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99 © IWA Publishing 2019 Hydrology Research | 50.1 | 2019
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Development of WEP-COR model to simulate land surface
water and energy budgets in a cold region
Jia Li, Zuhao Zhou, Hao Wang, Jiajia Liu, Yangwen Jia, Peng Hu
and Chong-Yu Xu
ABSTRACT
The Water and Energy transfer Processes in Cold Regions (WEP-COR) model is an improved version of
the Water and Energy transfer Processes in Large basins (WEP-L) model that integrates a multi-layer
frozen soil model to simulate the hydrological processes in cold regions and the heat fluxes at
different depths of frozen soil. The temperature, water content, freezing depth of the soil, and daily
discharge were simulated and compared with observations. The simulated and observed data were
used to analyze the runoff flow components. The results showed that the WEP-COR model can
effectively simulate the distributions of the soil temperature and water content. The average root
mean squared errors of the temperature, unfrozen water content, total water content, and freezing
depth of the soil were 1.21 WC, 0.035 cm3/cm3, 0.034 cm3/cm3, and 17.6 cm, respectively. The mean
Nash–Sutcliffe efficiency and relative error of the daily discharge were 0.64 and 6.58%, respectively.
Compared with the WEP-L model, the WEP-COR model simulated the discharge with higher accuracy,
especially during the soil thawing period. This improvement was mainly due to the addition of the
frozen soil mechanism. The WEP-COR model can provide support for agricultural and water
resources management in cold regions.
doi: 10.2166/nh.2017.032
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Jia LiEnvironmental Science and Engineering
Department,Donghua University,Shanghai 201620, China
Jia LiZuhao Zhou (corresponding author)Hao WangJiaJia LiuYangwen JiaPeng HuState Key Laboratory of Simulation and Regulation
of Water Cycle in River Basin,China Institute of Water Resources and
Hydropower Research,Beijing 100038, ChinaandEngineering and Technology Research Center for
Water Resources and Hydroecology of theMinistry of Water Resources,
Beijing 100038, ChinaE-mail: [email protected]
Chong-Yu XuState Key Laboratory of Water Resources and
Hydropower Engineering Science,Wuhan University,Wuhan 430072, ChinaandDepartment of Geosciences Hydrology,University of Oslo,Oslo, Norway
Key words | cold region, frozen soil, hydrological model, Second Songhua River basin, WEP-L (Water
and Energy transfer Processes in Large basins)
INTRODUCTION
The Qinghai-Tibet plateau, northwestern alpine area, and
Northeastern China are the three major cold regions of
China (Chen et al. ). They not only cover about 43.5%
of the total land area but are also the primary headsprings
of the water supply for the arid and semiarid regions of
China (Kang et al. ; Chen et al. a; Liu & Yao
). Due to their high latitude and high altitude, these
regions have a wide distribution of glaciers, snow cover, per-
mafrost, and seasonal frozen ground (Jiang et al. ;
Homan et al. ; Wang et al. ). The impermeability
of frozen soil changes its capacity for surface storage, infil-
tration, and evaporation; this influences the hydrological
cycle processes of the land surface (Gusev & Nasonova
; Yamazaki et al. ; Tian et al. ). Meanwhile,
global warming has led to shrinking glaciers and the
degeneration of permafrost (Liu et al. ; Smith et al.
; Cheng & Wu ; Niu et al. ). These changes
alter the runoff generation processes and runoff amounts
of these regions, which in turn affect their water supply
capacity (Barnett et al. ; Han et al. ; Zhang et al.
100 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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). Northeastern China is an important base for produ-
cing grain as a commodity. The freezing and thawing (FT)
processes of seasonal frozen soil in this region affect
changes in the water phase and are vital to crop cultivation
(Hejduk & Kasprzak ). Therefore, exploring the hydro-
logical cycle under frozen soil conditions is very important
for water resources management and agricultural pro-
duction in cold regions.
In the past decades, various models have been devel-
oped to simulate the transfer of water and heat fluxes in
frozen soil and improve the modeling parameterization for
frozen soil (Harlan ; Flerchinger et al. ; Jansson &
Moon ; Li et al. ). However, these models only
treat one-dimensional water flows (Takata ). They only
consider the vertical migration of water without considering
the lateral flow, so they cannot calculate the runoff and over-
land flow in cold regions. Therefore, some researchers have
tried coupling frozen soil mechanisms to land surface
models, such as the Variable Infiltration Capacity (VIC)
model (Liang et al. ; Cherkauer et al. ; Zhao et al.
