Optimum management of irrigated crops in regions with shallow saline
groundwater requires a careful balance between application of irrigation
water and upward movement of salinity from the groundwater. Few
field-validated surrogate models are available to aid in the management of
irrigation water under shallow groundwater conditions. The objective of
this research is to develop a model that can aid in the management using a
minimum of input data that are field validated. In this paper a 2-year
field experiment was carried out in the Hetao irrigation district in Inner
Mongolia, China, and a physically based integrated surrogate model for arid
irrigated areas with shallow groundwater was developed and validated with
the collected field data. The integrated model that links crop growth with
available water and salinity in the vadose zone is called Evaluation of the
Performance of Irrigated Crops and Soils (EPICS). EPICS recognizes that
field capacity is reached when the matric potential is equal to the height
above the groundwater table and thus not by a limiting hydraulic
conductivity. In the field experiment, soil moisture contents and soil salt
conductivity at five depths in the top 100 cm, groundwater depth, crop
height, and leaf area index were measured in 2017 and 2018. The field
results were used for calibration and validation of EPICS. Simulated and
observed data fitted generally well during both calibration and validation.
The EPICS model that can predict crop growth, soil water, groundwater
depth, and soil salinity can aid in optimizing water management in
irrigation districts with shallow aquifers.
Introduction
Irrigation water is a scarce resource, especially in arid and semi-arid
areas of the world. Irrigation improves quality and quantity of food
production; however, excess irrigation and salinization remain one of the
key challenges. Almost 20 % of the irrigated land in the world is affected
by salinization, and this percentage is still on the rise (Li et al., 2014).
Soil salinization and water shortages, especially associated with
surface-irrigated agriculture in arid to semi-arid areas, is a threat to the
well-being of local communities in these areas (Dehaan and Taylor, 2002;
Rengasamy, 2006).
In arid and semi-arid areas where people divert surface water for flood
irrigation and have poor drainage infrastructures, the groundwater table is
close to the surface because more water has been applied than crop
evapotranspiration. Capillary rise of the shallow groundwater can be used to
supplement irrigation, and thereby, in closed basins, can possibly save water
for irrigating additional areas downstream (Gao et al., 2015; Yeh and
Famiglietti, 2009; Luo and Sophocleous, 2010). However, at the same time,
capillary upward-moving water carries salt from the groundwater, increasing
the salt in the upper layers of the soil, leading to soil degradation and
possibly decreasing yields and change in crop patterns to more salt-tolerant
crops (Guo et al., 2018; Huang et al., 2018). The leaching of salt with
irrigation water is necessary and useful for irrigated agriculture (Letey et
al., 2011). In northern China, the fields are commonly irrigated in the fall
before soil freezing to leach salts and provide water for first growth after
seeding in the following year (Feng et al., 2005).
Tradeoffs between irrigation practices and soil salinity were studied by a
lot of researchers (Hanson et al., 2008; Minhas et al., 2020). Minhas et al. (2020) give a brief review of crop evapotranspiration and water management issues when coping with salinity in irrigated agriculture. Phogat et al. (2020) assessed the effects of long-term irrigation on salt build-up in the soil under unheated greenhouse conditions by the UNSA-TCHEM and HYDRUS-1D (Phogat et al., 2020).
Therefore, understanding the interaction of improved crop yield, soil
salinization, and decreased surface irrigation is important to the
sustainability of the surface irrigation water systems in arid and semi-arid
areas. This will require experimentation under realistic farmers' field
conditions as well as modeling to extend the findings beyond the plot scale.
Field-scale models for water, solute transport, and crop growth are widely
available. Crop growth models use either empirical functions or model the
underlying physiological processes (Liu, 2009). Models widely used for
simulating crop growth are EPIC (Erosion Productivity Impact Calculator;
Williams et al., 1989), DSSAT (Uehara, 1989), WOFOST (Diepen et al., 1989),
and AquaCrop (Hsiao et al., 2009;
Raes et al., 2009; Steduto et al., 2009). Models that focus on water and
solute movement in the vadose zone using some form of Richards' equation are
HYDRUS (Šimůnek et al., 1998) and SWAP (Van Dam et al., 1997).
Models that integrate crop growth and water-solute movement processes are
SWAP-WOFOST (Hu et al., 2019), SWAP-EPIC (Xu et al., 2015,
2016), HYDRUS-EPIC (Wang et al., 2015), and HYDRUS-DSSAT (Shelia et
al., 2018). These integrated models require input data that are usually not
available when applied over extended areas (Liu et al., 2009; Xu et al.,
2016; Hu et al., 2019). The EPIC crop growth model is often preferred in
integrated crop growth hydrology models because it requires relatively few
input data and is accurate (Wang et al., 2014; Xu et al., 2013; Chen et
al., 2019).
There is a tendency with the advancement of computer technology to include
more physical processes in these models (Asher et al., 2015; Doherty and
Simmons, 2013; Leube et al., 2012). Detailed spatial inputs of soil
hydrological properties and crop growth are required to take advantage of
the model complexity (Flint et al., 2002; Rosa et al., 2012). This greater
model complexity, both in space and time, requires longer model run times,
especially for the time-dependent models (Leube et al., 2012). These models
are useful for research purposes, but for actual field applications, the
required input data are not available and are expensive to obtain. In such
cases, simpler surrogate models are a good alternative (Blanning, 1975;
Willcox and Peraire, 2002; Regis and Shoemaker, 2005). Surrogate models
run faster and are as accurate as the complex models for a specific problem
(shallow groundwater here) but not as versatile as the more complex models
that can be applied over a wide range of conditions (Asher et al., 2015).
Simple surrogate models are abundant in China for areas where the
groundwater is deeper than approximately 10 m (Kendy et al., 2003; Chen et
al., 2010; Ma et al., 2013; Li et al., 2017; Wu et al., 2016) but are limited
and relatively scarce for areas where the groundwater is near the
surface in the arid to semi-arid areas (Xue et al., 2018; Gao et al., 2017;
Liu et al., 2019). In these areas with shallow aquifers, the upward
groundwater flux from groundwater is an important factor in meeting the
evapotranspiration demand of the crop (Babajimopoulos et al., 2007; Yeh and
Famiglietti, 2009). The advantage of applying surrogate models in areas with
shallow aquifers is that they can simulate the hydrological process with
fewer parameters, using simpler and computationally less demanding
mathematical relationships than the traditional finite-element or difference
models (Wu et al., 2016; Razavi et al., 2012).
The change in matric potential is often ignored in these surrogate models
for soils with a deep groundwater table. However, for areas with shallow
aquifers (i.e., less than approximately 3 m), the matric potential cannot be
ignored. The flow of water is upward when the absolute value of matric
potential is greater than the groundwater depth or downward when it is less
than the groundwater depth (Gardner, 1958; Gardner et al., 1970a, b;
Steenhuis et al., 1988). The field capacity in these soils is reached when
the hydraulic gradient is constant (i.e., the constant value of the sum of
matric potential and gravity potential). In this case, the soil water is in
equilibrium, and no flow occurs.
Xue et al. (2018) and Gao et al. (2017) developed models for the shallow
groundwater but used field capacities and drainable porosities that were
calibrated and independent of the depth of the groundwater. This is inexact
when the groundwater is close to the surface. Liu et al. (2019) used for
simulating shallow groundwater the same type of model as described in this
paper but calibrated crop evaporation and did not simulate the salt
concentrations in the soil. This made their model less useful for practical
application.
