The seasonal cycle of stratification is one of thestrongest of the physical phenomena that shape thedynamics of phytoplankton in the ocean. At any giventime, the depth of the mixed layer is determined by thebalance of 2 opposing trends: the stratifying tendencyof solar heating and precipitation; and the tendency ofwind mixing and surface cooling to erode stratification.The relative strengths of these 2 trends vary through-out the year. In general, the effect of wind is sustainedand strong during winter, whereas the effect of the sunis sustained and strongest during summer. That the2 trends are out of phase with each other accounts forthe annual cycle of stratification, and stratification in-creases as summer succeeds spring, decreasing asautumn gives way to winter.
The principal biological effect of this cycle is thatwhen the water column is stratified, the surface mixedlayer (the layer in which illumination is optimal forphotosynthesis) is isolated from the layer below (wherethe nutrient reservoirs are found). Once photosynthe-sis has exhausted the nitrate at the surface, re-supplythrough transport from below, against the density gra-dient, is difficult (Lewis et al.1986).At this stage, photo-synthesis may continue in the surface mixed layer, butusing only reduced (recycled) nitrogen as a substrate.In general this may be sufficient to meet the metabolicdemands of the pelagic community, but not to providesurplus production that could be used to increase sys-tem biomass; for example, biomass of exploitable fishstocks (Platt et al. 1992).
Of course, nutrients can be transported against thedensity gradient provided enough external energy is
Short-term changes in chlorophyll distribution inresponse to a moving storm: a modelling study
Yongsheng Wu1,*, Trevor Platt1, Charles C. L. Tang1, Shubha Sathyendranath1, 2
1Coastal Ocean Science, Bedford Institute of Oceanography, Dartmouth, Nova Scotia B2Y 4A2, Canada2Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH, UK
ABSTRACT: Using a 3-D ocean circulation model of the Labrador Sea, we investigated the imme-diate response, through vertical redistribution of the chlorophyll field, to a steadily moving storm.The model is forced by a prescribed wind and pressure field. The numerical experiments included acontrol run to analyze the horizontal and vertical structure of the chlorophyll field, and several sen-sitivity runs to investigate the response to changes in the storm parameters (translation speed, sizeand intensity) and the seasonal distribution of chlorophyll. The model results showed that after thepassage of the storm, surface chlorophyll in the Labrador Sea is generally increased by vertical mix-ing. The largest increase occurs in autumn. In summer (control run), the surface chlorophyll concen-tration is 1 to 3 mg m–3 higher than the concentration before the storm in almost all the areas underthe influence of the storm. In the shelf regions, however, the increase is very small. The changes insurface chlorophyll concentration are shown to be primarily controlled by the mixed-layer depth andthe initial chlorophyll distribution. Nitrate brought from the deep reservoir to the mixed layer byentrainment was estimated from the model. For a typical storm in summer, 3.35 × 103 mol of newnitrate is added to the mixed layer for each km of storm track. Primary production rates following theintroduction of new nitrate will contribute to further change in surface chlorophyll, but on a longertime scale.
KEY WORDS: Moving storm · Chlorophyll · Vertical distribution · 3-D model
Resale or republication not permitted without written consent of the publisher
Mar Ecol Prog Ser 335: 57–68, 2007
supplied. This can happen, for example, when a stormof sufficient strength passes over the area concerned(Platt et al. 2003). The vertical mixing induced by thestorm increases the depth of the surface mixed layerand in the process entrains nitrate from the deep re-servoir. The nitrate so entrained is referred to as newnitrogen, to indicate that its source is external to thelayer where photosynthesis occurs. New nitrate canbe used to increase biomass at any trophic level in thepelagic layer, and the biomass so produced may beremoved (for example by fishing) without destroyingthe integrity of the pelagic ecosystem (Platt et al.1992).
Using remotely sensed data, several authors havedemonstrated local biomass changes following thepassage of storms (Babin et al. 2004, Davis & Yan 2004,Fuentes-Yaco et al. 2005, Platt et al. 2005, Son et al.2006). Storms are, therefore, of fundamental impor-tance to the dynamics of the ocean ecosystem, and weshould try to understand in detail the way in whichthey exert their influence, and the limitations of theireffect. Remotely-sensed data can give the distributionof biomass at the surface but no information about thechange of vertical distribution and mixed-layer depth.Here, we apply a circulation model of the Labrador Seato examine changes in the vertical distribution ofphytoplankton biomass (indexed as the concentrationof chlorophyll) to an intense storm moving through thearea, and discuss the implications for nitrate distribu-tion. The biological processes involving nitrate are notaddressed. We seek to identify the physical mecha-nisms having the greatest control on the distribution ofchlorophyll and nitrate, and to understand the depen-dence of the responses on properties of the storm, suchas its size, intensity and translation speed. We discussthe spatial structure of the chlorophyll field followingthe storm and the extent to which the response mightchange with season.
