Influence of Different Meteorological Factors on the Accuracy of Back Propagation Neural Network Simulation of Soil Moisture in China

Abstract

Soil moisture is one of the most critical elements of the Earth system and is essential for the study of the terrestrial water cycle, ecological processes, climate change, and disaster warnings. In this study, the training sample was selected to divide the dataset according to months from 2000 to 2018 after the advantages of three training samples were compared using a backpropagation (BP) neural network model. Furthermore, the monthly surface soil moisture in China in 2019 and 2020 was simulated based on various meteorological elements. The results demonstrate that evapotranspiration has the greatest influence on soil moisture among the various meteorological factors, followed by precipitation on a national scale throughout the year. Additionally, the accuracy of the training and simulation results with BP neural networks in the national winter months is slightly worse. In the future, the training samples of the BP neural network can be optimized following the differences in the dominant influence of various meteorological factors on soil moisture in different areas at different times to improve the simulation prediction accuracy.

1. Introduction

Soil moisture (SM) is a vital component of the earth system [1,2]. It plays a vital role in various exchange processes on the earth’s surface [3] and influences the exchange of heat, water, momentum, and chemical substances between the earth’s surface and the atmosphere. Through the upward movement of evapotranspiration (EV) and the transpiration of soil and vegetation, a large amount of SM becomes atmospheric moisture [4]. Thus, SM is the main source of atmospheric moisture [5] and the basis of plant growth [6,7,8]. It affects plant growth by affecting ventilation, temperature, nutrient transport, uptake, and transformation [9]. In terrestrial ecosystems, SM controls plant growth as the link between the biosphere and the soil zone [10]. SM is closely associated with different meteorological factors. It is a storage component of precipitation (PR) and radiation anomalies [5], influencing soil surface albedo and soil heat capacity [11], as well as climate change through latent and sensible heat transfer. Therefore, the study of SM is essential for water resources management, ecological security evaluation, the judgment of climate change trends, and meteorological disaster prediction in the context of global climate change [12,13,14]. Understanding the multiple impacts of SM and climate and its relevance to climate change projections is critical. Reducing uncertainty in future climate scenarios will be substantially aided by a better comprehension and quantification of SM-climate-related processes [5]. Using estimates of SM based on water balance models and temperature observations, Whan, K., J. et al. investigated the effect of SM on summer monthly maximum temperatures from 1984 to 2013 in Europe and revealed a negative relationship between SM and summer monthly temperatures [15]. Over the past 40 years, the total explanatory power of PR, temperature, and vegetation in the permafrost region of the Qinghai-Tibet Plateau was 51%, and the contribution rate of PR was the highest, accounting for 47.2%. Concurrently, the contribution rate of PR was over 41%, and the combined explanatory power of the three components in the seasonal permafrost area was 69.1% [14]. Surface SM in northeastern and central China and eastern Inner Mongolia exhibited a consistent trend of dryness from 1979 to 2010, while soils on the Qinghai-Tibet Plateau presented a trend of wetness. PR is the main factor responsible for these trends, controlling the direction of SM change while increasing temperature also exacerbates soil drying during periods of reduced PR [16]. Zeng et al. discovered that PR variability dominated soil wetting in typical semi-arid and typical humid areas of China after 2005, and surface-atmosphere temperature contributed more to drought in drylands [2].

The decreasing trend of SM over East Asia in the 21st century is mainly induced by decreasing PR while increasing temperature has almost tripled soil drying [17]. Cheng et al.’s analysis of the global SM trend from 1948 to 2010 demonstrated primarily negative trends in SM. Although the temperature was the primary factor in the long-term trend of SM overall, PR had a dominant influence on the variability of SM at interannual to decadal time scales for the world average [18]. Deng et al. unveiled that the global average SM in 1979–2017 decreased markedly, 65.1% of the global soil drying trend was attributed to temperature rising, and the combined effects of PR, temperature, and NDVI were responsible for 82% of the wetting trend [19].

Generally, methods for estimating SM commonly include field measurements, remote sensing measurements, and model simulation [2]. While measuring SM in the field is reliable, retrieving samples and performing laboratory measurements both demand a sizable workforce [5]. Therefore, it is difficult to obtain large-scale measured SM in a relatively short time. Remote sensing measurements can provide a large range of near-surface estimation [20]. However, both the high temporal resolution and high spatial resolution of remote sensing measurement data can hardly be satisfied simultaneously [21]. Model simulations can obtain spatially continuous and temporally complete SM estimates under certain accuracy conditions while acquiring exact associations with SM-related factors. BP neural networks are widely adopted for data fitting and prediction with their good learning ability and self-adaptive capability. BP neural networks can respond to system changes by modifying the link values of the network. It is a multi-input and multi-output structural model with the ability to adapt to multivariate control systems.

