Hydrodynamic modelling and uorescent spectral …...and Greg, Roger, Carol, Tom, Sheree, Jos e,...

Hydrodynamic modelling and

fluorescent spectral methods for

characterising the spatial

distribution of phytoplankton

Ryan Alexander

B. Eng. (Hons.) (Environmental) University of Western Australia

This thesis is presented for the degree of

Doctor of Philosophy of Environmental Engineering of The University of Western

Australia

Centre for Water Research

2012

ii

Abstract

Identifying structure in aquatic environments and showing the relationship to

phytoplankton diversity is challenging because it is difficult to make direct

measurements of all relevant variables at the necessary temporal and spatial

scales. Two new approaches are demonstrated, which allow relationships be-

tween phytoplankton distribution and the aquatic environment to be better

understood.

The first approach involved the use of numerical modelling to resolve structures

in the aquatic environment at smaller spatial and temporal scales than tradi-

tional field sampling allows. A three-dimensional, coupled physical-biological

numerical model was used to reconcile a range of different unsteady processes

that influenced the spatial distribution of motile phytoplankton in a medium

sized reservoir located in central Argentina. It was determined that physi-

cal processes (with some influence from phytoplankton migration) control the

habitat of the motile phytoplankton rather than biological/chemical gradients.

The results suggest that numerical models can be used to characterise the

spatial habitat of other motile phytoplankton species in similar settings.

The second approach involved the use of fluorescence spectral measurements

as a proxy indicator of phytoplankton diversity. As fluorescence spectra can

be measured rapidly in situ, in principle, spectral measurements can be made

at a resolution that should allow many scales of phytoplankton patchiness to

be resolved. However, decoding the information contained within the spectral

measurements presents a challenge. Therefore, a method based on principal

component analysis (PCA) was developed for identifying patches of distinct

fluorescent groupings of phytoplankton from in situ spectral data. A series of

idealised spectral data sets were used to explain the conceptual basis of the ap-

proach. To demonstrate the method, a profiling multi-wavelength fluorometer

was cast at numerous locations throughout Winam Gulf, Kenya. Processing

the spectral data with PCA revealed that linear combinations of four funda-

mental base spectra could explain almost all of the variation in the spectral

measurements. Three of the base spectra were associated with spatially dis-

tinct patches of phytoplankton containing different species assemblages, while

the fourth base spectrum was due to fluorescence of coloured dissolved or-

ganic matter (CDOM). Strong relationships were found between the gradients

in spectral data and other environmental variables, which suggested several

underlying explanations for the phytoplankton and CDOM patchiness. The

PCA processing method has the capacity to summarise critical features con-

tained within large spectral data sets and can facilitate better optimisation of

traditional water sampling.

This work is dedicated to the memory of Frank Alexander Sr., Win Fisher

and my dearly missed friend Sam Kularatne.

Acknowledgements

Working towards a PhD can be a solitary experience in many ways, and yet I

can’t imagine how I would have ever reached this point without a tremendous

amount of help and support.

My parents, Frank and Lorraine, did everything they possibly could to give

me the upbringing and education that I needed just to be able to start this en-

deavour, and all the love and support I could ever wish for to help me finish. In

addition, my brothers, Joel and Cale, provided me with great encouragement,

support and friendship through this time.

To Sal, my partner, your love, support and direct assistance made sure I arrived

at the end in one piece. Thank you.

Jorg, my supervisor and co-author, gave me the inspiration to take on this

challenge in the first instance and instilled me with the belief that I could make

a worthwhile contribution. As my supervisor, Jorg deserves much direct credit

for my professional and personal development, but he also deserves indirect

credit as the driving force behind the intellectual and creative culture that

makes CWR a special place to do research. It’s been a long road, but along

the way I’ve had the opportunity to broaden my knowledge well beyond the

technical details contained in the manuscripts, and that’s something that I

truly value and will always carry with me.

Numerous colleagues made direct contributions to the field work that formed

the basis of the manuscripts. In particular, Andres and Sebastian in Argentina,

and Greg, Roger, Carol, Tom, Sheree, Jose, Kenji and Peter Gikuma-Njuru in

Kenya. Several people provided me with constructive feedback and encourage-

ment on the various manuscripts. I really appreciated comments from Tamar

Zohary, Colin Reynolds and Jason Antenucci on my first manuscript. Likewise

comments from Kenji Shimizu and two anonymous reviewers were of great help

with my second manuscript.

I carried out some contract research work in parallel with my PhD and was

fortunate to be under the management of Chris, Pete, Jason and Clelia at

various times, all of whom allowed me flexibility to balance my commitments

when needed.

A great feature of my time as a PhD student has been the camaraderie I have

experienced with fellow students at CWR. In particular, Andres, Ingrid, Trish,

Sandy, Sebastian, Daniel Botelho, Vadim, Geoff, Leon, Clelia, Arthur, Ro-

cio, Roman, Kenji, Yanti, Demet, Daniel Machado, Roberta, Sarah, Peisheng,

Cristina and Jessica. Thanks for the interesting conversations, adventures,

laughs, tears, and coffee. You are all unforgettable.

Declaration

This thesis contains published work and work prepared for publication, which

has been co-authored. The publications from this thesis are contained within

three chapters (Chapter 2 to Chapter 4) and each of these chapters is presented

as a standalone manuscript. Chapter 1 provides some context for the three core

chapters and Chapter 5 summarises the major outcomes of the work.

Chapter 2 has been published in Journal of Plankton Research as ”Alexander,

R. and J. Imberger. 2009. Spatial distribution of motile phytoplankton in a

stratified reservoir: the physical controls on patch formation. J. Plankton Res.

31: 101-118.” The field work, field data processing and numerical modelling

was conducted by myself under the scientific supervision of Jorg Imberger, who

provided particular input to the scaling analysis. The manuscript was written

by myself and edited thoroughly by Jorg Imberger.

Chapter 3 has been published in Limnology and Oceanography: Methods as

”Alexander, R., P. Gikuma-Njuru and J. Imberger. 2012. Identifying spatial

structure in phytoplankton communities using multi-wavelength fluorescence

spectral data and principal component analysis. Limnol. Oceanogr. Methods.

10: 402-415.” The idea for the method was my own but Jorg Imberger made

a significant contribution to the mathematical proof (Case A). Peter Gikuma-

Njuru provided the field data that was used to validate the method. The

manuscript was written by myself and edited by Jorg Imberger.

Chapter 4 has been published in Freshwater Biology as ”Alexander, R. and J.

Imberger. Phytoplankton patchiness in Winam Gulf, Lake Victoria: a study

using principal component analysis of in situ fluorescent excitation spectral

data. Freshwater Biol. 58: 275-291.” The scientific analysis for this work was

carried out by myself under the supervision of Jorg Imberger, who provided

particular input with regard to estimate of water residence time from the salin-

ity data. I was not involved in the field work, which was carried out by Jorg

Imberger and others as part of a larger study. The manuscript was written by

myself and edited by Jorg Imberger.

Contents

1 Introduction 1

2 Spatial distribution of motile phytoplankton in a stratified reservoir: the

physical controls on patch formation 3

2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Site description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.2 Field instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.3 The hydrodynamic model ELCOM . . . . . . . . . . . . . . . . . . . 8

2.3.4 External boundary conditions: inflows and meteorology . . . . . . . 9

2.3.5 Internal aquatic conditions: hydrodynamics and biological parameters 11

2.3.6 Simulation configuration . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Validation of the temperature field . . . . . . . . . . . . . . . . . . . 14

2.4.2 Phytoplankton patch formation . . . . . . . . . . . . . . . . . . . . . 16

2.4.3 Phytoplankton patch transport . . . . . . . . . . . . . . . . . . . . . 17

2.4.4 Phytoplankton patch persistence . . . . . . . . . . . . . . . . . . . . 20

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5.1 Critical analysis and sensitivity of results . . . . . . . . . . . . . . . 23

2.5.2 New insights on patch dynamics . . . . . . . . . . . . . . . . . . . . 27

2.5.3 Ecological consequences of wind driven patchiness . . . . . . . . . . 29

3 Identifying spatial structure in phytoplankton communities using multi-

wavelength fluorescence spectral data and principal component analysis 33

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

v

CONTENTS

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.1 Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.2 Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4.3 Case C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4.4 Case D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4.5 Field data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.6 Comments and Reccomendations . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Phytoplankton patchiness in Winam Gulf, Lake Victoria: a study using

principal component analysis of in situ fluorescent excitation spectral

data 55

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3.1 Site Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3.2 Field instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.3 Field sampling procedure . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.4 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4.1 Background environmental conditions . . . . . . . . . . . . . . . . . 61

4.4.2 Spectral data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4.3 Relationship between the spectral data and other environmental

variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5 Summary 81

References 83

vi

1

Introduction

Phytoplankton community composition affects the functioning of aquatic ecosystems

and is relevant to global climate because of the important role of phytoplankton in the

carbon cycle (Falkowski et al., 2004). Therefore, understanding why phytoplankton as-

semblages have high species diversity is an important but unresolved research question.

Hutchinson’s (1961) paradox of plankton encapsulated the conundrum concisely; if phy-

toplankton compete for a limited range of resources in an unstructured environment, then

the principle of competitive exclusion (Hardin, 1960) should lead eventually to low species

diversity, which is counter to common observation.

One approach to reconciling the paradox is to argue its inverse, that phytoplankton

species richness must be evidence of underlying structure and/or dynamic variability in

the aquatic environment. The issue then becomes how to identify structure in aquatic en-

vironments and show the relationship to phytoplankton diversity. However, because it is

impractical to measure phytoplankton diversity and related environmental variables over

the wide range of spatial and temporal scales that are relevant, it is necessary to make use

of proxy measurements and simplifying assumptions where appropriate. In particular, it is

useful to consider phytoplankton diversity from the perspective of functional traits rather

than lineage. This approach, known as functional classification (Reynolds et al., 2006) or

trait-based community ecology (Litchman and Klausmeier, 2008), considers diversity at

the level of the shared traits or characteristics that allow phytoplankton to specialise in

particular niches. Because different evolutionary pathways can converge towards similar

functional attributes, the number of functional niches is much smaller than the number

of phytoplankton species. However, although the functional classification approach pro-

vides an ideal conceptual framework to clarify the links between functional attributes and

environmental structure, the functional niches themselves are still somewhat imprecisely

defined by qualitative descriptors.

1

1. INTRODUCTION

This thesis aims to advance research efforts to relate phytoplankton assemblages to

environmental structure by introducing some new quantitative approaches. Specifically,

this thesis describes the use of numerical modelling to resolve structure in the aquatic

environment at relatively fine temporal and spatial scales, and the application of high

frequency in situ spectral fluorescence measurements as a proxy indicator of phytoplankton

diversity.

The first chapter examines how physical forcing of the aquatic environment combined

with vertical migration of phytoplankton caused phytoplankton patchiness in a medium

sized reservoir. A three dimensional numerical model was used to resolve the physical

structure of the aquatic environment. Field measurements made at coarser scales were

used to validate the model.

The second chapter introduces a new method for analysing fluorescence spectral mea-

surements. As fluorescence spectral data contains implicit information about phytoplank-

ton diversity that can be measured in situ and at high frequency, this kind of data can

potentially be used to resolve spatial and/or temporal gradients in the composition of

phytoplankton assemblages at much finer scales than is possible with traditional sam-

pling. However, due to ambiguity that is inherent to spectral data, the method is only

able to reveal relative changes in the overall composition of phytoplankton assemblages

rather than changes in the concentrations of individual phytoplankton species. Neverthe-

less, assuming changes in phytoplankton assemblages revealed by the spectral data can be

linked to changes in other environmental variables, the method represents a step towards

quantifying functional niches for phytoplankton.

The third chapter tests the validity of the approach developed in the second chapter by

applying the analysis method to field data measured in Winam Gulf, Lake Victoria. Spec-

tral data was used to infer spatial gradients in the phytoplankton assemblage, which were

shown to be closely related to large scale physical and chemical gradients in the aquatic

environment. The fine spatial scale of the field measurements allowed phytoplankton

patchiness to be resolved at smaller scales than previously, and furthermore, provided new

evidence about the drivers of phytoplankton diversity and abundance at this site.

2

2

Spatial distribution of motile

phytoplankton in a stratified

reservoir: the physical controls on

patch formation

2.1 Abstract

Changes in the spatial distribution of the dinoflagellate Ceratium hirundinella were

observed in a stratified, medium-sized (16 km2) Argentinean reservoir over several days.

A fluorescence profiling technique was used to identify persistent patchiness in the distri-

bution of the dinoflagellate. A three-dimensional numerical model was used to reconcile

a range of different unsteady processes and prove that the initial source of heterogeneity

in the system was the vertical migration of Ceratium. Once migration established vertical

heterogeneity, the dominant influence on the patch dynamics alternated between control

by migration and control by mixing and transport. This led to the development of per-

sistent horizontal patchiness. The analysis revealed that the region of the lake inhabited

by Ceratium was highly predictable and from this result it was determined that physical

processes (with some influence from migration) control the habitat of this dinoflagellate

rather than biological/chemical gradients. When the spatial habitat of a particular phyto-

plankton species can be isolated in this manner, the resources available to the species can

be more accurately determined by further study. The results are particularly applicable

to the study of motile/buoyant plankton in aquatic systems that are periodically subject

to moderate or strong wind forcing events.

3

PHYSICAL CONTROLS ON PATCH FORMATION

2.2 Introduction

The spatial distribution of phytoplankton in an aquatic system determines the prox-

imity of the cells to light and nutrients and therefore influences the capacity for primary

production. All established phytoplankton populations are subject to transport and mix-

ing in ambient flow but some phytoplankton taxa have evolved strategies to exert influence

over their spatial distribution, thereby enhancing access to resources. Active vertical mi-

gration strategies are common to most species that cause nuisance algal blooms (Paerl,

1988), especially dinoflagellates and cyanobacteria. Several different hypotheses have been

proposed to explain the dominance of these phytoplankton (Paerl, 1988), but it is difficult

to isolate the importance of many covariant influences because of the range of time and

space scales involved (Visser, 1995). This problem also extends to a broader objective

in ecology, i.e. to understand competition dynamics between species. When Hutchinson

(1961) considered a potential explanation for the paradoxically high species diversity of

phytoplankton, he reasoned that temporal changes in aquatic habitats functioned to shift

parameters of species competition. An alternative, but not mutually exclusive explanation

for high diversity is that spatially distinct ecological niches exist in aquatic systems, and

persist long enough for particular species to exploit to their advantage (Richerson et al.,

1970). Both of these hypotheses suggest that species competition is intricately linked to

habitat patchiness in time and space.

Patchiness is the net result of various differential growth, loss and/or transport pro-

cesses. This means that the direct measurement of all contributing processes is not prac-

tical and therefore the drivers of patchiness have tended to be investigated via indirect

techniques. Powell et al. (1975) used spectral analysis techniques to infer that turbu-

lence controlled patchiness at scales < 100 m in Lake Tahoe, but biological controls were

important at larger scales. Abbott et al. (1982) clarified this relationship, finding that

large scale phytoplankton patchiness only occurred in conjunction with similarly large

scale habitat variability (in this case nitrate patchiness), otherwise phytoplankton were

randomly distributed. Large-scale patchiness in phytoplankton is, therefore, primarily

attributed to variable availability of substrates or differential grazing (Richerson et al.,

1970). Motile phytoplankton are a special case because, not only does migration become

the primary determinant of vertical patchiness, but it also initiates horizontal patchiness

(George and Edwards, 1976).

The focus of this study is to explain how migratory behaviour combined with physical

forcing determines the patchiness of a nuisance algal bloom. While the methods applied

are intended to be generally applicable to motile phytoplankton, migratory behaviour

is species specific and the dinoflagellate, Ceratium hirundinella (O.F. Muller) Dujardin

4

2.2 Introduction

(1841) is examined in this study as a typical representative of a nuisance bloom species.

Ceratium hirundinella (O.F. Muller) (from now on referred to as Ceratium) is particularly

well adapted to compete in stratified conditions. Although Ceratium cells do not grow

rapidly, they have several compensating advantages. Ceratium has a large cell size that

resists grazing (Reynolds, 2006), is capable of making pronounced diel vertical migrations

to seek light and nutrients (Talling, 1971), has the ability to gain access to nutrients by

phagocytosis (Dodge and Crawford, 1970) and forms resting cysts when conditions are no

longer suitable for growth (Heaney et al., 1983). These competitive strategies go some way

to explaining why seasonal succession patterns in eutrophic, stratified, temperate lakes can

typically culminate with late summer domination by Ceratium (Reynolds, 1976).

Horizontal patchiness of Ceratium was previously observed by Heaney (1976) in a

small lake (1 km2) and recognised as a response to the interplay of vertical migration and

wind driven circulation. Harris et al. (1979) investigated the stimuli for vertical move-

ments of Ceratium, and found that Ceratium cells preferred to position at the depth of

the 1.4x10−4 mol quanta m−2 s−1 light level, avoiding higher light levels and depths below

the oxycline. However, the precise migration behaviour of Ceratium cannot be charac-

terised easily because cells migrate according to individual requirements. Observations of

Ceratium distributions in the field have indicated that some cells can remain near to the

surface while other cells from the same distribution migrate to the metalimnion in the

evening to access nutrients (George and Heaney, 1978). There is also evidence to indicate

that Ceratium species strains from different geographical locations have different migra-

tion characteristics. Whittington et al. (2000) observed Ceratium in Chaffey Reservoir,

eastern Australia, and found that the cells positioned at a light level that was signifi-

cantly higher than the optimum light level indicated by Harris et al. (1979). If horizontal

patchiness is highly sensitive to these intricate migration characteristics, general models

of patchiness are problematic because phytoplankton may evolve differently to deal with

different environmental conditions.

Despite the species-specific intricacies of phytoplankton migration, George and Ed-

wards (1976) offered a general explanation of phytoplankton heterogeneity that was in-

trinsically limited to small lakes, proposing that buoyant plankton were capable of sepa-

ration from the flow in downwelling regions when there was wind driven circulation flow.

Webster (1990) later elucidated this mechanism with an analytical model, showing that

the steady-state concentration of phytoplankton at the downwind end of a lake increased

with increasing floatation velocity and decreasing wind speed. At high wind speeds, the

mechanism breaks down because turbulent forces become large compared to the buoyancy

forces. In larger lakes, Verhagen (1994) noted that the duration of wind forcing would not

usually be long enough to allow steady-state conditions to establish, hence the limitation

5


of this mechanism to small lakes. However, Verhagen developed an unsteady solution to

the problem, which hinted at the possible development of wind driven horizontal patchi-

ness in larger lakes. The analytical models proposed by Webster and Verhagen are very

useful in their generality, but they consider vertical migration at a constant rate, steady

wind forcing and idealised lake bathymetry. Numerical models based on the Navier-Stokes

equations have the potential to incorporate more realistic migration behaviour and can

respond to variable boundary forcing.

This study relies on field measurements to validate the occurrence of Ceratium hori-

zontal patchiness on a scale that is an order greater than previous cases where Ceratium

patchiness has been observed. Similar to previous studies, we seek to explain whether

phytoplankton patchiness is controlled by hydrodynamics or biological influences, but we

use numerical modelling to enhance the spatial and temporal resolution of the analysis,

thereby overcoming some of the practical limitations of field sampling. The modelling ap-

proach does not attempt to resolve all processes contributing to patchiness, but is instead

deliberately limited to the minimum number of features that are hypothesised to explain

the patchiness to first order. The implication of this design is that successful validation

of the patchiness model also confirms that the key processes may have been identified

correctly.

2.3 Method

2.3.1 Site description

LDS

Dam Wall

64° 27’ 9" W

31° 22’ 34" S

San Antonio

Cosquin

Chorrillos

N

2 km

20m

10m

Figure 2.1: Bathymetry of San Roque Reservoir.

San Roque Reservoir (31◦ 22′ S,

64◦ 28′ W) in central Argentina is the

main drinking water supply for the city

of Cordoba. The dam was constructed

in 1884 at the junction of two major in-

flows, the Cosquın River to the north

and the San Antonio River to the south

west, forming a triangular-shaped reser-

voir (Fig. 2.1). At full storage capacity,

the reservoir has a volume of 1.96x108 m3

and covers an area of 1.61x107 m2. The

average annual residence time is around

8 months; large inflows typically occur be-

tween October and December and thermal

stratification develops from November.

6

2.3 Method

Harmful algal blooms became a management concern in this reservoir in the early

1980s. In the ensuing years, chlorophyll a (chl a) concentrations have typically been

of the order of 60 µg L−1 and total phosphorus has been measured at levels of 9.04

µM (Rodriguez et al., 2000). During summer stratification, cyanobacteria (Microcystis

aeruginosa) and/or Ceratium have dominated phytoplankton biomass. In the summer of

2001-2002, the reservoir experienced a large Ceratium bloom and this study focuses on

the peak period of that bloom.

2.3.2 Field instrumentation

Field data were collected over a 10-day period from 26 February to 8 March 2002. A

Lake Diagnostic System (LDS) was deployed at a fixed position in the lake (Fig. 2.1)

to record water temperature and atmospheric forcing at 1-min intervals. The LDS had

a submerged thermistor chain with thermistors spaced at 0.25 m intervals for depths be-

tween 0.5-6.25 m and 0.75 m intervals thereafter to a maximum depth of 19.75 m. The

station included above-lake sensors for measuring short wave radiation, net radiation,

air temperature, humidity, wind speed and direction. Intensive field measurements were

made on 6 March (09:30 and 17:30 h) and 8 March (10:30 and 17:30 h) along a transect

path from the Cosquın River to the San Antonio River (Fig. 2.1). A fine scale profiler

(F-Probe) with a Seabird SBE-3 thermometer (Fozdar et al., 1985) was used to measure

the temperature at a vertical resolution of approximately 0.02 m. A fluorescence profiler

(bbe Moldaenke Fluoroprobe) was cast after the F-Probe to measure chlorophyll and var-

ious other pigments associated with different phytoplankton groups (Beutler et al., 2002).