MODEL EQUATIONS AND MODEL SETUP
Ocean model. To simulate the short-term change ofthe chlorophyll distribution under perturbation by thestorm, we use a 3-D advection-diffusion equation em-bedded in a 3-D ocean circulation model. The oceanmodel is the Princeton Ocean Model (POM) imple-mented for the Labrador Sea. The model contains anembedded second-order turbulence closure sub-mo-del, which takes into account the effects of both windmixing and wave dissipation (Mellor & Blumberg2004). The vertical eddy viscosity is parameterized bya mixing length, the turbulence kinetic energy, and astability factor which depends on the vertical shearand buoyancy. The setup of the model has been de-
scribed in detail by Yao et al. (2000) and Wu et al. (un-publ.). The model domain is from 40° N to 66° N andfrom the Canadian east coast to 40° W, with a horizon-tal resolution of approximately 20 km × 20 km (Fig. 1).The vertical coordinate system is the generalized coor-dinate system which permits a z-level representationof the upper ocean everywhere in the model domainindependent of water depth (Mellor et al. 2002). Thereare 30 vertical levels consisting of ten 2 m levels in theupper water column and 20 sigma levels (fixed frac-tions of the water depth) below.
58
200
1000
2000
3000
4000
200
4000
5000
+
L
G
New-foundland
Greenland
LabradorSea
−65°W −60°W −55°W −50°W −45°W −40°W40°N
45°N
50°N
55°N
60°N
65°N
Labrador
Fig. 1. Model domain and storm track. The model boundariesare indicated by the thick lines. The bold solid line with soliddots indicates the storm track. The solid dots denote the stormposition at the time step of 6 h. +: marks the site referred to inFigs. 4 & 5. The box outlined by dashed lines defines the areaused in Figs. 6 & 9. Sites L and G (�) are used in Fig. 8. Thedotted line is the cross-track section in Figs. 7 & 10–13
Wu et al.: Modelling chlorophyll distribution in a moving storm
The conservation equation for the chlorophyllconcentration can be written as (Fennel & Neumann2004):
(1)
where C is the chlorophyll concentration in mg m–3; t istime; u is the velocity vector; z is the vertical coordinate(positive downward), w is the vertical velocity; KH isthe vertical diffusion coefficient; FC is the horizontaldiffusion term; and S is the source/sink term which isthe sum of biomass production and loss. We did notstudy the biological processes and hence set S to zero.The method for solving Eq. (1) is similar to the methodfor solving the equation of temperature or salinity. Zeroflux conditions are employed at the surface and bottomboundaries, and radiation conditions are used at lateralboundaries. In the present study, our focus is on physi-cal processes with time scales of several days. The con-tribution of the growth and loss terms to the change ofchlorophyll after the storms will be discussed else-where.
Storm model. We used a controllable wind and pres-sure field to simulate the effect of a moving storm. Thisapproach has been taken by a number of investigators(O’Brien & Reid 1967, Chang & Anthes 1978, Price1983, Tang et al.1998). Following O’Brien & Reid (1967)and Tang et al. (1998), the horizontal distribution of airpressure changes exponentially from the center to theperiphery of the storm:
(2)
where p(r) is the air pressure at distance r to the stormcenter. The quantities pc and pn are the pressures atthe center and at the outer periphery, respectively,and R is the radius of the storm. Using the gradientwind equations, we have the wind speed:
(3)
where ρa is the air density (assumed con-stant at 1.15 kg m–3) and ƒ is the Coriolisparameter. The radial and tangentialvelocities of surface wind, Vr and Vθ,respectively, can be calculated from:
(4)
(5)
where α is the inflow angle (the anglebetween the wind vector and the tangentto the local isobar), here set to 10°, and β isan empirical function of r:
(6)
where d (= 5.088 km) is an empirical distance scale ori-ginally given in miles in O’Brien & Reid (1967). Theseequations represent the wind field for an axially sym-metric storm.
A typical storm over the Labrador Sea moves fromsouthern Labrador or northern Newfoundland to-wards Greenland. As it moves across the ocean, itsintensity decreases. Some storms weaken and dissi-pate before reaching the coast of Greenland andsome veer to the southeast. Here, the storm trackused for all experiments was a straight line fromsouthern Labrador to southwestern Greenland (seeFig. 1). The typical parameter values for the refer-ence run (Table 1) are based on data from the Cana-dian Meteorological Centre and the European Centrefor Medium-range Weather Forecasts (Tang et al.1998): R = 100 km, pn = 101.3 kPa, pc = 94.0 kPa andthe translation speed, UH = 8.0 m s–1. Wind speedsacross the storm for 3 difference values of centralpressure are shown in Fig. 2. The cross-storm va-riation is characterized by a sharp drop in wind speedtoward the storm center and a gradual decrease fromthe maximum outward.
