A Downscaling Method of TRMM Satellite Precipitation Based on Geographically Neural Network Weighted Regression: A Case Study in Sichuan Province, China

Abstract

Spatial downscaling is an effective way to improve the spatial resolution of precipitation products. However, the existing methods often fail to adequately consider the spatial heterogeneity and complex nonlinearity between precipitation and surface parameters, resulting in poor downscaling performance and inaccurate expression of regional details. In this study, we propose a precipitation downscaling model based on geographically neural network weighted regression (GNNWR), which integrates normalized difference vegetation index, digital elevation model, land surface temperature, and slope data to address spatial heterogeneity and complex nonlinearity. We explored the spatiotemporal trends of precipitation in the Sichuan region over the past two decades. The results show that the GNNWR model outperforms common methods in downscaling precipitation for the four distinct seasons, achieving a maximum R² of 0.972 and a minimum RMSE of 3.551 mm. Overall, precipitation in Sichuan Province exhibits a significant increasing trend from 2001 to 2019, with a spatial distribution pattern of low in the northwest and high in the southeast. The GNNWR downscaled results exhibit the strongest correlation with observed data and provide a more accurate representation of precipitation spatial patterns. Our findings suggest that GNNWR is a practical method for precipitation downscaling considering its high accuracy and model performance.

1. Introduction

High-resolution precipitation data play a crucial role in various fields, including meteorological forecasting, climate research, water resource management, agriculture, ecology, disaster monitoring and prevention, urban planning and construction, and energy production [1,2]. In recent years, the frequency of extreme weather events and natural disasters has increased. Accurate and detailed precipitation data are now essential for human response to these disasters [3].

With the rapid development of remote sensing technology, existing meteorological satellite precipitation data have been widely utilized due to their wealth of information and convenient acquisition methods [4]. However, remote sensing satellite precipitation products are usually designed for global large-scale purposes. As research in hydrology, meteorology, and ecological environment advances, the resolution of such data struggles to support small-scale and refined research. Spatial downscaling methods have become an important research focus in the remote sensing field, aiding researchers in obtaining higher-resolution data in related fields [5]. Presently, three commonly employed downscaling methods exist: the simple downscaling method, dynamic downscaling method, and statistical downscaling method [6]. Among these, the simple downscaling method, also referred to as interpolation scaling, primarily reduces scaling by interpolating feature points individually [7]. However, due to the uncontrollable error of single-point interpolation, this method has similar challenges as ground monitoring precipitation data, namely, its inability to fully describe the terrain of the study area and its lack of spatial representation in complex terrain areas. The dynamic method’s downscaling model faces limitations in its application due to its high computational cost and inconvenient configuration [8]. The statistical downscaling method mainly utilizes various statistical techniques to establish mathematical relationships between meteorological factor variables at large and regional scales, aiming to enhance the resolution of remote sensing data [9]. Compared to the dynamic downscaling method, this approach requires fewer computing resources, is simpler to operate, has broader applicability, and has greater flexibility. The key to ensuring the effectiveness of precipitation downscaling is addressing the spatial heterogeneity and complex nonlinearity within the regression relationship between precipitation and related geographic factors. [10]. Previous studies have demonstrated that constructing a downscaling regression model of the tropical rainfall measurement mission (TRMM) precipitation data based on normalized difference vegetation index (NDVI) data can improve the resolution of regional TRMM precipitation data to 1 km [11]. By establishing multiple linear regression (MLR) models between TRMM and NDVI and digital elevation model (DEM), precipitation data with a 1 km resolution can be obtained. [12]. Some scholars have incorporated slope direction and the local Moran index, based on NDVI, DEM, slope direction, latitude, and longitude to develop a downscaling model of TRMM precipitation data using statistical regression methods, enabling an increase in the resolution of TRMM precipitation data to 100 m [13,14]. The commonly used algorithmic models include geographically weighted regression (GWR) and multi-scale geographically weighted regression (MGWR). Some researchers have also utilized various machine learning algorithms for precipitation downscaling, such as the random forest (RF) algorithm and XGBOOST [15,16].