This instrument had a vertical resolution of approximately 0.4 m. The Fluoroprobe al-

lowed different phytoplankton groups to be identified but could not distinguish between

dinoflagellates and diatoms, so cell counts were used to supplement the profile data. Water

samples were collected from depths of 0.2 and 14 m around 9:00 h 5 March at the location

of the LDS station during the field survey. The Federal Environmental Monitoring Agency

of Argentina (CIRSA) conducted cell counts and supplied additional cell count informa-

tion from regular monitoring stations before and after the experiment period. With the

exception of some water samples collected near inflows, Ceratium dominated the phyto-

plankton community in all water samples; therefore, the dinoflagellate/diatom response

of the Fluoroprobe was assumed to be Ceratium. The assumption of dinoflagellate domi-

nance was further supported by the observation of sharp vertical layers in the chlorophyll

distribution in calm conditions, typical of motile phytoplankton. In post-processing, the

abundance of Ceratium was converted from arbitrary fluorescence units to relative units

by dividing by the maximum fluorescence measurement obtained from each transect. The

7


fluorescence profiling technique indicated the presence of other phytoplankton groups but

concentrations were low relative to Ceratium and these data are not presented here.

2.3.3 The hydrodynamic model ELCOM

The Estuary, Lake and Coastal Ocean Model (ELCOM) (Hodges and Dallimore, 2006)

was used to simulate temperature, velocity, light and Ceratium distribution over a 10 day

period. The three-dimensional ELCOM model uses a fixed grid structure to solve the

Reynolds-averaged Navier-Stokes equations, subject to boundary forcing and the hydro-

static approximation. The numerical scheme is based on the TRIM code (Casulli and

Cheng, 1992), but uses a modified turbulence closure that is suited to coarse grids, and a

numerical diffusion filter (Laval et al., 2003) that is appropriate for stratified lakes. At the

free surface, radiation exchange is computed according to standard bulk transfer equations

(Imberger and Patterson, 1990), but the transfer of vertical momentum is solved for each

column using an approach that is more common to one-dimensional models (e.g. Imberger

and Patterson, 1981). At each time step, the depth of the mixed layer is determined by

an energy budget that balances the energy of turbulence produced by wind stirring and

velocity shear against the energy required to mix a given density gradient in one model

time step. To reduce the time-step dependence of the mixing routine, the model represents

incomplete mixing by carrying over unused mixing energy to the next time step.

A transportable, motile scalar was used to trace the distribution of Ceratium in the

reservoir. A conservative scalar was chosen because the net growth/loss of Ceratium

was considered small compared to changes due to transport, mixing and motility over

the timescale of the analysis, especially considering the slow growth and loss avoidance

strategies of this species. The scalar was subject to vertical mixing according to the

mixed layer routine, but to incorporate the effect of cell motility, a light-dependent vertical

advection term was added to the scalar to mimic Ceratium. The migration term set the

Ceratium to swim toward an optimum light level of 1.4x10−4 mol quanta m2 s−1 (Harris

et al., 1979) at a constant rate of 5 m day−1 in the daytime and sink at 1 m day−1

in the evening. The upward migration rate was determined from trial simulation runs

in which this parameter was adjusted to span a range of literature values (3, 5, 10 and

15 m day−1). The upward migration rate of 5 m day−1 was selected as it gave the best

comparison with the field data, but the sensitivity of the results to this choice will be

discussed. Based on the high concentration of inorganic nutrients in the surface layer (see

below), it was assumed that there would be no imperative for downward migration by

Ceratium cells. Therefore, the assumption was made that Ceratium cells would simply

sink at a slow rate in the evening, when there was no light stimulus for migration. We

concede here that the migration scheme used in the model was imperfect, but the focus

8

2.3 Method

was to test whether a simple migration scheme could help to explain horizontal patchiness

in the field, rather than demonstrate a species (and site) specific model calibration. This

objective is important because it relates to the general applicability of this methodology

to other species with similarly uncertain migration characteristics.

The light field was simulated using Beers law to distribute 45% of the surface short

wave radiation over depth as a function of a dynamic extinction coefficient determined

from the Ceratium concentration in each grid cell.

2.3.4 External boundary conditions: inflows and meteorology

Late season rainfall preceded the field campaign and this led to an inflow event that

was unusually large for the time of year. The cool underflow replenished the hypolimnion

of the reservoir and increased the water level above the spillway. Subsequently, there were

large outflows from the reservoir at the beginning of the field campaign (Fig. 2.2a). Due

to the spillway outflow, the water level in the reservoir remained quite constant during

the field campaign despite further minor inflows on 5 and 6 March. These smaller inflows

represented only 5% of the total reservoir volume, but they will be shown to have had a

localised influence on the Ceratium distribution.

During the field campaign, two distinct daily weather patterns were observed. The

most common pattern was one of warm weather (26-27 February, 2-4 March and 6-

8 March), characterised by maximum air temperatures in excess of 25◦C (Fig. 2.2b),

low wind speed in the morning (Fig. 2.2c and d), mostly clear skies (Fig. 2.2e) and brisk

afternoon northerly winds (Fig. 2.2c). We note here the use of the meteorological con-

vention that defines a northerly wind as coming from the north. The warm weather was

punctuated by cool weather periods on 3 days (28 February, 1 March and 5 March). Under

the cool weather pattern, the conditions were overcast and southerly winds prevailed. The

occasional switch between these two weather patterns will be shown to influence the spatial

distribution of Ceratium in San Roque. Semi diurnal patterns in the wind forcing (Fig.

2.3) also influenced the Ceratium distribution. During warm weather, the wind forcing

had three distinct sub-daily components; a calm period from the late evening to mid-

morning, a significant northerly breeze from the late morning until the late afternoon; and

finally, an easterly breeze in the early evening. The timing of the wind direction changes

was similar on each day, but the magnitude of the wind forcing was larger on 7 March,

and this prevented field sampling on this day.

9


25

50

75[m

3s-1

](a) Discharge

-10

-5

0

5

10

[ms-1

]

(d) East component wind velocity-10

-5

0

5

10

[ms-1

]

(c) North component wind velocity

27 28 01 02 03 04 05 06 07 08 090

0.5

1

[kW

m2]

(e) Short wave radiation

February/March 2002

10

20

30

40

[° C

]

(b) Air temperature

Figure 2.2: (a) Dam outflow from San Roque (dashed) and estimated inflow for San Antonio River(solid), inflow is offset by 25 m3 s−1. (b-e) Meteorological conditions measured at the LDS station.Date ticks on the horizontal axis indicate midnight (as in subsequent figures). Wind direction usesthe meteorological convention, e.g. positive north component indicates wind coming from the north.

10

2.3 Method

06 07 08 090

2

4

6

8

10[m

s-1]

Wind speed and direction March 2002

09:30 17:30 10:30 17:30

Figure 2.3: Expanded view of wind speed and wind direction. The solid line is the wind speed(10 min average), the arrows indicate the wind direction (centred 3 h average). The arrows pointin the downwind direction. Vertical markers indicate the time of transect surveys (as in subsequentfigures).

2.3.5 Internal aquatic conditions: hydrodynamics and biological param-

eters

The LDS station was located to give a high temporal resolution record of the tempera-

ture stratification in a deep region of the reservoir (Fig. 2.4a). The dynamics of the surface

layer were particularly significant for this study owing to the tendency of Ceratium to con-

centrate near the surface. Although the mixed layer depth in the model was calculated

with numerical accuracy, in the following text we define the mixed layer by a 1◦C temper-

ature difference from the temperature recorded by the surface thermistor. This is a lower

bound estimate of the mixed layer, but it gives a reasonable approximation for descriptive

purposes. According to this definition, the depth of the mixed layer ranged between the

near surface and a maximum depth of ≈10m, with the maximum depth distinguished by

the 22◦C isotherm (Fig. 2.4a).

The water column stability was investigated to identify periods that were most con-

ducive for Ceratium migration. Under daylight stimulus, Ceratium could migrate from

deep regions to the base of the mixed layer, but once in the mixed layer turbulent mixing

was most likely to control the vertical distribution. When stratification was dominant

over turbulent mixing, diurnal stratification formed close to the surface and the depth

range conducive for migration was increased. From 5 March onward, the effect of wind

mixing tended to dominate the formation of diurnal stratification, at least to a depth of

around 5 m (Fig. 2.5). Opportunities for Ceratium to migrate above a depth of 5 m in

stable conditions did not occur on 5 and 6 March, and only during the morning on 7 and

8 March. During the typically calm conditions of the morning, relatively weak, but stable

temperature gradients (≈0.25◦C) were common near the surface (e.g. 8 March, Fig. 2.5).

11


[°C

]

17

18

19

20

21

22

23

24

25

26

27

(a) LDS field temperature0

5

10

15

20

De

pth

[m

]

(b) ELCOM simulated temperature0

5

10

15

20

[°C

]

0.0

0.5

1.0

1.5

2.0

(c) Simulation RMSE

February/March 2002

27 28 01 02 03 04 05 06 07 08

0

5

10

15

20

Figure 2.4: (a) Field water temperature profile measured at the LDS station. (b) Simulated watertemperature, with output resolution of 60 s. (c) Root mean square error difference between the fielddata and the simulation.

[°C

]

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

26.0LDS field temperature

March 2002

De

pth

[m

]

09:30 17:30 10:30 17:30

06 07 08

0

2

4

6

8

10

12

14

Figure 2.5: Expanded view of the field temperature in the surface layer at the LDS station. Onlyisotherms above 22◦C are displayed.

12

2.3 Method

Internal seiching activity influenced the depth of the mixed layer, and therefore the

region inhabited by Ceratium. The isotherm response at the LDS station was clearly

related to the wind forcing, but the shape of the reservoir and the position of the thermistor

chain meant that there was a non-uniform response to forcing that depended on the wind

direction. The triangular geometry accentuated the isotherm oscillation at the LDS station

(Fig. 2.4a) when wind forcing had a strong westerly component (e.g. 7 March, Fig. 2.2d).

During the more frequent periods of northerly wind forcing, the isotherms at the LDS

station did not show the same degree of response to wind of similar magnitude. Owing to

these geometric irregularities, it was important to consider that while the thermistor chain

provided an accurate description of the surface layer depth and seiching in the region of

the LDS, it did not provide the full picture of the dynamics throughout the lake. However,

the numerical model was used to connect the thermocline behaviour throughout the lake

based on validation against the thermistor chain record at a deep, central location and

profiles measured at the extremities of the lake (see Results).

Previous long-term monthly water quality sampling conducted by CIRSA indicated

significant cell counts of the diatom Cyclotella and the cyanobacterium Anabaena from

June 2001, with both of these species reaching peak counts in December. During Decem-

ber, there were large counts of Microcystis and Ceratium and their appearance roughly

coincided with the establishment of stratification. By the time of the field campaign in

February, Ceratium dominated the cell counts. Water samples collected from the sur-

face layer between 21 February and 13 March showed Ceratium cell counts regularly

exceeding 106 cells L−1. Other numerically significant members of the phytoplankton

community identified to a genus level were Cyclotella, Anabaena, Microcystis, Aulacoseira

and Chlorella. However, when representative cell volumes were used to approximate the

biomass of each genus, the domination by the large Ceratium cells was much more ap-

parent, they comprised over 90% of the total cell volume. The only exception to this

dominance was in samples taken close to the entry points of the Cosquin River and San

Antonio River where there was a more mixed composition of species in the phytoplankton.

CIRSA monitoring after the field campaign ended showed a steady decline of Ceratium

through April to May, suggesting that during the field campaign the seasonal growth of

Ceratium was around its peak. The nutrient levels in the surface layer during the field

campaign were considered to be high based on the average of 12 water samples taken from

depths between 0.2 and 2 m, at various locations along the transect path and at the LDS

station. The mean nutrient concentrations were 0.30 µM phosphate, 3.9 µM ammonia,

2.4 µM nitrate and total phosphorus was 3.6 µM phosphorus.

13


2.3.6 Simulation configuration

The bathymetry grid for San Roque was constructed from satellite imagery, a coarse

depth survey of the reservoir with a resolution of ≈500 m2 and depth profiling along a

few transects. The resultant bathymetric map was used to generate a grid with a 50 m

by 50 m horizontal resolution and a vertical resolution of 1 m for the deepest 10 m of the

water column and 0.5 m for all shallower cells.

The atmospheric forcing data for the model were determined from the LDS station

measurements. The provincial water management authority (DIPAS) provided outflow

data, and inflow data were estimated from a water balance under the assumption that the

total inflow to the reservoir was evenly attributable to the two major inflows. An old dam

acts as a sill 100 m upstream of the outflow and this means that the outflow water was

in effect, removed from the upper 5 m of the surface layer. The inflow temperatures were

estimated using profile data collected at the San Antonio River bridge (31◦ 24′ 56.55′′ S,

64◦ 29′ 48.11′′ W) and the Cosquın River bridge (31◦ 19′ 9.80′′ S, 64◦ 27′ 20.02′′ W).

The model was initialised using a vertical temperature profile measured from the LDS

at 08:30 h on 26 February 2002; all initial velocities were zero and the initial temperature

field was assumed to be uniform in the horizontal. The dynamic component of the light

extinction coefficient was modelled using the empirical relationship for Ceratium found

by Harris et al. (1979) and assuming a ratio of 2.37x10−4 µg chl a cell−1 (Reynolds,

2006). The simulated Ceratium was initialised with a uniform distribution and at a con-

centration determined from the average of the water samples. There was no Ceratium

in the inflow water of the simulation. The simulation ran with a time step of 60 s from

26 February 08:30 h to 9 March 00:00 h.

Due to the dominance of northerly wind forcing during the survey period, it was

assumed that the main horizontal gradients in temperature and Ceratium distribution

would be captured along the axis of the north/south orientated transect.

2.4 Results

2.4.1 Validation of the temperature field

The performance of ELCOM was evaluated by comparing the thermistor chain record

(Fig. 2.4a) to the model output at the same location (Fig. 2.4b). It is not possible to make

a complete evaluation of the model with a single statistic because there are several distinct

aspects to consider. First, the total heat budget of the water column was calculated by

averaging the vertical field temperature profiles over depth and then over time and then

repeating this procedure for the simulated temperature profiles. Comparison revealed

14

2.4 Results

that the difference between the average temperature of model and the simulation was

less than 0.1◦C. Secondly, the phase and amplitude of the isotherm displacements should

be consistent in the simulation and the field data. This was evaluated by mapping the

root mean square error (RMSE) of the thermistor chain record compared to the simulation

(Fig. 2.4c). In this context, the RMSE simply equates to the absolute value of the residual

of between the field measurements and the model output at the same location and time.

Unlike the heat budget comparison, the RMSE approach is unforgiving of small errors in

the phase and displacement of internal waves.

The majority (81%) of the RMSE values calculated were less than 0.5◦C. In general,

the RMSE errors above 0.5◦C were concentrated at mid-depth because this is where the

temperature gradients were largest and therefore errors in the phase and amplitude of

internal waves in this region are more heavily penalised. The largest errors occur relatively

early in the simulation (27-28 February) during the period when the model was adjusting

from the state of zero initial velocity and the amplitudes of internal waves were under

predicted. Following this period, the only significant errors (above 1◦C) are on 1, 5 and

7 March. On these occasions, the errors were due to insufficient deepening of the surface

layer during relatively strong mixing events. In all three of these instances, the errors were

transient and this indicated an association with passing internal waves. Because the errors

did not propagate in time, it could be inferred that the average mixing applied across the

lake was reasonable even though there was some damping or phase lag of internal waves

at specific locations. The surface layer heating, cooling and mixing were well replicated

by the model and this can be judged by qualitative comparison of Fig. 2.4a and Fig. 2.4b,

or by observing the low RMSE in near surface region (Fig. 2.4c).

Horizontal temperature gradients were measured by profiling along the transect path

and these measurements were compared to model output at a similar time. The first

transect completed on 6 March is presented (Fig. 2.6a) along with the simulation results

(Fig. 2.6b). The RMSE value for the simulation was calculated at each point where there

was field data and then contoured to highlight the regions where the model performance

was weakest. The average RMSE value for all data points was 0.2◦C, indicating a good

comparison to the field data. The simulation reproduced the horizontal gradient in surface

temperature, but underestimated the volume of cool inflow water from the San Antonio

River (Fig. 2.6c). This underflow error reflected the uncertainty in the boundary condition

more so than model error. The upwelling of hypolimnion water around 3 km along the

transect path (Fig. 2.6a) was broadly captured by the simulation with similar intensity

(Fig. 2.6c).

15


21.0

21.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

[°C][°C][°C][°C][°C]0

5

10

(a) Field temperature: 6 March 8:05-9:41

C. S.A.

Dep

th [

m]

(b) ELCOM simulated temperature: 6 March 9:36

C. S.A.

0

5

10

0.0

1.0

2.0

[°C][°C][°C]

C. S.A.

(c) Simulation RMSE

Accumulated Distance [km]0 1 2 3 4 5 6 7 8 9 10 11 12

0

5

10

Figure 2.6: (a) Contour map of water temperatureprofiles taken along a transect path spanning from theCosquın (C.) River (left of figure, 0 km) to the SanAntonio (S.A.) River (right of figure, 12 km). Verticallines indicate profile locations. Start and finish timesfor the transect are given in the title. (b) Contourmap of simulated water temperature based on verticalprofiles of model output at 500 m horizontal intervals.Time of the model output is given in the title. (c)Contour map of the root mean square errors of thesimulation (see text for details).

Numerical diffusion is the most likely

explanation for the over damping of in-

ternal seiching in the simulation. Overall,

the model reproduced the major tempo-

ral changes in the vertical layer structure

(Fig. 2.4) and produced spatial temper-

ature gradients that were consistent with

those measured by profiling (Fig. 2.6).

2.4.2 Phytoplankton patch for-

mation

The model simulation of the distribu-

tion of Ceratium commenced on 26 Febru-

ary, but the first comparisons with the

field Ceratium measurements were made

after 8 days of simulation time. Be-

cause the simulation started with a uni-

form Ceratium distribution and there was

no differential growth or loss, the only

mechanisms that could have introduced

heterogeneity into the simulated system

were vertical migration, horizontal advection and inflow dilution. That is not to claim

these were the only mechanisms responsible for patchiness in the field observations, but a

validated simulation would imply the dominance of these mechanisms. The Ceratium dis-

tribution was surveyed on 6 March during the morning, and the observed data indicated

concentration of Ceratium near the surface and dilution near the entry of the Cosquın

River (Fig. 2.7a). These broad features were also reproduced in the simulated distribu-

tion (Fig. 2.7b). The low concentration of Ceratium in the Cosquın River side arm region

was due to wash out from inflow (Fig. 2.2a); this effect was strong because the reservoir is

narrow in this region (Fig. 2.1). In contrast, the inflow from the San Antonio River had

little influence on the Ceratium distribution because it plunged below the surface layer

due to greater bed slope and inflow density.

To highlight discrepancies between the simulation and the field data, the RMSE val-

ues were calculated (in the same manner as outlined previously for temperature) and

then expressed as a percentage error (Fig. 2.7c). With regard to the interpretation

16

2.4 Results

0.0

0.1

0.2

0.4

0.5

0.6

0.8

0.9

1.0

[R.U.][R.U.][R.U.][R.U.]0

5

10

(a) Field Ceratium: 6 March 8:05-9:41

C. S.A.

Dep

th [

m]

(b) Simulated Ceratium: 6 March 9:36

C. S.A.

0

5

10

0

10

20

30

40

50

[%][%][%]

C. S.A.

(c) Simulation RMSE


0

5

10

Figure 2.7: (a) Contour map of the Ceratium dis-tribution based on fluorescence profile measurementsgiven in relative units (R.U.). The relative units werederived by dividing the measured fluorescence valuesby the highest fluorescence measurement in the tran-sect. Dots indicate where data were measured. Startand finish times for the transect are given in the ti-tle. (b) Contour map of simulated Ceratium distri-bution constructed from vertical profile model outputat 500 m horizontal intervals. The relative units werederived by dividing the simulated fluorescence val-ues by the highest simulated fluorescence value in thetransect. Time of the model output is given in thetitle. (c) Contour map of the percentage errors of thesimulation (see text for details).

of Fig. 2.7c, an error value close to

100% in a particular location would imply

that the simulation predicted that loca-

tion to be highly concentrated with Cer-

atium when the field data indicated the

same area to be a region of low concentra-

tion, or vice-versa. From the RMSE map

in Fig. 2.7c, it is apparent that the simu-

lation overestimated the concentration of

Ceratium near the surface in the region

3-9 km along the transect, and underesti-

mated the concentration in the Cosquın

River side arm region (1-3 km). How-

ever, when all RMSE values were aver-

aged, the mean error of the simulation was

10.2%. To place this result in perspec-

tive, the RMSE calculated by comparing

the field data to a homogeneous distribu-

tion (the initial state of the simulation) is

27.3%. This quantitative comparison in-

dicates that the simulated Ceratium dis-

tribution did converge toward the struc-

ture of the field distribution. The quali-

tative match between the data sets (Fig.

2.7a and 2.7b) also supports this conclu-

sion.