Because of the shortcomings in the above complex models, we avoided the use
of a constant drainable porosity and considered the crop growth and thus
improved the surrogate model in our last study (Liu et al., 2019). The
objective of this research was to develop a field-validated surrogate model
that could be used to simulate the water and salt movement and crop growth
in irrigated areas with shallow groundwater and salinized soil with a
minimum of input parameters. To validate the surrogate model, we performed a
2-year field experiment in the Hetao irrigation district that investigated
the change in soil salinity, moisture content, groundwater depth, and maize
and sunflower growth during the growing season.
In the following section we present first the theoretical background of the
surrogate model. The model consists of a crop growth module and a vadose zone
module. This is followed by a detailed description of the 2-year field
experiments begun in 2017 in the Hetao irrigation district where maize and
sunflower were irrigated by flooding the field. The experimental results
consisting of climate data, irrigation application, crop growth parameters,
moisture and salt content, and groundwater depth are used to calibrate and
validate the model.
Model descriptionIntroduction of the model
In a recent study, we presented a surrogate model for the vadose zone with
shallow groundwater using the novel concept that the moisture content at
field capacity is a unique function of the groundwater depth after
irrigation or precipitation that wets up the entire soil profile. The model,
called the Shallow Vadose Groundwater model, is applied directly to
surface-irrigated districts where the groundwater is within 3.3 m from the
soil
surface (Liu et al., 2019). The model was a proof of concept with calibrated
values for evapotranspiration and soil salinity which was not simulated.
To make the Shallow Vadose Groundwater model more physically realistic, we
added a crop growth model and included the effect of salinity and moisture
content on evaporation and transpiration directly in this study. The new
model that combines parts of EPIC (Williams et al., 1989) with the Shallow
Vadose Groundwater model is called the Evaluation of the Performance of
Irrigated Crops and Soils (EPICS).
Structure of the EPICS model
In the EPICS model, the soil profile is divided into five layers of 20 cm
(from the soil surface down) and a sixth layer that stretches from the
100 cm depth to the water table below (Fig. 1).
Schematic diagram of model components and water movement.
The moisture content and salt content are calculated for each day (Fig. 1).
All flow takes place within the day, and the water and salt content are in
“equilibrium” (i.e., fluxes are zero) at the end of the day for which the
calculations are made. Daily fluxes considered in the vadose model are the
following: at the surface, the fluxes are irrigation, both irrigation water,
I(t), and salt, S0(t), and precipitation, P(t), and for each layer,
j, on days with irrigation and rainfall, the downward flux of water,
Rw(j, t), and salt, S(j, t), between the layers. On days
without water input at the soil surface, an upward groundwater flux
U(j, h, t) and salt S(j, t) are considered. The flux to the surface
depends on the groundwater depth. Finally, transpiration, T(j, t),
removes water from the layers with roots of the crops and evaporation,
E(j, t), from all layers.
The EPICS model consists of two modules: the VADOSE module and the CROP
module. The two modules are linked through the evapotranspiration flux in
the soil (Fig. 2).
Schematic diagram of the linked novel Shallow Aquifer-Vadose zone
surrogate module and EPIC module. Note: ET0 is the reference
evapotranspiration, Ep and Tp are the potential
evaporation and potential transpiration, Ea and
Ta are the actual evaporation and actual transpiration,
Kc is the crop coefficient, τ is the development stage of
the leaf canopy, and rj is the root function of soil layer j.
The CROP module employs functions of the EPIC model (Williams et al., 1989)
and root growth distribution (Novak, 1987; Kendy et al., 2003; Chen et al.,
2019). The CROP module calculates daily values of crop height, root depth,
and leaf area index (LAI) based on climatic data (Fig. 2).
The VADOSE module calculates the moisture and salt content in the root zone
and the upward movement of the groundwater (Fig. 2). Field capacity varies
with depth and is a function of the (shallow) groundwater depth and the soil
characteristic curve (Liu et al., 2019). Moisture contents become less than
field capacity when the upward flux is less than the actual
evapotranspiration.
Finally, the link between the VADOSE and CROP modules is achieved by
calculating the actual evapotranspiration with parameters of both modules
consisting of the moisture content and salt content simulated in the VADOSE
module and the root distribution and potential evapotranspiration in the
CROP module (Fig. 2).
Theoretical background of the EPICS model
In the next section, the equations of the CROP in the VADOSE modules are
presented. The calculations are carried out sequentially on a daily time
step. This model predicts field daily soil water, salt content, and crop
growth, which are critical parameters for irrigation water management. For
field and regional water management and irrigation policy development,
resolution of the daily time step is sufficient. Finer resolution is not
needed for managing water and salt content for irrigation. In the first step,
the
actual evaporation and transpiration are calculated for each layer in the
model. Next, the moisture content and salt content are adjusted for the
various fluxes. Since the equations for the downward movement on days of
rainfall and/or irrigation are different than for upward movement from the
groundwater on the remaining days, we present the upward and downward
movement in separate sections. The code was written in Matlab 2014Ra and
Microsoft Excel was used for data input and output.
CROP module
The crop module uses functions of EPIC (Williams et al., 1989) to calculate
LAI, crop height and the root depth (green boxes in Fig. 2), the potential
transpiration, Tp, and evaporation, Ep (orange boxes in Fig. 2). Input data for the CROP module included mean daily
temperature (Tmean), maximum daily
temperature (Tmx), minimum daily
temperature (Tmn), maximum crop height (Hmx),
maximum LAI (LAImx), maximum root depth (RDmx),
dimensionless canopy extinction coefficient (Kb), and total
potential heat units required for crop maturation (PHU).
The potential rates of evaporation, EP(j, t), and
transpiration, TP(j, t), of different layers are derived
from the total rates and a root function that determines the distribution of
roots in the vadose zone:
1aTP(j,t)=rT(j,t)Tp(t),1bEp(j,t)=rE(j,t)Ep(t),
where j is the number of soil layers and t is the day number,
TP(t) is the total potential transpiration, and
EP(t) is the total potential evaporation at time, t. Both are calculated
with the CROP module (Sect. S1 in the Supplement). Root functions (Sau et
al., 2004; Delonge et al., 2012) were used to calculate transpiration and
evaporation of different soil layers. rT(j, t) is the root
function for the transpiration and rE(j, t) is the root
function for the evaporation. Both have the same general equation but with a
different value for the constant δ.
rT(j,t)=11-exp(-δ)exp-δZ1jZ2j1-exp-δZ2j-Z1jZr,rE(j,t)=11-exp(-δ)exp-δZ1jZ2j1-exp-δZ2j-Z1jZr,
where z1j is the depth of the upper boundaries of the soil layer j.
For rT(j, t), if the root depth is smaller than the lower
boundaries of the soil layer j, Z2j is equal to the root depth, and if
the root depth is greater than the lower boundaries of the soil layer j,
Z2j is the depth of the lower boundaries of the soil layer j. For
rE(j, t), Z2j is the depth of the lower boundaries of the
soil layer j. Zr is the root zone depth, and δ is the
water use distribution parameter. Note that the sum of rT(j, t)
of all soil layers is equal to 1. In the study of Novark (1987), the value
of δ for corn is 3.64, and we used this value. To obtain
rE(j, t), δ was set to 10 (Chen et al.,
2019; Kendy et al., 2003). Sunflower root function simulation employed the
same δ values as for maize.
The actual evaporation rates, Ea(j, t), and transpiration,
Ta(j, t), for each soil layer, j, at time, t, are
calculated as a proportion of the potential values as
3aEa(j,t)=kE(j,t)Ep(j,t),3bTa(j,t)=kT(j,t)S(j,t)Tp(j,t),
where kE(j) and kT(j) are water stress coefficients
and S(j) is a salt stress coefficient. According to Raes et al. (2009), the
water stress coefficients are
4akE(j,t)=exp-2.5θfc(j)-θ(j,t)θfc(j)-θr(j)θ≤θfc,4bkE(j,t)=1θ>θfc,
where θfc(j) is the moisture content at field capacity for
layer j, or when the conductivity becomes limiting and
θr(j) is the moisture content at wilting point,
θ(j, t) is the soil moisture content for layer j at time t.