Although these statistics-based methods are widely used, they each have their drawbacks. Traditional statistical models struggle with nonlinear problems, while machine learning models face challenges in addressing local spatial non-stationarity, leading to unsatisfactory model accuracy and visual effects [17,18]. In small areas and refined studies, the demand for spatial details increases, making the regression relationship between precipitation and related geographic factors increasingly complex. Consequently, a higher accuracy of regression results is required [19,20]. Therefore, there is an increasing urgency to develop new operational models capable of handling spatial non-stationarity and complex nonlinearity in precipitation regression statistics, to obtain high-precision and high-resolution precipitation data.

The GNNWR model proposed by Wu et al. [21] recently utilized a spatially weighted neural network (SWNN) to replace the kernel function of GWR. This model can simultaneously handle spatial heterogeneity and complex nonlinear problems in regression relationships and has shown better fitting accuracy and prediction performance compared to GWR and neural network models. The application of the GNNWR model to the study of precipitation downscaling in complex spaces provides a new solution to improve the accuracy of precipitation downscaling and enhance the spatial details of downscaling data. Our objective is to construct a high-resolution precipitation downscaling model based on GNNWR and demonstrate its superiority. We took TRMM satellite precipitation data as an example, regarded them as independent variables, and chose DEM, slope, NDVI, and land surface temperature (LST), which have complex relationships with precipitation, as covariates to accurately capture the spatial heterogeneity and nonlinear characteristics of precipitation and multi-factor regression relationships, thereby obtaining a high-precision precipitation dataset suitable for small-area research [22,23,24,25]. Additionally, we quantitatively compared the downscaling accuracy of RF, GWR, and MGWR algorithms in different spatiotemporal environments and the visual effects of the downscaling results of each model. Furthermore, as an example, we verified GNNWR downscaling results based on measured site data and compared them with other precipitation datasets of the same resolution, highlighting the downscaling ability and effectiveness of GNNWR. In summary, this study aims to illustrate, from various angles, that the proposed GNNWR model provides high availability and accuracy for precipitation downscaling, as well as high rationality and practicality.

2. Data and Methods

2.1. Study Area

Sichuan Province is located in southwest China, between 92°21′~108°12′ east longitude and 26°03′~34°19′ north latitude. It stretches approximately 1075 km long from east to west and 900 km wide from north to south. The province shares borders with Chongqing to the east, Yunnan and Guizhou to the south, Tibet to the west, and Shaanxi, Gansu, and Qinghai provinces to the north. Its elevation ranges from 187 m to 7435 m, with higher terrain in the west and lower terrain in the east, and it is divided into three main regains: Sichuan Basin, northwest Sichuan Plateau, and southwest Sichuan Mountain. The landform of Sichuan Province is mainly mountainous, consisting of four landforms types: mountains, hills, plains, and plateaus [26]. It is also an important intersection and transportation corridor to connect South China and Central China, connect Southwest China and Northwest China, and communicate with Central Asia, South Asia, and Southeast Asia. The climate in the province is warm and humid, belonging to the subtropical humid monsoon climate. The total amount of precipitation varies greatly from season to season. Summers are rainy with plenty of precipitation, while winters are rainy. The vegetation is mainly subtropical evergreen broad-leaved forest [27]. The geographical location and distribution of precipitation stations in Sichuan Province are shown in Figure 1:

2.2. Experimental Data

In this study, NDVI, LST, DEM, and slope, which are closely related to precipitation, were selected as explanatory factors to include in building downscaling models. The experimental data are shown in

Table 1. Details and sources of each factor.