Model initialization. The initial conditions for thephysical components of the model, such as currents,temperature and salinity, were obtained from the re-sults of a diagnostic-prognostic spin-up. The 3-Docean temperature and salinity fields used in thespin-up are the seasonal climatology data obtainedfrom an objective analysis of bottle and CTD records(dating back to 1910) archived at the Bedford In-stitute of Oceanography (Tang & Wang 1996). Thevertical distribution of the initial chlorophyll concen-tration before the storm was specified with the para-
β = + −( )12
21d
r
V Vθ β α= 0 7. cos
V Vr = −0 7. sinβ α
VR
rp p
r rR r= − +⎡⎣⎢
⎤⎦⎥
−−
ρan c e( )
ƒ ƒ( / )/2 2 1 2
4 2
p r p p p R r( ) ( ) ( / )= + − × −c n c e
∂∂
+ × ∇ + ∂∂
= ∂∂
∂∂( ) + +C
tC w
Cz z
KCz
F Su H C
59
Run Chlorophyll Storm parametersprofile Translation Radius Air pressure
Table 1. Parameters used in the numerical experiments. *The parameter hasthe same value as the value in Run 1 (= Reference Run)
Mar Ecol Prog Ser 335: 57–68, 2007
meterization of Platt et al. (1991). The parameterswere extracted from 873 chlorophyll profiles obser-ved in the North Atlantic between 1960 and 1990,and sorted by season and region.
The vertical distribution of chlorophyll, C0 (z), is ex-pressed as a shifted Gaussian distribution:
(7)
where B is a background value, h is the total biomassat the peak, σ is the width of the chlorophyll peak, andzm is the depth of the chlorophyll maximum. The sea-sonal and regional characteristics of C0 (z) are charac-terized by these 4 parameters. To reduce the degreesof freedom from 4 to 3, a dimensionless parameter ρ,the ratio of the peak biomass to the background value,can be defined as:
(8)
The background value, B, can be determined if thesurface concentration Co(0) is known. We assume thatthe surface chlorophyll is horizontally homogeneous in
the entire model domain. The values fordifferent seasons, which are based onocean color data from satellites, are givenin Table 2. According to the classification ofPlatt et al. (1991), there are 6 regions in ourmodel domain. Each region in each seasonhas its own set of parameters. The parame-ter values for the Labrador Sea Region (lat-itude ranges from 51 to 70° N and depth is>2000 m) in different seasons are listed inTable 2. Fig.3 shows C0(z) computed fromEq. (7) and parameters in Table 2.
The response of the chlorophyll field to amoving storm was investigated using theresults of a series of numerical experiments(Table 1). The first (Run 1) is the referencerun with typical storm parameters and thechlorophyll distribution for summer. In agroup of 6 experiments (Runs 2 to 7), weused different translation speeds, air pres-
sure differences, Δp (= pn – pc), and radii. In anothergroup of experiments (Runs 8–10), we kept the stormparameters unchanged and specified the initial chloro-phyll distribution for the other 3 seasons. In eachexperiment, the model was run for 4 d. We note that
Table 2. Surface concentration B(0) and parameters of B(z) inLabrador Sea region for different seasons. (The vertical profile
in winter is uniform)
−400 −300 −200 −100 0 100 200 300 4000
10
20
30
40
50
r (km)
Win
d sp
eed
(m s
−1 )
pc = 92 kPapc = 94 kPapc = 96 kPa
pn = 101.3 kPaR = 100 km
Fig. 2. Wind speed profiles (Vr2 + Vθ
2)1/2 for different central pressures. r : distance to centre of storm. See Eqs. (2)–(6)
0 0.25 0.5
0
20
40
60
80
100
Dep
th, z
(m)
a0 1 2 3 4
b
0 2 4 6 8
0
20
40
60
80
100
Dep
th, z
(m)
c0 4 8 12 16
C0(z) (mg Chl m−3)
d
Fig. 3. Profiles of the vertical distribution (z) of chlorophyllC0(z). (a) Winter, (b) spring, (c) summer, (d) autumn. Note thedifferences in the scales of C0(z). The maxima of spring, sum-mer and autumn are 3.17, 7.86 and 15.0 mg m–3, respectively
Wu et al.: Modelling chlorophyll distribution in a moving storm
the time for the storm to cross the Labrador Sea is only34 h in the reference run (see Fig. 1). Since the heatbudget of the surface mixed layer following the pertur-bation is dominated by storm-induced entrainmentand mixing, we neglected heat exchange between theatmosphere and the ocean (O’Brien & Reid 1967,Chang & Anthes 1978). The surface flux of fresh waterwas also set to zero.