) and Community Land Model (CLM) (Niu & Yang
; Wang et al. ). In addition, the soil FT processes
have been incorporated into distributed hydrological
models, such as the Cold Regions Hydrological Model
(CHRM) platform (Pomeroy et al. ; Zhou et al. ),
Soil and Water Assessment Tool (SWAT), Distributed
Water–Heat Coupled (DWHC) model (Chen et al. a,
b), Water and Energy Budget-based Distributed Hydro-
logical Model (WEB-DHM) (Shrestha et al. ), and
Geomorphology Based Hydrological Model (GBHM)
(Zhang et al. ). However, with the exception of CRHM
and the DWHCmodel, most frozen soil modules in hydrolo-
gical models are simplified and empirical. Although CRHM
contains various modules for hydrological processes, it
cannot simulate the distributions of soil temperature and
water content at different depths and does not consider
the land use type. The DWHC model was set up by referen-
cing SWAT and Coup Model (Jansson & Moon ).
Because the calculation of some thermal parameters
depends on the results of other parameters, this correlation
increases the uncertainty of the model. In addition, the use
of many parameters increases the difficulty of modeling
hydrological processes in a cold region, which lacks detailed
hydrological and soil data. Therefore, a DWHC model that
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considers the land use type and frozen soil with some con-
ceptual parameters to compensate for the lack of detailed
data should be developed. The Water and Energy Transfer
processes in Large basins (WEP-L) model is a physically-
based and distributed hydrological model. Each
calculation unit of the model considers land use heterogen-
eity by adopting the mosaic method (Jia et al. ).
However, the WEP-L model does not contain a module to
simulate soil FT processes. Thus, the focus of this study
was to couple a frozen soil model to the WEP-L model
and improve the simulation performance for basins in cold
regions. The improved Water and Energy Processes in
Cold Regions (WEP-COR) model can consider the impact
of soil FT processes on hydrological processes in cold
regions. The WEP-COR model was applied to simulating
the soil heat and water fluxes, soil temperature, freezing
depth, and runoff of the Second Songhua River (SSR) basin.
METHODOLOGY
Description of the WEP-L model
The WEP-L model has been successfully applied to several
basins in Japan, Korea, and China (Jia & Tamai ; Jia
et al. ). It combines the merits of physically based
spatially distributed (PBSD) models (Refsgaard et al. )
and the soil–vegetation–atmosphere transfer (SVAT)
scheme to represent spatially variable water and energy pro-
cesses in soils with complex land covers. To consider the
impact of the topography and land cover on the water
cycle in large basins, the spatial calculation unit of the
WEP-L model is contour bands inside small sub-basins.
Each unit in the vertical direction includes five layers from
top to bottom: the interception layer, depression layer, soil
layer, transition layer, and aquifer (Figure 1). In addition,
each unit in the horizontal direction is classified into five
classes with the mosaic method: water body, soil–
vegetation, irrigated farmland, non-irrigated farmland, and
impervious area (Avissar & Pielke ). The soil layers of
the soil–vegetation and farmland classes are further divided
into three layers to describe soil evaporation and the water
uptake of vegetation roots. The average water and heat
Figure 1 | Vertical structure of the WEP-COR model.
101 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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flux is obtained by areally averaging those from each land
use in a contour band.
The time step of the WEP-L model is generally 1 day.
Evapotranspiration from the water body and soil is
calculated by using the Penman equation, while evapo-
transpiration with vegetation canopies is calculated by using
the Penman–Monteith equation (Monteith ). The
canopy resistance (Noilhan & Planton ) is related to
the soil moisture condition. The infiltration and surface
runoff during rainfall greater than 10 mm/d are calculated
with a generalized Green–Ampt model (Jia & Tamai ).
The soil moisture movement in unsaturated soils is calculated
with the Richards model. The air temperature is used to
adjust the calculation of the saturated hydraulic conductivity
in frozen soil (Jia et al. ). The snow melt is calculated
with the temperature index approach. The subsurface runoff
is generated according to the land slope and soil hydraulic
conductivity. The ground water flow is calculated by using
the Boussinesq equations (Zaradny ). The groundwater
outflow is calculated according to the hydraulic conductivity
of the riverbed material and the difference between the river
water stage and groundwater level. The overland flow and
river flow are calculated by using the kinematic wave
method (Jia et al. ). The model approaches for water
and energy processes are described in Jia et al. ().
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Model improvement: frozen soil scheme
Seasonal frozen soil commonly occurs in Northeast China.