2.4.3 Phytoplankton patch transport

In the time between the two transect surveys on 6 March, the spatial distribution of

Ceratium had altered significantly. Over a period as short as this, strong advection can

alter the distribution more quickly than biological processes associated with growth or

loss. When processes of growth or loss act slowly on a patch compared to changes due to

advection, the distribution can be considered as frozen inside the patch (Imberger et al.,

1983). By assuming no growth or decay of Ceratium in the simulation, it was possible

to test the hypothesis that the movement of the patch observed on 6 March matched the

criteria for frozen flow.

17


21.5

22.5

23.5

24.5

25.5

26.5

[°C][°C][°C]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0.0

1.0

2.0

[°C][°C][°C]

C. S.A.

(c) Simulation RMSE


0

5

10


The temperature distribution mea-

sured during the second 6 March transect

showed clear evidence of downwelling in

the surface layer at the San Antonio end

(Fig. 2.8a). The downwelling was consis-

tent with the northerly wind forcing and

the isotherm displacement was replicated

in the simulation results (Fig. 2.8b). The

simulation RMSE values did not exceed

1.5◦C (Fig. 2.8c) and the average RMSE

was 0.3◦C.

There was an obvious relationship be-

tween the downwelling region and the

Ceratium distribution (Fig. 2.9a). The

simulated Ceratium distribution (Fig.

2.9b) produced a reasonable match to the

field data (Fig. 2.9c), and gave a partic-

ularly good representation of the region

bounded by the 0.1 contour, which we ar-

bitrarily defined as the Ceratium habitat.

Comparing the afternoon distribution of

Ceratium cells (Fig. 2.9) to the distri-

bution measured earlier in the day (Fig.

2.7), the simulation was able to reproduce two main changes evident from the field data;

the general transport of Ceratium toward the San Antonio end of the reservoir and the

deepening of the Ceratium cells in the downwelling region. However, the RMSE map (Fig.

2.9c) highlighted that there was a higher concentration of field Ceratium cells in the near

surface region 2-4 km along the transect path, and that the field Ceratium cells were more

evenly mixed over depth in the downwelling region (≈7-10 km).

Several quantitative properties of the simulated Ceratium distribution were calculated

to track the changes in the simulated distribution for the times between field surveys. The

approach used is to detail the incremental changes in the simulated Ceratium distribution

using the modelling results together with periodic validation against the field surveys.

For this purpose, the boundary of the Ceratium patch was defined by the contour that

contained half the total mass in the x-z plane (x the distance along transect, z the depth),

and this was repeated for each time step. Only the x-z plane was considered because the

transect data are two-dimensional and this means the mass calculation must be per unit

18

2.4 Results

length in the y plane, now on referred to as the linear mass. Once the linear mass was

found, the centre of gravity of this cloud could be calculated and designated as the centre of

the patch. Several associated properties, including the length, width and dispersion rate,

were also computed at each time step and will be referred to subsequently as a means to

summarise the patch dynamics.

0.0

0.1

0.2

0.4

0.5

0.6

0.8

0.9

1.0

[R.U.][R.U.][R.U.][R.U.][R.U.]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0

10

20

30

40

50

[%][%][%]

C. S.A.

(c) Simulation RMSE


0

5

10


Returning to the period between tran-

sects on 6 March, the simulation results

demonstrate how the patch structure in

the field changed from the distribution

shown in Fig. 2.7a to that shown in Fig.

2.9a. Following the onset of the wind just

after 9:30 h on 6 March, the vertical layer

structure of the Ceratium distribution was

disrupted and spread over an increased

depth (Fig. 2.10a). The centroid posi-

tion of the patch moved rapidly down-

wind in response to the northerly wind

forcing (Fig. 2.10b), but the horizontal

width of the patch did not change sig-

nificantly until the patch encountered the

San Antonio end boundary of the reser-

voir (Fig. 2.10c). This represented a

frozen flow case because after initial verti-

cal mixing, the patch remained relatively

well mixed during downwind transport.

In the downwelling region, where the lake

boundary confined horizontal movement,

the patch was laterally compressed and

further deepened (Fig. 2.10d). Over a

period of 8 h, the Ceratium distribution

had shifted from the near surface region

of the lake interior to the southern boundary of the reservoir. In effect, this was a two-

stage process, first Ceratium migrated to the near surface and then vertical velocity shear

transported the near surface water downwind. This process saw the initial seed of vertical

heterogeneity created by Ceratium migration converted into horizontal heterogeneity by

action of the physical forcing.

19


06 07 08 09

-1

0

109:30

17:30 10:30

17:30

(e) Effective dispersion coefficient

[m2s-1

]

March 200206 07 08 09

20

25

30

35

09:30

17:30

10:30

17:30

(f) Linear mass

[gC

hl

a.m

-1]

March 2002

0

5

10

09:30

17:30 10:30

17:30(c) Maximum horizontal width

[km

]

2

4

6

8

10

12

09:30

17:3010:30

17:30

(a) Maximum vertical spread

[m]

8

10

12

09:30

17:30 10:30

17:30

(b) Horizontal centroid position

[km

]

0

2

4

09:30

17:30 10:30

17:30

(d) Vertical centroid position

[m]

Figure 2.10: Quantitative tracking of the simulated Ceratium distribution (see text for details).

2.4.4 Phytoplankton patch persistence

The high concentration of Ceratium at the San Antonio end of the reservoir developed

only after a few hours of northerly wind forcing. Given that the wind forcing was unsteady,

we now consider the longevity of this form of patchiness under the conditions that prevailed

in the field and use scaling to speculate on the longevity of patchiness under a broader

range of conditions.

The northerly wind forcing on 7 March was significantly stronger than that experienced

on the 6 March (Fig. 2.3) and it would have been reasonable to expect significant changes

in the actual and simulated Ceratium distribution during this period. While there were

no field measurements available on this day, the simulation results did not indicate any

major changes to the structure or horizontal position of the patch during this period (Fig.

2.10a c), but the vertical position of the centroid (Fig. 2.10d) did oscillate around a depth

of 2 m.

The simulation results show an increase in dispersion of the patch that was coincident

with the increased wind forcing on 7 March (Fig. 2.10e), but this did not have a large in-

fluence on the patch structure. Okubo (1974) developed an empirical relationship between

the size of a patch and its dispersion based on field measurements. This empirical rela-

tionship comes from measurements in the ocean rather than from measurements in lakes,

but it can give an independent estimate of the dispersion coefficient that can be compared

to the model. Okubo’s relationship scales the dispersion coefficient with the 4/3 power

of the patch length, and this relationship suggests a dispersion coefficient of ≈1 m2 s−1.

This calculation is probably an overestimate because the patch dispersion was bounded

20

2.4 Results

in the region of the San Antonio inflow. Consequently, the low values of patch dispersion

that were calculated from the simulation results appear reasonable. It is noted that the

simulated dispersion rate was negative on occasion and this artefact was mostly due to

periodic transverse dilation and contraction of the patch in the direction perpendicular to

the transect path. To a lesser extent, Ceratium migration also contributed to the negative

dispersion values.

Although the simulation results and the field data are presented as two-dimensional,

it is important to acknowledge that some changes in the Ceratium distribution were due

to net transport in the y plane, but the extent of this effect in the simulation can be

quantified. The transport of the simulated Ceratium in the direction perpendicular to the

transect path (the y plane) can be determined by computing a mass balance of Ceratium

in the x-z plane at each time step of the model. The mass was determined by multiply-

ing the Ceratium concentration in each grid element by the x-z surface area of the grid

element, which gave the linear mass of chlorophyll. Because Ceratium was conservative

in the simulation (excepting the small effect of outflow), any change in the linear mass is

attributed to transport in the direction transverse to the transect path. The simulation

results showed that the linear mass oscillated within a range of up to 25% of the initial

value and that this order of fluctuation could occur over a timescale of hours (Fig. 2.10F).

Therefore, these fluctuations were far from an insignificant component of the dispersion

estimates on short timescales, but over time, there was a tendency to return toward a

mean value. The fluctuations were periodic and therefore clearly associated with internal

seiching in the y plane. Considered over the entire simulation period, the linear mass was

approximately conserved and this result validated the assumption that in this period when

the east-west wind component was weak, the main heterogeneity in the system was along

the direction of transect path.

The influence of transverse mass fluctuation was excluded by averaging the dispersion

calculation over a convenient time interval where mass was conserved. This approach

confirmed that there was minimal dispersion of the simulated patch during 7 March.

Further reinforcing this conclusion, the horizontal width of the patch did not significantly

change during this period (Fig. 2.10c). Therefore, the simulation results suggested that

the rate of dispersion of the Ceratium patch was low even under the influence of strong

northerly wind forcing.

The time scale to double the size of the patch by dispersive mechanisms is represented

as:

Td ∼L2p

K

where Lp is the patch length and K is a dispersion coefficient. With a patch length

21


of 5 km and choosing a deliberately conservative estimate of K = 17 m2 s−1 (Stocker

and Imberger, 2003), based on observations of a less confined but similarly energetic lake

system, Td is approximately equal to 17 days. Again, the confines of the boundaries make

this a lower estimate but nevertheless the result is consistent with the simulation, both

approaches suggesting that the influence of dispersion was minimal over the time scale of

the survey period.

After the northerly wind forcing relaxed in the late afternoon of 6 and 7 March (Fig.

2.3), baroclinic forces began acting to reverse the downwind accumulation of warm surface

water and redistribute Ceratium in the process. Although the wind forcing was strong on

7 March, 12 h of calm had passed (Fig. 2.3) before the next morning survey on 8 March.

Whether the Ceratium distribution would be greatly changed during this calm period

depended on the time scale associated with the restoring forces. Monismith et al. (1990)

used a scaling argument to estimate a time scale for the stability restoring baroclinic

motions:

Tb ∼

√L2

α∆tgh

where L represents the length of the reservoir (10 km), α is the thermal expansion

coefficient (2x10−4 ◦C), ∆t is the temperature gradient (2 ◦C), h is the layer depth (4 m)

and g is gravitational acceleration (9.8 m s−2). This scaling approach yielded an estimate

for the baroclinic restoring time of around 1 day, so the 12 h of calm conditions that elapsed

would not quite have been enough time to equilibrate the surface layer. This scaling is

confirmed by the persistence of warm water at the San Antonio end of the reservoir in the

next transect on 8 March (Fig. 2.11a). If anything, the scaling approach overestimated

the influence of restoring forces. In contrast, the simulation suggested the persistence of

warm surface water at the San Antonio end of the transect and the upwelling feature at

the Cosquın end of the transect (Fig. 2.11b). The good performance compared to the

scaling estimate is because of the more realistic bathymetry used in the model.

The fluorescence profiling indicated that the Ceratium distribution remained closely

associated with the warm surface layer water (Fig. 2.12a). The simulation results (Fig.

2.12b) gave a reasonable reproduction of the Ceratium habitat defined by the 0.1 level con-

tour, but the match to the field data was not as strong as in the earlier comparisons. In par-

ticular, inside the Ceratium habitat region, there was poor agreement between the field ob-

servations and the simulation. Northerly wind forcing was dominant again during the pe-

riod between morning and afternoon field surveys on 8 March (Fig. 2.3). There was an even

more exaggerated accumulation of warm water at the San Antonio extreme of the transect

(Fig. 2.13a) in the second transect of the day and this was replicated in the simulation (Fig.

2.13b).

22

2.5 Discussion

21.5

22.5

23.5

24.5

25.5

26.5

[°C][°C][°C]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0.0

1.0

2.0

[°C][°C][°C]

C. S.A.

(c) Simulation RMSE


0

5

10


The field Ceratium distribution had be-

come more concentrated at the San An-

tonio extreme of the reservoir than previ-

ously (Fig. 2.14a) and this was also true

of the simulated distribution (Fig. 2.14b).

There was a higher concentration of Cer-

atium at the extremity of the transect in

the simulation (Fig. 2.14c), but the agree-

ment with the field data had actually im-

proved compared to the preceding tran-

sect.

2.5 Discussion

2.5.1 Critical analysis and sensi-

tivity of results

A notable feature of the simulation

was the strong comparison to the patch-

iness in the field data on 6 March, even

though the model started on 26 February

with a homogenous distribution of Cer-

atium. The simulation was not expected

to converge toward the field distribution so effectively because factors that were not in-

cluded in the model were expected to have more influence on the formation of the patch.

The primary reason for this good comparison was that there was sufficient lead in time in

the simulation to allow Ceratium to migrate to the surface layer regardless of the initial

depth of the cells. Given the depth of the lake and the migration rate of Ceratium, it

took around 3 days to seed vertical heterogeneity into the simulation. Once the migration

process established vertical heterogeneity, the physical processes were able to act on a

background gradient in Ceratium concentration. The horizontal heterogeneity that de-

veloped in the simulation from this point was definitely a product of the physical forces

because there was no horizontal component in the migration model to contribute. How-

ever, horizontal heterogeneity does not inevitably follow from vertical heterogeneity. For

example, there was little horizontal heterogeneity in the system after the first 8 days of

the simulation (Fig. 2.7), especially if the wash out effect of Cosquın River is discounted.

23


0.0

0.1

0.2

0.4

0.5

0.6

0.8

0.9

1.0

[R.U.][R.U.][R.U.][R.U.]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0

10

20

30

40

50

[%][%][%][%]

C. S.A.

(c) Simulation RMSE


0

5

10


The lack of horizontal heterogene-

ity in this first instance is explained by

southerly wind in the morning on 5 March

(Fig. 2.3) that generally dispersed Cer-

atium across the lake. Therefore, the

southerly wind forcing (that was semi-

regular during this season) had a disper-

sive effect on the most frequent mode of

horizontal patchiness in the lake, effec-

tively resetting the Ceratium distribution

to a well mixed state. Due to this semi-

regular mixing effect, Ceratium motility is

the only source of heterogeneity that per-

sists in the system over long-time scales.

The boundary of the simulated Cer-

atium habitat showed a good comparison

to the field data in almost all cases (ex-

cept Fig. 2.12). This was because the

0.1 concentration level was always asso-

ciated with the isotherm at the base of

the surface mixed layer and was not influ-

enced by Ceratium migration. This corre-

lation between the habitat boundary and

the mixed layer depth is not immediately

obvious from reviewing the transect data

because the temperature of the isotherm

at the base of the mixed layer was variable (Fig. 2.5). The reason for this relationship is

that when wind mixed the surface layer in the simulation, the Ceratium distribution was

similarly mixed, and this occurred with a frequency that ensured there was always some

remnant of the Ceratium distribution at the base of the mixed layer, this then formed the

edge of the habitat boundary. The good comparison to the field data was confirmation

that the same process was occurring in the field, that is to say, during strong wind forcing

the effect of turbulent mixing dominated over Ceratium motility.

Simulating the distribution of Ceratium inside this habitat proved to be a more

difficult task than simulating the habitat boundary alone. Discrepancies between the

simulation and the field measurements indicated that the simplified modelling approach

used could not fully describe the vertical distribution of the field Ceratium during calm

24

2.5 Discussion

21.0

22.0

23.0

24.0

25.0

26.0

27.0

28.0

[°C][°C][°C][°C]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0.0

1.0

2.0

[°C][°C][°C]

C. S.A.

(c) Simulation RMSE


0

5

10


conditions. The strongest example of

this was in the first transect measure-

ment (Fig. 2.7), when the model over pre-

dicted the accumulation of Ceratium near

to the surface. Although the field data

also showed that the highest concentra-

tion of Ceratium was near the surface, a

large proportion of cells (e.g. the 0.6 con-

tour) were positioned deeper in the water

column, especially in the region 4-5 km

along the transect path (Fig. 2.7b). This

instance highlights that while the Cer-

atium in the model behaved according to

a single rule, in the field the behaviour of

the population was not uniform. It was

inevitable that a simplified model of the

system would have some error of this kind

due to failure to recognise the physiolog-

ical variability that exists amongst cells.

However, the cumulative error due to this

effect was not large because the periodic

surface layer mixing effectively suppressed

the divergence between simulated data and the field data. On each occasion that the wind

mixed the surface layer, the vertical heterogeneity in field Ceratium distribution was elim-

inated to the depth of the mixed layer, and the comparison with the simulation improved.

Therefore, the agreement between the simulation and the field data was strongest in the

afternoon when wind forcing was active. The regular stirring of the Ceratium distribution

by the wind also meant that the simulated patch dynamics were not particularly sensi-

tive to the migration rate. This was because the velocity scales associated with stirring

and/or advection, when active, were large enough to dominate the migratory motion and

this would have been true for any reasonable estimate of the migration rate. This result

demonstrates that while a detailed understanding of phytoplankton migration may be

elusive for many species, as long as some mixing regularly occurs, the extent of spatial

habitats can still be accurately identified using the methods described.

The degree to which a simplified and approximate migration scheme is useful for mak-

ing predictions depends on the sensitivity of the simulation results to the choice of the

25


0.0

0.1

0.2

0.4

0.5

0.6

0.8

0.9

1.0

[R.U.][R.U.][R.U.][R.U.]0

5

10


C. S.A.

Dep

th [

m]


C. S.A.

0

5

10

0

10

20

30

40

50

[%][%][%][%]

C. S.A.

(c) Simulation RMSE


0

5

10


migration scheme. Results from two sim-

ulation runs that used upward migration

rates of 0 m day−1 and 10 m day−1 respec-

tively, are presented to demonstrate the

sensitivity of the results to the migration

scheme (Fig. 2.15). When the migration

rate was set to 0 m day−1 vertical het-

erogeneity could not be established in the

model and the Ceratium distribution re-

mained well mixed except for the influence

of the inflows (Fig. 2.15a). The inflow-

induced horizontal heterogeneity was ap-

parent at both extremes of the reservoir

when inflows were active, but when in-

flow discharge decreased after 6 March

(Fig. 2.2a), the horizontal heterogeneity

was dispersed, particularly at the San An-

tonio end (Fig. 2.15b). When the migra-

tion rate was set to 10 m day−1, the initial

structure of the patch on 6 March (Fig.

2.15c) was similar to the result found us-

ing 5 m day−1 (Fig. 2.7b), but the lower

boundary of the 0.1 contour level was 1-

2 m shallower. In this respect, the 10 m

day−1 migration rate appeared to be an

overestimate compared to the field data (Fig. 2.7a), but still gave a reasonable compari-

son. However, the 10 m day−1 migration rate over estimated the downwind accumulation

of Ceratium under northerly wind forcing (Fig. 2.15d) compared to both the field data

(Fig. 2.14a) and the 5 m day−1 simulation results (Fig. 2.14b). Increased downwind

accumulation as the vertical migration rate increases is consistent with the predictions

of Webster’s (1990) analytical model and this effect was further observed when the mi-

gration rate was set to 15 m day−1 (not presented). Although the 5 m day−1 migration

rate produced the best comparison to the field data, the initial formation of the patch,

the downwind transport of the patch and the persistence of the patch in time was also

simulated reasonably well using a rate of 10 m day−1. In this respect, the broad features

of the patch dynamics were not highly sensitive to the upward migration rate used in the

model.

26

2.5 Discussion

Dep

th [

m]

(a) Simulated Ceratium (0 m.day-1

) 6 March 9:36

C. S.A.

0

5

10

Dep

th [

m]

(b) Simulated Ceratium (0 m.day-1

) 8 March 17:31

C. S.A.

0

5

10

Dep

th [

m]

(c) Simulated Ceratium (10 m.day-1

) 6 March 9:36

C. S.A.


0

5

10

Dep

th [

m]

(d) Simulated Ceratium (10 m.day-1

) 8 March 17:31

C. S.A.


0

5

10

[Re

lative

Un

its]

0.0

0.1

0.2

0.4

0.5

0.6

0.8

0.9

1.0

Figure 2.15: (a) Simulated distribution of Ceratium on 6 March using an upward migration rate of0 m day−1. (b) Simulated distribution of Ceratium on 8 March using an upward migration rate of0 m day−1. (c) Simulated distribution of Ceratium on 6 March using an upward migration rate of10 m day−1. (d) Simulated distribution of Ceratium on 8 March using an upward migration rate of10 m day−1. In all panels the relative units represent the simulated fluorescence values normalisedby the highest simulated fluorescence value in each transect.

There is some evidence in the results that the selected migration rate of 5 m day−1

was too extreme. For example, there was a relatively high accumulation of Ceratium near

to the surface compared to the field data on 6 March (Figs 2.7 and 2.9). However, a

simulation trial with the migration rate set to 3 m day−1 (not presented) did not produce

the near surface accumulation of Ceratium in the morning on March 8 that was in the field

data (Fig. 2.12a). Even using the selected migration rate of 5 m day−1, the simulation

overestimated the proportion of cells that remained below a depth of 3 m (Fig. 2.12b).

The sensitivity analysis indicates that the constant 5 m day−1 rate was an appropriate

time average of the actual migration rate; but it is most likely that the actual migration

rate varied with time, above and below this value.

2.5.2 New insights on patch dynamics

Although horizontal patchiness induced by wind has been observed previously, the

mechanisms and scaling arguments that have been used to explain the phenomenon are

only applicable under a restricted set of conditions. The mechanism proposed by George

and Edwards (1976) to describe horizontal patchiness induced from wind has two prereq-

uisites; advection must be small compared to migration velocity and the duration of the

wind forcing must be long enough to give time for heterogeneity to establish. Above a

critical wind speed of 4 m s−1, they found that patchy phytoplankton distributions were

homogenised by this mechanism rather than created. In addition, according to the scaling

of Webster (1990), it is only possible for heterogeneity to develop if the duration of wind

forcing exceeds a timescale proportional to the length of the lake and the inverse of the

27


wind speed. Given the upper limitation on wind speed proposed by George and Edwards;

together these restrictions imply that this mechanism is limited to small lakes (e.g. George

and Heaney, 1978). Using a numerical modelling approach in this study has allowed all

of these restrictions to be relaxed and demonstrated that horizontal heterogeneity can

form under a much broader range of conditions and in larger systems. In particular, the

approach allowed the effect of different unsteady processes to be integrated over time and

this was necessary because control of the patch dynamics alternated between dominance

by motility in calm conditions and control by mixing and transport otherwise. Each of

these processes was transient, but because one process did not cancel the effect of the

other, the horizontal and vertical heterogeneity was persistent even though the drivers of

patchiness were alternating and unsteady.