RESULTS
Spatial and temporal changes in summer (Run 1)
We define the change of chlorophyll in the surfacemixed layer, Δchl, in response to the storm as:
(9)
where Cb and Ca are the chlorophyll concentrationsbefore and after the storm, respectively.
Vertical changes
The response of the chlorophyll field tothe storm may be divided into 2 stages.The first is the transient stage, which isrelatively short, lasting for several hoursafter the passage of the storm. The secondis the wake stage during which the cur-rent field is dominated by the inertialoscillation. When the storm passes over agiven location, the initial Gaussian distrib-ution is destroyed and the chlorophyll isredistributed uniformly within the upperlayer (Fig. 4a) by vertical water motion(Fig. 4b). Fig. 4c displays density at depthrelative to the surface value. The surfacemixed layer depth (MLD) can be estima-ted using a specific criterion of density dif-ference. For a density difference of 0.1 kgm–3, the MLD deepens from 15 m beforethe storm to 60 m after the storm. TheMLD is not sensitive to the value of thedensity difference, because the densitygradients at the base of the mixed layerare large. After the passage of the storm,the chlorophyll concentration remainsuniform within the surface mixed layer,and the MLD oscillates at the inertialfrequency. The surface chlorophyll con-centration increases slightly during up-welling and decreases slightly duringdownwelling as a result of the vertical mo-tion of the water (Fig. 4b).
Fig. 5 shows the chlorophyll and temper-ature profiles before and after the storm.
The surface chlorophyll increases from 1.0 to 2.8 mgm–3. The peak centered at 38 m is smoothed. In con-
Δchl C C= −a b
61
Fig. 4. Change in vertical distribution (z) of: (a) chlorophyll; (b) verticalvelocity (w) and (c) density (Δσt)relative to the surface value at the loca-tion denoted by the symbol + in Fig. 1. The solid dot at the top of eachpanel indicates the time at which the storm passes this location
0 2 4 6 8 10
0
20
40
60
80
100
120
140
160
180
200
Chl (mg m−3)
Dep
th z
(m)
a
After stormBefore storm
3 4 5 6T (°C)
b
Fig. 5. Vertical profiles (z) of (a) chlorophyll and (b) tem-perature before and 5 h after the storm in summer. The hori-zontal solid and dash-dotted lines in (a) denote zm and zm + 2σ
respectively
Mar Ecol Prog Ser 335: 57–68, 2007
trast, the sea surface temperature decreases by 1.6°Cas a result of mixing of the warm surface water and thecold subsurface water.
Horizontal changes
We focus the analysis of the model results on arectangular region around the storm track measuring600 km in the across-storm track direction and morethan 850 km in the along-storm track direction (see thebox in Fig. 1). Fig. 6a shows Δchl at t = 30 h when thestorm is 12 h from the Labrador coast (see Fig. 1), andFig. 6b shows Δchl when t = 58 h, when the storm haspassed the study area. The most prominent feature ofFig. 6a is an area of high concentration in the shape ofan inverted ‘U’. The apex of the inverted ‘U’ moveswith the storm. The storm eye lags the head by about120 km. After passage of the storm (Fig. 6b), the area ofhigh concentration forms 2 parallel bands on bothsides of the storm track, and between them is an areaof moderate concentration.
Fig. 7 shows Δchl, D (the depth of the base of themixed layer) and the cooling of the sea surface (ΔSST )along a section perpendicular to the storm track in themiddle of the Labrador Sea (see Fig. 1 for location).The 2 maxima are slightly shifted to the right. Δchl val-ues on the 2 sides of the track have similar magnitudes(the right side is larger). The ΔSST plot (Fig. 7c) sug-gests more intense cooling on the right side of thestorm. The asymmetry is caused by the higher windspeeds on the right side, owing to the movement of thestorm. The maximum cooling, –1.7°C, occurs at about55 km to the right of the storm track, which is at the
same location as the MLD maximum. It isapparent that ΔSST is closely related to theMLD. The slight difference in Δchl on the2 sides near the centre of the storm is associ-ated with the asymmetry in D. The peaks ofΔchl on the 2 sides occur at 160 km from thetrack. The mixed layers at these locationshave similar mixed layer depths (45 m).
The distribution of surface chlorophyll isdependent on the initial distribution and theintensity of mixing. For a given initialchlorophyll distribution (Fig. 5), the changeof surface chlorophyll is controlled by D,the depth of maximum chlorophyll concen-tration, zm (both D and zm are positive)and the width of the chlorophyll peak, σ(Fig. 7b). For D < zm, Δchl increases with in-creasing MLD. For D > zm + 2σ, on the otherhand, it decreases with increasing MLD.The response Δchl can be negative if sur-face chlorophyll concentration is high and
the final MLD is sufficiently deep. The maximum Δchloccurs when D falls between zm and zm + 2σ, i.e. 36 mand 56 m, respectively, for the initial distribution inFig. 5. Such a relationship among Δchl, D, zm and σ iseasy to understand. A shallow mixed layer can notreach the biomass below zm, whereas a deep mixedlayer can dilute the biomass at its maximum.