Phase changes of the soil water have a considerable influence
on the infiltration and evaporation (Konrad & Duquennoi
). In addition, the soil water flux and runoff generation
process in a cold region are strongly dependent on the soil
freezing depth (Hayashi et al. ). The heat fluxes at differ-
ent soil depths (i.e., soil layers) can change the soil water
phase and soil temperature, while the soil moisture content
and temperature difference between soil layers determine
the heat flux. Therefore, the soil temperature and soil solid
water need to be represented in a model through an energy
balance. Although the WEP-L model can be used to simulate
the soil surface temperature and heat flux of soil, the simu-
lation results cannot reflect the heat flux transfer in soil
layers. Besides, the WEP-L model divides the upper soil
(2 m) into three layers, so only three average values of the
soil moisture content can be shown at three depths. The dis-
tributions of the soil moisture and temperature in a soil group
cannot be revealed either. To overcome these deficiencies, we
added the calculation of the heat transfer and water phase
change for different soil layers. The improved model can be
used to simulate the soil temperature, soil solid water content,
and freezing depth. The depth of a soil layer is one of the
102 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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parameters for calculating the heat flux. Therefore, in con-
sideration of the computation time, the WEP-COR model
divides the upper soil (2 m) into 11 layers. The top two
layers are set to a depth of 10 cm because the surface soil is
sensitive to climate changes, and the other layers are each
set to a standard depth of 20 cm. The number of layers can
be adjusted if the soil thickness is less than 2 m. The calcu-
lations for the soil heat transfer and soil FT processes were
added to all three land use classes (i.e., soil–vegetation, irri-
gated farmland, and non-irrigated farmland). Figure 1 shows
the vertical structure of the WEP-COR model. The methods
for the coupled soil water–heat processes were mainly
derived from the Coup model and Shang’s model (Shang
et al. ; Wang et al. ). These models can clearly rep-
resent the water and heat flux transfer of soil FT processes
and parameters for different soil status. Thus, they are
coupled in the WEP-COR model. The water–heat continuous
equation of frozen soil is solved numerically based on the soil
freezing status and empirical formulas.
Soil freezing status
The soil freezing status is divided into three types. (1) For the
unfrozen type, the soil temperature (Ts) is above 0 WC, and
there is no solid water in the soil layer. (2) For the frozen
type, Ts is lower than Tf (i.e., the threshold temperature
value). The soil is assumed to be completely frozen with a
residual unfrozen amount. According to measurements,
when the soil temperature is less than �10 WC, the liquid
water content of the soil is stable at about 0.09 cm3/cm3
(Wu et al. ). Here, the Tf value was revised to �10 WC.
(3) For the partially frozen type, Ts is higher than Tf but
lower than 0 WC. Liquid water and solid water can coexist
in the soil.
Boundary condition and heat flux into soil
The WEP-COR model assumes that the upper boundary of
the soil group is the atmosphere, which controls the input
and output of the energy. The upper boundary energy trans-
fer can be calculated from meteorological variables
including the temperature, wind speed, hours of sunshine,
and relative humidity. The bottom boundary of the soil
group is the transition layer or aquifer, which has a constant
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temperature. The energy balance equation on land surface is
expressed as (Jia et al. ):
RN þAe ¼ 1EþH þG (1)
where RN (J/m2/d) is the net radiation, Ae (J/m2/d) is the
anthropogenic energy source, lE (J/m2/d) is the latent heat
flux, H (J/m2/d) is the sensible heat flux, and G (J/m2/d) is
the heat conduction into soil. The force-restore method
(FRD) (Hu & Islam ) is used to solve G and the surface
temperature of different land covers.