The interaction of migration and physical processes has been shown in this study

to produce horizontal patchiness on a large scale relative to the lake size. The general

consensus from previous studies that have compared temperature and chlorophyll spectra

(Richerson et al., 1970; Platt and Denman, 1975) is that chlorophyll behaves like a passive

tracer at scales <100 m, but above this scale patchiness is influenced by biological factors.

The observations of horizontal patchiness in this study do not directly contradict this

assertion because the source of patchiness is biological in origin, but in this case there is

coherence between temperature and phytoplankton at a larger scale of 5 km (estimated

from Fig. 2.10c).

Regardless of the particular mechanism that forms patchiness, the relevance of patch-

iness is in some respects considered proportional to its persistence. The classical theoreti-

cal KISS model (Kierstead and Slobodkin, 1953) suggests that patchiness can only persist

when growth dominates dispersive forces, but this model does not allow for migration.

The results presented here demonstrate that a slow growing patch can persist if vertical

migration plays a role in the patch formation. In this study, the simulated Ceratium had

zero growth rate but the horizontal patchiness was persistent for several days (in the both

simulation and field data), because the wind forcing that helped to establish the hori-

zontal patchiness recurred regularly. When it is considered how rapidly the horizontal

patchiness was established, the frequency of occurrence in this lake must be as regular

as the northerly wind forcing. Therefore, a heterogeneous horizontal distribution actually

represents the norm for a lake under these conditions.

In the design of this study, it was assumed that changes in the Ceratium distribution

due to growth/loss processes were small compared to the other processes. This implies

that the methodology is restricted to periods that are shorter than the time scales of

growth and loss. However, if the relative distribution of Ceratium is of interest rather

than the absolute concentration, the methodology is potentially applicable over longer

28

2.5 Discussion

periods. To justify such an extension, the vertical migration behaviour of Ceratium would

need to remain consistent over time and horizontal dispersion would need to act faster

than any horizontal differential growth/loss processes that cause changes in the relative

distribution.

The results of this study indicate that the spatial extent of the Ceratium habitat can

be accurately mapped out with a numerical modelling approach. Theoretical explanations

for high phytoplankton diversity hinge on the concept that lakes are far from isotropic

and that many different niches must exist within a lake to support diversity. However,

it is difficult to progress the idea of a niche beyond an abstract concept, at least partly

because it is impractical to measure all contributing parameters with adequate spatial

resolution. The modelling approach adopted in this study allowed the physical influences

on the boundaries of the Ceratium habitat to be identified. From this starting point, the

clear extension is to examine the boundary fluxes of resources in and out of the three-

dimensional habitat space, either by coupling to a biological model or by strategic field

measurement inside and outside the boundary to determine fluxes.

In larger aquatic systems where the domain is less bounded or unbounded, the same

patch forming mechanisms will still occur but the patch structure may not self organise in

the manner described in this study. In these cases, the simulation approach followed here

could still be applied if the patch structure was explicitly seeded into the simulation. Under

this methodology, it would at least be possible to isolate the effect of transport processes

on patch dynamics from biotic influences. It should be noted that the length scale of San

Roque reservoir meant that some mechanisms that are known to generate heterogeneity

were excluded from this analysis. Spatially variable wind stress, geographical features and

the earths rotation can make additional contributions to heterogeneity at larger scales. It

is possible to consider these influences using the methodology presented if the study area

is appropriately large. However, the experiment design did preclude the investigation of

heterogeneity at relatively small scales. In particular, the field sampling strategy could

not identify horizontal heterogeneity at scales smaller than the horizontal profile spacing.

Similarly, the detail of the numerical simulation was limited by the grid size. Therefore,

features such as Langmuir circulation, that have a width scale limited by the depth of the

mixed layer (Leibovich, 1983), could not be resolved using the methodology presented.

2.5.3 Ecological consequences of wind driven patchiness

If horizontal patchiness is created by physical structuring of a system rather than gra-

dients in biochemical processes, on the surface it may be questioned whether or not this

particular form of patchiness has any ecological significance or if it simply represents frozen

flow. It was clear from both the field observations and the simulation results that, when

29


active, the mixing associated with advective transport was sufficient to eliminate the layer

structure of Ceratium. Effectively, the periods of wind forcing rendered Ceratium inca-

pable of migrating to a preferred light level. However, the role of vertical migration was

critical during calm periods in the morning, leading to the formation of a distinct vertical

layer (Fig. 2.12a). During calm conditions, the patch did not satisfy the assumption of

frozen flow and the divergence that occurred between the simulation and field measure-

ments during these periods reflected this. Although the calm morning period represented

a short fraction of the day, this time was sufficient to allow Ceratium to re-concentrate

near the surface.

Ceratium has two competitive advantages over non-buoyant phytoplankton, the ability

to position at an optimum light level and the avoidance of sinking losses. In this study,

the simulated Ceratium population was only able to position at a preferred light level for a

short fraction of each day. Throughout most of the day, it could be inferred that the actual

distribution of Ceratium would not have been significantly different from the distribution

of any other the phytoplankton species that inhabited the surface layer. However, in

the case of Microcystis, Reynolds (1989) demonstrated that the vertical migration allows

cells to recover quickly after wind mixing to exploit favourable conditions as soon as they

present. Although the periods of calm were short in San Roque Reservoir, the field data

indicated that these periods allowed the fast swimming Ceratium to position at a preferred

light level, at least for a fraction of a day. However, given that calm conditions during

daylight hours were limited, it is unclear as to whether or not the boost in optimum light

dose could provide adequate compensation for the swimming energy expended. If the

net energetic benefits were negligible, then it would follow that any neutrally buoyant

phytoplankton would be similarly competitive in this habitat. If this were the case, it

would follow that Ceratium was dominant in this habitat simply because it was previously

established, not because migration capacity gave an advantage. Or else other strategies

such as loss avoidance were more important. In a similar respect, the association of the

field Ceratium with relatively warm water correlated with the warm water preference of

this species, but the association was clearly an artefact of the patch formation mechanism,

not an indication of a favourable growth region.

The loss rates that sinking phytoplankton experience are in direct contrast to the

competitive advantage conferred by upward migration in a stratified lake. In theoretical

terms, the survival of negatively buoyant cells in the surface layer can only occur if net

growth can compensate for sinking losses. Huisman et al. (2002) used a one-dimensional

model to examine the relationship between the net growth, mixing and mixed layer depth,

to investigate the critical balance between these parameters. However, the persistent

horizontal patchiness in this study demonstrates an environment that can not be well

30

2.5 Discussion

described by one-dimensional analysis. The trapping of Ceratium in the relatively shallow

region at the southern end of the reservoir changed the light availability for Ceratium and

at the same time, the upwelling of the metalimnion at the opposite end of the reservoir

provided a light dose to the metalimnion region that one-dimensional averaging would

eliminate. There is clearly potential for a wider range of distinct niches to be identified

by giving consideration to both vertical and horizontal patchiness in lakes. When better

recognised, this form of complexity might improve insight into the reasons for dominance

and/or diversity of phytoplankton.

31


32

3

Identifying spatial structure in

phytoplankton communities using

multi-wavelength fluorescence

spectral data and principal

component analysis

3.1 Abstract

Rapid in situ measurements of some components of fluorescent spectra are now pos-

sible with submersible multi-wavelength fluorometers, which implies that phytoplankton

composition can be measured, at least implicitly, at a spatial resolution that allows many

scales of patches to be resolved. We present a method for identifying the location of

patches of distinct fluorescent groupings of phytoplankton by using principal component

analysis (PCA) to process in situ spectral data. The processing method potentially allows

retention of more information from the raw data than existing methods because it depends

on fewer assumptions. Furthermore, it can be applied without the need for site-specific

calibration of the fluorometer. A series of idealised spectral data sets were used to ex-

plain the conceptual basis of the approach; the method was then applied to field spectral

data sampled in Lake Victoria, Kenya. The results demonstrate that the main features of

large sample sets of multi-component spectral data can be summarised in a single graph

that reveals the number of spectrally distinct groups of phytoplankton at the site, and

33

INTERPRETING SPECTRAL DATA WITH PCA

allows information about the spatial structure of those different phytoplankton groups

to be derived from subsequent analysis. In this way, fluorescent spectral data collected

at high spatial resolution can be used to identify the locations of patches and facilitate

targeted water sample collection from those locations to investigate the species diversity

and distribution at a study site.

3.2 Introduction

Linking changes in species diversity to underlying physical, chemical, and biological

gradients is an important general objective in ecology. However, gradients in phytoplank-

ton community composition are difficult to investigate because they generally take the form

of patches that occur at scales ranging from a few centimetres to hundreds of kilometres

(Martin, 2003). Furthermore, these patches are continuously modified by fluid advection

and dispersion, and by cell division, motility, and mortality. Characterising patches with

field measurements demands higher spatial and temporal resolution in sampling than is

practically achievable using traditional optical microscopy.

The potential to differentiate certain phytoplankton taxa based on the composition of

their photosynthetic pigments was first recognised by Yentsch and Yentsch (1979), in the

time since then, the techniques for pigment detection based on fluorescence have progressed

beyond the laboratory and now equipment can be deployed in situ without the need for

any manual handling of samples (e.g., Cowles et al., 1993; Desiderio et al., 1997). In par-

ticular, commercially available multi-wavelength fluorometers (e.g., Beutler et al., 2002)

take advantage of the fact that much of the pigment information that is discriminatory can

be captured using a limited number of excitation wavelengths and a single emission wave-

length (Hilton et al., 1989; Johnsen et al., 1994). However, the goal of rapid, automated

measurement of phytoplankton diversity is still work in progress, in part because the ca-

pabilities of new field equipment prototypes are still evolving (e.g., Beutler et al., 2003;

Chekalyuk and Hafez, 2008), but more so because in addition to taxa specific spectral

variability, the bio-optical properties of living cells can vary substantially in response to

different light (SooHoo et al., 1986; Hilton et al., 1988) and nutrient exposure (Cleveland

and Perry, 1987; Sosik and Mitchell, 1991). Bio-optical measurements thus carry informa-

tion about phytoplankton physiology that is potentially useful (Sosik and Mitchell, 1991;

Beardall at al., 2001), but at the same time, this additional information hinders attempts

to infer phytoplankton community structure from in situ fluorescent spectra (Jakob et

al., 2005). Furthermore, in natural waters, the fluorescence of dissolved organic matter

(CDOM) partially overlaps with phytoplankton fluorescence, which in effect, means that

the background signal is another unknown variable for in situ measurements (Babichenko

34

3.2 Introduction

et al., 2000). It is worth emphasising that because fluorescent detection is a highly sensi-

tive measurement (Holm-Hansen et al., 1965), there is no real issue in detecting changes

in spectra due to these influences; the problem is rather how to interpret the wide array of

information that is potentially contained in spectral measurements, particularly as these

measurements can now be accumulated at frequency of around 1 Hz (Beutler et al., 2002)

during the course of a typical field sampling campaign.

Different approaches have been applied previously to decode taxonomic information

from spectral data (see MacIntyre et al., 2010 for a detailed review). Some approaches have

the specific goal to identify particular harmful species (e.g., Millie et al., 1997; Zhang et

al., 2010), whereas others are designed to infer community composition (e.g., Seppala and

Balode, 1998; Beutler et al., 2002; MacIntyre et al., 2010), and this latter objective is the

focus here. Whereas the earliest studies of community composition were based on pigment

peak ratios (Yentsch and Phinney, 1985; Babichenko et al., 1999; Cowles et al., 1993), more

recently, the most common strategy has been to express measurements of spectra made on

phytoplankton assemblages of unknown composition, which we will call response spectra,

as linear combinations of more fundamental spectral components (Poryvkina et al., 1994;

Beutler et al., 2002) by using a least squares fitting procedure. This general approach

has been termed linear unmixing (MacIntyre et al., 2010). The fundamental spectral

components, called norm spectra (Beutler et al., 2002) or spectral fluorescence signatures

(Poryvkina et al., 1994), are typically determined by measuring the spectra of individual

phytoplankton species isolates that have been cultured in the laboratory (e.g., Beutler

et al., 2002; Bodemer, 2004). Alternatively, norm spectra can be inferred directly from

field samples using multivariate methods (Seppala and Olli, 2008), but to do this, the

phytoplankton composition of the calibration field samples must be known.

In practice, and regardless of how the norm spectra are determined, these spectra

are usually considered to be representative of major fluorescent groups of phytoplank-

ton, rather than individual species, because the differences between the norm spectra of

many species are potentially smaller than differences that may be due to changes in cell

physiology. At present, there is no way to differentiate the latter. Accepting this level of

uncertainty, four broad fluorescent groupings of species have been consistently identified

(Beutler et al., 2002; Poryvkina et al., 1994). The main groupings were categorised by

Beutler et al. (2002) as green (mainly chlorophytes), blue (cyanobacteria but excluding

red cyanobacteria that contain phycoerythrins), brown (diatoms, haptophytes, and di-

noflagellates), and mixed (cryptophytes). Beutler et al. (2002) determined typical norm

spectra for each of these groups based on measurements of several cultured species rep-

resentatives from each group (Fig. 3.1), and also found that these norm spectra were

linearly independent, which is an essential mathematical requirement for linear unmixing.

35


0

0.5

1

1.5

2 (c) Brown group (c

3)

Rel

ativ

e fl

uo

resc

ence

em

issi

on

in

ten

sity

wavelength [nm]

45

0

52

5

57

05

90

61

0

0

0.5

1

1.5

2 (a) Green group (c

1) (b) Blue group (c

2)

45

0

52

5

57

05

90

61

0

(d) Crypt. group (c4)

Figure 3.1: Norm spectra of four major fluorescentgroupings of phytoplankton reproduced from Beut-ler et al. (2002): (a) Green (Chlorophyta), (b) Blue(Cyanobacteria), (c) Brown (Heterokontophyta, Hap-tophyta, and Dinophyta), (d) Cryptophyta. Horizon-tal axes tick marks indicate the wavelengths used toexcite fluorescence. The relative fluorescence emis-sion intensity is the integrated intensity measured be-tween 680-720 nm with units of digitised photomul-tiplier voltage (digits) per measuring light intensity(µE m2 s−1) and per unit chlorophyll concentration(µ g L−1).

However, compiling a reference library of

norm spectra for widespread use is dif-

ficult because absolute measurement val-

ues from different fluorometers (including

those that are the same model) cannot

be directly compared unless appropriately

adjusted by a quantum correction proce-

dure (Kopf and Heinze, 1984). There-

fore, norm spectra should be uniquely

calibrated for a specific site and instru-

ment, and even then, the norm spectra

will be unstable in situ if subsequent en-

vironmental variations lead to physiolog-

ical changes in the living cells. At a

minimum, the uncertainty around norm

spectra means that some potentially sig-

nificant information contained in the re-

sponse spectra will be lost in the form

of the fitting errors of linear unmixing.

More problematically, intra-specific vari-

ability alone can be so significant as to

confound taxonomic assessment (MacIn-

tyre et al., 2010).

Given that the problem of defining norm spectra makes linear unmixing inherently

difficult, it is reasonable to consider an alternative processing technique for in situ spec-

tral data that approaches the problem from a new perspective. Specifically, instead of

attempting the decomposition of spectral measurements on an individual basis, we pro-

pose to examine the differences between spectral measurements from a particular site, in

essence, to focus on gradients in the entire spectral data set rather than on the absolute

features in individual measurements. If gradients in spectral data can be identified, then

it follows that they must either be associated with underlying changes in phytoplank-

ton community composition, phytoplankton physiology, and/or concentration of CDOM.

Whatever the underlying cause, the number of gradients at a particular site is likely to

be much smaller than the number of spectral samples collected. Therefore, once the gra-

dients are identified, targeted supplemental water sampling can be used to clarify their

nature. In particular, where spatial gradients in phytoplankton community composition

36

3.3 Method

are concerned, the gradient extremes are likely to represent the origins of spectrally distinct

phytoplankton patches.

The purpose of this work is to demonstrate how multivariate analysis, specifically

principal component analysis (PCA), can be applied to in situ spectral data to determine

the number and location of different patches of phytoplankton at a particular sampling

site. Multivariate methods similar to PCA have been applied previously to spectral data

to assist with the identification of norm spectra (Seppala and Olli, 2008; Zhang et al.,

2006), to determine optimum wavelengths for the discrimination of various phytoplankton

groups (Johnsen et al., 1994) and to classify response spectra with reference to known

norm spectra (MacIntyre et al., 2010). However, here we focus on using PCA as a basis

to reveal the relative differences between response spectra measured at the same site.

The critical advantage of this gradient approach is that it bypasses the need to classify

individual samples, which implies that the norm spectra (and the assumptions on which

their use is based) are not required. The method simply requires that some algal groups,

with linearly independent norm spectra, exist at the site (even if unknown a priori), and

are mixed in different proportions throughout the domain being investigated. A series

of simulated data sets are used to demonstrate the theoretical basis of this approach.

Because the underlying concentrations, compositions, and norm spectra of phytoplankton

in the simulated data sets are exactly known, both the effectiveness and idiosyncrasies of

the method are demonstrated explicitly. The practical applicability of the method is then

demonstrated using field data collected from Winam Gulf, Lake Victoria.

3.3 Method

A series of gradients in phytoplankton community composition, or coenoclines, form

the basis of four separate idealised examples. Each coenocline describes the community

composition and abundance of two or more fluorescent phytoplankton groups in a lake

of length L and depth H. Each coenocline is based on a set of simple equations that

specify how the concentrations of the fluorescent groups change over the domain, as briefly

summarised below:

• Case A: Opposing linearly increasing and decreasing horizontal variations of green

and brown fluorescent groups.

• Case B : Three partially overlapping Gaussian distributions representing one-dimensional

horizontal patches of green, blue, and brown fluorescent groups.

• Case C : Three partially overlapping Gaussian distributions representing two-dimensional

patches of brown, mixed, and green fluorescent groups.

37


• Case D : Same as Case C but with a random error included in the response spectra.

We assumed that the multi-wavelength fluorometer was configured identically to the

bbe Moldaenke Fluoroprobe (TS 7-07). The Fluoroprobe has five light-emitting diodes

(LEDs) that sequentially irradiate the water sample at different wavelengths (450, 525,

570, 600, and 610 nm) and a light detection sensor that captures the sum of the intensity

of fluorescence emission between 680 nm and 720 nm (Beutler et al., 2002). Hence, a single

measurement generates five variables from which the excitation spectrum for Chlorophyll

a florescence can be inferred.

The norm spectra used for the phytoplankton groups in the simulated in situ data were

taken from the typical norm spectra given by Beutler et al. (2002) shown in Fig. 3.1. It

is convenient to write the norm spectra as a matrix:

skm =

1.2 0.4 0.2 0.3 0.4

0.3 0.3 0.8 1.3 1.9

1.2 0.8 0.3 0.3 0.3

1.2 0.8 1.1 1.0 0.8

where the index m = 1, 2, 3, 4, 5 (columns) relates to the five wavelengths of excitation

(λm), and k represents the algal group, from k = 1, green; k = 2, blue; k = 3, brown to

k = 4, cryptophyte, as shown in Fig. 3.1. The rows of this matrix indicate the absolute

responses of the Fluoroprobe sensors per unit of chl a.

The response spectra of any sample that contains only these groups may be expressed as

a linear combination of the norm spectra of the constituent phytoplankton species present

in that sample, weighted by their concentrations. Therefore, wherever the composition of

phytoplankton is known, the response spectra at that location may be simulated by an

equation similar to that used by Millie et al. (1997):

S(xi, zj , λm) =4∑

k=1

cijkskm

where i and j are indices determining the spatial location (xi, zj), k designates the

algal group, defined in Fig. 3.1, m designates the excitation wavelength (λ), and cijk the

concentration of group k, present at location (xi, zj). For all case studies presented, we

constructed simulated field data sets by assuming that measurements of response spectra

were made at 101 evenly spaced stations along the length of a transect.

The simulated spectral data matrices were normalised before performing PCA. For

each sample, the normalisation procedure divided the five magnitudes associated with

each measurement by the mean of those five variables. In effect, this procedure discards

information about changes in fluorescence intensity, a proxy for changes in biomass, and

38

3.3 Method

instead emphasises changes in spectral shape, which relate to changes in pigment compo-

sition.

The central aim in applying PCA is to reduce a data set consisting of values from five

emission magnitudes to a smaller number of composite variables. The composite variables

are orthogonal so they can be displayed on a new set of axes known as the principal

component (PC) axes that better reveal the underlying variation in the data. The PC

axes each explain a separate and known proportion of the total variance in the original

data, so although there are always as many PC axes as there are variables in the original

data, the PC axes can be easily prioritised by magnitude. The first few PC axes often

explain a substantial proportion of the total variance, so the lowest ranked PC axes can

be neglected to reduce the data set.

The only input to PCA is a matrix that contains values for all of the different variables

that comprise each sample. In the present context, the input matrix has as many rows as

the number of samples collected and five columns that reflect the number variables used

to describe the response spectra.

