Meeting challenges on the calibrationof the global hydrological model

WGHM with GRACE data input

S. WerthA. Güntnerwith input from R. Schmidt and J. Kusche

Introduction

S: Water storage changeP: PrecipitationE: EvaporationR: Runoff

ΔS = P - R - E

Terrestrial water balance

Time-Variable Gravity and Surface Mass Processes: Validation, Processing and First Application of New Satellite Gravity Data (TIVAGAM)

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• Conceptual waterbalance model

• 0.5° spatial resolution

• Daily time-step

• Climate forcing data from CRU, GPCC, ECMWF

• Human water use accounted for

• Calibration for river dischargeat 1200 stations worldwide

ΔS = ΔScanop + ΔSsnow + ΔSsoil + ΔSgw + ΔSlakes + ΔSwetl + ΔSriver

The WaterGAP Global Hydrology Model (WGHM)

Total continental storage change:

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Correspondence between GRACE and WGHM

Aim: Improve WGHM model results by a new calibration with GRACE data.

mm w.eq.

Mean maximum annual storage change (Gaussian filtering, 500 km)

GRACE

WGHM

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Work plan for model calibration:

1) Analyze model propertiesa) Identification sensitive parametersb) Model uncertaintyc) Calibration test runs

2) Select adequate GRACE data and filter tools

3) Perform multi-objective model calibration

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Work plan for model calibration:

1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs

2) Select adequate GRACE data and filter tools

3) Perform multi-objective model calibration

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1c) Single-objective calibration

WGHM Monte-Carlo run

Standard WGHM

WGHM single-objective, one-parameter calibration

Ob

1.0 0.5 0.0 -0.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Nash-Sutcliffe coefficient for water storage change

Nas

h-S

utcl

iffe

coef

ficie

nt

for

river

dis

char

ge

6

perfect model

simulation

Calibration approach

current parameter

sets

Evaluationof error

stop ?

Parameter-

variation

parameter set

ranking

Optimalsolution

yes

no

initial parameter

sets

Model simulation

GRACE total

storage variation

RunoffMeasureme

ntdata

7

0

err

or

dis

charg

e

Pareto

Frontier

0

single model simulation

error total storage change

0

Work plan for model calibration:

1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs

2) Select adequate GRACE data and filter tools

3) Perform multi-objective model calibration

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2) GRACE filter tool evaluation

worldwide 22 largest WGHM river basins

Filter type Parameter Source

Gaussian filter (GF) filter width Jekeli, 1981

Optimized for basin shape (OF) max. satellite error Swenson and Wahr, 2002

Optimized for exp. signal model (MF) correlation length, signal variance Swenson and Wahr, 2002

GRACE signal-noise-ratio optimized (SF) factor of formal errors Seo et al, 2005

Correlation Error Filter (CEF) filter window properties Swenson and Wahr, 2006

Decorrelation Filter (DDK) covariance matrix parameter Kusche, 2007

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2) GRACE filter tool evaluation: Amazon

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

wN

SK

500 1000 1500

filterwidth (km)

5101520

max. Satellite error (mm)

DDK decorrelated

w =10, n =30a e

w=30, n =30

a

e

w=20, n =30

a

ew =10, n =30

a

e

w =20, n =30a e

w =30, n =30a e

GFCEF decorrelated

OFCEF decorrelated

0

w =30, n =30

a

e

w =20, n =30a

e

w =10, n =30a

e

SFCEF decorrelated

5 10 15 20

error factor

50

100

150

2004006008001000

corrlation length (km)

= 250 mmσs

w =30, n =30a e

w =20, n =30a e

w =10, n =30a e 20

MFCEF decorrelated

Gaussian filter (GF)

Optimized for basin shape (OF)

Optimized for exp. signal model (MF)

GRACE signal-noise-ratio optimized (SF)

Correlation Error Filter (CEF)

Decorrelation Filter (DDK)10

2) GRACE filter tool evaluation: Lena

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

wN

SK

500 1000 1500

filterwidth (km)

5101520

max. Satellite error (mm)

w=10, n

=30

a

e

w=30, n

=30

a

e

w=20, n =30

a

e

w =30, n =30a e

w =20, n =30

a

ew =10, n =30a

e

GFCEF decorrelated

OFCEF decorrelated

DDK decorrelated

SFCEF decorrelated

0 5 10 15 20

error factor

w =20, n =30a e

w =10, n =30a e

w =30, n =30a e

MFCEF decorrelated

2004006008001000

corrlation length (km)

w =30, n =30a e

50

250= 300 mm

200

150

100

20

Gaussian filter (GF)

Optimized for basin shape (OF)

Optimized for exp. signal model (MF)

GRACE signal-noise-ratio optimized (SF)

Correlation Error Filter (CEF)

Decorrelation Filter (DDK)11

2) GRACE filter tool evaluation

Basin WGHM GLDAS

Amazon OF, MF OF,MF

Ganges MF MF

Mississippi

GF DDK

Volga SF SF

Yukon OF, CEFMF

MFOptimal filter for 5 basin examples

ParameterParameter

ValuewNS

C

rg [km] 200 0.75

εmax [mm] 13 0.78

error factor 0.4 0.77

σs [mm], cl [km]

250, 200 0.78

wa, we, na, ne 30, 3, 2, 30 0.63

a, p 1014, 4 0.74Amazon wNSC values and filter parameter for different filter types

Filter

Gaussian filter (GF)

Optimized for basin shape (OF)

Optimized for exp. signal model (MF)

GRACE signal-noise-ratio optimized (SF)

Correlation Error Filter (CEF)

Decorrelation Filter (DDK)

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Work plan for model calibration:

1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs

2) Select adequate GRACE data and filter tools

3) Perform multi-objective model calibration

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Work plan for model calibration:

3) Calibration Realization

Implementation of Multi-objective calibration algorithms into WGHM:

DDS Dynamically Dimension Search► single-objective calibration algorithm extended for mutli-objective problems

NSGA-II Non-dominated Sorting Genetic Algorithm► evolutionary multi objective calibration algorithm

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Summary and Outlook

fulfilled steps:Model studies for selected river basinsAnalyses of GRACE filter toolsImplementation of calibration algorithm

next steps:Multi-objective calibration runsUse of differently processed GRACE data,

e.g. signal proportions from analysis of Schmidt et. al. 2007

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