Soil heat flux transfer
According to the law of energy conservation, the equation of
the soil vertical heat flux transfer can be written as (Shang
et al. ; Wang et al. ):
@
@zλs
@Ts
@z
� �¼ Cv
@Ts
@t� Liρi
@θi@t
(2)
where z is the soil depth (m) that represents each soil layer,
λs is the soil thermal conductivity (W/(m•WC)), Ts is the soil
temperature (WC), CV is the composite soil heat capacity
(J/(m3•WC)), t is the time (s), ρi is the ice density (920 kg/
m3), Li is the latent heat of fusion (3.35 × 106 J/kg), and θi
is the soil volumetric ice content. Equation (2) describes
the heat transfer among soil layers at different depths and
the changes in the soil temperature and water phase. We
can use the numerical iterative method to solve Equation
(2). Then, the finite difference scheme can be written as:
1(ΔZjþΔZjþ1)=2
λks,jþ(1=2) Tks,jþ1�TK
s,j
� �ΔZjþ1
�λks,j�(1=2) Tk
s,j�TKs,j�1
� �ΔZj
24
35
¼Ckv,i
Tkþ1s,j �TK
s,j
Δtkþ1
" #�Liρi
θkþ1i,j �θKi,jΔtkþ1
" #
(3)
ΔZj ¼ Zj � Zj�1 (4)
ΔZjþ1 ¼ Zjþ1 � Zj (5)
λks,jþ(1=2) ¼λks,jþ1 � λks,j
2(6)
103 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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λks,j�(1=2) ¼λks,j � λks,j�1
2(7)
where j is the number of soil layers and k is the time. If the
time step is 1 day, kþ 1 represents the day after. The other
variables are the same as those defined previously.
The composite soil heat capacity CV is expressed as
(Jansson & Moon ):
Cv ¼ (1� θs) × Cs þ θl × Cl þ θi × Ci (8)
where θs is the soil saturated water content, θl is the soil
liquid water content, and Cs, Cl, and Ci are the heat
capacities of soil, water, and ice, respectively.
The thermal conductivity is a complex function of the
soil moisture and constituents. The Coup model and other
models calculate the thermal conductivity by using different
equations depending on the soil freezing status; however,
this approach requires the determination of several par-
ameters. In consideration of the parameter determination,
here the soil thermal conductivity was calculated by using
the IBIS model (Foley et al. ):
λs ¼ λst × (56θl þ 224θi ) (9)
λst ¼ 0:300 × ωsand þ 0:265 × ωsilt þ 0:250 × ωclay (10)
where λst is the dry soil thermal conductivity (W/(m•WC)) and
ωsand, ωsilt, and ωclay represent the volumetric fractions of
sand, silt, and clay, respectively.
Soil temperature
The energy flux drives the changes in the soil temperature
and water phase, while the soil temperatures of different
soil layers impact the soil sensitive heat. The temperature
of the top soil layer is calculated with the FRD method.
For other soil layers, the temperature at the middle part of
a soil layer is used to represent its average temperature.
The soil temperature and heat flux between adjacent soil
layers can be calculated as follows (Chen et al. b):
Hi,iþ1 ¼ λs,izi þ λs,iþ1ziþ1
2
� �Ts,i � Ts,iþ1
0:5zi þ 0:5ziþ1(i � 1) (11)
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Ts,j ¼Hj�1,j �Hj,iþ1
Cs,jρs,jZj(j � 2) (12)
where Hi,iþ1 is the sensible heat flow between soil layers i
and iþ 1. The initial Ts of each soil layer is the input of
the model. The soil temperature and moisture content are
simulated by numerical iteration.
Soil water flux transfer
During soil FT periods, migration only occurs in liquid
water. The soil vertical heat flux transfer can be written as
(Shang et al. ; Wang et al. ):
@θl@t
¼ @
@zD(θl)
@θl@z
� �� @K(θl)
@z� ρiρl
@θi@t
(13)
where D(θl) and K(θl) are the hydraulic diffusivity and
hydraulic conductivity, respectively, for unsaturated soil
and ρl is the density of water (kg/m3). K(θl) is closely
related to the saturated hydraulic conductivity Ks, which
is corrected by the soil temperature (Jansson & Moon
):
K(θl) ¼Ks θl ¼ θs
Ksθl � θrθs � θr
� �n
θl ≠ θs
8<: (14)
Ks ¼K0 Ts > 0
K0(0:54þ 0:023Ts) Tf � Ts � 00 Ts < Tf
8<: (15)
where θr is the soil residual moisture content, n is
the Mualem constant, Ks is the saturated hydraulic
conductivity of the soil temperature correction (cm/s),
and K0 is the initial saturated hydraulic conductivity
(cm/s).
Modeling procedure of soil heat and water transfer
The WEP-COR model couples the calculation of the soil
heat and water transfer processes with the WEP-L model.
Figure 2 shows the simulation flowchart of the soil heat
and water transfer. Both vertical and lateral flows are
Figure 2 | Flowchart of the soil heat and water transfer.
104 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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calculated. In these charts, R is the soil lateral flow, E is
the evaporation of vegetation and bare soil, Q is the soil
gravity drainage, and QD is the water flow between adja-
cent soil layers. The WEP-COR model iteratively
calculates the finite difference scheme to compute the
soil temperature and soil water flow. The time index rep-
resents the time, and the change interval of the time
index is equal to the time step. Ttþ1 represents T the
next day. The cycle index represents the iterations.