Factor Name	Variable Name	Temporal Resolution	Spatial Resolution	Data Source
Normalized difference vegetation index	NDVI	monthly	250 m	MOD13Q1
Land surface temperature	LST	monthly	1 km	MOD11A2
Digital elevation model	DEM	/	90 m	SRTM3 DEM
Slope	Slope	/	90 m	SRTM3 DEM
Precipitation	PR	monthly	0.25°	TRMM 3B43

, which mainly include the data name, variable name, temporal resolution, spatial resolution, and data source.

(1)

TRMM precipitation data

The TRMM is a remote sensing satellite jointly developed by NASA, the United States National Space Administration, and NASDA of Japan. Equipped with three precipitation sensors, including the TRMM microwave imager (TMI), precipitation radar (PR), and visible and infrared scanner (VIRS), it enables accurate acquisition of global precipitation data [28].

In this paper, TRMM3b43 monthly precipitation figures were obtained from NASA’s website (https://search.earthdata.nasa.gov, accessed on 1 January 2001 to 12 December 2019), the temporal resolution was scaled, with a spatial resolution of 0.25 ° × 0.25 °, and the required time series was from 2001 to 2019. TRMM data were downloaded in NetCDF format, and the preprocessing mainly included NC to TIFF, projection conversion, clipping, monthly precipitation calculation, and resampling.

(2)

DEM and Slope

The relationship between topography and precipitation is closely intertwined, exerting influence not only on the generation of precipitation but also on its spatial distribution [29]. The DEM enables the digital representation of ground topography using limited terrain elevation data. In this study, we utilized the SRTM3 DEM dataset published in China, which has a spatial resolution of 90 m. The elevation datasets with spatial resolutions of 0.25° and 1 km underwent preprocessing steps, including clipping, projection, spatial alignment, and resampling. Subsequently, slope data were derived from the DEM dataset.

(3)

NDVI

The NDVI is a metric derived from multi-spectral remote sensing data, used to monitor the growth of surface vegetation. The growth of vegetation is significantly impacted by precipitation. In this study, NDVI serves as an indicator to demonstrate the influence of precipitation on the surface vegetation cover and growth status, with higher NDVI values typically corresponding to higher precipitation levels. The calculation formula for NDVI is as follows:

$$NDVI=\frac{NIR-RED}{NIR+RED}$$

(1)

The NDVI index value ranges from −1 to 1, with NIR representing the reflectance of the near-infrared band and RED representing the reflectance of the red band. A higher NDVI value indicates greater vegetation cover and better growth. Negative values typically indicate water bodies, and values close to 0 may suggest bare soil or very low vegetation cover, while values close to 1 signify dense green vegetation [30].

(4)

LST

The LST reflects the state of land surface energy balance and is closely related to surface evaporation (including plant transpiration and soil evaporation). Because heat is consumed by evaporation, regions with better water conditions generally exhibit lower LST values. This relationship makes LST an important indicator for understanding and inferring surface water conditions, and thus an indicator of the spatial distribution and intensity of precipitation [31].

Based on the provided data, this study aims to generate spatial downscaling results with a resolution of 1 km. To establish the relationship between precipitation and surface factors at the same spatial resolution, all factors were uniformly converted into the WGS_1984_UTM projection coordinate system. The data were then preprocessed and resampled to resolutions 0.25° and 1 km in preparation for the subsequent modeling.

2.3. Method

2.3.1. Precipitation Downscaling Method Based on GNNWR

Statistical regression is a classical statistical analysis method widely used in various disciplines [32]. By modeling the relationship between the independent variable and the dependent variable, changes in the dependent variable can be effectively predicted and explained. Based on the assumption of a “constant relationship scale”, an association model between rainfall and explanatory variables was constructed using low-resolution data, and then the model was applied to high-resolution data to refine the research scope [33]. Additionally, by introducing the residual correction mechanism, the prediction accuracy of the model can be effectively improved under high-resolution conditions [34]. In this study, this relationship is represented by the following equation:

$${PR}_{0.25°}=f({NDVI}_{0.25°},{LST}_{0.25°},{DEM}_{0.25°}{,Slope}_{0.25°})+∆T_{0.25°}$$