Then the water stress coefficient in Eq. (3b) is
kT(j,t)=1-exp1-θ(j,t)-θr(j)(1-p)θfc(j)-θr(j)fshape-1expfshape-1θ≤θfc,kT(j,t)=1θ>θfc,
where fshape is the shape factor of the kT(j,t)
curve and p is the fraction of readily available soil water relative to the
total available soil water. Finally, the salt stress coefficient S(j, t)
for
each layer in Eq. (3b) can be calculated as (Allen et al., 1998; Xue et al.,
2018)
S(j,t)=1-B100kyECe(j,t)-ECethreshold,
where ky is the factor that affects the yield, ECe is
the electrical conductivity of the soil saturation extract (mS cm-1),
ECethreshold is the calibrated threshold of the electrical
conductivity of the soil saturation extract when the crop yield becomes
affected by salt (mS cm-1), and B is the calibrated crop-specific
parameter that describes the decrease rate of crop yield when
ECe increases per unit below the threshold. The electrical
conductivity of the soil saturation extract can be calculated as (Rhoades et
al., 1989)
ECe=1.33+5.88×EC1:5,
where EC1:5 is the electrical conductivity of the soil extract of
soil samples mixed with distilled water in a proportion of 1:5.
VADOSE module
To model the daily soil moisture content and groundwater depth, first we need
to calculate the soil moisture content at field capacity and the
drainable porosity based on the soil moisture characteristic curve. Besides,
we assume that the water and salt move downward on rainy and/or irrigation
days, while the water and salt move upward on days without rain and/or
irrigation.
Parameters based on the soil moisture characteristic curve
for modelingMoisture content at field capacity
Field capacity with a shallow groundwater is different than in soils with
deep groundwater where water stops moving when the hydraulic conductivity
becomes limiting at -33 kPa. When the groundwater is shallow, the
hydraulic conductivity is not limiting and the water stops moving when the
hydraulic potential is constant, and thus the matric potential is equal to
the height above the water table (Gardner, 1958; Gardner et al., 1970a, b;
Steenhuis et al., 1988; Liu et al., 2019). Assuming a unique relationship
between moisture content at field capacity and matric potential (i.e., soil moisture characteristic curve), the moisture content at field capacity at any point above the water table is a unique
function of the water table depth. Thus, any water added above field capacity
will drain downward. When the groundwater is recharged, the water table will
rise and increase the moisture contents at field capacity throughout the
profile.
The moisture contents at field capacity were found by Liu et al. (2019)
using the simplified Brooks and Corey soil moisture characteristic curve
(Brooks and Corey, 1964):
8aθ=θsφmφb-λforφm>φb,8bθ=θsforφm≤φb,
in which θ is the soil moisture content (cm3 cm-3),
θs is the saturated moisture content (cm3 cm-3),
φb is the bubbling pressure (cm), φm is
the matric potential (cm), and λ is the pore size distribution index.
The moisture content at field capacity, θfc(z, h), for any
point, z, from the surface water for a groundwater at depth, h, can be
expressed as (Liu et al., 2019)
9aθfc(z,h)=θs(z)h-zφb-λforh-z>φb(z),9bθfc(z,h)=θs(z)forh-z≤φb(z),
where h (cm) is the depth of the groundwater and z (cm) is the depth of
the point below the soil surface. Thus (h-z) is the height above the
groundwater, and this is equal to the matric potential for soil moisture
content at field capacity.
For shallow groundwater, the matric potential at the surface is -33 kPa
when the groundwater is at 3.3 m depth. For this matric potential, as
mentioned above, the conductivity becomes limiting. This depth of the
groundwater is
therefore the lower limit over which the VADOSE module is valid.
Evapotranspiration can lower the soil moisture content below field capacity.
Thus, the maximum moisture content in the VADOSE module is determined by the
soil characteristic curve and the height of the groundwater table, and the
minimum is the wilting point that can be obtained by evapotranspiration by
the crop. Note that the saturated hydraulic conductivity does not play a
role in determining the moisture content because inherently it is assumed
that it is not limiting in the distribution of the water.
Drainable porosity
The drainable porosity is a crucial parameter in modeling the groundwater
depth and soil moisture content. According to the soil water characteristic
curve at field capacity, the drainable porosity can be expressed as a
function of the depth. The drainable porosity is obtained by calculating the
field capacity Wfc(h) (cm) for each layer at all groundwater
depths. The total water content at field capacity of the soil profile over a
prescribed depth with a water table at depth h can be expressed as
Wfc(h)=∑j=1nL(j)θfc(j,h),
where θfc(j, h) is the average moisture content at field
capacity of layer j that can be found by integrating Eq. (8) from the upper
to lower boundaries of the layer and dividing by the length L(j), which
is the height of layer j. The matric potential at the boundary is equal to
the height above the water table. The drainable porosity, μ(h), which is
a function of the groundwater depth h, can simply be found as the
difference in water content when the water table is lowered over a distance
of 2Δh.
μ(h)=Wfc(h+Δh)-Wfc(h-Δh)2Δh,
where Δh=0.5L(j) (cm).
Downward flux (at times of irrigation and/or precipitation)
and model output
During the downward flux period, the upward water flux from groundwater is
zero. Under this condition, the model can output the daily soil moisture
content of different soil layers, the percolation from each soil layer to
the soil layer beneath, the discharge from soil water to groundwater, the
salt concentration of groundwater and of soil water in each soil layer, and
the groundwater depth.
Water
A downward flux occurs when either the precipitation or irrigation is
greater than the actual evapotranspiration. In this case, upward flux will
not occur because the actual evapotranspiration is subtracted from the input
at the surface. We consider two cases when the groundwater is being
recharged and when it is not.
When the net flux at the surface (irrigation plus rainfall minus actual
evapotranspiration) is greater than that needed to bring the soil up to
equilibrium moisture content, the groundwater will be recharged and the
distance of the groundwater to the soil surface decreases, and the moisture
content will be equal to the moisture at field capacity. The fluxes from one
layer to the next can be calculated simply by summing the amount of water
needed to fill up each layer below to the new moisture content at field
capacity. Hence, the percolation to groundwater, Rgw(t), can be
expressed as
Rgw(t)=P(t)+I(t)-Ea(t)-Ta(t)-∑j=1nθfc(j,h)-θ(j,t-Δt)L(j)Δt,
where n is the total number of layers, θ(j, t) is the average soil
moisture content on day t of layer j (cm3 cm-3),
Ea(t) is the actual evaporation (mm), Ta(t) is the
actual transpiration (mm), P(t) is the precipitation (mm), and I(t) is
the irrigation (mm).
When the groundwater is not recharged, the rainfall and the irrigation are
added to the uppermost soil layer and when the soil moisture content will be
brought up to the field capacity and the excess water will infiltrate to
the next soil layer, bringing it up to field capacity. This process continues
until all the rainwater is distributed. Formally the soil moisture can be
expressed as
θ(j,t)=minθfc(j,h),θ(j,t-Δt)+Rw(j-1,t)ΔtL(j),
where θ(j, t) is the average soil moisture content on day t of
layer j (cm3 cm-3); Rw(j-1, t) is the percolation
rate to layer j (mm) and can be found with Eq. (12) by replacing j-1
for n in the summation sign.