The effects of various meteorological factors on SM have been investigated. Nevertheless, there is little research on seasonal differences in meteorological factors affecting SM at a large regional scale. In this study, a BP neural network model is employed to simulate and predict SM for each month of 2019 and 2020 based on PR, EV, air temperature (AT), surface net solar radiation (SR), surface temperature (ST), and air pressure (AP) in China. First, an optimal training sample is selected for the BP neural network model to obtain the best simulation results. Then, the influence of different meteorological factors on the SM is revealed using the BP neural network. Finally, the seasonal differences in the simulation accuracy of SM across China are investigated. This study contributes to the influence of meteorological factors on SM in China and lays a scientific foundation for decision-making on disaster warning and ecological security evaluation in the context of global change.

2. Materials and Methods

2.1. Data Sources

The monthly average data of SM (0–7 cm) (m³/m³) and PR, EV, AT, SR, ST, and atmospheric pressure in China from 2000 to 2020 were obtained from ERA5-Land (https://doi.org/10.24381/cds.68d2bb30 (accessed on 15 July 2021)) of the European Center for Medium-Range Weather Forecasts (https://cds.climate.copernicus.eu/ (accessed on 15 July 2021)). ERA5-Land is a reanalysis dataset that provides a globally uniform format for multiple meteorological factors and multi-layer SM with a spatial resolution of 0.1°.

2.2. Data Processing

The initial data of SM, PR, EV, AT, SR, ST, and AP from 2000 to 2020 provided by ERA5-Land reanalysis data are all in NetCDF format, which needs to be processed and finally converted into a CSV format dataset for BP neural network training and simulation prediction. The processing flow is illustrated in Figure 1. Firstly, a MATLAB program is applied to convert the global NetCDF format files into global GeoTiff format files. Then, the mask is adopted in the ArcGIS tool to extract the GeoTiff format file of the China region. Afterward, GeoTiff format files are converted into the ACSII format file. Finally, another MATLAB program is utilized to read the data in the ACSII file and write it into a CSV file. Since the China region contains 96,028 rasters, there are 96,028 monthly data in the CSV file.

2.3. Methods

The BP neural network is a multi-layer forward neural network based on an error backpropagation algorithm (BP algorithm). It is by far the most famous multi-layer network learning algorithm and the most widely used algorithm model in an artificial neural network. A typical BP network is a feed-forward network with three layers: The input layer, hidden layer, and output layer. Its structure is exhibited in Figure 2. Some relevant variables are detailed as follows:

(1)

Suppose there are d input neurons, l output neurons, and q hidden layer neurons.

(2)

Set the threshold of the jth neuron in the output layer as θ_j.

(3)

Set the threshold of the hth neuron in the hidden layer as γ_h.

(4)

The connection weight between the ith neuron in the input layer and the hth neuron in the hidden layer is v_ih.

(5)

The connection weight between the hth neuron in the hidden layer and the jth neuron in the output layer is w_hj.

(6)

The hth neuron in the hidden layer receives input α_h from the input layer.

$${\alpha }_h={\displaystyle \sum _{i=1}^d{v}_{ih}\cdot x_i}$$

(1)

Note that the input received by the jth neuron in the output layer from the hidden layer is β_j:

$${\beta }_j={\displaystyle \sum _{h=1}^q{w}_{hj}\cdot b_i}$$

(2)

where b_h denotes the output of the hth neuron in the hidden layer.

The weight from the input layer to the hidden layer is set as v_ih, and the threshold of the hth neuron in the hidden layer is set as γ_h. The weight from the hidden layer to the output layer is set as w_hj, and the threshold of the jth neuron in the output layer is set as θ_j. In Figure 2, there are d input neurons and q hidden neurons. The hidden layer has q hidden neuron thresholds and l output neurons. Thus, there are l output neuron thresholds.

$$b_h=f({\alpha }^h-{\gamma }^h)$$

(3)

The activation functions of the hidden layer and output layer are all Sigmod functions.