There are two parts to the iterative computations.
First, the water and heat equations of the frozen soil
are solved following Equations (3)–(7). Then, the soil
moisture migration caused by evaporation, infiltration,
and gravity drainage is calculated. n is the iterations
of the former, and m is the iterations of the latter.
An error of within 0.001 is acceptable; the iterative
calculation does not stop until the error value is
acceptable.
Figure 3 | Locations of the Second Songhua River basin and stations.
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STUDY SITES AND DATA
Study area
The WEP-COR model was applied to the SSR basin. The
SSR is a tributary of the Songhua River in Northeast
China and covers an area of 7.4 × 104 km2 (Figure 3). Obser-
vations from 1971 to 1995 indicated that the long-term
average annual air temperature is approximately 4.2 WC
and the average annual precipitation is 700 mm for the
SSR basin. The basin is located in a typical cold region
where seasonal frozen soil is common. The soil FT period
of this basin is usually from November to May. The water
and heat flux simulations of the WEP-COR model were eval-
uated by taking measurements from the Qianguo irrigation
experimental station (124W30030″E, 45W14000″N) and a
meteorological station (station 54266, 125W37059″E,
42W31059″N). To consider the integrity of the data, the
Table 2 | Soil moisture characteristics
Parameters Sand Loam Clay loam Clay
θs 0.4 0.466 0.475 0.479
θf 0.174 0.278 0.365 0.387
θr 0.077 0.120 0.170 0.250
SW 6.1 8.9 12.5 17.5
n 3.37 3.97 3.97 4.38
θf: field capacity; SW: suction at wet front of soils; n: constant parameter of Mualem.
Table 1 | Some soil physical properties and the permeability coefficient
Soil depth(cm)
Particle size distribution (%) Bulkweight(g·cm�3)
Permeabilitycoefficient(10�4 cm·s�1)<2 μm 2–50 μm >50 μm
0–15 28.0 41.0 31.0 1.2 3.24
15–28 30.5 35.8 33.7 1.4 1.25
28–100 18.5 28.9 52.6 1.5 2.81
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Wudaogou station (126W37043″E, 42W53051″N) was selected
to evaluate the modeling performance for the daily dis-
charge. This station is located upstream of the SSR.
Data description
Figure 3 shows the distribution of the rivers and main hydro-
meteorological stations in the SSR basin. The WEP-COR
model requires data on the geography (elevation, veg-
etation), land use, meteorology, and parameters (soil type,
hydraulic conductivity, and soil moisture characteristic).
Elevation data were obtained from SRTM90. Monthly veg-
etation information (LAI and area fraction of vegetation)
was obtained from the NOAA-AVHRR data. The soil data
(soil type and corresponding characteristic parameters)
were acquired from the National Second Soil Survey Data
and Soil Types of China. Land use data were obtained
from the Landsat TM data and statistical data in the year-
books of administrative districts. Meteorological daily data
including the precipitation, temperature, wind speed, sun-
shine, and humidity can be downloaded from the website
http://cdc.cma.gov.cn. Based on the DEM data and
observed river information, the SSR basin was divided into
1,305 sub-basins, each of which was assigned by using the
Pfafstetter code (Verdin & Verdin ). The meteorological
daily data were interpolated to each sub-basin by using the
inverse distance weighted method.
Parameter sensitivity analysis of the WEP-L model was
previously done by Jia et al. (). The conductivity of riv-
erbed material, soil layer thickness, maximum soil moisture
content, and groundwater aquifer hydraulic conductivity
were identified as parameters with high sensitivity. Most
parameters in the model do not need to be calibrated, but
the high-sensitivity parameters were adjusted by comparing
the simulated discharge with observed values during the
selected calibration period. The soil physical properties pre-
sented in Table 1 were measured at the Qianguo experiment
station. Based on the texture information, the soils were
reclassified into four categories: sand, loam, clay loam,
and clay. The main soil moisture characteristics in Table 2
were taken from Jia et al. (). The conductivity of the riv-
erbed was set to 1.728 m/d. The groundwater aquifer
hydraulic conductivity and specific yield in the basin were
deduced from groundwater simulation and geological
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exploration data. The hydraulic conductivity was set to
1.056 m/d, and the specific yield was set to 0.05 m/d.