(2)

where $f$ is the functional relationship between the variable factors of low-resolution decline water and the surface, and $∆T_{0.25°}$ is the regression residual. Then, each variable factor under high resolution was put into the regression function, ${PR}_{1\mathrm{k}\mathrm{m}}$ is the desired result.

$${PR}_{1\mathrm{k}\mathrm{m}}=f({NDVI}_{1\mathrm{k}\mathrm{m}},{LST}_{1\mathrm{k}\mathrm{m}},{DEM}_{1\mathrm{k}\mathrm{m}}{,Slope}_{1\mathrm{k}\mathrm{m}})+∆T_{1km}$$

(3)

GWR is a spatial-based regression analysis method that builds local parameter estimation on top of ordinary linear regression (OLR). The parameters in global regression do not consider the geographic location of the sample data. The first and second laws of geography show that the closer two things are, the more similar their relationship will be, but there is also heterogeneity. When performing geographic regression analysis, it is often difficult to accurately characterize the non-stationarity of spatial data.

GWR has taken into account the non-stationarity of space, assuming that all relationships are established at the same spatial scale with the same bandwidth. However, in practice, the performance of spatial non-stationarity is very complex, and it is difficult to simulate complex geographical processes with fixed bandwidth settings, so the bandwidth should be adjusted according to regional characteristics to accurately capture spatial variability in practice. MGWR derives the optimal bandwidth of different elemental processes by seeking the spatial scales of their processes, to verify different processes, that is, the influence of different variable factors on the dependent variable can be established at different spatial scales.

RF algorithm is a bagging-based ensemble learning method that can be used for classification and regression prediction of data by constructing a variety of decision trees to deal with the relationship between independent and dependent variables. By constructing a large number of tree models, RF integrates and screens the importance of multiple eigenvalues, fully considers the importance between different eigenvalues, selects the optimal sample eigenvalues, and then finds the optimal solution. Compared with traditional regression prediction methods, RF can handle complex multi-dimensional eigenvalues and regression predictions are more accurate.

Based on the ideas of GWR, the GNNWR model, combining OLS and SWNN, can better estimate spatial non-stationarity. GNNWR believes that the spatial variation in regression relation can be regarded as the fluctuation in the level of spatial non-stationarity regarding the “OLR regression relation” at different positions. By capturing this variation, the model more accurately reflects the spatial non-stationarity of regression relationships between different locations. In this way, the GNNWR model is constructed by integrating four factors of NDVI, LST, DEM, and slope. The model structure is defined as follows:

$$\begin{gathered} PR={\omega }_0\left(S_i\right)\times {\beta }_0+{\omega }_1\left(S_i\right)\times {\beta }_1\times {\mathrm{N}\mathrm{D}\mathrm{V}\mathrm{I}}_i \\ +{\omega }_2\left(S_i\right)\times {\beta }_2\times {\mathrm{L}\mathrm{S}\mathrm{T}}_i+{\omega }_3\left(S_i\right)\times {\beta }_3\times {\mathrm{D}\mathrm{E}\mathrm{M}}_i \\ +{\omega }_4\left(S_i\right)\times {\beta }_4\times {\mathrm{S}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}_i+{\epsilon }_i (i=\mathrm{0,1},2\dots ,n) \end{gathered}$$

(4)

where $S_i$ is the spatial coordinate of the $i-th$ point to be estimated and $\beta$ = (${\beta }_0,{\beta }_{1.}{\dots ,\beta }_4$) is the regression coefficient of the OLR model, which reflects the average global level of precipitation regression relationship in the whole region. The coefficient estimation matrix of the OLR model can be expressed as follows:

$$\widehat{\beta }={\left(X^{T}X\right)}^{-1}{X}^{T}LST$$

(5)

