Model-based and statistical methods for assessment of goal achievement

EEA, Copenhagen 21-22 February, 2005

Anders Grimvall

Department of Mathematics

Linköping University, Sweden

EEA, 21-22 Feb 2005

Outline of presentation

Statistical methods for separating human impact from natural fluctuations

Ensemble runs of process-based models

Validation of models for scenario analyses

EEA, 21-22 Feb 2005

Nitrogen load and water dischargeat Lobith on the Rhine

0

100

200

300

400

500

1988 1990 1992 1994 1996 1998 2000 2002 2004

Riv

eri

ne

loa

d o

f to

tal n

itro

ge

n (

10

00

to

n N

/yr)

0

20

40

60

80

100

Wa

ter

dis

ch

arg

e (

10

6 m3 /y

r)

Nitrogen load Water discharge

EEA, 21-22 Feb 2005

Observed and normalised nitrogen load at Lobith on the Rhine

0

100

200

300

400

500

1988 1990 1992 1994 1996 1998 2000 2002 2004

Riv

erin

e lo

ad o

f to

tal n

itro

gen

(10

00 t

on

N/y

r)

Normalised load Observed load

EEA, 21-22 Feb 2005

Simple flow-normalisation of the riverine load of phosphorus at Brunsbüttel on the Elbe River

0

5

10

15

20

1984 1988 1992 1996 2000

To

t-P

loa

d (

kto

n/y

r)

0

10

20

30

40

Wa

ter

dis

cha

rge

(1

09 m

3 /yr)

Tot-P load Water discharge

0

5

10

15

20

0 10 20 30 40

Water discharge (109 m3/yr)

To

t-P

loa

d (

kto

n/y

r)

0

5

10

15

20

1984 1988 1992 1996 2000

Flo

w-n

orm

alis

ed

To

t-P

loa

d (

kto

n/y

r)

EEA, 21-22 Feb 2005

Normalisation of the load of phosporuscarried by the Elbe River

0

5

10

15

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

No

rma

lise

d T

ot-

P lo

ad

(kt

on

/yr)

.

Schnackenburg Brunsbuettel Cuxhaven

Normalisation with respect to water discharge, salinity and load of suspended particulate matter

EEA, 21-22 Feb 2005

Conclusions- statistical normalisation

The combined effect of all past interventions in the drainage area can be clarified with a temporal resolution that is satisfactory for decision-making

The attribution of anthropogenic trends to specific interventions may require other tools

EEA, 21-22 Feb 2005

General structure of process-based models of the flow of water and substances through a catchment

The riverine load y at given time t and site z is a function

of all inputs at all occasions up to time t and all sites upstream of zz~)ofupstream~,);~,((),( zztszsfzt xy

Different types of model inputs:

• initial conditions (state of the system at the onset of the simulation)• anthropogenic forcing of the system• meteorological forcing of the system• model parameters

)~,( zsx

EEA, 21-22 Feb 2005

Ensemble runs for meteorological normalisationof riverine loads

20

40

60

80

100

120

1 11 2120

40

60

80

100

120

1 11 21

Physics-basedmodel

Anthropogenicforcing

Simulatedweather data 1

Step 2:

20

40

60

80

100

120

1 11 2120

40

60

80

100

120

1 11 21

Physics-basedmodel

Anthropogenicforcing

Simulatedweather data k Model output k

Model output 1

20

40

60

80

100

120

1 11 2120

40

60

80

100

120

1 11 21

Weathergenerator

Real weather dataSimulatedweather data

Step 1:

Average output for each time t

20

40

60

80

100

120

1 11 21

The natural variation is suppressed

EEA, 21-22 Feb 2005

Meteorologically normalised outputs of the Integrated Nitrogen in Catchments (INCA-N) model

A single sub-basin comprising only arable land and

receiving a constant level of ammonium and nitrate fertiliser

(combined total 156 kg N/ha/yr)

0

20

40

60

80

100

120

1 2 3 4 5 6 7Year

Nor

mal

ised

load

of

inor

gani

c N

(kg

/ha/

yr)

EEA, 21-22 Feb 2005

Ensemble runs clarifying the response to changes in the fertilisation scheme

Run the model with

(i) a given fertilisation scheme

(ii) a slightly adjusted scheme

and compute the difference between the two model runs.