In a training example (x_k, y_k), the training output of the neural network is assumed to be

$$g_{k^{\prime }}=(g_1^{k^{\prime }},g_2^{k^{\prime }},\cdots ,g_l^{k^{\prime }})$$

(4)

The output is an l-dimensional vector, where

$$g^{k^{\prime }}=f({\beta }_i-{\theta }_i)$$

(5)

In this study, the number of nodes in the hidden layer is set as 9. The monthly average data of six meteorological elements in China, such as PR, EV, AT, SR, ST, and AP, were used as the input, and the monthly average SM was used as the output. Epochs were uniformly set as 1000 iterations, the expected error goal was 0.001, and the learning rate lr was 0.01. The BP neural network sample training set, the validation set, and the test set are divided in a ratio of 7:2:1.

2.4. Data Sample

Deep learning models require a considerable number of data for training, provided that data integration and matching are required and datasets with a long-time span are used to ensure complete data features. In this paper, the SM of each month in 2019 and 2020 in China was simulated and predicted based on the relationship between the monthly average value of six meteorological elements, such as PR, EV, AT, SR, ST, AP, and SM at the corresponding time in China from 2000 to 2018.

In this paper, three sets of strategies are proposed to evaluate and select the most appropriate training samples:

• Group 1 used all the data of 12 months from 2000 to 2018 and simulated and predicted the SM of each month in 2019 and 2020 after overall training.
• Group 2 divided the data of 19 years and 12 months from 2000 to 2018 into four parts according to spring, summer, autumn, and winter. The data in March, April, and May of 19 years were used as spring data. After training, the SM in March, April, and May of 2019 and 2020 was simulated and predicted. The data of June, July, and August of 19 years were adopted as summer data. After training, the SM in June, July, and August 2019 and 2020 was simulated and predicted. The data of September, October, and November of 19 years were utilized as the autumn data. After training, the SM in September, October, and November 2019 and 2020 was simulated and predicted. The data of December, January, and February of 19 years were employed as winter data. After training, the SM in December, January, and February 2019 and 2020 was simulated and predicted.
• Group 3 divided the period from 2000 to 2018 into 12 datasets following 12 months. The January data of these 19 years were trained to simulate the prediction of SM in January 2019 and 2020, and 12 datasets were trained to simulate the prediction of SM in the 12 months of 2019 and 2020, respectively.

2.5. Performance Evaluation Measures

In this paper, the accuracy of the training set, validation set, and test set of training samples was evaluated by the Pearson correlation coefficient R, expressed as:

$$R=\frac{{\displaystyle {\sum }_{i=1}^n(x_i-{\overline{x}}_i)(y_i-{\overline{y}}_i)}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(x_i-{\overline{x}}_i)}^2{(y_i-{\overline{y}}_i)}^2}}}$$

(6)

where n denotes the total number of samples, x_i indicates the simulated value, y_i represents the verified value, ${\overline{x}}_i$ signifies the average value of the simulated sample, and ${\overline{y}}_i$ refers to the average value of the verified sample.

The accuracy of the simulated samples was evaluated by the Mean Squared Error (MSE) and R Squared (R²).

MSE is:

$$MSE=\frac{1}{n}{{\displaystyle \sum _{i=1}^n(y_{{}^i}-{\widehat{y}}_{{}^i})}}^2$$

(7)

R² is:

$$R^2=1-\frac{{\displaystyle {\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle {\sum }_{i=1}^n{(y_i-{\overline{y}}_i)}^2}}$$

(8)

where n represents the total number of samples, ŷ_i refers to the simulated value, y_i indicates the verified value, and ${\overline{y}}_i$ stands for the average value.

Partial correlation coefficients between SM and PR, EV, SR, AT, and ST are calculated as:

$$T=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \cdots \cdots & r_{1m}\\ r_{12}& r_{22}& \cdots \cdots & r_{2m}\\ ⋮& ⋮& ⋮& ⋮\\ r_{m1}& r_{m2}& \cdots \cdots & r_{mm}\end{array}\right)$$

(9)

In this paper, the sixth-order matrix T of the linear correlation coefficient between the two variables was obtained first to calculate the partial correlation coefficients between SM and PR, EV, SR, AT, and ST. With SM as an example, the linear correlation coefficients between SM and itself, PR, EV, net surface radiation, AT, and ST are r₁₁, r₁₂, r₁₃, r_1i4, r_15, and r₁₆, respectively. The inverse T⁻¹ of matrix T is expressed as:

$$T^{-1}=({c^{\prime }}_{ij})=\left(\begin{array}{cccc}{c^{\prime }}_{11}& {c^{\prime }}_{12}& \cdots \cdots & {c^{\prime }}_{1m}\\ {c^{\prime }}_{12}& {c^{\prime }}_{22}& \cdots \cdots & {c^{\prime }}_{2m}\\ ⋮& ⋮& ⋮& ⋮\\ {c^{\prime }}_{m1}& {c^{\prime }}_{m2}& \cdots \cdots & {c^{\prime }}_{mm}\end{array}\right)$$

