ANALYSIS OF THE DEPENDENCE OF THE OPTIMAL PARAMETER SET ON CLIMATE CHARACTERISTICS

Marzena Osuch, Renata Romanowicz, Emilia KaramuzInstitute of Geophysics Polish Academy of Sciences, POLAND

Aims Cross-validation of a conceptual rainfall-

runoff model (HBV) Analysis of the temporal variability of the

HBV model parameters Dependence of model parameters on

climate characteristics Assessment of influence of climate

characteristics on identifiability of model parameters

Study areas Selected catchments from the proposed

database : Allier River at Vieille-Brioude, France, area

2267 km2

Axe Creek at Longlea, Australia, area 236.9 km2

Bani River at Douna, Mali, Ivory Coast and Burkina Faso, 103 391.032 km2

Durance River at La Clapiere, France, 2170.0 km2

Garonne River at Portet-sur-Garonne, France, 9980 km2

Kamp River at Zwettl, Austria, 621.8 km2

Wimmera River at Glenorchy Weir Tail, Australia, 2000 km2

and an additional catchment located in Poland Wieprz River at Kosmin, Poland, area 10231

km2Wieprz River source panoramio.com

Methods: HBV Model Conceptual lumped rainfall-runoff model Inputs: precipitation, potential

evapotranspiration and discharges at daily time step

Objective function: the Nash–Sutcliffe efficiency criterion

Optimization algorithm: Simplex Nealder-Mead

Parameter units Lower limit

Upper limit

FC mm maximum soil moisture storage 1 1000β - Parameter of power relationship to simulate indirect

runoff1 6

LP - Limit above which evapotranspiration reaches its potential 0.1 1value

0.1 1

α - Measure for non-linearity of flow in quick runoff reservoir

0.1 3

KF day-1 Recession coefficient for runoff from quick runoff reservoir

0.0005 0.3

KS day-1 Recession coefficient for runoff from base flow reservoir

0.0005 0.3

PERC mm/day Constant percolation rate occurring when water is available

0.1 4

CFLUX mm/day the maximum value for capillary flow 0 4

Methods: calibration 5-year sliding window

calibration Different number of

periods for each catchment due to different size of dataset

River Start of data

End of data

Nr of periods

Allier 01/01/1961

31/07/2008 44

Axe 01/01/1973

13/12/2011 33

Bani 01/01/1959

31/12/1990 27

Durance

01/01/1904

30/12/2010 101

Garonne

01/01/1961

31/07/2008 42

Kamp 01/01/1978

30/12/2008 28

Wieprz 01/11/1965

31/12/1995 24

Wimmera

02/01/1965

31/08/2009 38

Calibration and validation Bani catchment

NS coefficients for calibration vary from 0.91 to 0.99

the y-axis shows start of the period for which the model is calibrated, the x-axis shows the beginning of the validation period

Models calibrated to the data from the 60s poorly verified on the data from the 80s

VALIDATION

CA

LIB

RA

TIO

N

1960 1965 1970 1975 1980 1985

1960

1965

1970

1975

1980

1985 -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1960 1965 1970 1975 1980 19850.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99NS

Temporal variability of the HBV model parameters: Bani catchment

1960 1970 19800

500

1000FC

1960 1970 1980246

1960 1970 1980

0.5

1LP

1960 1970 19800

0.5

1

1960 1970 1980

0.10.20.3

KF

1960 1970 1980

0.05

0.1KS

1960 1970 1980

1234

PERC

1960 1970 19800

2

4CFLUX

Analysis of significance of linear regression at 0.05 level

An increase of FC, KS, PERC values

A decrease of CFLUX values

1960 1965 1970 1975 1980 19850.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99NS

Temporal variability of the HBV model parameters

Catchment Decreasing trend ↘(significant at 0.05 level)

Increasing trend ↗(significant at 0.05 level)

Allier β, α, KS KFAxe PERC, CFLUX FC, β, α, LP

Bani CFLUX FC, KS, PERCDurance PERC -Garonne KF α, KS, CFLUX

Kamp - α, FC, PERC

Wieprz - -Wimmera LP, PERC FC, KF

The direction of changes and intensity of trend vary between the HBV model parameters and catchments.

Hydro-climatic characteristicsWe analysed the following climate characteristics: Sum of precipitation over 5 year period Maximum daily precipitation Sum of flows over 5 year period, Maximum daily flows

Sum of PET over 5 year period Maximum daily PET Sum of air temperature over 5 year period Maximum daily air temperature Aridity index (PET/P)

Temp-related

Water-related

Variability of climatic conditions, Bani catchment

1960 1970 1980

5000

6000

yearssum

of p

reci

p [m

m]

1960 1970 1980

30

40

yearsmax

pre

cip

[mm

]

1960 1970 19808500

8600

8700

years

sum

of p

et [m

m]

1960 1970 1980

5.6

5.8

years

max

pet

[mm

]

1960 1970 19804.8

4.9

5 x 104

years

sum

of t

emp

[0 C]

1960 1970 198030

31

32

yearsm

ax te

mp

[0 C]

1960 1970 19800

5

10

15 x 105

yearssum

of f

low

s [m

3 /s]

1960 1970 19800

2000

4000

years

max

flow

[m3 /s

]

1960 1970 1980

1.5

2

years

PET/

P

Decline in sum of precipitation

decrease in flow Increase of

maximum air temperature and PET

Increase of aridity index

Dependence of model parameters on climate characteristics Bani catchment

Pearson correlation coefficient

Bold red values are significant at 0.05 level

FC, LP, KS, PERC and CFLUX parameters are correlated with climatic characteristics

