1. Introduction
Maize is one of the most important food crops and forage grains worldwide [
1]. In 2021, China planted more than 43.33 million ha of maize and produced more than 272.55 million tons [
2]. Therefore, ensuring stable maize production is crucial. Soil moisture in the root zone is the primary source of water required for maize growth [
3]. The authors of [
4] showed that soil moisture stress can lead to more than 10% yield reductions in maize, which seriously threatens food security. Ensuring proper soil moisture in the root zone of maize plays a decisive role in the growth and final yield of the crop [
5]. Soil moisture in the root zone is a benchmark parameter for calculating the soil storage in the planned infiltration layer. Predicting soil moisture in the root zone in advance allows farms to plan the appropriate irrigation times and amount of irrigation, reduce the impact of meteorological disasters, and reduce the total amount of irrigation water [
6]. Therefore, examining moisture prediction models at different depths in the root zone of crops is essential for irrigation decision-making and agricultural water conservation.
Existing studies on soil water content simulations in the root zone of crops can be divided into mechanistic models based on the physical laws of water transport and machine learning models based on data characteristics. Machine learning soil moisture prediction methods represented by deep learning models are emerging areas of research [
7,
8,
9]. However, the high cost (data acquisition), computing power (model training), and threshold (model building) required for deep learning limit its application in soil water content (SWC) prediction [
10]. The SWC mechanism prediction model is different from the machine learning model, which is based on the soil–plant–atmosphere continuum (SPAC) theory and considers the effects of evapotranspiration, root uptake, rainfall, groundwater, runoff, and other factors on the soil moisture content in the root zone, thus achieving predictions of soil moisture by simulating soil water transport [
11]. Soil moisture simulations using mechanistic models usually require only a few accurately set key model parameters to achieve long time horizons and multi-depth soil profiles [
12]. Therefore, simulating soil moisture transport at a relatively low cost is possible. Various mechanistic models have been proposed for soil moisture simulations. For example, the FAO developed a “crop-water” productivity model, AquaCrop, in 2009, which simulates the yield response of herbaceous crops to water by combining the water consumption characteristics, irrigation systems, and environmental evapotranspiration in different growing periods to simulate the temporal variation in soil moisture content [
13]. Additionally, soil water simulation models have been developed based on different soil water dynamics models, including APSIM [
14], EPIC [
15], LEACHM [
16], SWAP [
17], and DSSAT [
18]. However, similar to the AquaCrop model, these models focus more on moisture-driven crop response problems and require more crop parameter configurations.
Hydrus is a numerical model developed by the USDA Saline Soil Laboratory to simulate water, solutes, and heat transport in unsaturated matrices. It is a finite-element computational model that uses soil hydraulic parameters to simulate water, heat, and solute transport in unsaturated soils [
19]. Hydrus includes several modules for water transport, solute transport, thermal transport, and root uptake, as well as parameter optimization algorithms for the inverse solution estimation of head and solute transport parameters for various soils. The flexibility in handling a wide range of boundary conditions allows Hydrus to be one of the most highly used models to simulate changes in SWC [
12]. The Hydrus-1D model uses the Richards equation to simulate the vertical transport of soil moisture in a one-dimensional unsaturated zone; the Galerkin finite element method was used to solve the values of the equation via spatial discretization of the soil profile, which is performed in an implicit difference format applicable to the simulation of soil moisture in the root domain of field crops under rainfed or sprinkler irrigation environments [
20].