The mathematics of PCA is detailed thoroughly in the existing literature (e.g., Jolliffe,

1986; Legendre and Legendre, 1998); the core of the methodology can be summarised

briefly in three steps. First, each column of a sample set matrix has its mean value

subtracted. Second, the covariances between all of the data columns are calculated and

expressed in the form of a symmetric covariance matrix. Third, the covariance matrix

is reduced to its canonical form by eigenvalue decomposition (Legendre and Legendre,

1998). The eigenvalue decomposition generates a matrix of eigenvectors, commonly called

loadings, that relate the original variables to the PC axes. A second matrix can then

be found by multiplying the original variables by the loadings, giving a score for each

sample. Each score is made up of multiple components that give the coordinates of the

original samples with respect to the new PC axes. In practice, eigenvalue decomposition

is solved numerically, and in this case, PCA was done using MATLAB (version 2008b,

The MathWorks). The proportion of total variance explained by each PC axis is also

determined as part of the procedure.

For the fourth case study presented in Results (Case D), a random measurement error

was incorporated into the response spectra data to show the effects on PCA when applied

to non-ideal spectral data. The magnitude of the introduced error was equivalent to an

instrument measurement precision of ± 1%. Due to effects caused by the addition of

random error, cluster analysis was required to facilitate the interpretation of the results.

The cluster analysis was performed in MATLAB using an algorithm that separated the

data set into 50 clusters. The algorithm adjusts the centroid locations of each cluster

iteratively to minimise the total distance between all scores and the centroid of their

39


cluster. The distance measure for the clustering was Euclidean, which is appropriate

given that transformation of data by PCA preserves the Euclidean distance between scores

(Legendre and Legendre, 1998).

3.4 Results

3.4.1 Case A

0 0.5L L

0

1

2

3

4

5

6

7

8

9

10

distance

chlo

rophyll

a [

µgL

-1]

Gradient A

Figure 3.2: Simulated coenocline for Case A depict-ing the changes in concentration of green (circles, ci1)and brown (squares, ci2) phytoplankton groups over ahorizontal spatial gradient of length equal to L. Onlyevery fifth sample is plotted for clarity.

Case A assumes a linearly increasing

concentration of the green plankton group

(Fig. 3.1a) and a linearly decreasing con-

centration of the brown algal group (Fig.

3.1c) from x = 0 to x = L, as depicted in

Fig. 3.2, uniform over depth.

As there is no depth variation in Case

A, the concentrations of the four phyto-

plankton groups reduces to:

cijm = cim

ci1 =10xiL

ci2 = 10(1 − xiL

)

ci3 = ci4 = 0

where the subscript i may be thought of as representing the sample number with sample

number increasing monotonically from x = 0 to x = L. Therefore, at any distance along

the gradient, the response spectra S(xi, zj , λm), can be expressed as:

S(xi, λm) =10

Lxis1m + 10(1 − xi

L)s3m

Evaluating the response spectra at 101 evenly spaced stations from xi = 0 to xi = L

40

3.4 Results

generates the matrix Sim:

Sim =

12.0 8.0 3.0 3.0 3.0

: : : : :

12.0 6.0 2.5 3.0 3.5

: : : : :

12.0 4.0 2.0 3.0 4.0

that shows a linear transition from spectral values conforming to the brown spectrum (Fig.

3.1c) to the green spectrum (Fig. 3.1a). Note that the central row shows the response

spectra values at the midpoint of the gradient (x51 = 0.5 L).

As discussed above, to focus attention on the composition of samples, we normalise

the matrix by dividing the rows of Sim by the mean value of each row. In addition, a

first step to calculating the covariances between columns is to subtract the mean of each

column from the values in that column, which leads to a new matrix Rim:

Rim =

−0.1574 0.2755 0.0558 −0.0394 −0.1345

: : : : :

−0.0042 0.0073 0.0015 −0.0010 −0.0036

: : : : :

0.1736 −0.3038 −0.0615 0.0434 0.1483

For this simple example, a close inspection of Rim can reveal that all of the columns

are correlated. This implies that for Case A, it is sufficient to have only one sensor, sensor

m = 1, as sensor responses m = 2, m = 3, m = 4, and m = 5 are simply different fractions

of that sensor (−7/4,−17/48,

1/4 and 41/48, respectively).

Seeking such simplifications may be formalised by applying a PCA to Rim, in which the

first step is to calculate the sample covariances between the five different sensor outputs.

When expressed in matrix form, the covariances between the five columns of Rim can be

calculated as:

Yml =RT

imRim

N − 1=

0 0 0 0 0

0 9.5x10−3 2.4x10−3 0 −2.4x10−3

0 2.4x10−3 6.0x10−4 0 −6.0x10−4

0 0 0 0 0

0 −2.4x10−3 −6.0x10−4 0 6.0x10−4

where RT

im is the transpose of Rim and N is the number of samples. The symmetric matrix

Yml can then be diagonalised by solving for the five eigenvectors (γ):

41


γ =

0.45 −0.81 −0.30 −0.02 0.22

−0.78 −0.53 0.29 −0.14 0.03

−0.16 −0.09 −0.12 0.97 −0.09

0.11 −0.20 0 −0.09 −0.97

0.38 −0.11 0.90 0.17 0.05

where each column of γ gives the loadings for one of the five PC axes. Multiplying

R(xi, z1, λm) by γ generates a set of sample scores (φ):

φ =

−0.35 0 0 0 0

: : : : :

−0.01 0 0 0 0

: : : : :

0.39 0 0 0 0

In this case, because only the first column (φ1) is nonzero, it can be inferred that all of

the variance in R(xi, z1, λm) is captured in the first PC axis. This result essentially arises

because, in its simplest form, the variation depicted in Fig. 3.2 is a linearly changing

ratio of two plankton groups with distance x; therefore, although the gradient in Fig. 3.2

-0.4 -0.2 0 0.2 0.4

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

PC axis 1

PC

axis

2

PCA of gradient A

n = 1n = 50

n = 100

Figure 3.3: Scores derived from PCA of responsespectral data from Case A (only every fifth score isplotted for clarity). The marker shadings give an indi-cation of the sample number of each score: the lightershading, the lower the sample number. Arrows anno-tate the first (x1 = 0), 50th (x50 ≈ 0.5 L), and 100th

(x100 ≈ L) scores.

was originally measured in terms of five

variables, the intrinsic variation captured

by these variables can be represented by

one variable (φ1) and plotted along a sin-

gle axis (Fig. 3.3).

As the PC axes in PCA are always or-

thogonal, if scores plot along a straight

line, as in Fig. 3.3, the underlying re-

sponse spectral variables must be chang-

ing in a fixed linear combination. In gen-

eral, its important to recognise that if all

scores in a particular data set plot in a

straight line, it reveals that all response

spectra in that data set can be explained

by exactly two types of linearly indepen-

dent spectra. Applying PCA to an in situ

data set that had only one type of lin-

early independent spectrum would have

produced a scores matrix filled with ze-

roes, and all scores would have simply

42

3.4 Results

plotted at the origin of the PC axes. In the other extreme, a set of samples with more

than two types of linearly independent spectra could not have produced a set of scores

that plot along a straight path in PC axes space, as this would violate linear indepen-

dence. In short, any straight path formed by the scores is significant because it indicates

the existence of an underlying gradient between exactly two linearly independent spectra.

In addition, the scores that plot at the extreme ends of any straight path are particularly

significant because they indicate the respective origins of that gradient. For example, the

scores highlighted at the two extremes of the straight path in Fig. 3.3, n = 1 and n = 100,

which will be referred to as end-points, are the scores that represent the purest examples

of norm spectra for the brown and green groups, respectively. Cross-referencing with Fig.

3.2 confirms this; the first (n = 1, x1 = 0) and last (n = 100, x100 ≈ L) samples correspond

with the maximum dominance by the brown and green groups, respectively. Apart from

the two end-point scores, the graduated shading of the other intermediate scores shown in

Fig. 3.3 indicates that all scores are ordered logically in the PCA axis space, that is, the

scores are ordered according to their corresponding relative positions along the coenocline

in Fig. 3.2.

3.4.2 Case B

0 0.2L 0.5L 0.8L L0

1

2

3

4

5

6

7

8

9

distance

chlo

rophyll

a [

µgL

-1]

Gradient B

Figure 3.4: Coenocline for Case B depicting changesin concentration of blue (circles), green (triangles),and brown (squares) phytoplankton groups over aspatial gradient of length L.

Case B (Fig. 3.4) differs from the

previous case in several ways: the phy-

toplankton group distributions are bell-

shaped rather than linear; the maximum

concentrations of phytoplankton are dif-

ferent for each group; and the maxima

do not coincide with the extreme ends of

the sampling transect. The distributions

of the groups follow three Gaussian type

functions centred at x = 0.2 L (blue), x

= 0.5 L (green), and x = 0.8 L (brown).

Despite the presence of three phyto-

plankton groups in this case, only the first

two PC axes were required to explain all of

the variance in the original response spec-

tral data. The scores of Case B plot along

two almost straight paths that intersect

each other (Fig. 3.5), and hence form a

total of three end-points (n = 20, n = 50,

43


and n = 80). Note that although the two paths are not parallel to either PC axis, they

still have the same significance as explained in Case A, that is, each path represents a

transition between two types of linearly independent spectra. However, as these paths

intersect, one linearly independent spectrum must be common to both gradients. By

cross-referencing Fig. 3.4 with Fig. 3.5, it can be seen that the first end-point (n = 20,

Fig. 3.5) corresponds to the region of the coenocline where the blue group dominates the

plankton composition most strongly (x = 0.2 L, Fig. 3.4). The tightly packed cluster of

scores between n = 80 and the last score (n = 100, Fig. 3.5) corresponds to the region

of the coenocline where the brown group always dominates the plankton composition (0.8

L < x < L, Fig. 3.4). The end-point that is at the intersection of the paths (n = 50,

Fig. 3.5) corresponds to the region of the coenocline where the green group (x = 0.5 L,

Fig. 3.4) had maximum dominance. There is very slight curvature in the path of the data

between n = 1 and n = 50 (Fig. 3.5), which is due to the small but variable influence of the

brown group in the transition between the blue and the green groups. As the blue, green,

and brown phytoplankton groups did not completely dominate the plankton composition

at x = 20, x = 50, and x = 80, respectively, the response spectra that directly associate

with these end-point scores are slightly different from the norm spectra for these groups.

-1.5 -1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

PC axis 1

PC

axis

2

PCA of gradient B

n = 1

n = 20

n = 50

n = 80n = 100

Figure 3.5: Scores derived from PCA of responsespectral data from Case B. The marker shadings in-dicate where each score was collected: the darker theshading, the nearer to the end of the gradient L thatits corresponding sample was collected from. Arrowsannotate the first (x1 = 0), 20th (x20 = 0.2 L), 50th

(x50 = 0.5 L), 80th (x80 = 0.8 L) and the 100th (x100

≈ L) scores.

Given this difference, it is appropriate

to make a distinction in terminology to

distinguish between the norm spectra de-

rived from pure samples (cf. Fig. 3.1)

and the purest examples of norm spec-

tra that can be found in a particular field

data set, which are hereafter referred to

as base spectra. Technically, the base

spectra occur where a particular fluores-

cent group makes its maximum contri-

bution to the spectral fluorescence mea-

surements; however, in practice, this oc-

currence is also likely to closely coincide

with the region where the fluorescent in-

tensity attributable to that group is high-

est. Furthermore, as fluorescent inten-

sity is usually closely correlated with cell

abundance, the location of the base spec-

tra should often coincide with where the

concentration of a particular fluorescent group is highest.

44

3.4 Results

It is not immediately intuitive why a one-dimensional coenocline featuring shifts be-

tween three norm spectra over distance L (Fig. 3.4) should manifest in PCA axes space

along a ’v’-shaped path. Nonlinear trends like this are commonly observed when PCA or

related ordination techniques are applied to ecological data sets (Austin 1985), and can

have several underlying causes (Podani and Miklos, 2002).

To explain why the v-shaped data arrangement is mathematically essential in this case,

it helps to first clarify that in the PCA axes space, the distance between any two scores is

a direct measure of the dissimilarity of their underlying response spectra. Dissimilarity is

defined by the root mean square (RMS) sum of the differences at each wavelength:

d =

√√√√ 5∑m=1

(R(xi, z1, λm) −R(xp, z1, λm))2

where R(xi, z1, λm) and R(xp, z1, λm) are response spectra measured at two different loca-

tions (xi, z1) and (xp, z1), and m designates the different wavelength components in the

response spectral measurement.

If the first response spectral sample from the coenocline in Fig. 3.4 (i.e., n = 1,

x = 0) is selected arbitrarily as a reference sample, the RMS differences between that

sample and every other sample can be calculated (Fig. 3.6). Note that it is possible

to derive the same data as in Fig. 3.6 (in relative terms) directly from Fig. 3.5 by

measuring the linear distances between the first score (n = 1) and every other score. Fig.

3.6 shows that the dissimilarity does not increase monotonically with sample number,

for example, after n = 50 (which corresponds with the main bend in Fig. 3.5), the

dissimilarity gradually decreases with sample number. The v-shaped arrangement of the

scores is the only arrangement that preserves the Euclidean distances between all the

different combinations of score pairs. Furthermore, in Case A it was explained that a

coenocline containing more than two linearly independent norm spectra cannot plot along a

straight path in PCA axes space, therefore, there must be a kink in the path formed by the

scores where the coenocline shifts from blue-green dominance to green-brown dominance

(i.e., at x = 0.5 L, n = 50, Fig. 3.4).

45


1 25 50 75 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Rel

ativ

e fl

uore

scen

ce e

mis

sion

inte

nsi

ty

wavelength [nm]

sample number

Eu

clid

ean

dis

tan

ce

0

1.5

(a) x=1

0

1.5

(b) x=20

0

1.5

(c) x=30

0

1.5

(d) x=50

0

1.5

(e) x=80

45

0

52

5

57

05

90

61

0

Figure 3.6: Main panel shows the RMS differences between the response spectral samples fromCase B relative to the response spectra at n = 1 (x = 0) for all simulated samples. Inset panels showresponse spectra (in black) at selected sample numbers (n = 1, 20, 30, 50, and 80) contrasted withthe reference response spectra (n = 1) in grey.

46

3.4 Results

3.4.3 Case C

(a) 0

0.25H

0.5H

0.75H

tota

l ch

l. a

[u

gL

-1]

2 4 6 8 10 12

(b) 0

0.25H

0.5H

0.75H

’bro

wn

’ g

rou

p [

%]

0 20 40 60 80 100

(c) 0

0.25H

0.5H

0.75H

’cry

pto

ph

yte

’ g

rou

p [

%]

0 20 40 60 80 100

(d)

distance

0 0.2L 0.4L 0.6L 0.8L L

0

0.25H

0.5H

0.75H

’gre

en

’ g

rou

p [

%]

0 20 40 60 80 100

Figure 3.7: The coenocline for Case C based ona rectangular shaped lake of length L and depth H.Panel (a) shows the spatial distribution of total chl a(µ g L−1) based on summation of the brown, cryp-tophyte, and green groups. Panels (b), (c), and (d)show the percentage contribution to the total chloro-phyll concentration made by the brown, cryptophyte,and green phytoplankton groups, respectively. Crossmarks in panels (b), (c), and (d) indicate the loca-tions of the 7648th, 9098th, and 2557th samples, re-spectively (samples that are cross-referenced in Fig.3.8).

Case C depicts a two-dimensional

coenocline in which horizontal and ver-

tical changes in the concentrations of

brown, mixed, and green phytoplankton

groups lead to three distinct patches (Fig.

3.7). The response spectral data set for

this coenocline was larger than that of

previous cases because the depth varia-

tions meant that the simulated sampling

required 100 vertical profile measurements

at each of the 101 sampling stations to

cover the domain. PCA found that the

first two PC axes completely captured the

variance in the spectral data, but in this

case, the scores formed a two dimensional

triple-pointed structure instead of a single

track (Fig. 3.8).

The end-point scores at the extremi-

ties of the three outward pointing tracks

(Fig. 3.8) correspond to samples mea-

sured near the centres of the three

patches, the locations of which are indi-

cated in Fig. 3.7. Given that the end-

point scores indicate the purest examples

of the three base spectra, the scores that

are intermediate to the three end-points

therefore correspond with the transition

regions between the patches. A useful in-

terpretation of Fig. 3.8 is that the rela-

tive positions of the scores in relation to

the three end-points indicate their plankton compositions in a manner that is similar to a

ternary plot. The meshed arrangement of the scores in Fig. 3.8 is caused by the idealised

Gaussian curvature of the simulated patches, combined with the regular sampling pattern.

If all possible combinations of the 3 groups were represented in the coenocline, then the

scores in Fig. 3.8 would take the shape of a filled triangle.

47


3.4.4 Case D

-0.4 -0.2 0 0.2 0.4

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

PC axis 1

PC

axis

2

PCA of gradient C

n = 2557 (green)

n = 7648 (brown)

n = 9098

(cryptophyte)

Figure 3.8: Scores derived from PCA of responsespectral data from Case C. Arrows annotate the7648th, 9098th, and the 2557th scores, and the phy-toplankton groups that dominate their correspondingsamples are indicated in brackets. The locations thatthese particular samples were measured are indicatedin Fig. 3.7.

Case D is based on the same coeno-

cline as Case C (Fig. 3.7), but the sim-

ulated data set incorporated random er-

ror into all five of the variables associated

with each response spectral measurement.

PCA on spectral data from Case D re-

vealed that the first two PC axes ex-

plained more than 99% of the total vari-

ance in the spectral data. When the scores

of Case D were plotted (Fig. 3.9), they

formed a triple-pointed structure similar

to that shown for Case C (Fig. 3.8), how-

ever, the effect of the random error ad-

dition was to disrupt the precise meshed

arrangement of the scores. This disrup-

tion meant that it was difficult to single

out three particular end-point scores as

was done in Case C. Therefore, data clus-

tering was used to identify collections of

scores that were near to the end-point re-

gions. The objective was to form three

clusters small enough to be closely associ-

ated with the end-point regions, but large

enough to approximately encompass the

scatter in the data. Initially, the data set

in Fig. 3.9 was split into 50 clusters to

ensure that the clusters were adequately

sized, but only the three end-point clus-

ters needed to be retained for further an-

nalysis.

-0.4 -0.2 0 0.2 0.4

-0.4

-0.2

0

0.2

PC axis 1

PC

axis

2

PCA of gradient C with measurement error

cluster D1

cluster D2

cluster D3

Figure 3.9: Scores derived from PCA of responsespectral data from Case D. Grey shading of se-lected scores indicates their membership of the clus-ter groups annotated by arrows. The locations wheretheir corresponding samples were measured are indi-cated in Fig. 3.10.

The measurement locations of the

samples associated with each of the three

clusters in Fig. 3.9 are indicated in Fig.

3.10. The measurement locations of these samples directly relate to the coenocline in

Fig. 3.7; samples from the D1, D2, and D3 clusters were located near the regions of

highest concentration for the brown, mixed, and green groups, respectively (Fig. 3.10).

48

3.4 Results

0 0.2L 0.4L 0.6L 0.8L L

0

0.25H

0.5H

0.75H

6

8

5

Spatial locations of data clusters

dep

th

distance

cluster D1

cluster D2

cluster D3

Figure 3.10: Summarised version of the coenoclinefor Case D showing regions of high concentration ofbrown (cluster D1), cryptophyte (cluster D2), andgreen (cluster D3) phytoplankton groups. The greydots indicate the measurement locations of the sam-ples that correspond with the clusters identified inFig. 3.9. The isoclines indicate the concentrationcontours for each phytoplankton group (µ g L−1) thatencircle the samples from each cluster. The crossmarks indicate the mean measurement location ofeach cluster based on the mean distance and meandepth of all the samples in each cluster.

Some phytoplankton concentration

isoclines from Fig. 3.7 are shown again

in Fig. 3.10 to demonstrate how the mea-

surement locations of the clustered scores

were constrained within the underlying

concentration contours of the three re-

spective phytoplankton groups.

It is useful to characterise each of the

three clusters by averaging the proper-

ties associated with their respective sam-

ples. The mean distances and depths of

the three clusters of scores were calculated

and are indicated by crosses in Fig. 3.10.

These crosses correspond closely with the

locations of the end-point scores that were

identified in Case C (Fig. 3.7). This shows

that the effect of averaging the properties

of the clusters is to smooth some of the

noise that was caused by the introduction

of random error.

3.4.5 Field data

Field data presented in this study were collected from Winam Gulf (0◦ 15′ S, 34◦ 35′ E),

which is a relatively large and shallow (2-10 m depth) expanse of water that is connected

to the northeast of Lake Victoria (40 m depth) through the Rusinga Channel (Okely et al.,

2010). Sampling stations spanning the Gulf and Channel (Fig. 3.11) were profiled with

a bbe Moldaenke Fluoroprobe (TS 7-07) during a two-day field campaign commencing on

14 Dec 2005. Water samples were also collected at three stations (S1, S7, and S10, Fig.

3.11). Further details of this sampling campaign can be found in Gikuma-Njuru (2008).