Rw(j-1,t)=P(t)+I(t)-Ea(t)-Ta(t)-∑1j-1θfc(j,h)-θ(j,t-Δt)L(j)Δt
For the uppermost soil layer, the water percolation can be expressed as
Rw(0,t)=I(t)+P(t)-Ea(t)-Ta(t).
Salinity
The salt concentration for layer j can be expressed by a simple mass
balance as
C(j,t)=θ(j,t-Δt)C(j,t-Δt)L(j)+Rw(j-1,t)C(j-1,t)-Rw(j,t)C(j,t)Δtθ(j,t)L(j),
where C(j, t) is the salt concentration of layer j at time t
(g L-1). The equation can be rewritten as an explicit function
of C(j, t):
C(j,t)=θ(j,t)L(j)1+Rw(j,t)Δtθ(j,t-Δt)C(j,t-Δt)L(j)+Rw(j-1,t)C(j-1,t)Δtθ(j,t)L(j).
For the surface layer j=1, we obtain
C(1,t)=θ(1,t)L(1)1+Rw(1,t)Δtθ(1,t)L(1)1+Rw(1,t)Δtθ(j,t-Δt)C(j,t-Δt)L(j)+I(t)CIΔtθ(j,t)L(j),
where CI is the salt concentration in the irrigation
water (g L-1).
The salt concentration of the groundwater Cgw(t) can be estimated
as
Cgw(t)=G(t-1)×Cgw(t-1)+C(5,t)×Rw(t)G(t-1)+Rw(t),
where C(5, t) is the soil salinity concentration of the soil
layer 5 on day t (g L-1), G(t-1) is the difference of the
groundwater depth and the depth of the largest groundwater table fluctuation
depth of the groundwater table on day (t-1) (m) (Xue et al., 2018), and
Cgw(t) is the soluble salt concentration of groundwater at
day t (g L-1).
Upward flux and model output
For the upward flux period, the downward water flux to groundwater is zero.
The evapotranspiration leads to the decrease in soil moisture content in the
vadose zone and lowers the groundwater table due to the upward movement of
groundwater to crop root zone and soil surface. The soil moisture content is
calculated by taking the difference of equilibrium moisture content
associated with the change in groundwater depth. Under this condition, the
model can output the daily soil moisture content of different soil layers,
the upward groundwater flux, the groundwater depth, and the salt
concentration of groundwater and of soil water in each soil layer.
Water
The groundwater upward flux Ugw(h, t) is limited by either the
maximum upward flux of groundwater Ugw,max(h) or the
actual evapotranspiration, formally stated as
20Ugw(h,t)=minEa(t)+Ta(t),Ugw,max(h),21Ea(t)=∑j=1nEa(j,t),22Ta(t)=∑j=1nTa(j,t),
where Ugw,max(h, t) is the actual upward flux from groundwater (mm), Ea(t) is the actual evaporation at day t (mm), Ta(t) is the actual transpiration at day t (mm),
Ea(j, t) is the actual evaporation at day t of
layer j (mm), and Ta(j, t) is the actual transpiration at
day t of layer j (mm).
The maximum upward flux can be expressed as (Liu et al., 2019; Gardner et
al., 1958)
Ugw,max(h)=aebh-1,
where a and b are constants that need to be calibrated and h is the
groundwater depth (cm).
Two cases are considered for determining the moisture contents of the layers
depending on whether the actual evapotranspiration is greater or less than
the maximum upward flux.
Case I: Ugw,max(h)>Ea(t)+Ta(t): in
this case, where the maximum upward flux is greater than the
evaporative demand, the groundwater depth is updated:h(t)=h(t-Δt)+Ea(t)+Ta(t)μ(h‾),where μ(h‾) is the average drainable porosity over the change
in groundwater depth h. The moisture content after the change in
groundwater depth becomesθ(j,t)=θ(j,t-Δt)+θfc(j,h(t))-θfc(j,h(t-Δt)).Note that when the layer is at field capacity and the upward flux is equal
to the evaporative flux, the layer remains at field capacity for the
updated
groundwater depth at time t.
Case II: Ugw,max(h)≤Ea(t)+Ta(t):
in this case, the groundwater depth is updated:h(t)=h(t-Δt)+Ugw,max(h)μ(h‾).When the upward flux is less than the sum of the actual evaporation and
transpiration, the moisture content is updated with the difference between
the two fluxes, Ugw,max(h) and
[Ea(t)+Ta(t)], according to a predetermined
distribution extraction of water out of the root zone:θ(j,t)=θ(j,t-Δt)+θfc(j,h(t))-θfc(j,h(t-Δt)-r(j)Ea(t)+Ta(t)-Ugw,max(h)L(j).The upward flux of water can be found by summing the differences in
moisture
content above the layer j similar to Eq. (14), but starting the summation
at the groundwater.
Salinity
The salt from groundwater is added to the soil layers according to the root
function. The soil salinity concentration in layer j at day t can be
expressed as
C(j,t)=θ(j,t-Δt)C(j,t-Δt)L(j)+r(j,t)Ug(h,t)Cgw(t)θ(j,t-Δt)L(j)+θfc(j,h(t))-θfc(j,h(t-Δt))L(j)-r(j,t)Ea(t)+Ta(t)-Ugw,max(h).
Since water is extracted from the reservoir that has the same concentration
as in the reservoir, the concentration will not change; hence, the equation
used to estimate the groundwater salt concentration can be expressed as
Cgw(t)=Cgw(t-Δt).
Data collectionStudy area
Field experiments were conducted in 2017 and 2018 in Shahaoqu experimental
station in Jiefangzha sub-district, Hetao irrigation district in Inner Mongolia, China (Fig. 3). Irrigation water originates from the Yellow River. The change in the irrigation water salinity is small and can be ignored during the crop growth period. The area has an arid continental climate. Mean annual precipitation is 155 mm a-1, of which 70 % falls from June to September. Pan evaporation is 2000 mm a-1 (Xu et al., 2010). The mean annual temperature is 7 ∘C. The soils begin to freeze in the middle of November and to thaw at the end of April or beginning of May. Maize, wheat, and sunflower are the main crops in Jiefangzha sub-district and are grown with flood irrigation. The groundwater depth is between 0.5 and 3 m. Regional exchange of groundwater is minimal due to the low gradient of 0.01–0.025 (Xu et al., 2010). Thus, the groundwater flows mainly
vertically with minimum lateral flow in the regional scale. Over 50 % of
the total irrigated cropland, 5250 km2 in the Hetao irrigation district
in the Yellow River basin, is affected by salinity (Feng et al., 2005).
The layout of the experimental fields is shown in Fig. 3. The areas of
fields A–D are 920, 2213, 1167, and 1906 m2, respectively. Fields A
and D were planted with maize on 10 May and harvested on 30 September 2017.
In 2018, fields A and D were planted with gourds and were therefore
not monitored in 2018. Fields B and C were seeded with sunflower in both 2017
and 2018. The sunflower was planted on 1 June 2017 and 5 June 2018. Harvest
was on 15 September in both years. The fields were irrigated by flooding the
field ranging from two to five times during the growing season (Table 1). The
salinity of the irrigation source water was measured three times during the
crop growth period and the mean value was used in the mass balance. The
salinity of the irrigation source water is assumed unchanged. A well was
installed in each experimental field to monitor the groundwater depth.
Irrigation scheduling for the Shahaoqu experimental fields in 2017
and 2018.
Daily meteorological data, including air temperature, precipitation, relative
humidity, wind speed, and sunshine duration, originated from the weather
station at the Shahaoqu experimental station. The soil moisture content for
the four experimental fields in 2017 and for field C in 2018 during the crop
growing season was measured every 7–10 d at the depths of 0–20, 20–40,
40–60, 60–80, and 80–100 cm by taking soil samples and oven drying.