(10)

According to the inverse matrix T⁻¹, the partial correlation coefficient can be calculated by:

$$r_{ij\cdot }=\frac{-{c^{\prime }}_{ij}}{\sqrt{{c^{\prime }}_{ii}\cdot {c^{\prime }}_{jj}}}$$

(11)

where r_ij· indicates the partial correlation coefficient between two specific variables x_i and x_j when two or more variables are fixed.

The test statistic of partial correlation analysis is the t-statistic, which is mathematically defined as:

$$t=\frac{r\sqrt{n-q-2}}{\sqrt{1-r^2}}$$

(12)

where r denotes the partial correlation coefficient, n refers to the number of samples, and q is the order. If the probability p-value of the test statistic is less than a given significance level α, the original hypothesis should be rejected.

3. Results

3.1. Selection of Optimal Training Samples

The characteristics and quantity of the BP neural network training data are the most imperative factors to determine the performance of the model. The larger the sample size, the more accurate the results. The selection of training samples of the BP neural network has a great influence on the generalization ability of the network. Particularly, selecting appropriate training samples from an enormous dataset is the key to the good or bad training effect of the model [22]. The best training samples of the model are those comprising frequently occurring features in the test data while avoiding over-selection of very frequently occurring features in the training data [23]. The correlation coefficients of the training set of BP neural network samples of the three modes are close to their corresponding validation set and test set (

Table 1. Accuracy of the six-factor sample training set, validation set, and test set.

	Sample	Training R	Validation R	Test R
Group 1	2000–2018	0.90372	0.90493	0.90331
Group 2	Spring	0.92263	0.92105	0.92074
	Summer	0.95706	0.95653	0.95676
	Autumn	0.91765	0.91655	0.91884
	Winter	0.85684	0.85747	0.85715
Group 3	January	0.86801	0.86797	0.86698
	February	0.85761	0.85869	0.85694
	March	0.90174	0.90185	0.90088
	April	0.93758	0.93359	0.93303
	May	0.95245	0.95328	0.95393
	June	0.96106	0.95165	0.95106
	July	0.95822	0.95783	0.95811
	August	0.95777	0.95639	0.95683
	September	0.95489	0.95225	0.95272
	October	0.93097	0.93003	0.93075
	November	0.90343	0.90212	0.90381
	December	0.89566	0.90046	0.89542

). The time span of the three groups of training sample data is the same, and they all use the data from 2000 to 2020. The number of training data is one of the most crucial factors to determine whether the developed model is effective, which is essential for the performance of deep learning models [24]. Group1 has the largest amount of data. Nonetheless, the accuracy after BP neural network training is not the highest. Compared to Group1, Group2 and Group3 have a much smaller number of data for training samples. The training sets for spring, summer, and autumn in Group2 and Group3 have higher accuracy after training with the BP neural network. Meanwhile, only the training sets for winter months have slightly lower accuracy. The lowest value of correlation coefficient R between Group2 and Group3 training sets and their corresponding verification and test sets is also above 0.85. The summer training set in Group2 and the training set from May to September in Group3 have a correlation coefficient R of more than 0.95 with their corresponding validation and test sets. Apart from sufficient data, the success of the deep learning process and the performance of the model are controlled by the diversity of high-quality data [25]. The data performance of Group2 is better compared to Group1, though the data volume of training samples for spring, summer, and autumn in Group2 and training samples from April to October in Group3 is much smaller than that of Group1. Similarly, the training samples in January, February, and December in Group3 are better than the winter training samples in Group2. Among the training samples of the three modes, Group3 has the best performance with a large number of data in the single monthly training sample.

Next, the SM in China in 2019 and 2020 for 12 months each year is predicted based on the three groups of training sample data. Generally, the annual variation trend of MSE and R² of the predicted and verified SM are similar. The MSE of predicted SM and verified SM obtained from the three groups of training sample data is high in January and February and then decreases gradually. It is low in June, July, and August, and then continues to increase, reaching the highest value in December (Figure 3a). In contrast to MSE, R² is low in January and February and gradually increases in spring, reaching a peak level in June, July, and August. Afterward, it gradually decreases, exhibiting a low level in December (Figure 3b).