62
Fig. 6. Surface Δchl during and after passage of the storm at (a) 30 h and(b) 58 h. The area is indicated by the dot-dashed rectangular box in Fig. 1.The solid dot in (a) indicates the location of the storm center at 30 h
Fig. 7. (a) Change in surface chlorophyll (Δchl), (b) surfacemixed layer depth (MLD) (D) before (heavy dash-dotted line)and 5 h after (heavy solid line) the storm; and (c) ΔSST, in thecross-track section indicated by the dotted line in Fig. 1. Thethin horizontal solid and dash-dotted lines in (b) denote zm
and zm + 2σ respectively
Wu et al.: Modelling chlorophyll distribution in a moving storm
In contrast to the case for the open ocean, where thesurface concentration increases by vertical mixing, thechlorophyll distribution on the Labrador shelf and westGreenland shelf has large areas of low Δchl (Fig. 6).The undulating structure along the shelves seen inFig. 6 can be associated with the topographic wavesexcited by the storm. During and after the passage ofthe storm, a complex horizontal velocity field is devel-oped over the shelf (Tang et al. 1998). The velocityfield is composed of permanent currents, direct wind-forced currents, topographic waves, low-frequencycurrents and trapped inertio-gravity waves.The divergence and convergence of the cur-rents over the topography can give rise tovertical motion. We propose that upwellingresulting from such vertical motion can con-tribute to the reduced Δchl on the shelf. Fig. 8shows the change in chlorophyll concentrationin the z-t plane at sites L (Fig. 8a) and G(Fig. 8b) on the shelf edge (see Fig. 1 for loca-tions). The surface chlorophyll first increasesduring the storm, and then drops to the ambi-ent value several hours after the storm. It isclear from Fig. 8 that the mechanism respon-sible for the variation of chlorophyll concentra-tion is more than vertical mixing.
The large vertical velocities generated dur-ing and after the storm are shown in Fig. 4b. Todetermine whether they can lead to upwelling,we integrated the vertical velocity at 50 mfrom 1 h (the start of the storm) to 30 h and58 h, corresponding to the times of Figs. 6a and6b, respectively. The resulting vertical dis-placement fields (Fig. 9) show that the verticaldisplacement is positive with a maximumvalue of 20 m in the areas of low chlorophyllconcentration off the Labrador and Greenlandcoast (Fig. 6b). Positive vertical displacementindicates upwelling. In the shelf regions, low-chlorophyll water below the mixed layer islifted to the mixed layer to replace the chloro-phyll-rich water created by vertical mixing.
Sensitivity to storm parameters (Runs 2 to 7)
The physical response of the ocean to mov-ing storms of dissimilar intensity, size andtranslation speed has been investigated in sev-eral previous numerical studies (Chang &Anthes 1978, Price 1981, Tang et al. 1998). Ourobjective in this subsection is to examine howthe chlorophyll field responds to the changesin translation speed, size and intensity of astorm.
Translation speed
Low (UH = 4 m s–1) and a high (UH = 12 m s–1) trans-lation speeds were used in Runs 2 and 3, respectively.As in the control experiment (Fig. 6), the high responseregion from these runs has the shape of an inverted ‘U’and 2 parallel lines (not shown). The MLD is highlysensitive to the translation speed (Fig. 10). The maxi-mum MLD from the low-speed run is 180 m, whereasthat from the high-speed run is only 100 m. The largedifference is easy to understand. A reduction in the
63
Fig. 9. Vertical displacement indicating upwelling/downwelling dur-ing and after the passage of the storm at (a) 30 h and (b) 58 h. The geo-graphic area is indicated by the dot-dashed rectangular box in Fig. 1.The solid dot in (a) indicates the location of the storm center at 30 h
Fig. 8. Vertical distribution (z) of chlorophyll with time at (a) Labrador coast, L; and (b) Greenland coast, G (see Fig. 1 for locations)
Mar Ecol Prog Ser 335: 57–68, 2007
translation speed means a longer time for wind mixingto operate on the ocean and hence more turbulencekinetic energy is generated in the ocean, resulting in adeeper mixed layer.