Among them,

$$PR=\left[\begin{array}{c}P{R}_1\\ P{R}_2\\ \cdots \\ P{R}_n\end{array}\right], \mathrm{X}=\left[\begin{array}{c}1 {NDVI}_1{ PR}_1{ DEM}_1 {Slope}_1\\ 1 {NDVI}_2{ PR}_2{ DEM}_2 {Slope}_2\\ \cdots \\ 1 {NDVI}_n{ PR}_n{ DEM}_n {Slope}_n\end{array}\right]$$

(6)

where n represents the number of samples. Thus, substituting OLR’s estimate ${\widehat{\beta }}_{\mathrm{m}}$ times m into Equation (8), we can obtain ${PR}_{\mathrm{i}}$:

$$\begin{gathered} \widehat{{PR}_{\mathrm{i}}}=\sum _{m=0}^4{w}_m\left(s_i\right)\times {\widehat{\beta }}_m\left(OLR\right)\times x_{im} \\ =x_i^{T}W\left(s_i\right){\left(X^{T}X\right)}^{-1}{X}^{T}PR \end{gathered}$$

(7)

where $W(si)$ is the weight diagonal matrix of (1 + k) × (1 + k) and k is the number of independent variables, namely,

$$W(si)=\left[\begin{array}{cccc}w0(si)& 0& 0& 0\\ 0& w1(si)& 0& 0\\ 0& 0& \dots & 0\\ 0& 0& 0& wk(si)\end{array}\right]$$

(8)

SWNN is unique in that it uses the spatial distance between the predicted point and the modeled sample point to construct the input layer, thereby reflecting the geospatial features. The model design contains several hidden layers to handle complex data relationships and finally forms a spatial weight matrix through the output layer, ensuring that the model can flexibly respond to diverse modeling needs. Finally, the spatial weight of the prediction point i can be calculated using the following formula:

$$Wi=W(si)=SWNN({[d_{i1}^s,d_{i2}^s,\dots ,d_{in}^s]}^T)$$

(9)

where $[d_{i1}^s,d_{i2}^s,\dots ,d_{in}^s]$ is the Euclidean spatial distance from the point to the sample set. The spatial weight matrix $W(si)$ is calculated by the SWNN, and then the predicted value can be obtained by the geographically weighted regression formula. Therefore, the definition of the downscaling model of precipitation based on GNNWR in this paper is shown in Figure 2.

GNNWR establishes a functional relationship between precipitation and physical parameters of the surface at low spatial resolution to derive a spatial downscaling model of precipitation, which is then applied to high spatial resolution. Unlike previous methods, GNNWR does not require residual interpolation for model correction [35].

2.3.2. Model Design and Implementation

To improve the optimization efficiency and solving capability of the spatially weighted neural network in the GNNWR model, the neural network architecture and implementation strategy are designed, as shown in Figure 3.

A fully connected network is used between the various levels of an SWNN, and the dropout technology proposed by Srivastava et al. [36] is also used to enhance the model’s generalization ability. In addition, the PReLU activation function is utilized to improve the efficiency of model optimization [37]. Furthermore, batch normalization technology is introduced in the hidden layer to reduce the impact of internal covariate transformation, thereby further improving the computing power of the GNNWR model [38]. The neural network structure has 5 layers, and the specific parameters are shown in

Table 2. Details of neural network parameter settings.

Input layer	Hidden layer 1	Hidden layer 2	Hidden layer 3	Hidden layer 4	Hidden layer 5	Output layer
4096	2048	1024	256	128	64	5
Epoch	Learning rate	Dropout rate	Batch size	Optimizer
1000	0.0001	0.8	512	Adam

.

