WEP-L Model Parameter Calibration and Application in Haihe River Basin

WEP-L Model Parameter Calibration and Application in Haihe River
Basin
LEI Xiaohui1, TIAN Yu2, JIANG Yunzhong1
1. China Institute of Water Resources and Hydropower Research, Beijing, P.R.China, 100044
2. School of Civil Engineering, Tianjin University, Tianjin, P.R.China, 300072
[email protected]
Abstract: Because of distributed hydrological model with lots of parameters, output variables,
complicated model structure and highly nonlinear characteristics, therefore, parameter calibration
becomes the important and difficult problem in the application and development of distributed
hydrological model. The paper couples SCE-UA method with WEP-L model, and parameter
automatically calibration in the above Daiying hydrologic station of Haihe River Basin, Nash efficiency
coefficient increases significantly. Research result presents sample in the big basin of WEP-L model,
and provides import hydrological basic support for water resources and water environment management
in Haihe River Basin.
Keywords: parameter calibration, Haihe River Basin, WEP-L model, distributed hydrological model
1 Introduction
Hydrological model contains model structure and model parameters. To confirm model structure is
called system structure identification. In condition of fixed system structure, to optimize model
parameters is called system parameter identification. Both of these are called system identification.
Model parameter optimization is to simulate and analyze historical information and to confirm model
parameters in forecast plan to achieve real-time forecast. Model parameter optimization is aimed to
explore the most satisfactory model and parameters in order to simulate objective system, for parameter
optimization is the main part of model identification [1].
In past 30 years, many methods of global optimum have been developed. Global optimum must be more
convincing than partial optimum. Many researchers try to classify these methods on the basis of some
standard, but no classification plan has been widely accepted till now. The usual global optimum
algorithms in distributed hydrological model parameter optimization are simulation anneal method,
genetic algorithm and SCE-UA Shuffled Complex Evolution . Remarks on algorithm can be classified
into: effectiveness and stabilization of the algorithm; execution efficiency of the algorithm. Through
comparative analysis, SCE-UA algorithm is more stable and efficient [2]. Therefore, the thesis will
apply SCE-UA algorithm to parameter optimization of WEP-L model and to hydrological circulation
simulation at Kuancheng Station of Haihe River basin.
（
）
2 Parameter Auto-optimization of distributed hydrological model
2.1 Parameter optimization algorithm
Distributed hydrological model is widely used in many areas such as hydrological circulation simulation
and flood forecast. Except reasonableness of model result, selecting model parameters is the key of
model simulation efficiency. Model parameter optimization means to decrease difference between model
simulation output and actual observation value to the minimum. Hydrological model parameters can be
classified into two types: one with clear physic meaning and confirmed according to actual situation;
another with no or unclear physical meaning and confirmed according to past observation data. Besides,
1*
Corresponding author. Tel: 010-68785608; Email:[email protected].
Fund project: This paper was jointly supported by funds from Joint Operation Technology of Three Gorge and the
reservoirs in the upstream of Yangtze River of the Funds for Creative Research Groups of China, and the National
Key-technologies Program (2008BAB29B08) of the 11th 5-year Plan of the People’s Republic of China.
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although some model parameters have some physical meanings, they need to be optimized due to lack
of actual measurement data or incorrect observation data [3].
Parameter optimization is an unavoidable important part of hydrological simulation. Usually, it is to get
a group of parameters by adjusting hydrological model parameters, and to make simulation output reach
actual observation value as much as possible. In the past, optimization operation is manual on the basis
of experience, but with the development of computers, mathematic method used to optimize model
parameters has been efficient [4]. Hydrological model optimization methods in domestic and foreign
studies mainly contain simplex method, SCE-UA and genetic algorithm.
2.2 SCE-UA Optimization Algorithm
In 1990s, Duan etc[5] from University of Arizona began to research on optimization of Sacramento
model parameters, and by combining advantages of simplex algorithm [6], biological competition
evolution[7] and species intercrossing method, they proposed SCE-UA Shuffled Complex Evolution
algorithm. The algorithm can consistently, effectively and quickly search global optimum solution of
hydrological model parameters. SCE-UA is regarded as one of the most effective parameter
optimization methods in continuous basins, and is widely used in basin hydrological model parameter
optimization [8]. Firstly, the algorithm selects an initial species group at random in possible parameter
space. Then, the species group will be cut into several complexes, and each complex will be
independently optimized in simplex method. Complexes shall be intersected to form a new complex
regularly in order to obtain more information. The method is based on integration of the following four
concepts: (1) combine certainty and probability; (2) system evolution of complex points in the scope of
parameters; (3) competition evolution; (4) complex re-wash.