PCA on the response spectral field data indicated that the first two PC axes explained

more than 97% of the variance in the field data. The PCA scores (Fig. 3.12a) plotted

along a triangular track similar to that seen in Case B (Fig. 3.5), but with more dispersion

in the data (like Case D). Based on similarity to Case B, it can be surmised that the v-

shaped structure in Fig. 3.12a is indicative of three base spectra. To isolate and investigate

those base spectra, the data were split into 15 clusters, and four were retained for further

analysis (B1 to B4, Fig. 3.12a). Due to the dispersion in the data, the end-points were

not very clearly defined and two clusters were needed to encompass one of the end-points

49


10 km

Log10

Accumulated Distance [km]

0 1.1 1.4 1.6 1.7

S10

S1

S7

0.58oS 34.12

oE

RusingaChannel

100 km

Figure 3.11: Shoreline map of Winam Gulf with Lake Victoria inset. Open circles indicate thelocations of profiling stations S1 to S10. The transect path is indicated by a grey line, and theaccumulated distance along the transect path can be referenced directly from the scale bar shown.The accumulated distance is presented in logarithmic form to assist comparison with Fig. 3.12b.

in particular (B1 and B2, Fig. 3.12a). Furthermore, retaining both of these clusters

separately allows an example of the dispersion of the data to be examined.

As mentioned previously, the v-shaped arrangement of the field data in the PCA axes

space (Fig. 3.12a) probably indicates the existence of three partially overlapping patches

of phytoplankton at the field site, as was shown in Case B. However, as PCA does not

give any information about the location of those patches, it is useful to superimpose the

sampling location of each data point onto the results of the PCA; this was done by colour-

shading each sample in the PCA axis space to indicate its east-west sampling location (Fig.

3.12b) and its sampling depth (Fig. 3.12c). Fig. 3.12b shows that the samples associated

with the three end-points were measured at three distinct horizontal locations along the

transect. Samples associated with the B1 and B2 clusters (Fig. 3.12a) were all measured

at the western extreme of the transect, which was in the open waters of Lake Victoria

(station S1, Fig. 3.11). The samples associated with the B4 cluster (Fig. 3.12a) were all

measured at the eastern extent of the transect, which was within Winam Gulf (stations

S9 and S10, Fig. 3.11). The samples associated with the B3 cluster (Fig. 3.12a) were

all measured at an intermediate location along the transect that was within the Rusinga

Channel (station S7, Fig. 3.11).

50

3.4 Results

-1 0 1 2

-1

0

1

B1

B3

B4

B2

(a)

-1

0

1

PC

2

Lo

g10 A

ccu

mu

late

d D

ista

nce

+ 1

[km

]

(b)

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.4 1.6

-1 0 1 2

-1

0

1

PC 1

Lo

g10 D

ep

th [

m]

(c)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 3.12: All panels show the results of PCAon response spectral data measured in Winam Gulf.Panel (a) shows all scores with colours to indicatemembership of cluster groups annotated by arrows.Panel (b) shows all scores with colour shades to in-dicate the sampling location of each sample with re-spect to the accumulated distance along the transectshown in Fig. 3.11. Panel (c) uses colour shades toindicate the depth at which each sample was mea-sured, but only the scores corresponding to samplesthat were measured at a depth exceeding 1 m areshown.

The sampling depths of the scores

from the field data set are indicated in Fig.

3.12c with the scores measured at depths

shallower than 1 m excluded. Compari-

son with Fig. 3.12a (or Fig. 3.12b) in-

dicates that these shallow scores, which

are missing in Fig. 3.12c, account for

a large amount of the general dispersion

in the data. Once they are removed,

the remaining data more closely resem-

ble Case B (Fig. 3.5). Furthermore, the

data from the B2 cluster (Fig. 3.12a) are

largely absent from Fig. 3.12c, so it can

be concluded that these data were mea-

sured very near to the surface. Data from

the B1 cluster was also measured near to

the surface, but below a depth of 1 m.

The sampling depths of all data from the

B4 cluster were also near to the surface

(Fig. 3.12b), but this mainly reflects the

shallow depth of Winam Gulf. The sam-

pling depths of the data belonging to the

B3 cluster were varied (Fig. 3.12c), in-

dicating that very similar response spec-

tra were measured throughout the depth

of the water column near station S7 (Fig.

3.11).

The base spectra associated with the

clusters B1 to B4 are presented in Fig.

3.13 along with the mean spectrum for

each cluster. The B3 base spectra (Fig.

3.13c) are distinguished by a shared peak

response to 470 nm, and in general, resem-

ble the norm spectrum for the brown flu-

orescent group (Fig. 3.1c). The B4 base

spectra (Fig. 3.13d) are distinguished by

51


peak responses to 610 nm, and generally resemble the norm spectrum for the blue fluores-

cent group (Fig. 3.1b). The response spectra of the samples from the near neighbouring

clusters, B1 and B2 (Fig. 3.13), all have a peak response at 525 nm but differ slightly in

their relative responses at 610 nm. Notably, the base spectra for B1 and B2 do not re-

semble any of the norm spectra shown in Fig. 3.1, and furthermore, cannot be accurately

approximated by any linear combination thereof (i.e., no norm spectra in Fig. 3.1 have a

peak at 525 nm).

0.5

1

1.5

2

2.5(a) B1

Rel

ativ

e fl

uo

resc

ence

em

issi

on

in

ten

sity

0.5

1

1.5

2

2.5(b) B2

0.5

1

1.5

2

2.5

(c)B3

0.5

1

1.5

2

2.5

47

0

52

5

57

0

59

0

61

0

(d) B4

wavelength [nm]

Figure 3.13: Response spectra for the cluster groupsindicated in Fig. 3.12a. Grey lines indicate the re-sponse spectra of the individual samples belonging toeach cluster group, and black lines indicate the meanresponse spectra for each cluster.

Water samples were collected to vali-

date the main finding that the three sets

of end-point scores in Fig. 3.12a represent

three different phytoplankton assemblages

located in: the open waters of Lake Vic-

toria, the Rusinga Channel and Winam

Gulf, respectively. The water samples col-

lected from these three regions (S1, S7,

and S10, Fig. 3.11) confirmed the exis-

tence of three distinct algal assemblages.

Water samples from the offshore station

(S1) were co-dominated (in terms of wet

weight biomass, estimated from cell bio-

volumes) by cyanobacteria (Aphanocapsa

sp., 71% of total wet weight biomass)

and diatoms (Nitzschia sp., 27%), samples

from the Rusinga Chanel (S7) were dom-

inated by diatoms (mainly Nitzschia sp.,

72%), and the Winam Gulf samples (S10)

were dominated by cyanobacteria (mainly

Cyanodictyon sp. and Aphanocapsa sp.,

80%). Further details of the water sam-

pling results are presented in Gikuma-

Njuru (2008).

3.5 Discussion

The ultimate objective of any processing method for situ spectral data is to extract

useful information from the raw signal. Both PCA and linear unmixing, the most com-

monly applied alternative method (e.g., Beutler et al. 2002), have the potential to reveal

52

3.5 Discussion

the same information in a given spectral data set. However, PCA can reveal that informa-

tion without the need to define norm spectra, so the method has a significant advantage

whenever there is uncertainty about the norm spectra. In effect, uncertainty about norm

spectra feeds uncertainty into the output of linear mixing, which is particularly undesir-

able given that the raw fluorescence measurements are known to be highly sensitive in

terms of their precision (Holm-Hansen et al. 1965).

Multivariate methods (including PCA) have been used previously to enhance the anal-

ysis of spectral data but with a different emphasis to this current work. In particular,

Seppala and Olli (2008) applied a method that is closely related to PCA as a means to

obtain norm spectra that were site-specific; in doing so they eliminated some potential

sources of error in the norm spectra while still staying within the framework of the linear

unmixing approach. However, this method depends on calibration samples being repre-

sentative of subsequent field samples, and that the spectra of individual species conforms

closely to the generalised norm spectra that are determined during the calibration phase.

Once norm spectra have been established, multivariate methods have also been applied

to improve classification of unknown samples. In particular, a multidimensional scaling

approach proposed by MacIntyre et al. (2010) produces two-dimensional plots that are

functionally similar in their interpretation to the results presented here. However, Mac-

Intyre et al. (2010) interpret these plots with reference to norm spectra. Essentially, by

applying multidimensional scaling to calibration samples as well as field data, norm spectra

samples can be overlaid on the same two-dimensional plot as field data, thereby providing

a frame of reference in which the field spectral samples can be classified. In contrast, the

PCA approach followed here references base spectra rather than norm spectra, which in

effect amounts to a focus on the relative differences within a spectral data set. Therefore,

the main distinction between these two ordination approaches is not so much due to the

ordination methods themselves but more so how the spectral data are interpreted after

the ordination methods are applied.

While PCA doesn’t give any direct information about the underlying causes of the

gradients that it reveals, the gradients in response spectra revealed by PCA are not limited

to those caused by changes in species composition, and in principle may be attributable

to anything that can influence response spectra. Under the linear unmixing approach,

deviations from the norm spectra are discarded when response spectra are imperfectly

matched to a linear combination of the calibrated norm spectra. In effect, deviations

from the norm spectra become linear fitting errors even though they may contain useful

information. An implication of this approach is that dinoflagellates and diatoms are

considered inseparable because there are no dependable distinctions between the norm

spectra of species from these phyla that apply generally (Beutler et al., 2002); however,

53


it is conceivable that there may be detectable differences between two specific species at

a particular site. As the PCA approach only contends with the variations in spectra at a

particular site, rather than the much wider range of variations amongst species and phyla

that are possible, detectable differences between species from the same fluorescent group

can afford to be retained in the results, rather than discarded.

Given that PCA reveals where gradients in response spectral data exist at a particular

site but not what causes them, water samples represent a valuable addition to a spectral

data set. By collecting samples at locations coinciding with patches identified from PCA,

the spatial resolution of the fluorescence measurements can be supported by the taxonomic

information revealed by microscopy. Furthermore, collecting samples coinciding with flu-

orescent patches identified from the PCA could provide a means to guide adaptive water

sampling. However, this presumes that it is practical to revisit relevant sites for water

sampling after the spectral data have been measured. If not, two alternative approaches

could still be used instead. First, PCA could be performed on all available data after

each profile; in this way, the final results of the analysis would be progressively revealed in

’real-time’, and adaptive sampling could be done on the basis of this preliminary analysis.

Second, if spectral data from a previous field sampling campaign (with the same instru-

ment) is available, then PCA could be performed on a composite data set consisting of

historical and newly acquired spectral data as it is collected. This would allow the newly

acquired data to be placed in the context of the historical data so that water samples

could be collected whenever substantial differences emerged.

Future iterations on the current generation of multi-wavelength fluorometers may in-

clude more sensors to detect finer distinctions in response spectra as this becomes feasible

(e.g., Beutler et al., 2003; Desiderio et al., 1997). In this regard, it is convenient that

the application of PCA is equally valid when there are a larger number of input sensors.

Furthermore, even if the number of input sensors expands beyond the point of redundancy

for a particular field site, the output from PCA will still only be limited to the number of

spectrally distinct patches that can be identified at that site.

3.6 Comments and Reccomendations

The case studies demonstrate that gradients embedded in large spectral data sets

can be revealed from direct analysis of the raw data, bypassing the need to first identify

the plankton composition of individual samples in terms of norm spectra. Although this

analysis was focused on spatial gradients, there is no reason, in principle, that would

prevent the same method being used to interpret changes in response spectra over time

as measured at a fixed monitoring station.

54

4

Phytoplankton patchiness in

Winam Gulf, Lake Victoria: a

study using principal component

analysis of in situ fluorescent

excitation spectral data

4.1 Abstract

In order to characterise phytoplankton patchiness at fine scales, a profiling multi-

wavelength fluorometer was cast at numerous locations throughout Winam Gulf in Lake

Victoria to measure fluorescent excitation spectra, which are indicators of both phyto-

plankton diversity and coloured dissolved organic matter (CDOM). Processing the spec-

tral data with principal component analysis (PCA) revealed that linear combinations of

four fundamental base spectra could explain almost all of the variation in the spectral

measurements. Three of the base spectra were associated with spatially distinct patches

of phytoplankton containing different species assemblages, while the fourth base spec-

trum was due to CDOM fluorescence. The locations of the phytoplankton patches were

traced to the southeast of Winam Gulf, the western end of the Rusinga Channel and the

open waters of Lake Victoria adjacent to Winam Gulf, respectively. The high CDOM

fluorescence was traced mainly to relatively deep water in the Rusinga Channel. The phy-

toplankton and CDOM patchiness was interpreted in the context of physical and chemical

55

PHYTOPLANKTON PATCHINESS IN WINAM GULF

gradients that were measured at the site at the same scale as the spectral data. Strong

relationships were found between the gradients in spectral data and other environmen-

tal variables, which suggested several underlying explanations for the phytoplankton and

CDOM patchiness.

4.2 Introduction

Patches of phytoplankton are modified continuously by both physical and biotic pro-

cesses (e.g. Alexander and Imberger, 2009). The biotic processes, which include cell

division, motility and mortality, proceed at rates that are determined by the distribution

of resources for growth as well as by the functional traits of phytoplankton (Reynolds

et al., 2002; Litchman and Klausmeier, 2008), where the latter allow those resources to

be exploited at different rates by different species. This implies that there should be a

relationship between phytoplankton patchiness and species traits, although homogenis-

ing processes like fluid mixing and dispersion (Martin, 2003) will always act to obscure

that relationship. To investigate the coupling of phytoplankton species distributions to

resource gradients, the relevant variables need to be sampled simultaneously at length

scales smaller than the patchiness and over periods shorter than the mixing time scales.

Owing to variations in the composition of photosynthetic pigments amongst phyto-

plankton taxa, certain groupings of phytoplankton can be differentiated based on mea-

surement of fluorescent excitation spectra (Beutler et al., 2002; MacIntyre et al., 2010).

In particular, Beutler et al. (2002) demonstrated the capacity to distinguish between four

main phytoplankton groups in situ using a five-wavelength spectral fluorometer. These

researchers identified: a green group (chlorophytes) that have a maximum in their exci-

tation spectra at 450 nm due to chlorophyll a (chl a), chlorophyll b and xanthophyll; a

brown group (including diatoms, dinoflagellates and haptophytes) that also have a peak

at 450 nm but are distinguished by a shoulder in their spectra at 525 nm because of fu-

coxanthin or peridinin; a mixed group (cryptophytes) that have a peak at 570 nm because

of phycoerythrin; and a blue group (cyanobacteria) that have a high response at 610 nm

because of phycocyanin.

Although the detection of fluorescence per se is considered highly sensitive (Holm-

Hanson et al., 1965), there is still significant ambiguity with regard to the interpretation of

spectral data (MacIntyre et al., 2010). Simply put, although the spectra of most individual

species can be broadly classified into one of the four major spectral groups (Beutler et

al., 2002), there is a degree of spectral variability within these groups (and also within

species) that makes it challenging to interpret fine gradients in excitation spectra that

may be detected at a particular site (Jakob et al., 2005). A further complicating factor is

56

4.3 Method

that the fluorescence of coloured dissolved organic matter (CDOM), which has a spectral

peak around 370 nm, partially interferes with spectral measurement of phytoplankton

(Babichenko et al., 2000).

One approach to deal with the ambiguity that is inherent to in situ spectral data is

to focus on the relative changes in spectra measured at a site. In this way, investigation

is limited to determining the specific causes of the gradients in spectra at a particular

site, rather than the multitude of factors that might influence individual spectrum mea-

surements. Applying principle component analysis (PCA) to spectral data (Alexander et

al., 2012) facilitates such an approach. Specifically, PCA allows the number of spectrally

distinct groups of phytoplankton at a particular site to be identified, as well as sub-sets

of spectral samples (called base spectra) that associate most closely with each group.

Furthermore, referencing the sampling locations of the base spectral samples reveals how

the spectrally distinct phytoplankton groups are spatially distributed, which means that

patchiness can be characterised at scales that are only limited by the horizontal and ver-

tical resolutions of spectral profile measurements.

The purpose of this work is to demonstrate that phytoplankton patchiness inferred from

vertical profiles of spectral data can be closely related to gradients in other environmental

variables measured simultaneously at the same site. The chosen site of Winam Gulf

is ideally suited for this kind of investigation because physical, chemical and biological

gradients between the Kenyan waters of Lake Victoria and Winam Gulf are persistent

and relatively well documented (e.g. Gophen et al., 1995; Gikuma-Njuru and Hecky

2005; Sitoki et al., 2012). We first provide some context for the spectral data set by

reviewing information about the site from previous investigations and then summarise the

environmental conditions at the time of our investigation. Set against this background, we

show that spectral data measured at the site can be interpreted to reveal information about

phytoplankton patchiness that is broadly consistent with previous studies. Moreover,

resolving phytoplankton patchiness at finer scales than previously will add to information

about the underlying drivers of patchiness in the Gulf.

4.3 Method

4.3.1 Site Description

Lake Victoria is one of the world’s largest lakes having an area of 68 800 km2 and a

mean depth of 40 m (Bootsma and Hecky, 1993). Winam Gulf (also known as Nyanza Gulf

or Kavirondo Gulf) is a relatively large expanse of water that is connected to Lake Victoria

in the northeast through the Rusinga Channel (Fig. 4.1). The Gulf has an area of 1400 km2

57


(Calamari et al., 1995) and a mean depth of around 5 m, which is shallow compared to

Lake Victoria. The main inflows to the Gulf are the Sondu River (1.3x109 m3yr−1) and

the Nyando River (5x108 m3yr−1), which are indicated in Fig. 4.1. Both inflows carry

high loads of nutrients due to human population density and agricultural practices in the

catchment (Calamari et al., 1995; Hecky et al., 2010) but their combined annual inflow

is small compared to the water mass fluxes to and from the Gulf due to direct rainfall

and evaporation respectively (Gikuma-Njuru, 2008). Similarly, evaporation and direct

rainfall dominate the annual water balance of Lake Victoria, with approximately equal

contributions (Piper et al., 1986). A gradient in salinity has been measured consistently

between Lake Victoria and the Gulf waters (Calamari et al., 1995; Gikuma-Njuru 2008;

Sitoki et al., 2012). In addition, hydrodynamic modelling has demonstrated that the

exchange between Winam Gulf and Lake Victoria is limited (Okely et al., 2010). The

same modelling has also identified an anti-clockwise residual circulation current in Winam

Gulf.

easting

0 10 20 30 40 50 60 70 80km

nort

hin

g

0

10

20

30

40

50km

0.58oS 34.12

oE

Sondu R.

Nyando R.

RusingaChannel

HomaBay

Kisumu

R4

T2

0 10 20 30 40

Depth (m)

1 profile

2 profiles

3 profiles

4 profiles

5 profiles100 km

Figure 4.1: Bathymetry of Winam Gulf with contour lines to indicate 5 m depth intervals. Eastingand northing scales indicate distances from the reference coordinate indicated by the + symbol.Circles indicate the locations of field sampling stations and the markings within the circles indicatethe total number of profiles measured at each station (see small inset). The large inset indicates theshoreline of Lake Victoria with the Winam Gulf sub domain shaded.

58

4.3 Method

The Gulf waters are characterised by high levels of turbidity and CDOM, particularly

in the shallow near shore regions (Loiselle et al., 2008). As a result, the light extinction

coefficient (KPAR ≈ 4 m−1) is high enough to imply that phytoplankton growth within

the Gulf might be light limited (Gikuma-Njuru and Hecky, 2005; Loiselle et al., 2008).

However, the phytoplankton composition within the Gulf is dominated by cyanobacteria,

and in particular Microcystis cells that are strongly buoyant. Therefore, the importance

of light limitation in the Gulf is equivocal (Sitoki et al., 2012). As phytoplankton biomass

in the Gulf is relatively high (Sitoki et al., 2012), photosynthesis and/or respiration can

be expected to drive large diurnal fluctuations in dissolved oxygen as has been observed

in other bays of Lake Victoria (e.g. Ramlal et al., 1995).

The physical and chemical characteristics of the Lake Victoria waters that are adjacent

to Winam Gulf are quite distinct from those of the Gulf. Compared to the Gulf, the waters

of Lake Victoria are deep, less turbid and have different nutrient status. In particular,

the waters of Lake Victoria are characterised by nitrogen depletion, which is believed to

be due to denitrification in the hypolimnion (Hecky, 1993). Silica concentrations in Lake

Victoria waters are also significantly lower than in the Gulf (Gikuma-Njuru and Hecky,

2005). The major seasonal variation of phytoplankton biomass in Lake Victoria occurs

in conjunction with the annual overturn of nitrogen-depleted hypolimnion waters between

June and August (Hecky, 1993). As phytoplankton growth in the deep waters of Lake

Victoria is light limited, annual biomass in the deep waters is at a minimum during July-

August when the surface mixed layer is at its deepest (Hecky, 1993). However, it should be

noted that the same seasonal dynamic is absent from Winam Gulf because it is too shallow

to stratify persistently. The stratification and nitrogen depletion in the deeper waters

of Lake Victoria generally promote the growth of buoyant nitrogen fixing cyanobacteria,

particularly species from the Cylindrospermopsis and Anabaena genera (Kling et al., 2001).

Following overturn, however, the relative abundance of cyanobacteria in Lake Victoria

waters decreases and the relative abundance of diatoms increases (Lung’ayia et al., 2000;

Sitoki et al., 2012).

The Rusinga Channel is a transition region between deep offshore waters and the

shallow Gulf in terms of its depth as well as its location. Lung’ayia et al. (2000) observed

that the phytoplankton composition in the Rusinga Channel was generally similar to

that observed in the deeper waters of Lake Victoria. However, they also noted that the

abundance of chlorophytes in the Channel was relatively high during the month of August.

Similarly, Sitoki et al. (2012) observed a relatively high abundance of chlorophytes in the

Channel during September, although diatoms still dominated the assemblage.