The training and verification process of the GNNWR model is shown in Figure 4. In this paper, the monthly data of each variable involved in modeling were weighted and summed by season, and then the dataset of each season was randomly selected as the training set, validation set, and test set according to the ratio of 8:1:1. To ensure the robustness and reliability of the model construction, the randomly divided data should cover the entire research area in terms of spatial distribution, reducing the estimation bias caused by the difference in sample selection. During the model training, the training set was used to optimize the bias value and the network weight, while the validation set was used to assess if the model overfitted after each training iteration. After completion of the training process, the test set was used to test the model’s predictive ability. Therefore, validation sets and test sets did not participate in the training process of the model network.

In this study, the random gradient descent algorithm was used for training, with mean square error (MSE) selected as the training loss function for the GNNWR model and MSE of the validation set selected as the overfitting evaluation index. Overfitting was determined by monitoring the overfitting index, which exhibits a continuous upward or stable trend exceeding the predefined tolerance threshold, indicating that the model is overfitting and necessitating termination of the training operation.

2.3.3. Model Evaluation

In this study, four commonly used indexes, namely coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), were used to evaluate and compare the accuracy of the downscaling model. All algorithms used the same explanatory variables as GNNWR.

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

(10)

$$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(yi-\widehat{y}i)}^2}}{n}}$$

(11)

$$MAE=\frac{{\displaystyle \sum _{i=1}^n|yi-\widehat{y}i|}}{n}$$

(12)

$$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|\frac{yi-\widehat{y}i}{yi}\right|}\times 100\%$$

(13)

In the above formula, $yi$ the observed value, $\widehat{y}i$ is the predicted value, and $\overline{yi}$ is the mean of the observed value.

3. Results

3.1. Model Performance Comparison and Analysis

To assess the regression accuracy and fitting performance of the GNNWR downscaling model, this study employed four performance evaluation indices, namely R², RMSE, MAPE, and MAE, to quantitatively evaluate and compare the four models.

Table 3. Regression evaluation indexes of results of different downscaling models at quarter scale.

Season	Model	Regression Indicators
		R2	RMSE/mm	MAE/mm	MAPE
Spring	GNNWR	0.957	8.367	6.149	8.174
	MGWR	0.929	15.058	11.422	12.793
	GWR	0.933	12.944	10.165	12.707
	RF	0.816	32.995	26.58	14.052
Summer	GNNWR	0.931	18.565	10.40	12.765
	MGWR	0.919	24.180	18.457	19.780
	GWR	0.886	33.885	21.449	24.172
	RF	0.756	54.077	40.795	31.404
Autumn	GNNWR	0.955	7.211	4.184	6.740
	MGWR	0.929	14.973	9.612	12.431
	GWR	0.916	14.824	13.206	14.367
	RF	0.776	31.833	25.119	22.552
Winter	GNNWR	0.929	3.551	3.247	5.887
	MGWR	0.909	4.401	3.269	4.021
	GWR	0.874	5.311	4.019	5.954
	RF	0.857	6.103	5.220	6.006

presents the specific regression evaluation indices for each season across the four algorithmic models.

The precipitation varies significantly in different seasons and regions due to strong spatiotemporal heterogeneity. In this study, we extracted the accumulated rainfall data for the Sichuan region from 2001 to 2019 using the original TRMM data and the annual average rainfall was calculated. The annual cumulative rainfall for each year was then compared to the annual average rainfall to determine the rainfall deviation for each year. After comparing the deviation, it was found that 2013 had the closest rainfall deviation to the multi-year average. Therefore, we took the precipitation data for each season in 2013 (spring: March to May; summer: June to August; autumn: September to November; winter: December to February) as samples. All algorithms used the same set of explanatory variables as in the GNNWR model. To ensure that all variables had a consistent time scale, we first weight-summed the monthly data of precipitation and all explanatory variables by season and then built the model.