Methods of evaluation
Experimental data fromOctober 2011 to May 2012 were used
to evaluate the simulation results of the soil FT processes at the
Qianguo experiment station. The daily freezing depth of
station 54266 and daily discharge data of the Wudaogou
station were split into two parts: data from 1971 to 1985 for
calibration and data from 1986 to 1995 for validation. The
modeling performancewas statistically evaluated by a qualitat-
ive assessment though graphs first and then a quantitative
assessment with statistical measures. The root mean squared
error (RMSE), Nash–Sutcliffe coefficient (NSE), and relative
error (RE) were used for the quantitative evaluation. The
RMSE, NSE, and RE can be calculated as follows:
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n
Xni¼1
Oi � Sið Þ2h ivuut (16)
NSE ¼ 1�Pn
i¼1 Oi � Sið Þ2Pni¼1 Oi � �O
2 (17)
Pn Pn
107 J. Li et al. | Development of WEP-COR model to simulate land surface water and energy budgets Hydrology Research | 50.1 | 2019
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RE ¼ i¼1 Si� i¼1 OiPni¼1 Oi
� 100% (18)
where n is the number of observations, Oi is the observed
value, �O is the mean observed value, and Si is the simulated
value. For the NSE, the best value is 1, and a negative value
means that the model is not credible.
RESULTS AND DISCUSSION
Soil temperature simulation
Figure 4 shows the simulated and observed daily mean soil
temperatures at different depths from 24 October 2011 to 11
May 2012 at the Qianguo experiment station. The temperature
of the upper layers (0–20 cm) fluctuated wildly, and the soil
temperature and its fluctuation diminished with depth. This
result agrees with other studies (Guo et al. ; Xiang et al.
). The simulated soil temperature of the upper soil layers
matched the observations well, but the temperatures of the
middle and lower layers were slightly underestimated during
the thawing period. This underestimation may have been due
to the homogenized soil hydraulic conductivity and thermal
parameters in the experiment (Table 1); the parameters were
the same from the third to11th layers. In addition, theminimum
simulated soil temperature was lower than that observed. This
previous error may have resulted in the later underestimation
during the thawing period. The soil thermal conductivity may
also be greater than the simulation, so the simulated soil temp-
erature rose slower than that observed during the thawing
period. Table 3presents theNSEandRMSEof the soil tempera-
ture at different depths. The layer at 120 cm had missing data,
which led to a higher NSE value compared to other layers
because only the freezing period was represented and not the
FT periods. The mean NSE was 0.92, and the mean RMSE
was 1.21 WC. Overall, the soil temperature simulated with the
WEP-COR model was similar to the observed data.
Soil moisture simulation
Figure 5 illustrates the simulated and measured volumetric
liquid water and total water (both unfrozen and frozen
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moisture) of the soil at different depths during the FT
periods from 2011 to 2012. The liquid water content was
equal to the total water content on 2 November, which
means that there was no solid water at all and the soil was
unfrozen. As the air temperature decreased, the soil froze
from top to bottom (Figure 5(b) and 5(c)) (Slater et al.
). At the early stage of soil freezing, solid water appeared
in the upper soil layers. As the liquid water shifted from
unfrozen soil to frozen soil, the liquid water content of the
top layer decreased, and its total water content increased
(Iwata &Hirota ; Sheshukov &Nieber ). Figure 5(b)
and 5(c) show that the simulated total water content was
less than that measured, which may have resulted from the
higher simulated values of evaporation. The simulated
liquid water content was higher than that measured, which
was probably caused by the differences in soil temperature.
On 22 February, the soil water distribution showed a ‘V’
shape, which indicates that the soil frozen depth was
almost at the maximum (Cheng & Wu ; Hayashi et al.
). Figure 5(e) shows an ‘O’ shape for the water distri-
bution, which means that both the upper and bottom soil
layers were thawing. However, the simulated thaw rate
was less than that measured. The heat flux of the middle
layer was overestimated, so the liquid water content was
higher than that measured. Figure 5(f) shows that the total
water content was equal to the liquid water content, which
indicates that the soil thawing process was completed.
Table 4 presents the statistical values, and the mean
RMSEs for the unfrozen water content and total water con-
tent were 0.035 and 0.034 cm3/cm3, respectively.
Soil freezing depth simulation
Figure 6 shows the simulated and observed soil freezing
depths during the FT periods from 2011 to 2012. As the temp-
erature decreased, the soil began to freeze in mid-November
and reached the maximum frozen depth in early March.