59


4.3.2 Field instrumentation

A multi-wavelength fluorometer (bbe Moldaenke Fluoroprobe TS 7-07) coupled with

a Centre for Water Research fine scale conductivity, temperature, depth (CTD) profiler

(Imberger and Head, 1994) was used to profile the water column in situ. The fluorometer

has separate light emitting diodes (LEDs) that permit the measurement of fluorescence

emission at six wavelengths (370 nm, 470 nm, 525 nm, 570 nm, 590 nm and 610 nm).

The LEDs are pulsed sequentially at a frequency of 5 kHz and a single photomultiplier

(bandwidth range between 680 nm and 720 nm) measures the emission stimulated by these

LEDs. The photomultiplier is synchronised with the LED pulses so that distinct responses

to each LED are isolated. To complete a single sample, the fluorometer averaged the high

frequency measurements over a time interval of 2 s. The fluorometer was trimmed so that

the maximum fall speed was close to 0.5 ms−1, which implies a vertical sampling resolution

of approximately 1 m. The fluorometer was accompanied by software (Fluoroprobe 2.1

bbe Moldaenke) that estimated total chl a [µgL−1] based on a factory-calibrated algorithm

that considered both the measured fluorescence excitation spectrum and the transparency

of the sample (Beutler et al., 2002). The fine scale CTD also measured turbidity, pH and

dissolved oxygen. The CTD has a sampling resolution of 50 Hz, which implied a vertical

sampling resolution of around 0.01 m.

Meteorological data was measured at a fixed monitoring station positioned 2 m above

the surface of the water in the Rusinga Channel (T2, Fig. 4.1). The station was attached

to a thermistor chain that measured the temperature structure of the water column. An

Acoustic Doppler Current Profiler (ADCP, Sontek) was positioned approximately 100 m

southeast of the meteorological station at a depth of 23 m in order to measure flow velocity

in the overlying water column continuously. Additional details concerning the meteoro-

logical, temperature and velocity measurements can be found in Okely et al. (2010).

4.3.3 Field sampling procedure

Winam Gulf and the adjacent waters of Lake Victoria were sampled over a ten-day

period commencing on 6 August 2005. The profile stations formed multiple transects

through a large sampling domain that spanned from east Winam Gulf to 10 km west of

the Rusinga Channel exit (Fig. 4.1). Profiling was conducted mainly during daylight

hours and some of the profile stations were sampled on multiple occasions, as indicated in

Fig. 4.1.

60

4.4 Results

4.3.4 Data processing

Each spectral measurement in the profile data from the Fluoroprobe was associated

with measurements from the fine scale CTD data at the same depth, after depth-based

linear interpolation of the CTD data. This effectively reduced the sampling resolution

of the fine scale CTD data but allowed each spectral measurement to be associated with

additional measurements of chl a, sample depth, salinity, turbidity, dissolved oxygen and

the spatial coordinates of the profiling sites.

The excitation spectra measurements were normalised by dividing the six emission

intensities of each measurement by the mean intensity of that measurement, following

the approach detailed in Alexander et al. (2012). This data normalisation focuses the

subsequent PCA on changes in pigment composition rather than pigment concentration;

otherwise, the high to low gradient in chl a between the epilimnion and hypolimnion waters

would dominate the analysis. PCA was performed on the normalised excitation spectra,

which are hereafter referred to as response spectra. The input response spectral data was

a matrix with 2310 rows and six columns and the PCA was done with MATLAB (R2006a

The MathWorks). The direct outcome of the PCA was that almost all of the information

contained in the input response spectral data could be represented in a three-dimensional

axes space that contains one data point for each spectral sample. This axes space has

two important general properties that provide the basis for its interpretation. Firstly, the

distance between any two data points (scores) is a measure of the dissimilarity of their

associated response spectra, where dissimilarity is defined by the sum of root mean square

differences between two response spectra over each of the six different wavelengths of the

fluorometer (Alexander et al. 2012). Secondly, scores that are arranged along straight

paths in the axes space are particularly significant because they indicate a transition in

spectra involving precisely two base spectra groups.

4.4 Results

4.4.1 Background environmental conditions

Throughout the period of sampling the wind forcing in Winam Gulf followed a diurnal

pattern that was dominated by a lake breeze. Wind measured at station T2 (Fig. 4.1)

on 12 August is presented in Fig. 4.2a as representative of the overall period, and shows

the onset of the westerly lake breeze in the mid afternoon. A complete record of the wind

and other meteorological forcing data for this period can be found in Okely et al. (2010).

In addition, these researchers also showed that the regional wind field caused differences

in water elevation between the Gulf and Lake Victoria, which in turn drove a barotropic

61


current that was amplified in its passage through the narrow Rusinga Channel. The speed

and direction of that current was not always uniform over depth because of the direct

influence of wind near the surface; nevertheless, water column averaged current speed and

direction oscillated regularly over a period of several hours (Fig. 4.2b). At station T2,

there tended to be very little (< 0.2 ◦C) if any temperature stratification in the early

morning before 6:00 AM, but diurnal stratification typically developed from the morning

onwards and persisted while the wind speeds were relatively low (Fig. 4.2c). The onset of

the Lake breeze caused at least partial mixing of the diurnal thermocline in the afternoon.

0

5

10

sp

ee

d [

ms

-1]

(a)

0

10

20

30

40

sp

ee

d [

cm

s-1

]

(b)

depth

[m

]

temperature [°C]

(c)

02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

0

5

10

15

2023.6 24.4 25.2 26.0 26.8 27.6

Figure 4.2: A representative selection of 24 hours of field data measured at station T2 (Fig. 4.1)on 12 August 2005. Panel (a) shows wind speed and direction, averaged over 15 and 60 minuteintervals respectively. Panel (b) shows water current speed and direction, averaged over the depthof the water column. The current speed and direction data were also time averaged over 15 and 60minute intervals respectively. Panel (c) shows water column temperature averaged over 15 minuteintervals with contour lines indicating changes of 0.2 ◦C. Magenta circles indicate thermistor depths.

Although the water currents oscillating about Rusinga Channel were locally significant,

the excursion caused by these currents over one period was only of the order of 2 km, which

is much shorter than the length of the Channel itself (≈ 20 km, Fig. 4.1). This implies

that the direct exchange between Winam Gulf and Lake Victoria by this mechanism was

limited. Further evidence of the limited nature of horizontal mixing between Winam Gulf

and Lake Victoria waters was provided by the salinity data. The gradients in salinity

measured across the site were not large enough to affect water density but were a useful

62

4.4 Results

tracer of mixing between different water masses. The horizontal distribution of salinity

(Fig. 4.3a) showed an increase from Lake Victoria waters through to the western half of

Winam Gulf, which is consistent with previous findings (Gikuma-Njuru 2008; Sitoki et al.,

2012). However, within the Gulf itself there was also a slight decrease in salinity measured

from west to east, which was particularly evident in the southeast near the Sondu River

mouth (Fig. 4.1).

The salinity gradient measured in the eastern half of Winam Gulf provided a basis to

estimate the water residence time in this region. To define the region simply we assumed

that the bathymetry of Winam Gulf could be represented by a circular quadrant with a

radius of 35 km and a uniform depth h (4 m), which is partially outlined in Fig. 4.3a.

The surface area of this quadrant (α = 9.6x108 m2) is approximately equivalent to that

of the Gulf (excluding Rusinga Channel and Homa Bay) and its origin (73 km east, 30

km north, Fig. 4.3a) is approximately coincident with the Sondu River (Fig. 4.1). We

assumed that all inflow to the quadrant entered at the origin at a constant flow rate Qi

[m3s−1] and with a constant salinity Si [kgm−3]. Similarly, the rate of outflow from the

perimeter of the quadrant at any radius r is equal to Qr [m3s−1] with salinity equal to Sr

[kgm−3]. The other flux is through the surface via evaporation, and we defined the rate

of net evaporation vn [ms−1] as the rate of evaporation minus the rate of rainfall.

A balance between inflow and net evaporation determines the velocity (vr) of the

outward radial flow at any radius r:

vr =2Qi

πrh− vnr

2h(4.1)

To calculate the time (t) for fluid to travel from the origin of the segment out to a

radius of r, we integrate the reciprocal of the velocity (vr) with respect to r, which leads

to:

t =h

vn

(ln

(2Qi

πh

)− ln

(2Qi

πh− vnr

2

2h

))(4.2)

Because the annual average rate of net evaporation in Winam Gulf is positive, salinity

should increase with distance from the inflow origin. Furthermore, conservation of mass

implies that the mass of salt entering the quadrant at the origin (QiSi) is equal to the salt

mass leaving the perimeter at any radius r (QrSr), as no salt is lost through evaporation.

In addition, because of the idealised quadrant geometry, the flow rate Qr at r must be

equal to 0.5rhvr. Therefore, using conservation of mass and substituting equation (4.1)

leads to the following non-dimensional expression:

SrSi

=

(1 − vnπr

2

4Qi

)−1(4.3)

63


Figure 4.3: Panel (a) shows depth averaged salinity distribution throughout the field site. Atsampling stations where multiple profiles were available (see Fig. 4.1) the salinity values were basedon an average of all available profiles. Dots indicate the locations of sampling stations. A nearestneighbour interpolation scheme was used to estimate the salinity values between sampling stations.Panel (a) also shows the partial outline of a 90◦ circular sector shaped control volume with a radiusof 35 km, which will be referred to later in Results. Larger circles around some dots in panel (a)indicate the particular sampling stations that define the cross sectional transect shown in panel (b),which shows dissolved oxygen profiled on 12 August. Dotted vertical lines in panel (b) indicate theprofiling stations and sampling times are indicated for some stations.

64

4.4 Results

By setting Si = 0.058 (from Fig. 4.3a), Qi = 57.1 m3s−1, which is equal the combined

annual mean flow rate of the Sondu and Nyando Rivers (Calamari et al., 1995), and choos-

ing vn = 2.4x10−8 ms−1 based on 12 month averaged rates of precipitation and evaporation

from two stations weather stations at opposite ends of Winam Gulf (see Gikuma-Njuru,

2008), equation (4.3) can be used to calculate theoretical values for salinity as a function

of radius (Fig. 4.4). Furthermore, from equation (4.2) it can be calculated that the time

for the inflow waters to reach a radius of 35 km is longer than 1300 days; therefore, the

use of annual average flow and evaporation data is appropriate. The theoretical values of

salinity were directly compared with equivalent values of salinity derived from the con-

toured field measurement (Fig. 4.3a). The field values were determined by calculating

the mean salinity along the arc perimeter of a quadrant for different values of r. For radii

greater than 23 km the mean values are only based on where the arc perimeters coincided

with the surface area of the Gulf. The salinity gradient derived from field measurements

0 10 20 30

0.06

0.07

0.08

0.09

0.1

salin

ity [pss]

radius [km]

(Q i

α vn= 2 . 5)

field

theory

Figure 4.4: Mean values of salinity as a function ofthe radius of the circular sector control volume de-fined in Fig. 4.3a. The field values were calculatedbased on Fig. 4.3a with radial increments of 2 km.For each incremental quadrant of radius r, the meansalinity was computed along the outer perimeter ofeach quadrant. The parameters of the theoretical so-lution are expressed as the non-dimensional ratio ofinflow (Qi) to net evaporation (vn) times the totalarea (α) of the 35 km quadrant. The symbols at theright of the figure indicate the overall mean salinity(volume adjusted) of the 35 km segment based on thefield (+) and theoretical (x) salinity data.

(Fig. 4.4) was relatively diffuse after

10 km due to the advection and dispersion

of salt that occurs under field conditions,

which is unaccounted for in the theoretical

model. Nevertheless, the volume weighted

mean salinities for the field and theoreti-

cal data were quite similar (see symbols,

Fig. 4.4), and the good agreement be-

tween these values is evidence that the

salinity gradient observed in Winam Gulf

can be explained by evapoconcentration

of salt.

Spatial gradients in temperature, pH

and dissolved oxygen were more difficult

to interpret from the profile data than

salinity because these variables were un-

steady over the semi-diurnal period of a

typical transect, particularly near the wa-

ter surface. Therefore, the transect of

dissolved oxygen profiles measured over

10 hours that is presented in Fig. 4.3b represents a composite of spatial and tempo-

ral gradients. Nevertheless, it can be seen that a strong vertical gradient in dissolved

oxygen was well established at the time of the first profile of the day (9:23 AM, Fig. 4.3b)

65


even though the diurnal temperature stratification as measured at station T2 (Fig. 4.1)

had only begun to establish around three hours earlier (Fig. 4.2c).

4.4.2 Spectral data

The results of PCA on the response spectral data set revealed that the first three

spectral similarity axes captured 99.6% of the variance in the response spectral data set

(88.3%, 10.1% and 1.2% respectively). The scores derived from the results of PCA formed

a triangular structure in the PCA axes space, the vertices of which are labelled A, B and

C in Fig. 4.5a. The outer edges of the triangular structure were particularly straight

between A-C and B-C. With respect to the third axis, which is represented by colour

shading in Fig. 4.5a, there was a relatively steep upward gradient in the scores (out of

the page) between the points labelled A and D. Otherwise, the variation in the scores

in the direction of the third axis was relatively small and/or gradual, which is why the

contribution to the total variance due to that axis was only 1.2% .

Given that the first two similarity axes together captured almost all of the variance

in the response spectral data set, much of the analysis can be simplified to focus on the

two-dimensional plane formed by these axes. However, in order to present the data set

comprehensively, it is important to assess the extent to which the scores were unevenly

distributed and/or overlapping in the two-dimensional plane. This was done by calculating

and graphing the areal densities for the scores (Fig. 4.5b).

The three vertex end-points of the triangular data structure formed by the scores (A,

B and C in Fig. 4.5a) have a critical significance because they designate three different

base spectra (Alexander et al., 2012). Furthermore, if the variation in the scores in the

direction of the third axis is also considered, the samples near the D label (Fig. 4.5a) also

represent an extremity of the same kind. Formal distinction of these four base spectra

requires that small groups of samples be associated with each of them. This was done

by first measuring the straight-line distances (in three-dimensions) between all individual

scores and the various end-points labeled A to D in Fig. 4.5c. Secondly, all of the samples

that were within a given distance of one of the base group end-points were allocated to

that base group. Because the areal sample densities were unevenly distributed (Fig. 4.5b),

the distance limits for each group were adjusted differently so that there could be at least

25 samples per base spectral group. In particular, the distance limit for group B was made

relatively large because the data were particularly sparse near the B end-point (Fig. 4.5b).

Furthermore, two of the main base spectral groups (B and C, Fig. 4.5c) were divided into

subgroups for reasons that will be explained later in Results.

Although the method of distinguishing the base spectra groups was slightly subjective,

the base spectral groupings are fit for purpose as long as the samples within each base

66

4.4 Results

-1 -0.5 0 0.5 1 1.5 2

-0.6

-0.4

-0.2

0

0.2

0.4

1st

spectral similarity axis (88.3%)

2nd s

pectr

al sim

ilarity

axis

(10.1

%)

(a)

A

B

C

D

-0.6 -0.4 -0.2 0.0 0.2 0.4

3rd

spectral similarity axis (1.2%)

-1 -0.5 0 0.5 1 1.5 2

-0.6

-0.4

-0.2

0

0.2

0.4

(b)

1 3 5 7 9

samples per grid cell

-1 -0.5 0 0.5 1 1.5 2

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

(c)

A

B

C

D - A (n=27)- B1 (n=49)- B2 (n=15)- B3 (n=11)- C1 (n=11)- C2 (n=13)- C3 (n=9)- D (n=26)- Oth. (n=2149)

Figure 4.5: All panels show the scores from PCA of the response spectral data set. Panel (a) showsthe arrangement of the scores with respect to the first three axes of the PCA, with colour shadingused to represent the third dimension. The percentage of the total variance in the spectral data thatis explained by each axis is given in brackets. Panel (b) shows the density of samples in the two-dimensional plane formed by the first two PCA axes. The sample density was determined by defininga fine uniform grid (see inset for example) and then computing the number of samples located withinthe area of each grid cell. Panel (c) uses colour shading to show four groupings of samples (A to D)that have been identified as base spectra; samples from groups B and C are further divided into sub-groups by internal markings (see legend inset). The straight line connecting A to B indicates wheretheoretical pure blends of the A and B base spectra would be located in the axes space, and likewisefor the straight lines connecting B to C and A to C. The number of samples in each group/sub-groupis indicated inside the legend in brackets, as is the number of samples not included in any of the basespectral groups (Oth.).

67


group have similar response spectra. To validate the within group spectral similarity, the

response spectral data for each of the major groups were plotted (Fig. 4.6) and each panel

in Fig. 4.6 also shows the distribution of response spectral data within each group set

against the overall spread in the response spectral data set (indicated by thin vertical

grey lines). Comparison of the four panels confirmed that the spectra samples within each

group were very similar and it can also be seen that there was always one wavelength at

which the base spectral response was the maximum of the entire data set. Specifically,

the base spectra groups A to D showed maxima relative to the entire data set at 470, 610,

370 and 525 nm, respectively.

0

1

2(A)

0

1

2(B)

0

1

2(C)

0

1

2(D)

rela

tive flu

ore

scence e

mis

sio

n inte

nsity

370

470

525

570

590

610

wavelength [nm]

Figure 4.6: Panels A to D show the mean responsespectra of the base spectra groups A to D respectively.Thick, coloured vertical bars at each wavelength showthe range in response spectra within each group ateach excitation wavelength. Thin, grey bars at eachwavelength show the range in response spectra overthe entire data set.

The spectra of groups A (Fig. 4.6a)

and D (Fig. 4.6d) were very similar, which

can be expected given that these base

groups were near to each other in the PCA

axes space (Fig. 4.5c). Both of these

groups had a peak response at 470 nm,

which is broadly characteristic of a large

fluorescent grouping of algae that includes

chlorophytes, diatoms and dinoflagellates

(Beutler et al., 2002). The group B

base spectra had a peak at 610 nm (Fig.

4.6b), which is indicative of cyanobacte-

ria (Beutler et al. 2002). The group C

base spectra had a 370 nm peak, which in-

dicates that this base spectral group was

due to the fluorescence of CDOM.

4.4.3 Relationship between the

spectral data and other environ-

mental variables

In general, there was a high degree of

coherence between the sampling locations

of individual samples and membership of

the various base spectral groups and subgroups. The sampling locations and sampling

depths of all of the samples associated with the four base spectral groups are shown in

Fig. 4.7. Fig. 4.7 shows that all samples from groups A and D were situated near the

west end of the Rusinga Channel, and their depths were approximately between 5 - 10 m

68

4.4 Results

for group A (Fig. 4.7c), and between 0 - 15 m depth for group D (Fig. 4.7d). In contrast,

the locations of the samples from group B were concentrated in three different regions: in

the southeast near the Sondu River (B1), in the northeast near the city of Kisumu (B2),

and in the eastern half of the Rusinga Channel (B3). However, the number of samples

in the B1 group was twice as large as the number of samples in the other B subgroups

combined (see legend Fig. 4.5c). Therefore, the group B samples primarily associate with

the southeastern portion of Winam Gulf. All of the samples from the B1, B2 and B3

subgroups had sampling depths that were relatively near to the surface, particularly the

B2 subgroup (Fig. 4.7c). The group C samples were all located in relatively deep regions of

the sampling domain, and always near to the sediment (Fig. 4.7d). The samples from the

three subgroups C1, C2 and C3, were located just west of Rusinga Channel, in the middle

of the Channel and in the eastern half of the Channel respectively. The west-east spatial

separation of the C1, C2 and C3 samples (Fig. 4.7) matched the left-right arrangement of

these subgroups in the PCA axes space (Fig. 4.5c).

- A

- B1

- B2

- B3

nort

hin

g [km

]

(a)

0

10

20

30

40

50

(b)

- D

- C1

- C2

- C3

0 10 20 30 40 50 60 70 80

0

10

20

30

40

- A

- B1

- B2

- B3

depth

[m

]

easting [km]

(c)

0 10 20 30 40 50 60 70 80

easting [km]

(d)

- D

- C1

- C2

- C3

Figure 4.7: All panels show sampling locations of individual samples from the base spectra groups(A to D, see Fig. 4.5c). Panels (a) and (b) show the location of sampling stations where base spectrasamples were profiled, while panels (c) and (d) show the depths that those samples were measured.Gray dots show the location of all other samples.

In addition to establishing base spectra sample locations, the base spectral samples

were also characterised in terms of the other variables that were measured in conjunction

with the response spectral data (Fig. 4.8). Note that all of the variables in Fig. 4.8 except

69


for chl a were measured independently of the response spectral data. The salinity data

associated with the base groups (Fig. 4.8a) showed general trends that were consistent with

the main east-west salinity gradient at the site (Fig. 4.3a). For example, the measurements

made at the locations of the base spectral groups located west of Rusinga Channel (i.e.

groups A and D) were associated with relatively low salinity while the B subgroups, which

were located further east (Fig. 4.7), had relatively high median salinities reflecting the

higher salinity of Winam Gulf water (Fig. 4.3a).

Within these large-scale trends there were also finer details in the salinity data that

revealed information about the origins of the different water masses associated with each

base group and subgroup. For example, the C1 subgroup had a significantly lower salinity

than C2 and C3 (Fig. 4.8a), which indicated that the C1 water was sourced from the

relatively low salinity waters of Lake Victoria (see Fig. 4.3a) while C2 and C3 must have

been mostly sourced from the higher salinity Winam Gulf water. Both the A and the D

groups had relatively low salinity, which indicates that both of these groups were originally

sourced from Lake Victoria waters like C1. However, because the median salinity value of

group A was slightly higher than that of D and C1 (Fig. 4.8a), its water mass is likely to

have incorporated a small fraction of higher salinity water from Winam Gulf.