For the chlorophyll concentration, we divided thearea affected by the storm into an inner region (be-tween the 2 chlorophyll peaks) and the outer region
(outside the chlorophyll peaks). In the inner region, thesurface chlorophyll increases with the translationspeed. In the outer region, the relationship is reversed.The reason for the different behaviours is that in theinner region D > zm + 2σ and Δchl is inversely propor-tional to the MLD, and in the outer region D < zm andΔchl is proportional to the MLD. The peak values of
Δchl on both sides of the storm track, how-ever, are not sensitive to the translationspeed. This is because the peak values arecontrolled mainly by D, which does notchange much with the translation speed atthe locations of the peaks.
Storm size and intensity
In Runs 4 and 5, radii R of 60 km (smallstorm) and 140 km (large storm) wereused. For the same pn and pc, the largestorm covers a greater area with highwind, although the maximum wind speedis lower than the maximum in the smallstorm. Fig. 11 shows the change of Δchland MLD in the cross-track section for dif-ferent storm sizes. The final MLD increaseswith the storm size. The response Δchl de-creases in the inner region and increases inthe outer region with the storm size. Thesechanges are primarily a result of verticalmixing, which smoothes out the verticaldistribution and thus changes the surfacevalue of chlorophyll concentration. Theaffected area increases with the storm sizeas expected, but the maximum Δchl is notsensitive to R.
The air pressure difference Δp = pn – pc isa measure of the intensity of the storm. Itcan be altered by keeping the ambientpressure pn constant and changing thecenter pressure pc. The results for 3 differ-ent Δp are shown in Fig. 12. With an in-crease of Δp from 3.3 kPa to 11.3 kPa, themaximum MLD increases from 50 m to200 m. Δchl decreases and increases with Δpin the inner and outer regions, respectively.The maximum Δchl is not sensitive to Δp.
Chlorophyll response in different seasons (Runs 8 to 10)
The response of the chlorophyll field topassage of a storm depends on the degreeof stratification in the water column, which
64
Fig. 10. (a) Change of surface chlorophyll (Δchl), (b) MLD (D), over thecross-track section indicated by the dotted line in Fig. 1, for 3 translationspeeds (UH). The thin horizontal solid and dash-dotted lines in (b) denote
zm and zm + 2σ respectively
Fig. 11. (a) Change of surface chlorophyll (Δchl), (b) MLD base depth (D),over the cross-track section indicated by the dotted line in Fig. 1, fordifferent radii (R) and UH = 8 m s–1. The thin horizontal solid and dash-
dotted lines in (b) denote zm and zm + 2σ respectively
Wu et al.: Modelling chlorophyll distribution in a moving storm
is a seasonally varying property. If the water column isalready well mixed (for example winter condition intemperate latitudes), the passage of even a strongstorm may have only a limited effect. In early spring,even with incipient stratification, the surface mixedlayer may still be nutrient replete, so that entrainmentof more nutrients by vertical mixing will have littleeffect on primary production. However, any newlyproduced biomass at the surface may be redistributedin the vertical plane, with an initial apparent reduction
in chlorophyll. It is in the summer and autumn that wemight expect the most pronounced effect. At this time,nutrients are usually exhausted at the surface, and anyentrainment of nitrate into the surface mixed layershould provoke a rapid response in phytoplanktongrowth. The strength of the response will be greaterthe longer conditions have been stable (free of pertur-bation by wind). If several storms pass through an areain rapid succession, the response to the later stormswill be attenuated because the earlier ones will have
already mixed the water column, entrai-ning nitrate. Hence, further disturbancehas little further effect.
To investigate the response in differentseasons, we ran the model (Runs 8 to 10)with the initial chlorophyll profiles given inFig. 3 and Table 2. The storm has no effecton the surface chlorophyll in winterbecause initial chlorophyll distribution isuniform. The initial chlorophyll distribu-tion for spring is characterized by a surfacevalue much higher than values below 60 m(Fig. 3b). As a result, the surface chloro-phyll in much of the inner region decreasesafter the storm, because of deep mixing.The different initial distributions in autumnand summer (Fig. 3) lead to different maxi-mum values of Δchl and locations (Fig. 13a)although the mixed layer depths in the2 seasons (Fig. 13b) are similar. The mixedlayer deepens toward winter and reaches amaximum in spring. The asymmetry acrossthe storm track shown in the spring MLD iscaused by the change in ocean densityfrom southern to northern Labrador Sea.