Basic thinking of SCE-UA algorithm is to combine complex search technology based on certainty and
biological competition evolution in nature. The key part of the algorithm is CCE. In CCE, every
complex peak is a potential father, and it possibly participates in calculation of next generation’s species.
The role of each sub-complex is the same as the relationship of son-father. Randomness’ application in
establishing sub-complex can make search more complete in feasible zone. The detailed steps of
SCE-UA algorithm are as follows [9]:
(1) Initialization. Suppose optimization is dimension n, select complex number P(P≥1) in evolution and
peak number m(m≥1) in each complex calculate sample point number s=P×m.
(2) Create sample points. Create s sample points in feasible zone at random x1 ,… xs calculate each
（
）
，
point x i ’s function value f i = f ( xi )
， ，
， i = 1，…，s .
(3) Make sequence of sample points. Make ascending order of s sample points
( xi , f i ) ，then mark it as
，…，s ，amongst f ≤ f ≤ …f ，mark D = {( x , f ) , i = 1,… s}
( xi , f i ) ， i = 1
1
2
s
(4) Classify complex groups. Classify D into P complexes A1 ,
，
points amongst, Ak
=
{( x , f ) x
k
j
k
j
k
j
…,A
i
i
p
, each complex contains m
…
= xk + m( k −1) , f jk = f j + m( k −1) , j = 1, , m k = 1, 2,
…p}
(5) Complex evolution. Evolve each complex according to CCE.
(6) Complex mixture. All peak points of each complex after evolution are combined to form a new point
group, and make ascending order of function value fi . Mark D after that, and make ascending order of
D according to objective function.
(7) Astringency judgment. Stop if it meets astringency conditions, or return to D.
3 Application Case
3.1 General description of Haihe River Basin
Haihe River basin, located in E112 120°, N 35
～
～43°, faces Bohai on the east, Yellow River on the
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south, Yunzhong and Taiyue Mountain on the west and Mongolian Plain on the north. The total area of
the basin is 320, 000 km2, accounting for 3.3% of national land, including 189,000 km2 mountainous
area and 131,000km2 plain. Average annual precipitation is 535mm and it has minimum precipitation in
eastern costal China with great fluctuation of average annual precipitation. Annual evaporation capacity
in Haihe River basin and intermountain basin usually is l 000 1300 mrn while 850 1 000 mm in hilly
region.
～
～
3.2 WEP-L distributed hydrological model construction of Kuancheng Station of Haihe River
basin
The thesis adopts day-to-day precipitation data at 9 upstream precipitation stations of Kuancheng Station
in Haihe River basin, day-to-day weather elements at one weather station, and day-to-day actual runoff
measurement information at Kuancheng Hydrometrical Station. Under-laying surface environmental
materials contain 1:100,000 land utility map, land DEM information, 1:250,000 geological data, soil and
characteristic information in 1980, 1985 and 2000, and these are used to establish WEP-L distributed
hydrological model at upstream of Kuancheng Station in Haihe River basin. The distribution of
upstream precipitation station and weather station of Kuancheng Station is shown in Fig.1.
Fig.1 General description of upstream research zone of Kuancheng Station
3.3 Parameter automatic optimization process
The process of applying SCE-UA algorithm to WEP model parameter optimization is: (1)confirm upper
and lower limit of parameters; (2)establish objective function; (3) confirm stop iterative criteria; (4)
parameter optimization result.
Parameters of WEP-L model can be divided into runoff parameter and conflux parameter according to
runoff and conflux process. Please refer to Table 5-1. Runoff parameter can be classified into ground
surface process parameter (modified coefficient of depression storage of land surface), soil water
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transfer process parameter (the first, second and third soil layer, and modified coefficient of soil
hydrological conductivity), groundwater runoff process parameter (modified coefficient of hydrological
conductivity of riverbed bottom materials and modified thickness coefficient of mountain aquifer), and
vegetation evaporation process parameter (modified coefficient of stomatal resistance). Conflux
parameter contains modified coefficient of Manning roughness factor of slope conflux inside sub-basin
and modified coefficient of Manning roughness factor of river-way conflux between sub-basins. Upper
and lower limit of optimized parameters in the paper are shown in Table 1.
1
HSSFCoef
Table 1 Optimize parameter range
Lower Upper
Remarks
limit
limit
0.1
3
Modified coefficient of maximum depression storage
2
SoilDE1
0.1
1
3
SoilDE2
0.2
2
No.