Currently, the Hydrus-1D model is widely used to examine water recharge transport and water balance in agricultural soils (mainly surface infiltration, soil evaporation, transpiration, and deep seepage) because it requires fewer parameter configurations and yields satisfactory simulation results [
12]. Several studies have evaluated the simulation accuracy of the Hydrus-1D model in different environments. The authors of [
21] evaluated the performance of the Hydrus-1D model for simulating soil moisture in irrigated winter wheat under different water management conditions in the semi-arid zone of Morocco, with a mean simulated root mean squared error (RMSE) of approximately 3%. The authors of [
22] reported a soil moisture simulation RMSE of below 9% for a typical horticultural cropping system for watermelon cultivation in southern Italy using the Hydrus-1D model. Additionally, an increasing number of studies have used Hydrus-1D simulations as true values to analyze other critical indicators derived from soil moisture changes. In [
23], the authors simulated SWC changes in mature citrus orchards in southern China based on the Hydrus-1D model to analyze seasonal water deficit phenomena and demand. The authors of [
24] combined Hydrus-1D with geographic information systems to assess the impact of climate change on soil salinity and irrigation management. In [
25], the authors simulated irrigation scheduling thresholds based on the multi-depth soil field water holding capacity with Hydrus-1D in Alabama, USA. The authors of [
26] used the APSIM and Hydrus-1D models to predict the effects of climate change on the soil moisture dynamics of summer maize between 1981 and 2089, concluding that climate change has shortened the growing season of summer maize by 12 to 27 days. Many studies have directly used the physical Hydrus-1D model to generate large spatial–temporal vertical soil moisture datasets for deep learning model training and validation owing to limited regional soil moisture observation data, especially in large-scale SWC estimation studies combined with remote sensing technology [
27,
28,
29,
30].
Determining the appropriate soil hydraulic parameters for the van Genuchten equation is key to achieving accurate and effective simulations with the Hydrus-1D model [
12]. Previous studies have used three main methods to obtain hydrodynamic soil parameters in the Hydrus-1D model: (1) obtaining default parameters derived from relevant studies based on soil texture types [
31]; (2) predictions by sampling the mechanical composition of the soil, including the proportion of the grain size (sand, powder, and clay), soil field water holding capacity, and bulk density soil parameters [
32]; and (3) an inverse solution for historical data (soil moisture and meteorological processes) based on the built-in Levenberg–Marquardt estimation method to derive key soil hydrodynamic parameters [
33]. Existing Hydrus-1D model studies, in which soil hydrodynamic parameters are obtained, are predominantly based on methods (2) (requiring field excavation of soil samples and laboratory measurements) [
34] and (3) (requiring the consumption of at least one planting cycle of actual measurements for an inverse solution) [
33], whereas method (1) is mainly used in studies where the complete acquisition of actual measurements is complex, such as large-scale studies [
35]. However, existing studies have typically chosen one of these approaches as the basis for model runs; only some studies have comparatively assessed the effects of different hydrodynamic soil parameter acquisition approaches on soil moisture simulations in the maize root zone.
Additionally, with the rapid development of remote sensing technology, satellite data can be used to obtain SWC and meteorological information on a large scale. For example, the SMAP satellite can provide soil moisture content information in the soil profile, which is one of the most widely used SWC data sources [
36,
37]. However, the SMAP data return period was seven days: the provided SWC was a relative value of the volumetric water content (ratio of the absolute SWC to field water holding capacity), such that it is challenging to use SMAP data for the inverse solution of the parameters in the Hydrus-1D model [
38]. Reanalysis data can obtain historical meteorological, soil, and crop data with an accuracy similar to that of in situ ground monitoring by assimilating information from ground station observations, satellite remote sensing, and numerical model simulations [
39]. The ERA5-Land reanalysis dataset produced by the European Center for Medium-Range Weather Forecasts (ECMWF) provides hourly historical reanalysis data for more than 50 indicators, including environmental meteorology and soil moisture, with a high degree of consistency in the data-production process [
40]. Meanwhile, the new generation of cloud-based planetary scale platforms for Earth science data and analysis applications, represented by the Google Earth Engine (GEE), has made access to reanalysis data more convenient [
41]. Reanalysis data can be used in place of historical measured data for the inverse solution of the hydrometric parameters in the Hydrus-1D model. Considering the more complex process of field soil extraction for measuring soil parameters, the use of remote sensing data reduces the cost of data acquisition while expanding the volume of historical data. Therefore, it is novel to introduce remote sensing and reanalysis data for Hydrus-1D model parameter optimization and to compare the effects of different soil hydrodynamic parameter inverse solutions. Related findings can contribute to applying the Hydrus-1D model on a global scale and with a unified framework.