In 2018, in addition, the soil moisture content at the same depths was
monitored daily using Hydra Probe Soil Sensors (Stevens Water Monitoring
System Inc., Portland, OR, USA) in field B except the oven drying method. The
Hydra Probe
was calibrated using the intermittent manual measurements. In 2017, the
groundwater depths were manually measured in all four experimental fields
about every 7–10 d. In 2018, the groundwater depth in fields B and C was
recorded at 30 min intervals using an HOBO Water Level Logger-U20 (Onset,
Cape Cod, MA, USA). The sensors of the soil moisture content and groundwater
depth were connected to data loggers and downloaded via wireless
transmission. The crop leaf area and crop height were manually measured
every 7–12 d.
Undisturbed soil samples were collected in 5 cm high rings with a diameter
of 5.5 cm from the five soil layers where the soil moisture was taken and
used for textual analysis, saturated soil moisture content, field
capacity, and soil bulk density. The soil texture was analyzed with a laser
particle size analyzer (Mastersizer 2000, Malvern Instruments Ltd., United
Kingdom). The American soil texture classification method was used in this
study. Finally, the soil samples were collected 7–10 d apart to monitor
the change in electrical conductivity (EC). The soil samples were mixed with
distilled water in a proportion of 1:5 to measure the electrical
conductivity of the soil water by a portable conductivity meter. It is
assumed that 1 ms cm-1 corresponds to 640 mg L-1 of the total
dissolved salts (Wallender and Tanji, 2011; Xue et al., 2018).
Model calibration and validation
The observed soil moisture contents, groundwater depths, crop heights, LAIs,
and salinity concentrations for field A with maize and sunflower fields B
and C in 2017 were used for calibration, and the sunflower data of fields B
and C in 2018 and the maize data in field D in 2017 were used for
validation. The initial θfc was based on the measured data
(Table 2). The initial values of θs and θr
were derived from the soil texture with the method of Ren et al. (2016)
(Table 2). The default values of EPIC for sunflower and maize were used as
initial values for simulating crop growth (Kcmax and
LAImx in Eq. S3, Kb in Eq. S4, Hmx in
Eq. S7, PHU in Eq. S9, Tb in Eq. S10, ad in Eq. S12,
T0 and Tb in Eq. 16, and RDmx in Eq. S18). The
initial value maximum crop coefficient (Kcmax) in Eq. (S3) in
Sect. S1 for evapotranspiration calculation was taken from Sau et al. (2004).
The initial values of two groundwater parameters (a and b in Eq. 23) were
based on Liu et al. (2019). The Brooks and Corey soil moisture characteristic
parameters (φb, λ in Eq. 8) were obtained by
fitting the outer envelope of the measure moisture content and water table
data.
Soil texture and bulk density of the experimental fields in
Shahaoqu.
Statistical indicators were used to evaluate goodness of fit of the
hydrological model for both calibration and validation (Ritter and
Muñoz-Carpena, 2013). The statistical indicators included the root mean
square error (RMSE) (Abrahart and See, 2000),
RMSE=1N∑i=1NPi-Oi2,
the mean relative error (MRE) (Dawson et al., 2006; Nash and Sutcliffe,
1970),
MRE=1N∑i=1NPi-OiOi×100%,
the Nash–Sutcliffe efficiency coefficient (NSE) (Nash and Sutcliffe, 1970),
NSE=1-∑i=1NPi-Oi2∑i=1NOi-O‾2,
and the determination coefficient (R2) and regression coefficient (b)
(Xu et al., 2015)
33R2=∑i=1NOi-O‾Pi-P‾∑i=1NOi-O‾0.5∑i=1NPi-P‾0.52,34b=∑i=1NOi×Pi∑i=1NOi=12,
where N is the total number of observations; Pi and Oi are the
ith model predicted and observed values (i=1, 2, 3 … N),
respectively; O‾ and P‾ are the mean observed values
and predicted values, respectively. The RMSE is used to evaluate the bias of
the measured data and predicted data. The MRE can evaluate the credibility of
the measured data. The NSE is usually used to evaluate the quality of the
hydrological models. The R2 is used to measure the fraction of the
dependent variable total variation that can be explained by the independent
variable. And the regression coefficient represents the influence of the
independent variable on the dependent variable in the regression equation.
The values of RMSE and MRE close to 0 indicate good model performance. The value of NSE ranges from -∞ to 1. NSE = 1 means a perfect fit, while the negative NSE values indicate the mean observed value is a better predictor than the simulated value (Moriasi et al., 2007). For b and R2, the value closest to 1 indicates good model predictions.
Parameter sensitivity analysis
A sensitivity analysis was performed to determine how the input parameters
affected output of the models (Cloke et al., 2008; Cuo et al., 2011). Each
parameter was varied over a range of -30 % to 30 % to derive the
corresponding impact on the model output of soil moisture, groundwater
depth, soil salinity, leaf area index, and actual evapotranspiration. The
change in output values was plotted against the change in input values.
Results
The 2017 and 2018 experimental data of the Shahaoqu farmers' fields in the
Hetao irrigation district (Fig. 3) are presented first, followed by the
calibration and validation results of the CROP and VADOSE modules of the
EPICS model.
Reference evapotranspiration (ET0) and precipitation during the
crop growth period in 2017 and 2018.
Results of the field experimentWater input
The precipitation was 63 mm in 2017 (10 May to 30 September) and 108 mm
in 2018 (1 June to 15 September). The precipitation from the greatest
rainstorm was 26 mm on 1 September 2018 (Fig. 4). Irrigation provided most
of the water for the crops. Field A (maize) was irrigated four times for a
total of 736 mm and field D (maize) was irrigated five times for a total of
588 mm in 2017. Sunflower fields B and C were both irrigated twice with
total water amounts of 261 and 160 mm, respectively, in 2017. In 2018,
fields B and C were irrigated five and two times, respectively, with total
water amounts of 478 and 240 mm, respectively. The reference
evapotranspiration ranged from 1 mm d-1 to a maximum of
6.4 mm d-1 during the crop growing period (Fig. 4). The total
reference evapotranspiration from 10 May to 30 September 2017 was 595 and
368 mm from 1 June to 15 September 2018. The reason was that there were more
rainfall days in June, July, and September in 2018 than in 2017, which
increased the amount of water available for the evapotranspiration by the
crop in 2018. In addition, the wind speed was high so that the increase in the evapotranspiration was elevated. In the studies of Ren et al. (2017) and Miao et al. (2016), the mean ET0 was over 6 mm per day in May. Hence, the ET0 during the study period in 2017 was greater than in 2018.
Soil physical properties
Based on the soil textural analysis in Table 2, the soils were classified as
silt, silt loam, and loamy sand. Bulk densities varied from 1.24 to
1.47 Mg m-3, with the greatest bulk densities in the 0–20 cm soil
layer. There was generally more sand in the top 40 cm than below. The
subsoil was heavier and had the greatest percentage of silt (Table 2). The
moisture content at -33 kPa (0.33 bar) varied from 0.25 to
0.35 cm3 cm-3 and at 1.5 Mpa (wilting point at 15 bar) ranged
from 0.08 to 0.15 cm3 cm-3 (Table 2).
