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.