The predicted SM in 2019 and 2020 was consistent with the annual variation trend of MSE and R² of verified SM (Figure 3a,b). The smaller the MSE, the larger the R². The training sample data of Group 1 were used for prediction, and the MSE of predicted SM and verified SM was the largest and R² was the smallest. The training sample data of Group 3 were used for prediction. The MSE of predicted SM and verified SM was the smallest, and R² was the largest. Using the training sample data of Group 2 for prediction, MSE and R² for predicting and verifying SM were in the middle. Therefore, the Group 3 training sample data constitute the best method for SM prediction.

3.2. Simulation of SM in China Based on Optimal Training Samples

In Group 3, the training samples in February had the lowest accuracy and the training samples in June had the highest accuracy. The training results for a single month of the 12 months in Group 3 were used to predict SM across the country for 12 months in 2019 and 2020. In these two years, the accuracy of the prediction results was the lowest in January and the highest in July. The R² of the prediction results in January and July 2019 was 0.702 and 0.919 (Figure 3b and Figure 4), and the MSE was 0.00638 and 0.00184, respectively (Figure 3a). The R² of the prediction results in January and July 2020 was 0.725 and 0.927 (Figure 3b and Figure 5), and the MSE was 0.00495 and 0.00173 (Figure 3a), respectively.

Subsequently, the SM in each month of 2019 and 2020 in China was simulated with the Group 3 training sample data. The simulation results suggested that the slope of the unary linear regression equation between the simulated SM value and the verified SM value in most months was greater than 1 (Figure 4 and Figure 5). Hence, most simulated SM values were greater than the verified SM value. However, the simulated values of SM at sites with high actual SM (>0.5 m³/m³) are almost less than the verified SM values throughout the year. SM has significant spatial variability [26], consistent with the national monthly SM in 2019 and 2020 (Figure 6 and Figure 7).

Furthermore, the national spatial distribution pattern of verified and simulated SM values in 2019 was compared month by month (Figure 6 and Figure 8). The simulated and verified SM values in 12 months of 2020 demonstrated a similar spatial distribution pattern (Figure 7 and Figure 9). In the middle summer of 2019 and 2020, R² was the largest, and the spatial distribution pattern similarity between simulated and verified SM values was the highest. In winter, R² was small, and the spatial distribution pattern similarity between simulated and verified SM values was slightly lower (Figure 6, Figure 7, Figure 8 and Figure 9). From the national perspective, a small part of the northern and northeastern parts of the Qinghai-Tibet Plateau has perennial SM higher than 0.5 m³/m³, ranking among the top in China. Since all of these regions have simulated SM values less than 0.5 m³/m³, the spatial distribution of simulated SM cannot reflect this local characteristic. Compared with the actual spatial distribution pattern of SM, the fragmentation degree of the simulated spatial distribution pattern of SM was considerably reduced, while the national spatial distribution pattern of the simulated and verified SM values was similar.

3.3. Effect of Different Meteorological Factors on the Accuracy of BP Neural Network Training Samples

The simulated SM in China has seasonal variations, as revealed by the relationship between SM and six meteorological factors, such as PR, EV, AT, net surface radiation, ST, and AP. Then, the accuracy of simulated SM training samples of a single meteorological factor was compared over 12 months from 2000 to 2018 to understand the differences in the effects of different meteorological factors on SM in different months. According to Table 1, the correlation coefficients of the training set and its corresponding validation set and test set are close, and only the correlation coefficients of the test set are compared (

Table 2. Accuracy of the single-factor sample training set.

Sample	PR	EV	AT	SR	ST	SP
January	0.6977	0.7240	0.6138	0.3425	0.5645	0.3966
February	0.6880	0.7391	0.5807	0.4498	0.5023	0.4006
March	0.7574	0.7963	0.4197	0.5682	0.3882	0.4142
April	0.8162	0.8429	0.3078	0.5849	0.2998	0.4275
May	0.8644	0.9105	0.1820	0.6726	0.3995	0.4073
June	0.8745	0.9008	0.3848	0.6531	0.5583	0.4080
July	0.8924	0.9203	0.4244	0.5395	0.6416	0.4717
August	0.9032	0.9301	0.3943	0.5462	0.5856	0.4648
September	0.8773	0.9140	0.3223	0.3900	0.2931	0.4264
October	0.8164	0.8663	0.4198	0.4119	0.4099	0.3686
November	0.7527	0.7894	0.5420	0.3158	0.4760	0.3932
December	0.6490	0.7375	0.6244	0.2657	0.5482	0.3933