Repeat such pairs of runs for a representative distribution of meteorological forcings and compute the mean output for each time t.

If the adjustment is zero for the second year and onwards, we can summarise the results in impulse response functions for the impact of fertiliser application.

EEA, 21-22 Feb 2005

Predicted response of riverine loads of inorganic nitrogen to an impulse in fertiliser application

A single sub-basin comprising only arable landBase-flow index 0

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7Year

Cu

mu

late

d r

esp

on

se

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7Year

Re

lativ

e f

req

ue

ncy

Travel time of the extra nitrogen added Ratio of the cumulated increase in

riverine loads to the increase in fertiliser application

EEA, 21-22 Feb 2005

Predicted response of riverine loads of inorganic nitrogen to an impulse in fertiliser application

A single sub-basin comprising only arable landBase-flow index 1

0.0

0.2

0.4

0.6

0.8

1.0

1 4 7 10 13 16 19 22 25 28Year

Cu

mu

late

d r

esp

on

se .

0.00

0.05

0.10

0.15

0.20

1 4 7 10

13

16

19

22

25

28

Year

Re

lativ

e f

req

ue

ncy

Ratio of the cumulated increase in riverine loads to the increase in

fertiliser applicationTravel time of the extra nitrogen added

EEA, 21-22 Feb 2005

Ensemble runs clarifying water travel times

The response to changes in the input of an inert substance can be clarified by performing ensemble runs in which:

all processes involving transformation or immobilisation

of nitrogen are switched off

An inert substance moves like the water in which it is

dissolved

EEA, 21-22 Feb 2005

Distributions of travel times for inorganic nitrogen and water

Base-flow index 0

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7

Year

Rel

ativ

e fr

eque

ncy

Water Inorg. N

0.00

0.05

0.10

0.15

0.20

1 3 5 7 9 11 13 15 17 19 21

Year

Rel

ativ

e fr

eque

ncy

Water Inorg. N

Base-flow index 1

Preferential removal of nitrogen taking long pathways

EEA, 21-22 Feb 2005

Conclusions- ensemble runs

Ensemble runs involving artificially generated meteorological inputs can be employed to:

Extract model features that might otherwise be hidden by the total variation in the model output

Compute meteorologically normalised model outputs for retrospective or scenario analyses of riverine loads

EEA, 21-22 Feb 2005

Conventional model validation

0

50

100

150

200

250

300

350

400

450

500

1991-01-01 1992-01-01 1992-12-31 1993-12-31 1994-12-31

Nitr

ate

tra

nsp

ort

(g

N/s

)

Observed transport Modelled transport

Proper validation requires data sets having a

substantial variation in the input under consideration

EEA, 21-22 Feb 2005

Conclusions- validation of process-based models

Proper validation of models for scenario analyses can only be done in catchments where substantial interventions have been undertaken

It can be questioned whether the INCA-N model, and many other models, are able to predict long lags in the water quality response to interventions in the drainage area

EEA, 21-22 Feb 2005

Overall conclusions

Statistical normalisation can give added value to observed data

Ensemble runs can give added value to process-based models

The currently used model validation techniques can be questioned

EEA, 21-22 Feb 2005

Further reading

Hussian, M., Grimvall, A., and Petersen, W. 2004. Estimation of the human impact on nutrient loads carried by the Elbe River. Environmental Monitoring and Assessment 96:15-33.

Wahlin, K., Shahsavani, D., Grimvall, A., Wade, A. and Butterfield, D. 2004. Reduced models of the retention of nitrogen in catchments. In C. Pahl-Wostl, S. Schmidt, A.E. Rizzoli, and A. J. Jakeman (eds.) Complexity and Integrated Resources Management, Transactions of the 2nd Biennial Meeting of the International Environmental Modelling and Software Society, iEMSs: Manno, Switzerland, 2004.

EEA, 21-22 Feb 2005

Flow normalisation of the nitrogen load carried by the Göta River - data from Trollhättan

Normalisation with respect to water discharge

0

5000

10000

15000

20000

25000

1975 1980 1985 1990 1995 2000 2005

Tot-N load (ton N/yr) Normalised Tot-N load (ton N/yr)