Entrainment of nitrate
As an application of the storm model, weestimated the nitrate entrained into themixed layer by storm-induced vertical mix-ing using a simple 2-layer model for ni-trate. The conceptual change of the nitratedistribution before and after the storm isshown in Fig. 14. If we know the initial sur-face and deep-water values, Nb and Nd,and MLD after the storm, Da, the nitratebrought from the deep reservoir to the ini-tial mixed layer, F, by the storm is given by:
(10)
where Db is the MLD before the storm andNa is the nitrate concentration after the
F D N N= −b a b( )
65
Fig. 13. (a) Change in surface chlorophyll (Δchl), (b) MLD, over the cross-track section indicated by the dotted line in Fig. 1, for different seasons
Fig. 12. (a) Change of surface chlorophyll (Δchl), (b) MLD (D), over thecross-track section indicated by the dotted line in Fig. 1, for different airpressure differences. The thin horizontal solid and dash-dotted lines in
(b) denote zm and zm + 2σ respectively
Mar Ecol Prog Ser 335: 57–68, 2007
storm. By assuming the total nitrate in the water col-umn is conserved before and after the storm, Na can becomputed given Da:
(11)
The amount of nitrate entrained from the lower layerto the mixed layer per unit distance of the storm trackis given by:
(12)
where y is in the cross-track direction and the integra-tion is over the dotted line in Fig. 1. Given the valuesNb = 0.5 mmol m–3 and Nd = 1.0 mmol m–3, and Da fromRuns 1 to 7 and additional runs, we obtain M as afunction of the translation speed, radius and depres-sion (Fig. 15).
Fig. 15 shows that for a typical storm in summer(Run 1), 3.35 × 103 mol of nitrate for each km of thestorm track is added to the mixed layer, and the sur-face value increases by 47%. The quantity M decrea-ses with the translation speed and increases with theradius and depression. More nitrate will be brought tothe surface by slower, larger and more intense storms.Although the total masses of chlorophyll and nitratecannot be changed by the storm (leaving aside phyto-plankton growth), new nitrate is entrained from thedeep reservoir to the mixed layer by the storm, and canbe used to increase biomass at any trophic level.
DISCUSSION
We have demonstrated that changes in surfacechlorophyll through redistribution are highly sensitiveto the final MLD. The effect of the MLD, is howevernonlinear, i.e. a greater MLD may not always lead to ahigher concentration. An interesting question that wenow address is: for a given initial vertical distribution,does there exist an optimum final MLD that willproduce the maximum increase in surface chlorophyll?We use a simple analytical model to answer thisquestion.
In terms of surface chlorophyll Bs, the chlorophylldistribution before the storm can be rewritten as:
(13)
where(14)
The chlorophyll within this layer is assumed to beredistributed evenly after the storm and is given by:
(15)CD
C z zD
0 0
1’ = ∫a
da
( )
az
=+ −
1
12 22ρ σe m /( )
C z C az z
( )(
( ))
= +⎛
⎝⎜⎞
⎠⎟− −
021
2
2ρ σem
M F yy
= ∫ d
ND N D D N
Dab b a b d
a
= × + − ×( )
66
Nb Na Nd
Db
Da
Nitrate (mmol m−3)
z (m
)
4 6 8 10 123
3.5
4
UH (m s–1)
a
60 80 100 120 1402
3
4
5
R (km)
b
3.3 5.3 7.3 9.3 11.31
2
3
4
5
M (x
103
mol
) km
–1
Pn − Pc (kPa)
c
Fig. 14. Schematic diagram of vertical profiles (z) of nitratedistribution before (dot-dashed line) and after (solid line) thestorm. See Eqs. (10) to (12) for definitions of other terms
Fig. 15. Change of nitrate mass M entrained to the mixedlayer with: (a) storm speed (UH); (b) size (R: radius) and (c) air
pressure difference Pn – Pc
Wu et al.: Modelling chlorophyll distribution in a moving storm
The ratio of the surface chlorophyll concentrationafter the storm to that before the storm is:
(16)
where Erf(x) is the error function. E can be expressedas a function of biological parameters and the finalmixed-layer depth, Da. As an example, we use thevertical profile for Region 9 in Platt et al. (1991) andcompute E as a function of Da for summer, autumnand spring (Fig. 16). For each season, there exists anoptimum MLD which gives the maximum E. This isbecause a small Da cannot entrain chlorophyll atdepth to the mixed layer, and a large Da dilutes thechlorophyll. The optimum Da falls between zm and zm
+ 2σ. Fig. 16 shows Da = summer and autumn, re-spectively. The corresponding values of E are 1.78(spring), 4.17 (summer) and 10.4 (autumn). Theseresults are consistent with the seasonal variation ofmaximum Δchl and the corresponding MLD from thenumerical model (Fig. 13). Since the MLD increaseswith the intensity of the storm (Fig. 12), Fig. 16 sug-gests that a relatively weak storm in autumn cancause a greater increase in surface chlorophyll than astronger storm in summer. The concept of optimum Da
can also be used to explain the band structure inFigs. 6, 7 & 10–13. Across the storm track, the maxi-mum chlorophyll concentration is not around thestorm centre but at a distance where the final mixedlayer depth is between zm and zm + 2σ.