). After training, the results of the 12-month data in this study implied that the correlation coefficient of SM simulated by EV was the largest, and the annual correlation coefficient ranged from 0.6490 to 0.9301. Furthermore, the correlation coefficient of PR-simulated SM was the largest, and the annual correlation coefficient ranged from 0.6490 to 0.9032. The correlation coefficient of SM simulated by SR in spring was also large. For example, the correlation coefficient of April was 0.5849, which was second only to the correlation coefficient of SM simulated by EV (0.8429) and SM simulated by PR (0.8162). The correlation coefficients of SM simulated by ST in summer and temperature in winter were also high.

Six meteorological factors including PR, EV, AT, SR, ST, and AP were combined pairwise. The two meteorological factors from 2000 to 2018 were employed to simulate the comparison of the accuracy of SM training samples in 2019 and 2020. Moreover, the correlation coefficient of the test set was also compared (

Table 3. Accuracy of single factor sample training set.

Sample	PR-EV	PR-AT	PR-SR	PR-ST	PR-SP	EV-AT	EV-SR	EV-ST	EV-SP	AT-SR	AT-ST	AT-SP	SR-ST	SR-SP	ST-SP
January	0.7238	0.7328	0.7133	0.7289	0.7354	0.7143	0.743	0.6807	0.6650	0.6843	0.8110	0.7099	0.7054	0.5657	0.7119
February	0.7360	0.7621	0.7667	0.7388	0.7754	0.7000	0.7453	0.6466	0.6720	0.6763	0.677	0.6495	0.6632	0.5961	0.6379
March	0.7854	0.8636	0.7689	0.8232	0.7938	0.7461	0.7765	0.7833	0.6988	0.6579	0.6971	0.5511	0.6822	0.6725	0.5296
April	0.8503	0.8453	0.8365	0.8584	0.8482	0.7860	0.837	0.8216	0.749	0.6651	0.7828	0.5617	0.6782	0.6803	0.6036
May	0.9063	0.8868	0.8806	0.8958	0.8936	0.8112	0.864	0.8562	0.7968	0.7791	0.8412	0.5905	0.8016	0.7524	0.6782
June	0.9097	0.8912	0.8848	0.9044	0.9005	0.8357	0.8805	0.8608	0.8245	0.8012	0.8399	0.6912	0.8300	0.7785	0.7873
July	0.9221	0.9062	0.8983	0.9075	0.9167	0.8826	0.8891	0.8897	0.8755	0.7375	0.8673	0.7852	0.7987	0.7611	0.859
August	0.9296	0.9225	0.9215	0.926	0.9307	0.8966	0.8971	0.9015	0.9013	0.7908	0.8622	0.7173	0.8201	0.7844	0.8082
September	0.9135	0.8943	0.8856	0.8959	0.9092	0.8784	0.8882	0.8855	0.879	0.5965	0.7873	0.5283	0.5416	0.6472	0.6046
October	0.8612	0.8488	0.8406	0.8536	0.858	0.8072	0.8419	0.8162	0.7837	0.6312	0.5035	0.5988	0.6132	0.6125	0.5847
November	0.7873	0.7961	0.7903	0.7768	0.7935	0.7908	0.7954	0.7242	0.7363	0.669	0.782	0.6896	0.6605	0.5819	0.6811
December	0.7512	0.7217	0.689	0.6937	0.7202	0.7539	0.7592	0.714	0.7442	0.6904	0.8256	0.7164	0.6789	0.5527	0.7176

). From May to October, the correlation coefficient of SM simulated by PR-EV was the largest. In March, April, and November, the correlation coefficient of SM simulated by PR-AT or PR-ST was the largest. In January and December, the correlation coefficient of SM simulated by AT-ST was the largest. From the perspective of the whole country, only second to PR and EV, SR has a relatively large impact on SM change in summer, and the temperature has a relatively large impact on SM change in winter (Table 2 and Table 3). Furthermore, the effect of AP on SM change is modest and can be ignored compared with PR, EV, AT, SR, and ST.