The objective of the study was to assess the feasibility of using “low-cost” multi-source remote sensing and reanalysis data for parameter optimization of the Hydrus-1D model and conduct a comparative analysis with various typical approaches. Two spring maize crops were grown in 2021 and 2022 at the Tongzhou base of the Maize Research Institute, Beijing Academy of Agricultural and Forestry Sciences, China. We collected meteorological, soil, and crop data during the corn growing period and analyzed the soil moisture and evapotranspiration characteristics during maize growth. Five typical methods for soil hydrodynamic parameter acquisition in the Hydrus-1D model were selected to analyze the boundary flux characteristics of the model simulation results and the effect of differences in the parameter acquisition methods on the accuracy of the multi-depth SWC simulations from three perspectives: overall root zone, growth stage, and soil depth.
2. Methods
This study aimed to evaluate differences in the accuracy of SWC simulations in the Hydrus-1D model using different methods for soil hydraulic parameter acquisition (
Figure 1). By conducting experiments with two corn crops, we collected data on the meteorological environment, soil moisture, crop growth, and soil parameters of the planted fields. The daily potential evapotranspiration, daily potential evapotranspiration, daily potential transpiration rate, and daily leaf area index (LAI) were used as necessary inputs for the simulation of the SWC in the Hydrus-1D model based on the measured data, and then the characteristics of SWC variation and soil water depletion in the root zone profile. Meanwhile, the historical remote sensing dataset was introduced through the GEE platform to obtain the meteorological environment, SWC, and LAI change process for the same period from 2015 to 2019 in the planting field to extend the historical dataset. The soil hydraulic parameters obtained by the five approaches were substituted into the Hydrus-1D model and simulated for each sample. The variation characteristics of the boundary fluxes in the root zone were analyzed to evaluate differences in the simulation accuracy from three perspectives: overall root zone, growth stage, and soil depth.
2.1. Hydrus-1D Model
The Hydrus-1D model has a modular design with a preprocessing section for configuring the base parameters, an execution section for carrying out iterative modeling of soil water transport, and a post-processing section providing run results and process information (
Figure 2). The model was set up sequentially to progressively configure the model parameters and adjust the subsequent parameter options according to differences in the settings. The core of this study focused on the configuration of the soil hydrodynamic parameters within the water flow module of the preprocessing session. The SWC variation in the maize root zone was simulated by substituting the soil hydrodynamic parameters obtained in different manners. Six observation points at depths of 10, 20, 30, 40, 50, and 60 cm in the soil profile were set up to output the simulation results. By default, the Hydrus-1D model uses centimeters as the base unit of measurement for the input/output. To facilitate comparison, we converted the output results to millimeters as the base unit for analysis and discussion in the Results section. The remaining modules were configured using the parameters recommended by similar studies or the Hydrus-1D model.
Soil moisture in the inclusion zone mainly undergoes one-dimensional vertical soil moisture transport. Therefore, the Richards equation [
42] was used to calculate the soil moisture variation in the vertical profile (the axes are positive downward):
where
is the specific water capacity (cm
–1),
is time (d),
is the soil hydraulic conductivity (cm/d),
is the pressure head (cm),
is the vertical soil depth coordinate (cm), and
is the soil root water uptake rate (cm/d).
The soil moisture characteristic curves were fitted using the van Genuchten model in the Hydrus-1D model [
43]:
where
is the saturated water content (cm
3/cm
3);
is the residual water content (cm
3/cm
3);
,
, and
are empirical shape factors in the water retention function;
is the saturated hydraulic conductivity (cm/d);
is the shape factor (pore connectivity parameter) in the hydraulic conductivity function; and
is the relative saturation,
.
This study focused on six key soil hydraulic parameters in the van Genuchten model: saturated water content (, cm3/cm3), residual water content (, cm3/cm3), saturated hydraulic conductivity (, cm3/d), the inverse of inlet suction (, cm–3), pore size distribution index (, n > 1), and soil pore connectivity parameter ().
The potential evapotranspiration of the crop (
) was calculated using the Penman–Monteith (P–M) equation recommended by the FAO [
44]. Here,
denotes the potential evapotranspiration rate (mm/day), expressed as follows:
was calculated as follows [
45]:
where
is the leaf area coefficient (m
2/m
2) and
is the dimensionless plant canopy radiation attenuation coefficient (0.4) [
46].
The root water uptake rate can be expressed as the volume of water consumed per unit volume of soil per unit of time. Hydrus-1D uses the Feddes model to simulate the root uptake rate process [
47], expressed as follows:
and
where
is the water stress response function (dimensionless),
is the standardized root water uptake distribution function (dimensionless),
is the potential crop transpiration rate (cm/d),
and
are the soil water potential at which the root water uptake rate decreases from 1 cm and decreases to 0 cm, respectively.
