Development of WEP-COR model to simulate land surface...

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

s://iwaponline.com/hr/article-pdf/50/1/99/524597/nh0500099.pdf FORUM user

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.

mailto:[email protected]

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.



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. ().


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



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


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)



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)


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.


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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.


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



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


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)

http://cdc.cma.gov.cn

http://cdc.cma.gov.cn

Pn Pn



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


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



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.


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.



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,


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%



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


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



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.


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%



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.


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



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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