As can be seen from Table 3, in terms of seasonal scale, the GNNWR model improved its fitting accuracy and had the best error control compared with other classic downscaling models in the four seasons, followed by the MGWR and GWR models, but with differences. RF had the worst accuracy, and the error control was not ideal. For example, in spring precipitation in the study area, the R² of GNNWR increased by 0.028, 0.024, and 0.141, compared with the other three models. The precipitation in Sichuan is generally higher in summer and lower in spring, autumn, and winter. This may be due to the spatial heterogeneity of precipitation, and the RMSE of summer precipitation in the four models is the largest, with RF up to 54.077 mm. The other three models have significantly lower values than RF, and GNNWR is 23.22% lower and 45.21% lower than MGWR and GWR, respectively. The error of each model is relatively well controlled in winter. The GNNWR model increases R², while reducing RMSE by 19.31%, 33.13%, and 41.81%. In addition, the MAE and MAPE of the GNNWR model decreased by 13.44% and 18.23%, on average.

In addition, in terms of model calculation time, RF < GWR < GNNWR < MGWR. However, with the exception of GNNWR, all other models needed to carry out interpolation conversion of coefficient and residuals. Therefore, the total downscaling time of the GNNWR model is much smaller than that of the other models.

In summary, in the four seasons with obvious precipitation differences, the GNNWR model has the best comprehensive performance of indicators, which has good stability and variance explanation.

3.2. High-Resolution Spatial Distribution Comparison of Precipitation

To provide a more intuitive demonstration of the downscaling effect of the GNNWR model, the original resolution TRMM image of Sichuan Province (0.25°) and the downscaled result images of the four models were visually compared. The downscaled result images were processed with anomaly removal, blank value interpolation, and raster alignment. Figure 5 shows the spatial distribution details of precipitation in Sichuan Province for the four seasons in 2013 for the four models.

As can be seen from Figure 5, compared with the original 0.25° TRMM data (Figure 5a), the downscaling data of the four models (Figure 5b–e) depict the spatial distribution of rainfall patterns in Sichuan in a more detailed way. However, among the four models, RF (Figure 5b) is greatly affected by the DEM factor and the spatial texture characterization is too obvious, which is inconsistent with the actual precipitation situation [39]. MGWR (Figure 5d) and GNNWR (Figure 5e) have relatively good performance. However, concerning the spatial distribution of precipitation, the downscaling of the GNNWR model is more consistent with the spatial distribution of the original data and the details are smoother and more exquisite. Particularly in summer, the downscaling effect of GNNWR (Figure 5e2) is comparatively superior.

4. Discussion

4.1. Availability and Advantages of Downscaling Results of GNNWR Model

To further assess and validate the reliability and precision of the GNNWR model’s downscaled data, this paper took the locations of 42 precipitation measurement stations within Sichuan Province as the reference points, and extracted the monthly TRMM values, GNNWR downscaled results, and values from other precipitation datasets at the same resolution for the years 2001 to 2019 [40]. Three commonly used accuracy evaluation indices, namely determination coefficient (R²), root mean square error (RMSE), and relative deviation (BIAS), were employed for verification and assessment.

From

Table 4. Accuracy evaluation of TRMM data after downscaling.

Time Scale	Accuracy Evaluation Object	Regression Indicators
		R2	RMSE/mm	BIAS/%
Spring	Original value—meteorological station value	0.80	22.39	4.66
	Other dataset value—meteorological station value	0.77	58.03	10.50
	Downscaling value—meteorological station value	0.82	27.07	6.38
Summer	Original value—meteorological station value	0.64	59.63	7.01
	Other dataset value—meteorological station value	0.74	179.09	14.56
	Downscaling value—meteorological station value	0.89	71.05	8.04
Autumn	Original value—meteorological station value	0.76	35.30	5.72
	Other dataset value—meteorological station value	0.66	67.76	–0.30
	Downscaling value—meteorological station value	0.75	37.29	6.03
Winter	Original value—meteorological station value	0.62	6.90	6.69
	Other dataset value—meteorological station value	0.67	20.34	11.83
	Downscaling value—meteorological station value	0.86	10.37	7.92

, it can be seen that, compared with other precipitation datasets of the same resolution, the R² value of the precipitation data after being downscaled by the GNNWR model is higher, indicating that the downscaled precipitation data by the GNNWR model has a better correlation with the real precipitation data and can better reflect the actual precipitation situation. Similarly, the RMSE value of the downscaled precipitation data by the GNNWR model is lower than that of other datasets of the same resolution, indicating that the downscaled precipitation data by the GNNWR model have a better error control level. In summary, the downscaled precipitation data by the GNNWR model have higher precision and better data quality than other precipitation datasets, which are reliable and can be used for subsequent research.