When heat from the atmosphere was less than the energy
required to keep the basal freezing state, the frozen soil
began to thaw on the surface and at the bottom (Cherkauer
& Lettenmaier ; Woo et al. ), and the thawing pro-
cess finished on 25 April. The simulated freezing depth
matched the measurement during the freezing period but
was a little greater than that measured during the thawing
Figure 4 | Simulated and observed soil temperatures at different depths.
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Table 3 | Statistical values from the soil temperature simulation
Depth (cm) 10 20 35 60 90 100 110 120
NSE 0.95 0.97 0.90 0.86 0.91 0.92 0.90 0.98
RMSE 1.47 0.94 1.17 1.23 1.14 1.27 1.48 1.04
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period. The deepest simulated frozen depth was 8 cm deeper
than the measurement. The simulated FT periods were 10 d
shorter than that measured. The average RMSE of the simu-
lated freezing depth was 17.68 cm.
The soil frozen depth affects both the lateral and vertical
soil water fluxes in cold regions (Hayashi et al. ). The
long-term observations of the daily freezing depth at station
54266 were used to evaluate the modeling performance.
Figure 5 | Simulated and observed soil moisture contents at different depths.
Table 4 | Statistical values from the soil water content simulation
Depth (cm) 0–10 10–20 20–40 40–60
Unfrozen 0.030 0.048 0.031 0.029
Total 0.031 0.025 0.027 0.048
Unfrozen: unfrozen water content; total: sum of unfrozen and frozen water contents.
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Figure 7 shows the daily simulated and observed soil freez-
ing depths from 1971 to 1995. The simulated freezing
depth generally matched the observed result well. The
NSE and RMSE of the calibration were 0.95 and 11.3 cm,
respectively. The NSE and RMSE of the validation period
were 0.92 and 13.2 cm, respectively.
Water discharge simulation
Figure 8 presents the simulation results of the WEP-L and
WEP-COR models for the daily discharge, and Table 5 pre-
sents the statistical test. The graphs indicate that the
variation tendencies of the simulations were consistent
with the observations. However, the WEP-L model without
60–80 80–100 100–120 120–140 140–160
0.028 0.024 0.016 0.041 0.069
0.026 0.017 0.014 0.043 0.076
Figure 7 | Daily simulated and observed soil freezing depths at station 54266. (a) Calibration (1971–1985). (b) Validation (1986–1995).
Figure 6 | Simulated and observed soil freezing depths during the FT period.
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the frozen soil scheme systematically underestimated the
stream flow. The NSE and RE were 0.38 and �53.69%,
respectively, for the calibration period. The WEP-L model
performed better during the validation period than the cali-
bration period with an NSE and RE of 0.64 and �41.62%,
respectively. As frozen soil has a considerable impact on
the surface storage capacity, hydrological modeling of a
basin in a cold region must include a frozen soil scheme,
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and the model performance cannot be improved solely by
parameter adjustment. The model performance was
obviously improved when coupled with a frozen soil
scheme. The WEP-COR model achieved an NSE and RE
of 0.42 and �0.97%, respectively, for the calibration
period. For the validation period, the NSE was similar to
that of the WEP-L model, but the RE endpoint showed a
35.04% decrease. Figure 8 shows that the simulated daily
Figure 8 | Observed and simulated daily discharges of the Wudaogou station from 1971 to 1995. (a) Calibration (1971–1985). (b) Validation (1986–1995).
Table 5 | Statistical values for the daily discharge simulation from 1971 to 1995
Calibration (NSE/RE) Validation (NSE/RE)
WEP-L 0.38/�53.69% 0.64/�41.62%
WEP-COR 0.42/�0.97% 0.64/6.58%
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discharge during the thawing period (February–May) tended
to underestimate the observations, and the simulations were
consistent with the highest observations. We inferred that
the high RE values were mainly due to the underestimation
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of the runoff during the thawing period (from February to
May). In general, the WEP-COR model demonstrated an
acceptable performance for the SSR basin and achieved effi-
ciency coefficients of NSE> 0.6 and RE< 10% for the
validation period. The simulated discharge can be used for
further analysis.
Analysis of flow components
Based on the analysis presented in the last section, we
inferred that the improved performance of the WEP-COR
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model was mainly for the thawing period. To further clarify
the improvement, the simulated daily river discharge from
February to May was compared with observations for the
validation period (Figure 9). Table 6 presents the statistical
test. In addition, the flow components from February to
May were calculated, and the monthly statistical results
are shown in Figure 10. As shown in Figure 9, the simu-
lated daily river discharge of the WEP-L model was
lower than that observed, while the simulation result of
the WEP-COR model showed good agreement with the
observation. The RE of the WEP-L model was �73.33%.
