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 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
km2
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 NealderMead
Parameter
units
Lower limit
Upper limit
FC
mm
maximum soil moisture storage
1
1000
β
-
Parameter of power relationship to simulate indirect runoff
1
6
LP
-
Limit above which evapotranspiration reaches its potential 0.1 1
value
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

1960
0.8

0.6
1965
CALIBRATION
0.4
0.2
1970
0 
-0.2
1975
-0.4
-0.6
1980
-0.8
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
NS
0.99
0.98
0.97
0.96
-1
1985
1960
1965
1970
1975
VALIDATION
1980
1985
0.95
0.94
0.93
0.92
0.91
1960
1965
1970
1975
1980
1985
Temporal variability of the HBV model
parameters: Bani catchment

FC
1000
6
500
4
0
1960
2
1970
LP
1980
1960
1
1
0.5
0.5
1960
1970
KF
1980
0.3
0.2
0.1
1960
0
1960
1970

1980


1970
KS
An increase of FC, KS, PERC
values
A decrease of CFLUX values
1980
0.1
0.05
NS
0.99
1970
PERC
1980
4
3
2
1
1960
Analysis of significance of linear
regression at 0.05 level
1960
1970
CFLUX
1980
0.97
4
0.96
2
1970
1980
0
1960
0.98
0.95
1970
1980
0.94
0.93
0.92
0.91
1960
1965
1970
1975
1980
1985
Temporal variability of the HBV model
parameters
The direction of changes and intensity of trend vary between the HBV model
parameters and catchments.
Catchment
Decreasing trend ↘
(significant at 0.05 level)
Increasing trend ↗
(significant at 0.05 level)
Allier
β, α, KS
KF
Axe
PERC, CFLUX
FC, β, α, LP
Bani
CFLUX
FC, KS, PERC
Durance
PERC
-
Garonne
KF
α, KS, CFLUX
Kamp
-
α, FC, PERC
Wieprz
-
-
Wimmera
LP, PERC
FC, KF
Hydro-climatic characteristics




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
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
0
sum of temp [ C]
5.8
5.6
1960 1970 1980
years
15
x 10
5
10
5
0
1960 1970 1980
years
max flow [m 3/s]
sum of flows [m 3/s]
1960 1970 1980
years
5
x 10
sum of pet [mm]
1960 1970 1980
years
30
8500
1960 1970 1980
years
4
4.9
4.8
1960 1970 1980
years
4000
2000
0
1960 1970 1980
years

8600
32


31
30
1960 1970 1980
years
2
PET/P
5000
40
8700
max temp [ 0C]
max precip [mm]
6000
max pet [mm]
sum of precip [mm]
Variability of climatic conditions,
Bani catchment
1.5
1960 1970 1980
years

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
β
FC


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
KF
KS
PERC CFLUX
-0.66
0.18
0.31
-0.31
-0.22
-0.83
-0.63
0.56
0.11
0.01
0.38
-0.34
-0.30
-0.29
-0.21
-0.03
sum of PET
0.24
-0.09
-0.19
0.21
0.15
0.27
0.22
-0.18
maximum PET
sum of air
temp.
maximum
temp
0.57
-0.21
-0.34
0.26
0.13
0.77
0.55
-0.48
0.19
-0.08
-0.19
0.21
0.15
0.24
0.18
-0.16
0.57
-0.16
-0.32
0.29
0.16
0.80
0.57
-0.50
sum of flows
-0.52
0.22
0.45
-0.20
-0.20
-0.89
-0.60
0.53
maximum flow
-0.57
0.22
0.41
-0.18
-0.17
-0.85
-0.60
0.51
0.67
-0.19
-0.28
0.31
0.23
0.77
0.61
-0.53
aridity index
KS
FC
0.055
1200
0.05
1000
0.045
800
0.04
FC

Pearson correlation
coefficient
KS

sum of
precipitation
maximum
precipitation
α
LP
0.035
600
0.03
400
0.025
200
0.02
0.015
0
2
4
6
8
sum of flows [m 3/s]
10
12
14
5
x 10
0
1.3
1.4
1.5
1.6
1.7
aridity index
1.8
1.9
2
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
1.0
0.8
0.6
FC
alpha
0.2
KF
KS
0.0
sum_precip
max_precip
sum_flow
max_flow
aridity_index
sum_PET
max_PET
sum_temp
max_temp
PERC
LP
Beta
-0.4
-0.6
-0.8
-1.0
Water-related
Air temperature-related
Temp-related
CFLUX
-0.2
Water-related
Correlation coefficient
0.4
Influence of sum of precipitation on
identifiability of model parameters: Bani
Si()
Si(FC)
0.6
0.4
4500
5000
5500
sum of precip [mm]
Si(LP)
6000
0.05
5000
5500
sum of precip [mm]
Si(KF)
0
4500
6000
-3
Si(KS)
5000
5500
sum of precip [mm]
Si(PERC)
6000
6000
5000
5500
sum of precip [mm]
Si(KS)
6000
5000
5500
sum of precip [mm]
Si(CFLUX)
6000
0
6000
5000
5500
sum of precip [mm]
6000

8
6
-3
0.02
5000
5500
sum of precip [mm]
x 10
4500
Si(CFLUX)
Si(KF)
Si(PERC)
10
0.01
-0.02
4500
5000
5500
sum of precip [mm]
Si( )
0.01
0.02
0
4500

0.02
Si( )
Si(LP)
0.05
0
4500
0.1
0
4500

0.1
Si()
Si(FC)
0.8
1
x 10
0
-1
4500
Two groups of
parameters
First group (waterrelated): 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
Si()
Si(FC)
0.6
0.4
1.4
1.5
1.6
1.7
aridity index
Si(LP)
1.8
1.9
0.05
1.5
1.6
1.7
aridity index
Si(KF)
1.8
0
1.4
1.9
Si(KS)
10
1.5
1.6
1.7
aridity index
Si(PERC)
1.8
1.9
1.8
1.9
1.5
1.6
1.7
aridity index
Si(KS)
1.8
1.9
0
1.6
1.7
aridity index
8

6
1.5
1.6
1.7
aridity index
Si(CFLUX)
1.8
1.9
1.5
1.6
1.7
aridity index
1.8
1.9
-3
0.02
1.5
x 10
1.4
Si(CFLUX)
Si(KF)
Si(PERC)
1.6
1.7
aridity index
Si( )
-3
0.01
-0.02
1.4
1.5
0.01
0.02
0
1.4

0.02
Si( )
Si(LP)
0.05
0
1.4
0.1
0
1.4

0.1
Si()
Si(FC)
0.8
1.8
1.9
1
x 10
0
-1
1.4
Two groups of
parameters
First group (waterrelated) : 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.