The highest correlation 0.89 is between KS parameter and sum of flows

FC β LP α KF KS PERC CFLUXsum of precipitation -0.66 0.18 0.31 -0.31 -0.22 -0.83 -0.63 0.56maximum precipitation 0.11 0.01 0.38 -0.34 -0.30 -0.29 -0.21 -0.03sum of PET 0.24 -0.09 -0.19 0.21 0.15 0.27 0.22 -0.18maximum PET 0.57 -0.21 -0.34 0.26 0.13 0.77 0.55 -0.48sum of air temp. 0.19 -0.08 -0.19 0.21 0.15 0.24 0.18 -0.16maximum temp 0.57 -0.16 -0.32 0.29 0.16 0.80 0.57 -0.50sum of flows -0.52 0.22 0.45 -0.20 -0.20 -0.89 -0.60 0.53maximum flow -0.57 0.22 0.41 -0.18 -0.17 -0.85 -0.60 0.51aridity index 0.67 -0.19 -0.28 0.31 0.23 0.77 0.61 -0.53

0 2 4 6 8 10 12 14x 105

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

sum of flows [m3/s]

KS

KS

1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

200

400

600

800

1000

1200

aridity index

FC

FC

Influence of climate characteristics on identifiability of model parameters We applied a sensitivity analysis (SA) by Sobol method to

assess the identifiability of the HBV model parameters The Sobol method is a well recognized variance-based

method

SA aims at establishing effect of model parameters on model output

The identifiability was assessed by First order sensitivity index – quantifies influence of parameter i

on the NS criterion Total order sensitivity index - quantifies influence of parameter i

on the NS criterion taking into account its interactions with the other parameters

Influence of climate characteristics on Sobol first order sensitivity index: Bani

sum_pr

ecip

max_pr

ecip

sum_flo

w

max_flo

w

aridit

y_inde

x

sum_PE

T

max_PE

T

sum_te

mp

max_te

mp

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

FCalphaKFKSPERCCFLUXLPBeta

Corr

elat

ion

coeffi

cien

t

Water-related Air temperature-related

Water-relatedTem

p-related

Influence of sum of precipitation on identifiability of model parameters: Bani

Two groups of parameters

First group (water-related): FC, α, KF and PERC – their identiliability increases with an increase of the amount of water

Second group (air temperature-related): β, LP and CFLUX -their identifiability decreases with an increase of the amount of water

4500 5000 5500 60000.4

0.6

0.8

sum of precip [mm]

Si(F

C)

Si(FC)

4500 5000 5500 60000

0.05

0.1

sum of precip [mm]

Si(

)

Si()

4500 5000 5500 60000

0.05

0.1

sum of precip [mm]

Si(L

P)

Si(LP)

4500 5000 5500 60000

0.01

0.02

sum of precip [mm]

Si(

)

Si()

4500 5000 5500 60000

0.01

0.02

sum of precip [mm]

Si(K

F)

Si(KF)

4500 5000 5500 6000

6

8

10x 10

-3

sum of precip [mm]

Si(K

S)

Si(KS)

4500 5000 5500 6000-0.02

0

0.02

sum of precip [mm]

Si(P

ER

C)

Si(PERC)

4500 5000 5500 6000-1

0

1x 10

-3

sum of precip [mm]

Si(C

FLU

X)

Si(CFLUX)

Influence of aridity index on identifiability of model parameters: Bani

Two groups of parameters

First group (water-related) : FC, α, KF and PERC – their identiliability decreses with an increase of aridity index (and sum of PET, sum of air temp, maximum PET, maximum air temp)

Second group (air temperature-related): β, LP and CFLUX - their identifiability increases with an increase of aridity index

1.4 1.5 1.6 1.7 1.8 1.90.4

0.6

0.8

aridity index

Si(F

C)

Si(FC)

1.4 1.5 1.6 1.7 1.8 1.90

0.05

0.1

aridity index

Si(

)

Si()

1.4 1.5 1.6 1.7 1.8 1.90

0.05

0.1

aridity index

Si(L

P)

Si(LP)

1.4 1.5 1.6 1.7 1.8 1.90

0.01

0.02

aridity index

Si(

)

Si()

1.4 1.5 1.6 1.7 1.8 1.90

0.01

0.02

aridity index

Si(K

F)

Si(KF)

1.4 1.5 1.6 1.7 1.8 1.9

6

8

10x 10

-3

aridity index

Si(K

S)

Si(KS)

1.4 1.5 1.6 1.7 1.8 1.9-0.02

0

0.02

aridity index

Si(P

ER

C)

Si(PERC)

1.4 1.5 1.6 1.7 1.8 1.9-1

0

1x 10

-3

aridity index

Si(C

FLU

X)

Si(CFLUX)

Summary (1) The HBV model was calibrated on a series of 5 year periods

and validated on other periods in 8 catchments. The results of calibration are very good. Validation of models shows two different patterns: a combination of good and bad years (Allier, Durance, Garonne) or poor validation of almost every model for the last periods (Axe, Wimmera)

We analysed the temporal variability of the HBV model parameters in 8 catchments by linear trend analysis. In most catchments (except Wieprz) there was a statistically significant linear trend. The direction of changes and intensity of trend vary between the HBV model parameters and catchments.

Summary (2) In the next step we estimated a dependence of model

parameters on climate characteristics (sum and maximum values of precipitation, air temperature, PET, flow and aridity index). Derived regressions are statistically significant at 0.05 level. The direction of changes and intensity vary between catchments and model parameters.

Influence of climate characteristics on identifiability of model parameters was assessed by Sobol sensitivity analysis. Results indicate strong dependency between first order Sobol sensitivity index and climatic characteristics. The HBV model parameters were classified into two groups: water-related and air temperature-related.