Soil moisture content
Moisture content, rainfall, and irrigation amounts are depicted for the five
layers and the four fields in 2017 and two fields in 2018 in Fig. 5. Blue
closed spheres indicate that the moisture content was determined on cored
soil samples (Fig. 5a–c, e, and f) and close-spaced spheres when the hydra
probe was used (Fig. 5d). The moisture contents were near saturation when
irrigation water was added and subsequently decreased due to crop
transpiration and soil evaporation (Fig. 5). In all cases, the moisture
contents during the main growing period remained above the moisture content
at -33 kPa that ranged from 0.25 to 0.34 cm3 cm-3 for the
60–80 cm depth (Table 2, Fig. 5). Only after the last irrigation and during
harvest of the crop did the moisture content in the top 0–40 cm for maize
and 0–60 cm for sunflower decrease below the moisture content at
-33 kPa. During the growing season, the variation of moisture content was
greater in the top 60 cm with the majority of the roots than in the lower
depths where, after the first irrigation, it remained nearly constant close
to saturation.
Observed (blue dots) and simulated soil moisture content of the
Shahaoqu experimental fields during model calibration (a–c) and
validation (d–f).
Salinity
Overall the salt concentration is greatest at the surface and increases at
all depths during the growing season. Sunflower is more salt tolerant than
maize and the overall salt concentration was greater in the sunflower fields
(Fig. 6) at comparable times of the crop development for field B but not for
field C. Comparing the salt concentration and soil moisture patterns
(Fig. 5), we note that they behave similarly but opposite to each other
(Fig. 6). The soil salinity concentration was decreasing during an irrigation
event due to dilution and then gradually increasing partly due to
evaporation of the water. Some of the soil salt was transported to the
layers below during irrigation and some salt was moving upward with the
evaporation from the surface. As expected, after the harvest, the fall
irrigation decreased the salt concentration from fall 2017 to spring 2018.
Observed (blue dots) and simulated soil salinity concentration of
the experimental fields in Shahaoqu during model calibration (a–c)
and validation (d–f).
Groundwater observations
The variation in groundwater depth during the growing season was very
similar for both years and in all fields. The groundwater depth for all
fields was between 50 and 100 cm from the surface after an irrigation event
and then decreased to around 150 cm before the next irrigation or rainfall
(Fig. 7). Only after the last irrigation in August 2017 did the water table
decrease to below 250 cm and to around 200 cm in 2018. Field D followed the
same pattern, but the groundwater was more down from the surface. In several
instances, the groundwater table increased without an irrigation or rainfall
event in sunflower field C (Fig. 7c and e). This was likely related to an
irrigation event either from an irrigation in a nearby field that affected
the overall water table or an accidental irrigation that was not properly
documented. We estimated the amount of irrigation water based on the change
in moisture content in the soil profile (orange bars in Fig. 7c and e).
Finally, there was a notable rise in the water table of a mean 375 mm “fall
irrigation” after harvest between the end of 2017 (Fig. 7a–c) and the
beginning of 2018 (Fig. 7d–f), which is a common practice in the Jiefangzha
irrigation district to leach the salt that has accumulated in the profile
during the growing periods.
Observed (blue dots) and simulated groundwater depth of the
experimental fields in Shahaoqu during model calibration (a–c) and
validation (d–f).
Note that in Fig. 7, after an irrigation event, the groundwater depth was
between 50 and 80 cm, while the whole profile was saturated (Fig. 5). This
is directly related to the bubbling pressure of the water. After the
irrigation event stopped, the water table was likely at the surface but then
immediately decreased because a small amount of evaporated water will bring
the water table down to a depth of approximately equal to the bubbling
pressure, φb, in Eq. (8). The bubbling pressures are listed
in Table 3.
LAI and plant height
Plant height and LAI followed the typical growth curve that started slowly
to rise in the beginning, accelerated during the vegetative stage, and then
became constant during the seed setting and ripening stages (Fig. 8). In the
maturing stage, the leaf area index decreased.
Observed crop height (a) and leaf area index (b)
of the experimental field in Shahaoqu in 2017 and 2018.
Soil moisture characteristic curve and drainable porosity
To simulate the soil moisture content and to derive drainable porosity as a
function of water table depth, the soil moisture characteristic curves were
derived by plotting the observed soil moisture content in 2017 and 2018
versus the height above the water table to the soil surface for the five
soil layers in Fig. 9. The Brooks–Corey equation (Brooks and Corey, 1964)
was fitted through the outer envelope of the points. The parameters of the
Brooks–Corey equation were adjusted through trial and error to obtain the
best fit (Table 3a). In Fig. 9, points on the left-hand side of the soil
moisture
characteristic curve (moisture content smaller than the field capacity) were
due to water removal at times when evaporative demand was greater than the
upward water flux. Under these conditions the conductivity is limiting in
the soil and there is no relationship between groundwater depth and matric
potential. Since we take the water table depth as a proxy for matric
potential, these points are omitted when drawing the soil characteristic
curve. The few points at the right of the soil moisture characteristic curve
indicate the soil moisture was greater than field capacity and matric
potential and groundwater were not yet at equilibrium after an irrigation
event.
Soil moisture characteristic curves of five soil layers in the
experimental fields. The pink line is the fit with the Brooks–Corey
equation.
Parameter sensitivity analysis for (a) soil moisture
content, (b) groundwater depth, (c) salt salinity
concentration, (d) LAI, and (e) ET.
The fitted parameter values are consistent. Field A had a greater bubbling
pressure and moisture content at -33 kPa than the other fields, indicating
that this field had more clay. This was confirmed by the data in Table 2.
For fields B–D, the bubbling pressure was greater at the 60–80 cm depth or
the 80–100 cm depth, which was also in accordance with the data in Table 2.
(a) Calibrated soil hydraulic parameters in the Brooks and
Corey soil moisture characteristic curve. (b) Calibrated groundwater
parameters.
Note: θs is the soil moisture at
saturation (cm3 cm-3), φb is bubbling
pressure (cm), and λ is the pore size distribution index.
Parameter sensitivity analysis
The results of sensitivity analysis of the 15 input parameters on 5 output
parameters are shown in Fig. 10. The evaluated output parameters are soil
moisture content, groundwater depth, soil salinity concentration, field
evapotranspiration, and crop LAI. Steeper lines indicate a greater
sensitivity of the parameter.
The results of the sensitivity analysis show that moisture content
predictions (Fig. 10a) are the most sensitive to the input value of the
saturated moisture content (θs). None of the other
parameters are very sensitive. This includes the shape parameters for the
soil characteristic curve, bubbling pressure φb, and
exponent λ. The input parameter with the most sensitivity to
groundwater depth (Fig. 10b) is the saturated moisture content as
well. Other less sensitive parameters are the exponent b and constant a
in Eq. (23) in predicting the upward flux and the bubbling pressure,
φb, of the soil moisture characteristic curve (Eq. 8a).
Likewise, in the case of the salinity predictions (Fig. 10c), the
saturated moisture content gives the greatest relative change in salt
content. Less sensitive, but still important, are the field capacity,
θfc, the bubbling pressure, φb, and the
exponent λ of the soil characteristic curve (Eq. 8a) and b in
Eq. (23). The sensitivity parameters for the leaf area index (LAI) (Fig. 10d) are the maximum potential leaf area index, LAImx, and fraction of the growing season when leaf area declines (DLAI) followed by total potential heat units required for crop maturation (PHU). Finally, for the evapotranspiration (Fig. 10e), the saturated soil moisture content is the most sensitive parameter, and other less sensitive parameters are the exponent b and field capacity.
Thus, the model output is most sensitive to the input parameters that define
the soil hydraulic properties, groundwater flux, and crop growth. As
expected, since the soil remains near field capacity, the parameters that
relate to the reduction of evaporation when the soil dries out are
insensitive. When used in the simulation practices, the model needs to be
calibrated and verified to avoid high error from parameter uncertainty.