4. Discussion

Multi-factor uncertainty co-influences the accuracy of SM estimates [27,28,29]. SM has a complex dependence on various meteorological factors [26,30]. There is a close relationship between SM and PR [16]. The correlation coefficients between simulated and validated SM test sets of a single meteorological factor in 12 months of the year revealed that the correlation coefficient of simulated SM with evaporation was the largest, followed by the correlation coefficient of simulated SM with PR. Overall, nationwide PR and EV are the main controlling factors of SM in different regions, consistent with the research results of Meng et al. [31]. According to the correlation coefficient between the simulated and validated SM test set of combined meteorological factors, the maximum correlation coefficient of simulated SM of combined meteorological factors varied in different seasons. In other words, the main controlling factors of SM varied with the shift of seasons. The effects of summer PR on SM and winter temperature on SM were significant.

The AP factor, which has almost no influence on SM, was neglected to further elaborate on the influence of different meteorological factors on SM and to further analyze the reasons for the low accuracy of SM training and simulation in winter. The average annual changes in five meteorological factors (PR, EV, AT, SR, and ST) from 2000 to 2018 were compared with those in 2019 and 2020. SM was low in January and flat or slightly increased in February, March, and April. It fell to the lowest level in the whole year in April, increased in the following months, reached the highest level in July and August, and decreased steadily after September (Figure 10a). The annual changes of EV, net surface radiation, AT, and ST were similar. All of them were lowest in January and December in winter, increased from January to June, reached the peak of the year in June, July, and August, and declined steadily after August to winter. EV, AT, and ST lagged behind the rise of net surface radiation in spring and the fall of net surface radiation in autumn (Figure 10c–f). Compared with meteorological factors such as EV, AT, and land ST, PR was low in the winter months and high in the summer while increasing sharply after May and decreasing sharply after September. This change was significant from the average level of 2000–2018 (Figure 10b).

The BP neural network was applied to train the relationship between six meteorological elements and SM in the corresponding month over 19 years from 2000 to 2018. The training set accuracy was the lowest in January and the highest in June, and in July it was close to June (Table 1). PR, EV, AT, and ST were fundamentally the lowest in January and the highest in July (Figure 10). There was a degree of correlation between the factors affecting SM, and they were scale-dependent [28]. For example, the rising AT increased surface EV and decreased SM [18]. A partial correlation analysis of SM and five influencing factors such as PR, EV, SR, AT, and land ST in January and July from 2000 to 2020 was conducted at the pixel scale to clarify the significant differences in the influence of PR, EV, AT, SR, and ST on SM across the country in winter (represented by January) and summer (represented by January) (Figure 11). Then, the respective partial correlation coefficient (Rp) was obtained.

In January, SM was mainly positively correlated with PR, with Rp values ranging from −0.87 to 0.96. The ratio of areas with positive correlations to areas with negative correlations was 9:2. The Sichuan Basin and the middle and lower reaches of the Yangtze River were significantly positively correlated regions (Figure 11a). There was a positive correlation between SM and PR in July, with Rp values ranging from −0.89 to 0.99. The area of positive correlation area accounted for one-third of the total area of China, mainly located in the North and Qinghai-Tibet Plateau (Figure 11b). In January, SM and EV were mainly negatively correlated, with Rp values ranging from −0.99 to 0.86. The ratio of areas with positive correlations to areas with negative correlations was 1:70. North China, Northwest China, southeast China, and Southwest China were significantly negatively correlated regions (Figure 11c). In July, SM and EV were mainly negatively correlated, with Rp values ranging from −0.99 to 0.87. The ratio of areas with positive correlations to areas with negative correlations was close to 1:43. The positive and negative correlation areas were significantly compared. The areas with significant negative correlation were mainly located in the Northeast, North China, and southeast and scattered in the Northwest (Figure 11d). There was a negative correlation between SM and SR. The Rp value of partial correlation between SM and SR in January was −0.92–0.88, and the area ratio of positive correlation to negative correlation was 1:9. The regions with a significant negative correlation were primarily in the Pearl River Basin, Southwest China, and the Sichuan Basin (Figure 11e). The Rp value of SM and SR in July ranged from −0.97 to 0.94, and the area with a negative correlation was one-fifth of the total national area. The area with a significant negative correlation was primarily in the eastern region (Figure 11f). The partial correlation between SM and AT in January was mainly positive, with Rp values ranging from −0.9 to 0.92. The area ratio of positive correlation to negative correlation was 3:1. The significantly positive correlation dominated in the central South and Qinghai-Tibet Plateau (Figure 11g). In July, SM and AT were mainly negatively correlated, with Rp values ranging from −0.96 to 0.92. The ratio of areas with positive correlations to areas with negative correlations was 1:3, and significant negative correlations were mainly observed in North China, Southwest China, and part of the Qinghai-Tibet Plateau (Figure 11h). The partial correlation between SM and land ST in January was mainly negative. The Rp value of partial correlation was −0.97–0.93. The area ratio of positive correlation to negative correlation was 1:4, and a significant negative correlation appeared in the southern part and the Qinghai-Tibet Plateau (Figure 11i). The Rp value was −0.94−0.94. The ratio of areas with positive correlations to areas with negative correlations was close to 1:1, and the areas with significant negative correlations were in the Northeast and Northwest (Figure 11j). On the whole, PR was mainly positively correlated with SM, while EV, SR, and temperature were negatively correlated with SM, consistent with the research results of Cho et al. [32].