The salinity data from the B1 subgroup (Fig. 4.8a) had a relatively large spread in its

distribution and included some low values of salinity relative to B2 and B3. This is because

the B1 subgroup was associated with the region of low salinity water in the southeast of

Winam Gulf (see Fig. 4.3a). The similar salinities of B2 and B3 indicate that both of

these subgroups had water origins from within Winam Gulf, or possibly Homa Bay (Fig.

4.1).

The highest chl a values were associated with the three B sub-groups, and with group

A to a lesser extent (Fig. 4.8b). The trends in the distribution of turbidity data (Fig.

4.8c) were broadly consistent with the trends in salinity across the groups (Fig. 4.8a).

This is because the waters of Winam Gulf are much more turbid than the offshore waters

of Lake Victoria; therefore, turbidity acts as a tracer of mixing between these water masses

in a similar manner to salinity. The distributions of dissolved oxygen (Fig. 4.8d) indicated

that the three C subgroups had the lowest dissolved oxygen levels. The distribution of pH

data amongst the groups (Fig. 4.8e) showed very similar trends to the dissolved oxygen.

70

4.4 Results

0.02

0.04

0.06

0.08

0.1

0.12

salin

ity [P

SS

]

(a)

0

50

100

150

chl. a

[µ

L-1

]

(b)

0

20

40

60

80

100

turb

idity [F

TU

]

(c)

0

2

4

6

8

10

D.O

. [m

gL-1

]

(d)

A B1 B2 B3 C1 C2 C3 D Oth.6

7

8

9

pH

(e)

Figure 4.8: Box plots summarising the distribution of environmental variables that were measuredin the field together with the response spectral data. All field samples are grouped according to theirmembership of the base spectral groups (A to D, Fig. 4.5c) with other remaining samples allocated toa single group (Oth., Fig. 4.5c). The lower and upper limits of the boxes indicate the 10th and 90th

percentiles respectively and the dots above and below the boxes show all samples that are outside ofthis percentile range. The thick horizontal lines spanning the widths of the boxes indicate the groupmedians. Vertical whiskers indicate confidence intervals for the median values (i.e. the median ± thestandard error); if the vertical whisker ranges of any two boxes do not overlap then their medians aredifferent at the 5% significance level. The box widths differentiate groups and sub-groups.

71


It is possible to summarise how changes in response spectra were correlated with the

other measured variables by overlaying those other variables onto the PCA axes space

(Fig. 4.9). In Fig. 4.9, the various panels tend to show gradients that are orientated

either left/right (first spectral similarity axis) or up/down (second spectral similarity axis).

Specifically, values of the easting coordinates (Fig. 4.9a), salinity (Fig. 4.9d) and turbidity

(Fig. 4.9f) all had their most substantial variation in the direction of the first spectral

similarity axis. This implies that these three variables were all correlated with a shift in

response spectra from group A (Fig. 4.6a) to group B (Fig. 4.6b). Similarly, the values

for depth (Fig. 4.9c), chl a (Fig. 4.9e), dissolved oxygen (Fig. 4.9g) and pH (Fig. 4.9h)

mainly exhibited gradients in the vertical direction of the secondary similarity axis. This

indicates that the response spectral data showed more resemblance to the group C spectra

(Fig. 4.6c) as water depth increased and oxygen, chl a and pH decreased.

-0.6-0.4-0.2

00.20.4

easting [km]

(a)

A

C1 C3

B

0 20 40 60 80

northing [km]

(b)

A

C1 C3

B

0 20 40 60

-0.6-0.4-0.2

00.20.4

log10

(depth + 1) [m]

(c)

A

C1 C3

B

0.2 0.6 1.0 1.4 1.8

salinity [PSS]

(d)

A

C1 C3

B

0.05 0.06 0.08 0.09

-0.6-0.4-0.2

00.20.4

log10

(Chl. a + 1) [µL-1

]

(e)

A

C1 C3

B

0.5 1.0 1.5 2.0

turbidity [FTU]

(f)

A

C1 C3

B

0 20 40 60

-1 -0.5 0 0.5 1 1.5 2

-0.6-0.4-0.2

00.20.4

D.O. [mgL-1

]

(g)

A

C1 C3

B

0 4 8

-1 -0.5 0 0.5 1 1.5 2

pH

(h)

A

C1 C3

B

6 7 8

Figure 4.9: All panels show relationships between the arrangement of the PCA scores and otherenvironmental variables that were sampled together with the response spectra. Where multiple scoresoccupy a similar position in the two-dimensional axes space (see Fig. 4.5b) the environmental valuesshown above are based on a median value. Easting and northing coordinates are relative to the scalesshown in Fig. 4.1.

72

4.4 Results

To this point, the analysis of the response spectral data set, which was measured at

different times of the day and over a period of 10 days, has not explicitly considered

temporal variation. Therefore, profiles of response spectral data from station R4 (Fig.

4.1) were used to provide an example of temporal variation in response spectra. Station

R4 represents a somewhat extreme case because it was located near to the mixing front

between relatively high salinity Winam Gulf water and the lower salinity water of the

Rusinga Channel (Fig. 4.3). The response spectral data measured at station R4 on 9

August is highlighted in the PCA axes space in Fig. 4.10a. The evenly spaced arrangement

of the scores along a straight line in Fig. 4.10a indicates a linear gradient between two base

spectra with depth. Specifically, Fig. 4.10a shows that the response spectra transitioned

from group B-like spectra near the surface to group C-like spectra near the sediment (Fig.

4.5c, Fig. 4.6b and c). The vertical gradient in response spectra was consistent with a

stable vertical gradient in the temperature structure that was measured at the same time

(Fig. 4.10b). On the following day, the response spectra measured near to the sediment

at station R4 (Fig. 4.10d) was basically unchanged; however, near the surface the spectra

had changed substantially to resemble the group A spectra. The accompanying salinity

profiles (Fig. 4.10c and Fig. 4.10f) indicated that the change in response spectra near the

surface was due to an influx of lower salinity water in the upper half of the water column,

which was most likely caused by either the oscillating current (Fig. 4.2b) or wind driven

transport near the surface. Similarly, the vertical profile of response spectra measured

on 11 August (Fig. 4.10g) and its associated salinity profile (Fig. 4.10i) indicated that

higher salinity Winam Gulf water had flowed back past station R4 in the preceeding

hours. Comparing the profile data measured on 9 and 11 August shows that mixing of

stratification near the surface (Fig. 4.10b and Fig. 4.10h) caused the scores from the

upper 5 m of the water column to collapse on top of each other in the PCA axes space

(Fig. 4.10a and Fig. 4.10g). This implies that the mixing of the surface layer caused the

gradient in response spectra to be eliminated.

Although the main purpose of PCA on response spectral data is to identify base spec-

tral samples, the vast majority of samples in the PCA axes space do not belong to any of

the base spectral groups (i.e. gray samples, Fig. 4.5c). In order to assess general trends

across these ungrouped samples, the PCA axes space was simplified by disregarding vari-

ation along the third similarity axes (thus neglecting spectral variation due to group D).

This meant that two-dimensional distances between each sample and the three remaining

end-points A, B and C (Fig. 4.5c) could be calculated. These distance values were then

scaled between zero and one by dividing by the distance between A and B. The resul-

tant scaled distance values were then transformed into a colour map in which magenta,

cyan and yellow colour intensity was inversely proportional to distance from the A, B and

73


-1 0 1 2

-0.5

0

0.5

Station: R4

Date: 09-Aug-2005

Time: 13:56

(a) 0

5

10

Temp. [°C](b)

Salinty [PSS](c)

-1 0 1 2

-0.5

0

0.5

Station: R4

Date: 10-Aug-2005

Time: 10:47

(d) 0

5

10

De

pth

[m

](e) (f)

-1 0 1 2

-0.5

0

0.5

Station: R4

Date: 11-Aug-2005

Time: 12:35

(g) 0

5

10

24

.4

24

.9

25

.4

(h)0

.06

9

0.0

74

0.0

79

(i)

Figure 4.10: Field data measured at profile station R4 (Fig. 4.1) at three different times. Panel (a)shows PCA scores associated with a vertical profile of response spectra data (coloured dots) as wellas all other scores from the spectral data set (grey dots). The sample depths are indicated by thecolour shading of the dots, which can be directly referenced with panels (b) and (c). Panels (b) and(c) show the temperature and salinity data measured at the same station and time as listed in panel(a). Similarly, panels (d) to (i) show information from the two other profiling instances.

74

4.5 Discussion

C end-points respectively (see inset Fig. 4.11). In this way the horizontal and vertical

gradients in response spectra over the entire site (except group D) could be summarised

by cyan-yellow-magenta colour shading (Fig. 4.11). Note that the most intense magenta,

cyan and yellow colouring in Fig. 4.11a and b coincide with the sampling locations of the

base spectral groups (Fig. 4.7). Furthermore, the mixed colour shades in Fig. 4.11 show

how the patches associated with base spectral groups were mixed in different proportions

throughout the site.

4.5 Discussion

It was established prior to this investigation that the phytoplankton species compo-

sition in Winam Gulf is distinct from that found in the deeper offshore waters of Lake

Victoria (e.g. Lungayia et al., 2000; Sitoki et al., 2012). This large-scale spatial gradient

in species composition was confirmed by the main horizontal trends in the spectral data

measured during this study, which showed a shift from group D type spectra (i.e. Fig.

4.6d) in the Lake Victoria waters to group B type spectra (i.e. Fig. 4.6b) in Winam Gulf

(Fig. 4.11). Furthermore, according to the spectral characteristics described by Beutler

et al. (2002), the particular changes in spectra measured across this site were consistent

with a transition from an assemblage dominated by cyanobacteria in Winam Gulf to a

diatom-dominated assemblage in Lake Victoria, which is expected following the period of

annual overturn in Lake Victoria (Kling et al., 2001). However, the additional contribution

of this study was to identify smaller scales of patchiness within this large gradient.

Previous field sampling of the Rusinga Channel (Lungayia et al., 2000; Sitoki et al.

2012) had suggested that the phytoplankton composition in the Channel was distinct

from that in the neighbouring waters either side of it. However, confirmation and char-

acterisation of relatively small-scale patchiness within the Channel is difficult without

high-resolution sampling. In addition, surveying patchiness within the Channel is compli-

cated by temporal variations caused by the oscillating current (Fig. 4.10). In this context,

the distinction in spectra between group A and group D was significant. Specifically, the

results of the PCA revealed that the group A spectra could not be explained by linear

combinations of the group B and group D spectra. This implies that the spectrum of

group A was not simply due to a mixture of Lake Victoria and Winam Gulf phytoplank-

ton assemblages but rather was representative of a different phytoplankton assemblage

located in the Channel.

Several factors could potentially explain a difference in phytoplankton composition and

abundance between the western part of the Rusinga Channel and the waters of Lake Victo-

ria slightly further west. Firstly, given the asymmetric nutrient status of the Lake Victoria

75


Figure 4.11: Contour maps showing spatial distribution of the response spectral data with respectto the three main base spectra (A, B and C, Fig. 4.5c). Panel (a) inset presents a triangular colourscheme that follows the same shape as that outlined in Fig. 4.5c; the intensity of magenta, cyan andyellow colour shading in the scheme is inversely proportional to the distances from the A, B and Cvertices respectively. The horizontal spatial distribution of response spectral data shown in panel (a)is based on vertical averages of response spectral data from the upper 5 m of the water column. Thecontouring method and station symbols used in panel (a) were the same as described in Fig. 4.3a.Panel (b) shows the horizontal-vertical spatial distribution of response spectral data using the samecolour scheme as panel (a). The data used in panel (b) is from the same transect as described in Fig.4.3a.

76

4.5 Discussion

and Gulf waters (Gikuma-Njuru and Hecky, 2005), the mixing of these water masses at

the western end of the Channel would have locally enhanced nitrogen and silica concen-

trations relative to those found in the westward adjacent Lake Victoria waters. Secondly,

the western half of the Channel has a shallower depth than the westward-adjacent Lake

Victoria waters, which implies higher average light availability when the water column is

mixed (Hecky, 1993). Thirdly, vertical mixing in the Channel was likely to have been more

active than in the westward-adjacent Lake Victoria waters because of shear generated by

the oscillating current (Fig. 4.2b); the effect of the increased mixing would have been to

modify the light climate for cells and to reduce the advantage of cell buoyancy or motility.

Given these differences, it is reasonable to expect a different phytoplankton assemblage in

the western half of the Rusinga Channel.

The particular differences between the group A and group D spectra provide a guide

to the difference in species composition between these assemblages. According to Beutler

et al. (2002), the steep negative slope of the group A spectra (Fig. 4.6a) between 450 nm

and 525 nm relative to group D (Fig. 4.6d) suggests that the group A assemblage had

a higher proportion of green algae than group D. This interpretation is consistent with

previous findings of both Sitoki et al. (2012) and Lungayia et al. (2000), who observed

relatively high (but still minority) proportions of green algae at sampling stations situated

in the western half of the Channel at about the same time of the year as this study.

Within Winam Gulf itself, previous investigations of the phytoplankton assemblage

have indicated that the dominance of cyanobacteria is perennial (e.g. Sitoki et al., 2012),

but whether the phytoplankton biomass in the Gulf is limited by light is unclear. Given

that the majority of the group B samples (i.e. the B1 subgroup) were located within a

10 km patch of water that was relatively low in salinity (Fig. 4.3a), particularly high

in turbidity (Fig. 4.8c) and very close to the mouth of the Sondu River (Fig. 4.1),

it is probable that the relatively high concentration of cyanobacteria in this region was

supported by nutrient input from the nearby rivers. Certainly, given the high turbidity in

this region, there was no evidence to suggest that this patch was the product of particularly

high light availability in this region of the Gulf. Given that the size of the patch formed

by the B1 samples is around 10 km (Fig. 4.7), equation (2) can be used to estimate a time

length of around 90 days for the inflow water to advect through this region beyond a radius

of 10 km, which is slow relative to the time scales of nutrient uptake and phytoplankton

growth. Although this estimate does not consider dispersion, Okely et al. (2010) estimated

that it would take a similarly long time (130 days) to flush this region by dispersive

mechanisms.

The locations of the samples from the B2 subgroup were distinct from the other group

B samples in that they were situated towards the western end of Winam Gulf and were also

77


relatively concentrated near to the surface. Given the diurnal rate of vertical mixing of

the near surface waters due to the lake breeze (Fig. 4.2), the vertical patchiness in the B2

spectral data must have been the product of vertical migration by buoyant cyanobacteria

cells rather than differential rates of growth in the vertical. Buoyancy-driven accumulation

of cyanobacteria near the surface would also explain the extremely high chl a values

associated with the B2 subgroup (Fig. 4.8b). The existence of vertical patchiness in itself

confirms that the timescales of vertical migration were shorter than the diurnal timescale

of vertical mixing. This means that the potential for light limitation of cyanobacteria in

the Gulf must have been moderated by cell buoyancy to some extent. Similarly, the same

logic must apply in the east of Winam Gulf where the shallower depth implies an even

shorter timescale for vertical migration. This suggests that previous estimates of the light

limitation of phytoplankton in the Gulf based on a well-mixed water column assumption

(e.g. Loiselle et al., 2008) probably overestimate the light limitation of the buoyant cells.

Therefore, it is conceivable that non-buoyant (or non-motile) phytoplankton cells may be

light limited in Winam Gulf while buoyant cells, particularly strongly buoyant cells like

Microcystis, are able to overcome light limitation, at least during the calm periods that

are typical early in the day. If so, light limitation may drive the competitive selection of

Microcystis but the biomass of phytoplankton in the Gulf may be limited by nutrients, as

was suggested by the relationship of the B1 group to the Sondu River inflow.

The base spectral samples associated with group C all had spectra that were dominated

by fluorescence from CDOM rather than chl a (Fig. 4.6c). The group C base spectral

samples were all measured near to the sediment in relatively deep waters (Fig. 4.7), as

were most of the other samples that had spectra similar to that of group C (see yellow

coloured areas in Fig. 4.11b). The regions where CDOM dominated the fluorescence

in Fig. 4.11b were correlated with regions of low dissolved oxygen (Fig. 4.3b). The

association of group C samples with low oxygen suggests that the primary source of this

CDOM was internal decomposition of organic matter rather than external input of CDOM.

However, the dominance of CDOM in the spectra data from the deeper waters was only

measured in relative terms, which means that it could be attributable to low phytoplankton

concentrations as much as high CDOM concentrations. Therefore, the present results

are not necessarily inconsistent with Loiselle et al. (2008), who found highest absolute

concentrations of CDOM in the shallow near shore regions. However, as their focus was on

near surface waters it is possible that their sampling missed high CDOM concentrations

in the deeper waters of the Rusinga Channel, or alternatively the high CDOM observed

in this study may be a seasonal phenomenon. Assuming the concentrations of CDOM in

the deep waters of the Rusinga Channel are significant, and are the product of internal

78

4.6 Conclusion

decomposition of organic matter, the diurnal vertical mixing of these waters may provide

a significant nutrient source to phytoplankton in the Channel.

4.6 Conclusion

The spectral data indicated that the general patchiness in phytoplankton distribu-

tion at the site was largely attributable to the mixing and dispersion of three distinct

phytoplankton assemblages, which were concentrated in three main locations. Not all

phytoplankton species can be discriminated from spectral data, which implies that the

patchiness described here may only be a subset of actual patchiness; however, the reaf-

firmation of gradients in phytoplankton composition reported by previous investigations

suggests that spectral data are well suited as a proxy indicator of phytoplankton diversity

at this site. High-resolution spectral data and processing with PCA allowed the locations

of the different phytoplankton assemblages, and physiochemical characteristics of these lo-

cations, to be resolved at a much finer scale than previously. In particular, cyanobacteria

were particularly concentrated in the southeast of Winam Gulf where inflows enter, which

is a region that has been under-sampled in previous investigations. Similarly, a distinct

phytoplankton assemblage in the Rusinga Channel was traced to the western edge of the

Channel, which is a region where water sourced from Lake Victoria is slightly diluted by

outflow from Winam Gulf. Assuming these particular aspects of phytoplankton patch-

iness persist at the site, future water sampling programmes may be targeted to further

characterise the dynamics of these assemblages.

79


80

5

Summary

The unifying objective of this thesis has been to develop and implement quantita-

tive measures to relate phytoplankton assemblages to environmental structure. Each of

the previous chapters has advanced this objective in different respects. Specifically, the

chapters address the use of a numerical model to resolve the drivers of phytoplankton

patchiness at small spatial and temporal scales (Chapter 2); the development of a new

PCA based method for identifying patchiness in phytoplankton assemblages from high

frequency in situ spectral measurements (Chapter 3); and finally, the application of the

PCA method to give new insights into phytoplankton patchiness in Winam Gulf, Lake

Victoria (Chapter 4).

In Chapter 2, a sophisticated three-dimensional hydrodynamic model was coupled to a

simple biological model of a motile dinoflagellate. While this was not the first application

of a coupled three-dimensional hydrodynamic and biological model, the extent to which

the simulated phytoplankton patchiness was verified by accompanying field measurements

was novel. Furthermore, the manner in which the phytoplankton patchiness was shown

to self organise from a homogeneous initial distribution was an interesting and unex-

pected result. More generally, the good agreement between the simulation and the field

data demonstrated that meaningful insight could be gained from modelling phytoplank-

ton patchiness, at least in similar circumstances. This is significant because if coupled

physical-biological models can be used to quantify the spatial boundaries of niches occu-

pied by phytoplankton, the same modelling could be extended in order to make better

estimates of light and nutrient fluxes to those niches.

Chapter 3 introduced a new method for revealing information about phytoplankton

assemblages that is contained intrinsically within fluorescence spectral measurements. The

method is distinct from alternatives approaches in that it does not require calibration

samples in the post processing of the raw signal. This feature of the method is significant

81

SUMMARY

because suitable calibration samples are often difficult to obtain. Moreover, uncertainty

about the representativeness of the calibration samples leads to errors in the analysis

of spectral data. Although PCA had been applied to spectral data previously, the way

in which the results of PCA were interpreted was novel. The new insight involved the

recognition that as long as there is patchiness in the phytoplankton assemblages at a

particular site, and those assemblages have norm spectra that are linearly independent,

then it follows from the mathematics of PCA that the mixing of two different assemblages

will manifest along a straight path in the PCA axes space. The most significant implication

of the new method is that high spatial resolution spectral data can now be used to identify

the locations of distinct fluorescent assemblages of phytoplankton at a particular site, and

thereby allows water sampling to be optimised.

In Chapter 4, the method developed in Chapter 3 was applied to spectral data mea-

sured in Winam Gulf, Lake Victoria. The field transects covered a relatively large area

and consisted of over 2000 individual spectral samples. The application of the method

demonstrated that this large data set could be distilled to reveal a small number of primary

sources that were responsible for the variation in spectral data. Novel approaches were

used to summarise the main features in the field data set. Firstly, physical and chemical

variables were superimposed onto the PCA axes space, which showed concisely how the

trends in the spectral data were correlated with these other variables (Fig. 4.9). Secondly,

spatial trends in the spectral data were able to be summarised using a tricolour scheme

(Fig. 4.11). The results of the analysis added to existing understanding about the spatial

distribution of phytoplankton in Winam Gulf. In particular, a phytoplankton assemblage

dominated by cyanobacteria was traced to a region in the south-east of Winam Gulf that

has been under sampled in previous studies. More generally, the analysis will provide a

basis to guide future field sampling in Winam Gulf.

82

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