Model calibration and validation with field data
The model parameters were calibrated and validated using the observed
moisture content, groundwater depth, plant height, leaf area index, and
calculated evapotranspiration. The data of sunflower fields B and C and
maize field A were collected and used for calibration. Since farmers did not
grow maize in 2018, the 2017 data of maize field D, together with sunflower
fields B and C in 2018, were used for validation. The optimal parameter set
was determined using graphical similarity between observed and predicted
results together with near-optimum performance of the statistical indicators
while keeping all values within physically acceptable ranges.
As a way of reducing the number of parameters that needed to be calibrated,
we initially selected one to three most sensitive parameters for each of
the observed time series, starting with evapotranspiration (including LAI and
crop height) and followed by moisture content, groundwater depth, and salt
content in the soil. This cycle was repeated several times until changes
became small. The last stage of the calibration consisted of fine-tuning the
remaining least sensitive parameters.
To calibrate the parameters in the CROP module, we calculated
evapotranspiration during the crop growth period with the observed soil
moisture content and groundwater depth by the soil water balance method. In
addition, we used the observed LAI measurements in 2017 and plant height in
both 2017 and 2018. LAI was not measured in 2018. The DLAI,
LAImx, and Hmx in the crop module were adjusted
to fit the observed LAI and crop height values. In addition, we fitted the
θfc moisture content to obtain a good fit of the
evapotranspiration. The saturated moisture content values were not adjusted
since they were already determined for fitting the soil characteristic curve.
The exponent b and constant a in Eq. (23) were adjusted to fit the
observed soil moisture content and groundwater depth.
Evapotranspiration, crop height, and leaf area index
The predicted evapotranspiration and that calculated from the mass balance
show a good agreement with Nash–Sutcliffe values ranging from 0.96 to 0.89
during calibration and validation (Fig. 11 and Table 4). The calibrated
predictions of plant height fitted the observed values well during
calibration and validation with Nash–Sutcliffe values ranging from 0.77 to
0.96 for the individual fields (Table 4) and over 90 % when the data were
pooled for the fields during calibration and validation (Fig. 12). LAI was
not
measured in 2018. During calibration, Nash–Sutcliffe-predicted LAI values
were good for sunflower but not as good for maize, but the coefficients of
determination and slope in the regression were acceptable (Table 4, Fig. 13).
In addition, the overall trend was predicted reasonably well (Fig. 13b).
Comparison of predicted and observed actual evapotranspiration:
(a) calibration and (b) validation.
Comparison of predicted and observed crop height:
(a) calibration and (b) validation.
Comparison of predicted and observed LAI: (a) calibration
and (b) validation.
Soil moisture and groundwater depth
Next, the moisture contents and groundwater table were fitted with the
parameters in the vadose model without changing the parameters in the CROP
module. Saturated moisture content was the most sensitive parameter for
calibrating the moisture content (Fig. 10a). Since this value was already
determined a priori from the soil characteristic curve (Table 3a), we could
not use other parameters to obtain a better fit since none were sensitive
(Fig. 10a). Therefore, we calibrated the groundwater parameters (i.e.,
a and b parameters; Eq. 23) together with the moisture content to obtain
the best fit for both. The fitted a and b values are listed in Table 3b.
The fitted parameters between the four experimental fields were similar but
not the same. This can be expected in river plains, where soils can vary over
short distances.
Overall, the moisture contents were predicted well during calibration and
validation (Figs. 5 and 14 and Table 4), with the exception of field B during
validation (Table 4) with a NSE of 0.43. The moisture contents were predicted
most accurately in the layers from 40 to 100 cm, where the soil moistures
were at field capacity during most of the growing season (Fig. 14). In the
top 40 cm, the predicted soil moisture content deviated from
observed moisture contents, especially at the drier end (Figs. 5 and 14).
Unlike at deeper depths, evapotranspiration determined the moisture contents
at shallow depths. Prediction of evapotranspiration introduced additional
uncertainties such as the distribution of the root system. This uncertainty
is also likely the reason why the 2018 moisture contents during the
validation are acceptable but not predicted as well as in 2017.
Comparison of predicted and observed soil moisture content:
(a) calibration and (b) validation.
The predicted and observed groundwater depths are in good agreement during
both calibration and validation (Figs. 7 and 15). The MRE values were within
±10 % and the NSE values ranged from 0.52 for field D during validation
to 0.91 in field C during calibration, where some of the recharge events were
estimated (Table 4).
Comparison of predicted and observed groundwater depth:
(a) calibration and (b) validation.
Model error statistics for calibration and validation of models
in 2017 and 2018 (mean relative error, MRE; root mean square error, RMSE;
Nash–Sutcliffe efficiency, NSE; coefficient of determination, R2; regression coefficient).
ProcessFieldVariableMRERMSENSER2Regression(%)(cm3 cm-3 cmcoefficientor g L-1 orslopemm)Calibration2017 field ASWC (0–1 m)2.90.040.80.561.01(maize)GWD4.533.80.640.640.97LAI-17.40.780.110.920.89hcrop0.0416.20.950.990.97C (0–1 m)13.90.5*0.491.072017 field BSWC (0–1 m)-1.20.040.710.740.97(sunflower)GWD6.022.90.860.980.96LAI4.70.580.90.920.91hcrop6.833.50.830.961.1C (0–1m)11.00.55*0.71.12017 field CSWC (0–1 m)8.50.040.880.91.05(sunflower)GWD-7.319.10.910.940.94LAI48.61.00.590.931.29hcrop5.4227.40.880.981.07C (0–1 m)-1.60.52*0.080.94ETa12.240.50.920.961.11Validation2018 field BSWC (0–1 m)-2.30.030.430.680.98(sunflower)GWD4.8616.10.830.841.01hcrop12.526.90.860.990.95C (0–1 m)4.00.35*0.721.062018 field CSWC (0–1 m)17.30.060.640.721.04(sunflower)GWD2.113.80.860.871.01hcrop-10.336.40.770.970.84C (0–1 m)0.510.33*0.731.022017 field DSWC (0–1 m)6.10.040.680.771.05(maize)GWD0.6439.10.520.711.01LAI-10.70.79-0.020.580.93hcrop-1.713.60.960.981C (0–1 m)9.80.51*0.541.11ETa8.042.40.890.890.95
Note: * relative bias was over 5 %, invalidating the
calculation of NSE. SWC is the soil moisture content, GWD is the groundwater
depth, LAI is the leaf area index, hcrop is the height of the crop, C is the
soil salinity concentration, and ETa is the actual
evapotranspiration.
Soil salinity
The only parameter that could be adjusted each year for calibration of the
salt concentrations was the initial salt concentration. The predicted salt
concentrations in the top layers decreased after an irrigation event similar
to the limited observed values (Fig. 6). Despite the salt concentration
fitting visually reasonably well as shown in Figs. 6 and 16,
there was a bias of 8 % in the data, and consequently the Nash–Sutcliffe
efficiency could not be applied (Table 4) (Ritter and Muñoz-Carpena,
2013). Similarly to the moisture contents, the salt concentrations in the
layers below 40 cm were predicted more accurately than the layers above
40 cm. More data should be collected during the whole year on the salt
concentrations in the soil in order to accurately predict the salt
concentrations.
Comparison of predicted and observed salt concentration during
calibration (a) and validation (b).
Discussion
The EPICS model is a surrogate model that can be applied in areas with
shallow groundwater. It can simulate the soil moisture content and salt
concentration for layers in the soil, the groundwater depth, upward movement
of water from groundwater, evapotranspiration, and plant growth.