The strongest partial correlation coefficients in January suggest that EV plays a dominant role in SM changes nationwide at the pixel scale, EV plays a dominant role in north, northwest, southeast, and southwest China, SR plays a dominant role in south-central China, and PR plays a dominant role in the Sichuan basin and parts of the middle reaches of the Yangtze River. The area ratio of PR, EV, SR, AT, and ST for the dominant role of SM is approximately 10:56:17:7:16 nationwide. The area of the region with a significant bias correlation between SM and the five meteorological factors accounts for approximately 55% of the total area of the country, and the area of the region with a significant bias correlation with PR and EV accounts for approximately 34% of the total area of the country (Figure 12a). PR in July plays a dominant role in SM changes nationwide at the pixel scale, a mixture of PR and EV plays a dominant role in the northern, western, and southwestern regions, a mixture of EV and SR plays a dominant role in the northeastern region, and the dominant role of SR is evident in most of the southern regions except the southwest. The area ratio of PR, EV, SR, AT, and ST to SM was approximately 10:9:6:1:1, the area with a significant bias correlation between SM and the five meteorological factors occupied approximately 84% of the total area of the country, and the area with significant bias correlation between PR and EV accounted for approximately 58% of the total area of the country (Figure 12b).

Among the five meteorological factors (PR, EV, SR, AT, and ST), PR and EV had a mixed dominance on the effect of SM (Table 2 and Table 3). However, the results of the partial correlation analysis revealed that EV dominated the effect of SM in winter. Commonly, high EV led to a significant reduction in surface SM [33]. In winter, the ST was higher than the AT, and the soil water EV was impacted by the ST [34]. Simultaneously, the effective amount of PR was minor, resulting in a low SM. Compared with summer, the area of SM nationwide with a significant bias correlation either with PR and EV or with five meteorological factors was considerably lower than that of summer. As a result, the accuracy of training data and the prediction effect in winter were lower compared to summer when the national SM was simulated by the BP neural network model.

5. Conclusions

In this paper, the SM for each month of 2019 and 2020 was simulated and predicted using the BP neural network trained on the relationship between monthly averages of six meteorological elements (including PR, EV, AT, net radiation, ST, and barometric pressure) and SM at the corresponding time for the whole country from 2000 to 2018. Generally, the spatial distribution pattern of simulated and verified SM values was similar. However, the degree of fragmentation of the simulated spatial distribution pattern of SM was considerably reduced compared with the verified spatial distribution pattern of SM.

The results suggested that the SM was affected by numerous meteorological factors, among which EV was most closely correlated. The atmospheric pressure was scarcely correlated with the SM changes. The SM was positively correlated with PR and negatively correlated with EV, SR, and temperature. When the BP neural network was employed to simulate SM for 12 months, the accuracy of training and simulation results in summer was high, while it was slightly worse for winter. The area with a significant partial correlation between SM and five meteorological factors such as PR, EV, SR, AT, and land ST in summer accounted for approximately 84% of the total area of China, while it reached 55% in winter. As a result, the accuracy of the BP neural network simulation of SM in winter was lower than that in other seasons.

To summarize, there was spatial variability not only in SM but also in the dominant meteorological factors influencing SM. Although the accuracy of the BP neural network simulating SM across the country in winter was slightly lower, the results of the BP neural network simulating SM variation in China throughout the year were acceptable. In the future, the training samples of the BP neural network should be optimized according to the difference in the influence of various meteorological factors on soil moisture in different regions at different times, so as to improve the simulation effect.