The crop root water uptake rate was more sensitive to the SWC. Crops can more easily uptake soil water between the soil capillary break water content and the field water holding rate. Crop uptake of soil water is more difficult when the SWC is between the wilting point and soil capillary rupture water content. The parameters of the maize root water-uptake configuration provided by the Hydrus-1D model were chosen for this study [
48].
Table 1 lists the details of the maize root water uptake rate parameters.
In this study, days were used as the units of the prediction time step. The surface soil of the corn plantation plots was directly exposed to air, and standing water was not produced during rainfall. Therefore, the upper boundary condition was chosen as the atmospheric boundary condition with a surface layer with crop cover:
where
is the maximum potential evaporation or infiltration rate under the current atmospheric conditions,
is the maximum allowable surface pressure head under the existing soil conditions, generally set to 0,
is the minimum allowable surface pressure head under the current soil conditions, as obtained from the equilibrium conditions between the water vapor and soil water in the atmosphere, and
was calculated as follows:
where
is the air humidity,
is the mass of water molecules, usually set as
= 0.018015 kg/mol,
is the acceleration due to gravity (
= 9.81 m/s
2), and
is the universal gas constant [
= 8.314 J/(kg·K)].
The groundwater at the corn plantation plot was deep without groundwater recharge; the plot envelope was in a free drainage state. Therefore, the lower boundary condition of the Hydrus-1D model adopted free drainage.
2.2. Methods for Obtaining Soil Hydraulics Parameters
This study referred to the method used to obtain the soil hydraulic parameters for the Hydrus-1D model in existing studies. Three main acquisition methods were used: default parameters for soil types, predictions from soil mechanical parameters, and inverse solutions from historical data. Five typical soil hydraulic parameter acquisition methods were designed, considering the convenience and cost of parameter acquisition (
Figure 3). The estimation of the soil hydraulic parameters using the soil mechanical composition was implemented using a neural network prediction module [
32]. This module has a built-in Rosetta transformation dynamic link library (dll) developed by the U.S. Salinity Laboratory [
49] based on a neural network approach to estimate soil water retention. Five typical soil hydraulic parameters were obtained using the following methods.
Default soil hydrodynamic parameters (DSHP) were used to determine the soil texture type. Based on the results of [
31], the Hydrus-1D model provided the average soil hydrodynamic parameters for 12 soil texture types as optional default parameters. The soil texture in the root zone of maize in the different years in this study was clay loam (
Table 2).
Neural network prediction using three soil mechanical composition parameters (NNP3). Soil particle size ratios (ratios of sand, silt, and clay particles; %) were used to estimate five soil hydraulic parameters (, , , α, and ) for each soil depth. The soil pore connectivity parameter () was set to the default value of 0.5.
Neural network prediction using five soil mechanical composition parameters (NNP5). Five soil hydraulic parameters (, , , α, and ) were estimated for each soil depth using the soil particle size ratio (ratio of sand, silt, and clay particles; %), soil field water capacity (SWC at 33 kPa; %), and soil bulk density (g/cm3) as inputs. The soil pore connectivity parameter () was set to 0.5.
Inverse solutions from measured historical data (ISHD). We selected all measured data (meteorological, soil moisture, and LAI) from the JKT363 plot during the growth period for the inverse solution of the six soil hydraulic parameters (
,
,
, α,
, and
). The initial values of each parameter were set to the default values for the clay loam soil texture. The inverse solution module of Hydrus-1D allows the optimization of a maximum of 15 parameters; simultaneous optimization of excessive parameters is not recommended [
50]. A hierarchical approach was used to optimize the parameters. The soil depths were optimized from shallow to deep in the order of six parameters for that layer depth; the default parameters were replaced with the optimized parameters.
Inverse solution from historical remote sensing data (ISRS). This process was the same as that of the historical data inverse solution process. Remote sensing data were used instead of measured historical data for inverse parameter solutions. This is because the division of the soil depth in the reanalysis data is difficult to match with that of the SWC sensor. We regarded the depth of 0–100 cm as a whole. Only one inverse solution was performed for each year of remote sensing data.
