Assessing Ecological Changes in Freshwaters using Statistical Models

Claire FergusonAdrian Bowman, Marian Scott

Laurence Carvalho (CEH, Edinburgh)http://www.antarcticconnection.com/antarctic/science/images/climate2.jpg

A Case Study of Loch Leven

Loch Leven Dataset

Length of dataset: 1968 - 2002

150 variables measured,

covering…

• Physics

• Lake chemistry

• Lake biology

• Weather

Sampling frequency: weekly to monthly

Gaps in data: 1984, 1986-87

Loch Leven – TrendsLog SRP

Years

Lo

g(S

RP

, m

ug

/l)

1970 1980 1990 2000

-10

12

34

Log TP

Years

Lo

g(T

P,

mu

g/l)

1970 1980 1990 2000

3.5

4.0

4.5

5.0

5.5

Log Chlorophyll

Years

Lo

g(C

hlo

rop

hyl

l, m

ug

/l)

1970 1980 1990 2000

12

34

5

Water Temperature

Years

Wa

ter

Tem

pe

ratu

re,

oC

1970 1980 1990 2000

05

10

15

20

Log Daphnia

Years

Lo

g(D

ap

hn

ia,

ind

/l)

1970 1980 1990 2000

-4-2

02

4Log NO3N

Years

Lo

g(N

O3

N,

mg

/l)1970 1980 1990 2000

-4-2

0

trend – a pattern in the long run average over time

Loch Leven – Seasonality

Log SRP

Month

Lo

g(S

RP

, m

ug

/l)

2 4 6 8 10 12

-10

12

34

Log TP

MonthL

og

(TP

, m

ug

/l)

2 4 6 8 10 12

3.5

4.0

4.5

5.0

5.5

Log Chlorophyll

Month

Lo

g(C

hlo

rop

hyl

l, m

ug

/l)

2 4 6 8 10 12

12

34

5

Water Temperature

Month

Wa

ter

Tem

pe

ratu

re,

oC

2 4 6 8 10 12

05

10

15

20

Log Daphnia

Month

Lo

g(D

ap

hn

ia,

ind

/l)

2 4 6 8 10 12

-4-2

02

4Log NO3N

Month

Lo

g(N

O3

N,

mg

/l)

2 4 6 8 10 12-4

-20

seasonality – a yearly cyclic pattern in monthly data

For each key variable:

Model: )month()year()SRPlog( 21 mm

Correlated Errors (V ) based on AR(1) correlation.

Circular smoother incorporated for month term (month 12 effect joins up smoothly with month 1 effect).

Additive Models

n

jijiji xmy

1)(

),0(~ 2 VN

Log SRP

a) estimate of m1(year)

year

m1

(ye

ar)

1970 1980 1990 2000

-1.0

-0.5

0.0

0.5

1.0

b) estimate of m2(month)

month

m2

(mo

nth

)

2 4 6 8 10 12

-1.0

-0.5

0.0

0.5

1.0

)month()year()SRPlog( 21 mm

p-value = 4.0 x 10-4 p-value = 0

Log NO3-N

a) estimate of m1(year)

year

m1

(ye

ar)

1970 1980 1990 2000

-2-1

01

b) estimate of m2(month)

monthm

2(m

on

th)

2 4 6 8 10 12

-2-1

01

)month()year()N-NOlog( 213 mm

p-value = 0.011 p-value = 0

Log Chlorophylla

a) estimate of m1(year)

year

m1

(ye

ar)

1970 1980 1990 2000

-0.5

0.0

0.5

1.0

1.5

b) estimate of m2(month)

month

m2

(mo

nth

)

2 4 6 8 10 12

-0.5

0.0

0.5

1.0

1.5

)month()year()lchlorophyllog( 21a mm

p-value = 6.0 x 10-5 p-value = 9.5 x 10-7

Log Chlorophylla

)month year,()lchlorophyllog( a m

year

1970

1980

1990

2000

month

2

4

6

8

10

12

m(year,m

onth)

3.6

3.8

4.0

4.2

Log SRP - Seasonally

)year()SRPlog( m

1970 1980 1990 2000

01

23

4

log srp spring

Year

log(

srp,

mug

/l)

1970 1980 1990 2000

01

23

4

log srp summer

Year

log(

srp,

mug

/l)

1970 1980 1990 2000

01

23

4

log srp autumn

Year

log(

srp,

mug

/l)

1970 1980 1990 2000

01

23

4

log srp winter

Year

log(

srp,

mug

/l)

),0(~ 2 N

p-value = 0.05

p-value = 0.09

p-value = 0.04

p-value = 0.05

Conclusions

Additive and nonparametric regression models –

Flexible tools for modelling

Non-parametric trends and seasonality simultaneously with correlated errors.

Changes in seasonality throughout time.

Nonparametric trends within each season.

Methodological modifications are required including circular smoothers and correlated errors.

Other Work

Modelling chlorophylla in terms of nutrients, water temperature and Daphnia.

To explore:

Lagged relationships

Effects of covariates

Changing relationships over time

Modelling multiple responses of chlorophylla and Daphnia to incorporate feedback relationships.