Data that can be used to compare the model resultsare scarce, because of the difficulty of collecting sur-face and sub-surface data during and immediately
after a storm. However, available remotely senseddata are consistent with our model predictions. Hurri-cane Kate passed the southern Labrador Sea on Octo-ber 4, 2003. From an analysis of ocean color data,Platt et al. (2005) found the surface chlorophyll in-creased 3- to 6-fold 14 d after passage of the hurri-cane. The increase on the right side of the hurricanepath was greater than the increase on the left side.The model results for autumn (Fig. 13) indicate amaximum increase of 10 times and an average(across the storm) increase of 5 times the pre-stormvalue (Fig. 3). Fig. 13 also shows that the increase isgreater on the right side of the storm path. To investi-gate the impact of storms on time scales longer than afew days, simulation models that input realistic windsand includes all the important biological processesare required.
CONCLUSIONS
The vertical redistribution of chlorophyll in responseto a moving storm has been investigated numericallyusing an idealized moving storm and initial chlorophyllfields. The suite of numerical experiments includes acontrol run and 9 sensitivity runs. The results are sum-marized as follows.
In the area covered by the storm, the surfacechlorophyll increases from its initial value after thepassage of the storm, except in the shelf regions andin spring. The mixed layer deepens and sea surfacetemperature decreases primarily as a result of verticalmixing. The change in chlorophyll concentration
across the storm track is characterized bya peak on each side of the track. The loca-tion of the peak is directly related to thefinal mixed layer depth, MLD. The changein the MLD and sea surface temperature,on the other hand, has a maximum closeto the storm center.
The major factors controlling the changein surface chlorophyll are the initialchlorophyll distribution and the intensityof vertical mixing induced by the storm,specifically, the relative depth of peakconcentration zm, versus the final mixedlayer depth. If the MLD is shallower thanzm, the surface chlorophyll increases withincreasing MLD. If the MLD is deeperthan zm + 2σ, the surface chlorophylldecreases with increasing MLD. In the re-ference run (summer conditions), the sur-face chlorophyll concentration increases1 to 3 times relative its initial value of1.0 mg m–3. The maximum increase is
ECC
aaD
Erz
Erz D= = + − −⎡
⎣⎢⎤0
0 2 2 2
’ π ρσσ σa
m m af f( ) ( )⎦⎦⎥
67
20 40 60 80 100 120 140 160 180 2000
2
4
6
8
10
12
SpringSummerAutumnzm
zm + 2σ
Da (m)
E r
atio
s
Fig. 16. Surface chlorophyll concentration ratio post-storm:pre-storm (E)as a function of the base of the mixed layer post-storm (Da) for spring,
summer and autumn
Mar Ecol Prog Ser 335: 57–68, 2007
about 3.2 mg m–3, which occurs at about 160 km fromthe storm track, where the MLD is about 45 m.
In contrast to the response in the open ocean, wherethe change in surface chlorophyll is large (except inspring), the surface chlorophyll changes little after thepassage of the storm in the shelf regions off the Labra-dor and west Greenland coast. The different responseof the open ocean and the shelf is shown to be causedby upwelling of the subsurface water on the shelf. As aresult of upwelling, the high-chlorophyll surface wateris replaced by low-chlorophyll water below the mixedlayer
For a given chlorophyll distribution, the change insurface concentration is sensitive to the translationspeed, size and intensity of the storm. The surface con-centration increases with the translation speed and de-creases with the size and intensity in the area betweenthe 2 peaks. The change with the storm parameters isthe opposite in the area outside the peaks. The maxi-mum, however, changes little with the storm para-meters.
The chlorophyll response is strongly dependent onthe seasonal variation of the initial chlorophyll fields.The storm has no effect on surface chlorophyll in win-ter because the initial chlorophyll distribution is uni-form. In spring, surface chlorophyll in much of areaunder the storm decreases after the storm. Summerand autumn have the largest response. The maximumincrease in surface chlorophyll concentration is 3.0 mgm–3 for summer and 4.9 mg m–3 for autumn.
Nitrate brought from deep reservoir to the mixedlayer by the storm is estimated from a simple 2-layernitrate model. For a typical storm in summer, about3.35 × 103 mol of new nitrate is added to the mixedlayer for each km that the storm travels. This quantitydecreases with the translation speed, and increaseswith the size and intensity of the storm. The influx ofnew nitrate will also promote a change in chlorophyllthrough primary production, but this effect is outsidethe scope of this paper.
Acknowledgements. The research was supported by theCanadian Space Agency under the Ocean’s Pulse (TOP) pro-ject and Program for Energy Research and Development(PERD). The authors thank D. Brickman and C. Fuentes-Yacofor reading an early version of the manuscript and givinghelpful comments.
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Editorial responsibility: Howard Browman (Associate Editor-in-Chief), Storebø, Norway
Submitted: May 24, 2006; Accepted: September 10, 2006Proofs received from author(s): April 2, 2007