The model is different from traditional models that are based on the Richards
equation; instead of calculating the fluxes first, in the EPICS model, the
groundwater depth is calculated first based either on the amount of water
removed by evapotranspiration on days without rain or irrigation or recharge
to groundwater on the other days. Subsequently, when the groundwater is
sufficiently shallow and the potential upward flux from the groundwater is
greater than the evaporative demand, the moisture contents are adjusted so
that soil moisture and groundwater depth are in equilibrium (i.e., field
capacity). In this case, the matric potential is equal to the height above
the water table, and the moisture contents can be found with the soil moisture
characteristic curve. When the upward flux is less than the evaporative demand of the atmosphere and crop, the difference between the upward moisture content is determined by first decreasing the moisture content below the field capacity. The flux of water in the soil is then calculated based on the changes in water content. The advantage is fewer input parameters needed when compared with other numerical models (Šimůnek et al., 1998; Van Dam et al., 1997). For example, the hydraulic conductivity is not used in EPICS.
Although the uncertainties of field experimental observations and input data
of the model affected the accuracy of simulation results, EPICS compares
well with other models. Xu et al. (2015) tested SWAP-EPIC for two lysimeters
grown with maize on the same experimental farm in the Hetao
irrigation district where our experiment was carried out. The SWAP model
solves the Richards equation numerically with an implicit backward scheme and
is combined by Xu et al. (2015) with the EPIC model. The accuracy of our
simulation results, despite the difference in complexity, is very similar.
The moisture contents were simulated slightly better with EPICS, the
groundwater depth was nearly the same, and the LAI values were predicted
more accurately in the SWAP-EPIC model. Xu et al. (2015) did not simulate
the salt content of the soil. Compared to fewer data and computationally
intensive models that are applied in the Yellow River, the soil moisture
content was simulated more accurately by EPICS than in the North China Plain,
with 30 m deep groundwater by surrogate models of Kendy et al. (2003)
and Yang et al. (2015a, b) and in the Hetao irrigation district by Gao et
al. (2017b) and Xue et al. (2018) during the crop growth period.
To obtain more accurate results in the future, the upward capillary flux
from groundwater needs to be improved. The salinity of irrigation source
water also needs to be measured, especially for the areas irrigated by
groundwater or the hydrologically closed basins. In addition, the
evapotranspiration measured independently, using eddy covariance (Zhang et
al., 2012; Armstrong et al., 2008) and the Bowen ratio–energy balance method
(Zhang et al., 2007), should be further used to test the performance of the
model in future study.
The limitation of the EPICS model is it can only be applied in areas where
groundwater is generally less than 3.3 m deep. When the groundwater is
deeper than 3.3 m, the field capacity of the surface soil is determined by
the moisture content when the hydraulic conductivity becomes limiting and
not by the depth of the groundwater.
Overall, the present model has the advantage that it greatly simplifies the
calculation of the moisture content, groundwater depth, and salt content and,
despite that, gives results similar to or better than other models applied
in the Yellow River basin.
Conclusions
A novel surrogate field hydrological model called Evaluation of the
Performance of Irrigated Crops and Soils (EPICS) was developed for irrigated
areas with shallow groundwater. The model was tested with 2
years of experimental data collected by us for sunflower and 1 year of maize
on replicated fields in the Hetao irrigation district, a typical arid to
semi-arid irrigation district with a shallow aquifer. The EPICS model uses
the soil moisture characteristic curve, upward capillary flux, and
groundwater depth to derive the drainable porosity and predict the soil
moisture contents and salinity. The evaporative flux is calculated with
equations in EPIC (Erosion Productivity Impact Calculator) and the root
distribution equation.
The simulation results show that the EPICS model can predict the soil
moisture content and salt concentration in different soil layers,
groundwater depth, and crop growth on a daily time step with acceptable
accuracy during calibration and validation. The saturated soil moisture
content is the most sensitive parameter for soil moisture content, salt
concentration, and ET in our model.
In the future, the model should be tested in other areas with shallow
groundwater that can be found in surface-irrigated sites and in humid
climates in river plains. Once fully tested, the EPICS model can be used for
optimizing water use on the local scale but, more importantly, on a watershed
scale in closed basins where every drop of water counts.
Nomenclature.
ET0Reference evapotranspiration (mm)pFraction of readily available soil water relative to the total available soil water (–)ETPPotential evapotranspiration (mm)SSalt stress coefficient (–)EpPotential evaporation (mm)BCrop-specific parameter (%)TpPotential transpiration (mm)kyFactor that affects crop yield (–)EaActual evaporation (mm)ECeElectrical conductivity of the soil saturation extract (mS cm-1)TaActual transpiration (mm)ECethresholdThreshold of the electrical conductivity of the soil saturation extract when the crop yield becomes affectedby salt (mS cm-1)KcCrop coefficient (–)EC1:5Electrical conductivity of the soil extract that soil samples mixed with distilled water in a proportion of1:5 (mS cm-1)τDevelopment stage of the leaf canopy (–)θsSoil moisture content at saturation (cm3 cm-3)rTRoot function for transpiration (–)φbBubbling pressure (cm)rERoot function for evaporation (–)φmMatric potential (cm)jNumber of soil layer (–)λPore size distribution index (–)LAILeaf area index (–)hGroundwater depth (cm)TmeanMean daily temperature (∘C)zDepth of the point below the soil surface (cm)TmxMaximum daily temperature (∘C)Wfc(h)Total water content at field capacity of the soil profile over a prescribed depth (cm)TmnMinimum daily temperature (∘C)L(j)Height of layer j (cm)LAImxMaximum leaf area index (–)μDrainable porosity (–)RDmxMaximum root depth (cm)PPrecipitation (mm)KbDimensionless canopy extinction coefficient (–)IIrrigation (mm)PHUTotal potential heat units required for crop maturation (∘C)nNumber of soil layers (–)Z1jDepth of the upper boundaries of soil layer j (cm)RgwPercolation to groundwater (mm)Z2jDepth of the lower boundaries of the soil layer for rE(j, t); root depth or the lower boundaries of the soillayer for rT(j, t) (cm)Rw(j-1, t)Percolation rate to layer j from layer j-1 at day t (mm)δWater use distribution parameter (–)C(j, t)Salt concentration of layer j at day t (g L-1)kEWater stress coefficient for evaporation (–)CISalt concentration of irrigation water (g L-1)kTWater stress coefficient for transpiration (–)CgwSalt concentration of groundwater (g L-1)θSoil moisture content (cm3 cm-3)UgwActual upward flux of groundwater (mm)
θfcSoil moisture content at field capacity (cm3 cm-3)Ugw,maxMaximum upward flux of groundwater (mm)θrSoil moisture content at wilting point (cm3 cm-3)aConstant used for calculation of Ugw,max (–)fshapeShape factor of kT curve (–)bConstant used for calculation of Ugw,max (–)
Data availability
The observed data used in this study are not publicly
accessible. These data have been collected by personnel of the College of
Water Resources and Civil Engineering, China Agricultural University, with
funds from various cooperative sources. Anyone who would like to use these
data should contact Zhongyi Liu, Xianghao Wang, and Zailin Huo to obtain
permission.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-24-4213-2020-supplement.
Author contributions
LZ and XW collected the data. ZL, ZH, CW, GH, XX, and
TS contributed to the development of the model. The simulations with the
model were done by ZL, ZH, and TS. Preparation and revision of the paper were
done by ZL under the supervision of TS and ZH.
Competing interests
The authors declare that they have no conflicts of
interest.
Acknowledgements
Peggy Stevens helped greatly with polishing the English. We thank the technicians in the Shahaoqu experimental station who helped in collecting data.
Financial support
This research has been supported by the National Key
Research and Development Program of China (grant nos. 2016YFC0400107
and 2017YFC0403301) and the National Natural Science Foundation of China
(grant nos. 51639009 and 51679236).
Review statement
This paper was edited by Alberto Guadagnini and reviewed by
two anonymous referees.
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