ANALYSIS OF THE DEPENDENCE OF THE OPTIMAL PARAMETER SET ON CLIMATE CHARACTERISTICS Marzena Osuch, Renata Romanowicz, Emilia Karamuz Institute 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 km 2  Axe Creek at Longlea, Australia, area km 2  Bani River at Douna, Mali, Ivory Coast and Burkina Faso, km 2  Durance River at La Clapiere, France, km 2  Garonne River at Portet-sur-Garonne, France, 9980 km 2  Kamp River at Zwettl, Austria, km 2  Wimmera River at Glenorchy Weir Tail, Australia, 2000 km 2  and an additional catchment located in Poland  Wieprz River at Kosmin, Poland, area km 2 Wieprz 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 ParameterunitsLower limitUpper limit FCmmmaximum soil moisture storage11000 β -Parameter of power relationship to simulate indirect runoff16 LP-Limit above which evapotranspiration reaches its potential value 0.11 α -Measure for non-linearity of flow in quick runoff reservoir0.13 KFday -1 Recession coefficient for runoff from quick runoff reservoir KSday -1 Recession coefficient for runoff from base flow reservoir PERCmm/dayConstant percolation rate occurring when water is available0.14 CFLUXmm/daythe maximum value for capillary flow04

Methods: calibration  5-year sliding window calibration  Different number of periods for each catchment due to different size of dataset RiverStart of data End of dataNr of periods Allier01/01/196131/07/ Axe01/01/197313/12/ Bani01/01/195931/12/ Durance01/01/190430/12/ Garonne01/01/196131/07/ Kamp01/01/197830/12/ Wieprz01/11/196531/12/ Wimmera02/01/196531/08/200938

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

Temporal variability of the HBV model parameters: Bani catchment Analysis of significance of linear regression at 0.05 level  An increase of FC, KS, PERC values  A decrease of CFLUX values

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 KF AxePERC, CFLUX FC, β, α, LP BaniCFLUXFC, KS, PERC DurancePERC- GaronneKF α, KS, CFLUX Kamp- α, FC, PERC Wieprz-- WimmeraLP, PERCFC, KF The direction of changes and intensity of trend vary between the HBV model parameters and catchments.

Hydro-climatic characteristics We 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  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 FCβLPαKFKSPERCCFLUX sum of precipitation maximum precipitation sum of PET maximum PET sum of air temp maximum temp sum of flows maximum flow aridity index

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 Water-relatedAir temperature-related Water-related Temp-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

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

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.