In contrast, the RE of the WEP-COR model was �6.26%.
Although both models underestimated the daily river dis-
charge, the WEP-COR model clearly showed an
improved performance.
Figure 10 shows the monthly mean variations in flow
components from February to May during the validation
period. The flow components represent the sources of
the river discharge, which include the surface flow (snow-
melt runoff and rainfall runoff), subsurface flow, and base
flow (groundwater discharge). As shown in Figure 10(a),
snowmelt runoff occurred in March and April as the air
temperature rose. There was no distinct difference
between the simulations of the two models. As shown in
Figure 10(b) and 10(c), there was slight rainfall runoff
Figure 9 | Observed and simulated discharges from February to May (1986–1995). (a) WEP-L.
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and infiltration in February as the soil was frozen. Sub-
sequently, the rainfall runoff of the two models tended
to increase, but the WEP-L model showed a lower rainfall
runoff than the WEP-COR model. The results indicated
that the frozen soil decreased the soil infiltration capacity.
The differences in the snowmelt runoff, rainfall runoff,
and infiltration between the two models were small. The
main differences were from the groundwater discharge
and recharge. In this study, the groundwater discharge
represented the water flux from the groundwater or aqui-
fer layer into the river, and the groundwater recharge
represented the water flux from the soil layer to the
groundwater or aquifer layer. Due to the impermeability
of frozen soil, the soil water flux could not further transfer
to the deep layer and formed an aquifer layer above the
frozen soil layer. The flow above the frozen soil layer
was classified as base flow. Therefore, the calculated
groundwater level was higher, so the lateral flow was
higher. The WEP-L model without the frozen soil
scheme underestimated the base flow. Regardless of the
occurrence of frozen soil, the water flux infiltrated into
the deep layer, and the groundwater level was lower
with hardly any lateral flow. These may be the main
reasons for the improved results with the WEP-COR
model.
(b) WEP-COR.
Table 6 | Statistical values for the simulated daily discharge from February to May
(1986–1995)
WEP-L WEP-COR
(NSE/RE) �0.06/�73.33% 0.33/�6.26%
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CONCLUSIONS
The WEP-COR model was developed to improve the model-
ing performance of the WEP-L model by adding a soil
heat–water coupled module to help simulate the land sur-
face water and energy budgets in a cold region. In
Figure 10 | Components of runoff from February to May during the validation period. (a) Snow
groundwater.
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addition, the number of soil layers was increased from
three to 11 to simulate the soil temperature and soil moist-
ure content at different depths. The simulated soil thermal
and moisture distributions were compared with measure-
ments taken at Qianguo irrigation experimental station.
The results showed that the WEP-COR model can be used
to simulate the vertical distributions of the soil temperature,
soil liquid and solid water contents, and soil freezing depth
in a cold region. The mean RMSEs of the soil temperature,
liquid moisture content, total water content, and freezing
depth were 1.21 WC, 0.035 cm3/cm3, 0.034 cm3/cm3, and
17.6 cm, respectively. The average NSE of the soil
melt runoff. (b) Rainfall runoff. (c) Infiltration. (d) Groudwater discharge (e) Recharge
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temperature was 0.92. The simulated daily freezing depth
was compared with observations at station 54266 from
1971 to 1995. The simulated freezing depth generally
matched the observed result well. The WEP-COR model sig-
nificantly improved the predicted discharge for the SSR
basin, especially during the soil thawing period. The analysis
of the daily discharge and runoff components demonstrated
that frozen soil needs to be considered when modeling the
hydrological processes in a cold region. The simulated
results showed an obvious improvement in the model per-
formance when it was coupled with the frozen soil
scheme. When the observed and simulated daily discharges
were compared, the NSE of the WEP-COR model was 0.64,
and the RE was 6.58%. In conclusion, the developed WEP-
COR model contributes to the qualitative evaluation and
prediction of the spatial and temporal distributions of
frozen soil and change in water resources. It can act as a
reference for agricultural and water resource management
in a cold region. It can also be used to explore the hydrother-
mal transfer and hydrological cycle response to climatic
change.
ACKNOWLEDGEMENTS
This work is supported by the National Natural Science
Foundation of China (51179203), and the National
Science and Technology Major Project for Water
Pollution Control and prevention (2008ZX07207-006,
2012ZX07201-006).
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First received 11 December 2016; accepted in revised form 23 February 2017. Available online 9 June 2017