2.3. Model Evaluation Metrics
As suggested by [
51], three classic error indicators were chosen to evaluate the accuracy of the model to facilitate a comparison of the simulation accuracy of the Hydrus-1D model in different studies.
The mean absolute error (
MAE):
The mean squared error (
MSE):
The root mean squared error (
RMSE):
In the above formulas, is the predicted value, is the true value, and is the average value. The MAE reflects the actual situation of the predicted error value. The MSE is the expected value of the square of the difference between the estimated and observed values, which can evaluate the degree of change in the data. The smaller the MSE value, the better the accuracy of the prediction model. The RMSE is the arithmetic square root of the MSE.
2.4. Model Implementation and Analysis
Version 4.17 of the Hydrus-1D model was used in this study. This version of the software can be downloaded and used for free from the Hydrus website (
https://www.pc-progress.com, accessed on 10 August 2021). Origin Pro (version 2022a) was used for data analysis and graphing; SPSS Statistics 24.0 was used for LAI function fitting. The Anaconda platform was used as the base platform for evaluating the accuracy of the simulated data. The underlying Python version was 3.7.
6. Conclusions
In this study, to evaluate the feasibility of using remote sensing data to optimize hydrodynamic soil parameters in the Hydrus-1D model, five types of soil hydrodynamic parameter acquisition methods were designed for a comparative evaluation from three parameter acquisition categories: parameters based on soil type default (DSHP), parameters based on soil mechanical composition prediction (NNP3 and NNP5), and parameters based on inverse solutions of historical data (ISHD and ISRS). Two crops of spring maize were planted in 2021 and 2022 at the Tongzhou base at the Maize Research Institute, Beijing Academy of Agricultural and Forestry Sciences, Beijing, China. Meteorological, soil, and crop data were collected during the maize-growing season. The boundary flux characteristics of the model simulation results were analyzed, and the accuracy differences in the five parameter acquisition methods were compared from three perspectives: overall root zone, growth stage, and soil depth. The results showed that (1) evapotranspiration was the main method for soil water depletion in the root zone of maize; the total actual evapotranspiration accounted for 68.26 and 69.43% of the total precipitation in 2021 and 2022, respectively, of which the root water uptake accounted for approximately 62.64% of the total actual evapotranspiration. (2) The accuracy of the SWC simulations in the root zone for different approaches were all acceptable in the following order: NNP5 (RMSE = 5.47%) > ISRS (RMSE = 5.48%) > NNP3 (RMSE = 5.66%) > ISHD (RMSE = 5.68%) > DSHP (RMSE = 6.57%). The ISRS approach based on remote sensing data achieved almost the best performance while effectively reducing the workload and cost. (3) The accuracy of the SWC simulation for different growth stages was ranked as follows: seedling stage (MAE = 3.29%) > tassel stage (MAE = 4.68%) > anthesis maturity stage (MAE = 5.52%). (4) The SWC errors simulated by all methods tended to decrease with increasing soil depth, whereas the ISHD method, based on measured historical data, achieved the best performance at a depth of 60 cm (MAE = 2.8%). Additionally, the results of the Pearson correlation analysis between each indicator (meteorology, soil, and crop) and MAE showed that the daily order of maize after planting (DOY) had the highest correlation with the MAE (R = 0.42), reflecting the time-cumulative nature of the model simulation errors.
However, there are still some limitations to this study in terms of soil texture complexity, crop species, and model optimization. In future studies, we will continue to enrich the diversity of the soil and crop species coverage in planting plots to obtain more widely representative results. At the same time, we will further expand the evaluation range and combination mode of remote sensing data sources; for example, other studies [
61] have pointed out that the GLDAS-2.1 reanalysis dataset released by NASA has a better SWC correlation than ERA5-Land in some arid regions of China. This can be used for the parameter inverse solution of the Hydrus-1D model. Additionally, [
33] pointed out that the Feddes model in the Hydrus-1D model is deficient for the fine simulation of dynamic crop growth processes. Studies have been conducted to couple crop models, such as DSSAT [
35] and AquaCrop [
68], with the Hydrus-1D model to achieve more accurate SWC simulation via crop models for enhancing the simulation accuracy of water uptake and Tp in the root zone of crops. Improving model simulation accuracy is also an important area for future research.