4
Parameter
Classification
Name
（）
Second soil layer thickness（m）
Third soil layer thickness（m）
First soil layer thickness m
SoilDE3
0.4
3
AKCoef
0.1
10
6
RCDTCoef
0.1
10
7
ATHKCoef
0.1
10
Modified coefficient of soil hydrological conductivity
Modified coefficient of hydrological conductivity
of riverbed bottom materials
Modified thickness coefficient of mountain aquifer
8
RCMIcoef
0.1
10
Modified coefficient of stomatal resistance
RivMNCoef
0.01
1
Modified coefficient of river-way conflux between sub-basins
SubMNCoef
0.01
1
Modified coefficient of slope conflux inside sub-basin
5
9
10
Runoff yield
parameter
Conflux
parameter
(1) Establish objective function
Objective function is used to evaluate inosculation of actual measurement flow and simulated flow
process. Selection of objective function is the key to get optimized result. The thesis chooses residual
sum of squares of simulated flow and actual measured flow as objective function. Please refer to
Formula (1):
2
n
SS Q =
∑ (X
sim , i
− X o bs , i )
i =1
（1）
(2) Confirm stop iterative criteria
If it is unable to improve precision of 0.01% after 10 cycles of objective function, the points
corresponding to the parameter values are in flat-topped surface of the feasible zone and iteration stops;
if it is unable to change parameter remarkably after 10 iterations and simulation result is not improved
obviously, object function is thought to be optimized and the iteration stops.
(3) Parameter result after auto-calibration at Kuancheng Station
Through parameter optimization of steps above, we can get optimization results of 10 most important
parameters in WEP-L model. Please refer to Table 2. Before parameter optimization, sensibility analysis
can be used to confirm three parameters to be optimized, namely W3DE2, AKCoef and ATHKCoef, but
others are still initial parameters.
Parameter Name
Table 2 Parameters after auto-calibration at Kuancheng Station
Initial Parameter
Parameter after Auto-calibration
HSSFCoef
1
1
W3DE1
0.2
0.2
W3DE2
0.4
0.29
W3DE3
0.8
0.8
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AKCoef
1
0.1158
rcdtCoef
1
1
ATHKCoef
1
9.08
RCMIcoef
1
1
RivMNCoef
1
1
SubMNCoef
1
1
3.4 Calibration and verification of model parameters
The thesis selects data from 1976 to 1980, and day time step is used for simulation calculation and
model calibration. After the calibration, data from 1981 to 1985 is used to authenticate the result. Fig.2
and Fig.3 respectively show comparison of simulation result of monthly runoff process and actual
measurement result during calibration period and verification period at Nanzhuang Station, while Table
3 shows runoff simulation calibration and verification result at Kuancheng Station.
0
250
100
200
)s
/3150
m(
ff
on
uR100
Precipitation（mm）
200
Simulated（m3/s）
300
Observed（m3/s）
400
50
0
197601
500
)
m
m
(
n
o
i
t
a
t
i
p
i
c
e
r
P
600
197701
197801
Time
197901
198001
Fig.2 Comparison between runoff simulation process and actual runoff measurement process during regular
term at Kuancheng Station
0
100
100
80
Precipitation（mm）
)
s
/
3 60
m
(
f
f
o 40
n
u
R
200
Simulated（m3/s）
300
Observed（m3/s）
400
20
0
198001
500
)
m
m
(
n
o
i
t
a
t
i
p
i
c
e
r
P
600
198101
198201
198301
Time
198401
198501
Fig.3 Comparison between runoff simulation process and actual runoff measurement process during
verification period at Kuancheng Station
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Year
1976-1980
1981-1985
Table 3 Runoff simulation calibration and verification result at Kuancheng Station
Average difference of average Nash efficiency coefficient
monthly runoff process
annual runoff
11.09
0.66
9.82
0.71
（﹪）
of
In Table 3, we can see that average difference of average annual runoff is 11.09% and Nash efficiency of
monthly runoff process is 0.66 during calibration period; average difference of average annual runoff is
9.82% and Nash efficiency of monthly runoff process is 0.71 during verification period. Since Haihe
River basin is located in a plain, the hydrological equilibrium in the basin is influenced by human
activities and hydrological circulation simulation process is not easy. The Nash efficient coefficient
above 0.6 is a relatively good result.
4 Conclusion and Prospect
In this thesis, SCE-UA algorithm is used in parameter optimization of WEL-L model, and hydrological
circulation simulation of Kuancheng Station in Haihe River basin is made. Since hydrological
equilibrium in Haihe River basin is influenced by human activities, there are new changes in
hydrological equilibrium. Therefore, the simulation result is improved relatively. Parameter optimization
can promote the application and practice of distributed hydrological model to some extent, but there still
are many complicated issues to be explored. We shall attach importance to the combination of human
wisdom and computer automation, and develop intelligent auto-optimization method integrating human
wisdom and experience.
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