4.2. Rationality and Accuracy of GNNWR Downscale Precipitation Spatial Mapping

The annual total precipitation in Sichuan Province from 2001 to 2019 showed an upward trend, then a downward trend, and then an upward trend again. As shown in Figure 6a, precipitation increased from 831.04 mm in 2001 to 886.49 mm in 2004, then sharply decreased to 729.48 mm in 2006, and finally increased to 919.71 mm in 2017. The fluctuation of precipitation changes was divided by 2012 as a dividing point. Before 2012, the annual precipitation fluctuated greatly, and the overall precipitation was relatively small. After 2012, the precipitation showed a high level of small fluctuation, with values fluctuating around 900 mm. To further quantify the monthly precipitation change characteristics of Sichuan Province, the monthly total precipitation was averaged from 2001 to 2019 to obtain the monthly precipitation time series. From Figure 6b, it can be seen that the monthly precipitation in Sichuan Province showed an upward and then a downward trend. Precipitation increased from 7.23 mm in January to 164.48 mm in July, then decreased to 6.99 mm in December. July’s precipitation reached the highest value of the year, followed by June and August, with precipitation fluctuating around 145 mm. June to August are in the summer, with summers being hot and rainy, and precipitation being abundant. However, December, January, and February are winter months, with winter being cold and dry and precipitation being relatively scarce.

According to the GNNWR downscaled monthly precipitation data from 2001 to 2019 in the Sichuan region, we calculated the annual average monthly precipitation in the study area over the past two decades and presented its spatial distribution diagram in Figure 7. From Figure 7, it can be seen that the spatial distribution pattern of monthly average precipitation in each year from 2001 to 2019 has significant differences: the monthly average precipitation in 2001 ranged from 29.40 to 174.11 mm, with high-precipitation areas mainly located in the southern part of the Sichuan Basin and low-precipitation areas distributed in the northwest of Sichuan Province; in 2002–2004, the range of monthly average precipitation values compared to 2001 was smaller, but the high-precipitation area expanded from the central Sichuan Basin to the entire Sichuan Basin in eastern Sichuan, and the low-precipitation area remained in the northern part of the study area; in 2005 and 2006, the spatial distribution range of the extremely high- and low-precipitation values in these two years was reduced, but the overall distribution pattern did not change much; in 2007 and 2008, the monthly average precipitation ranged from 31 to 143 mm, and the high-precipitation area shifted to the eastern part of the Sichuan Basin, with the high-precipitation area distributed in the northwest; from 2009 to 2011, the low-precipitation area expanded from the northwestern part of the Sichuan Basin to the southern part of the Sichuan Basin, and the high-precipitation area was mainly distributed in the central part of the Sichuan Basin and the eastern part of the Sichuan Basin, without an obvious shift; in 2012 and 2013, the high-precipitation area shifted to the southern part of the Sichuan Basin, and the low-precipitation area shifted to the northwestern part of the Sichuan Basin; from 2014 to 2019, the spatial distribution range of the high-precipitation area was reduced, and it shifted within the range of the Sichuan Basin in the southwestern part and the southeastern part, while the low-precipitation area.

In summary, there was a significant spatial difference in the monthly precipitation distribution in Sichuan Province from 2001 to 2019. From 2001 to 2008, there was a shift in the spatial distribution of high-precipitation areas, but the low-precipitation areas did not change. From 2009 to 2011, there was a significant shift in the spatial distribution of low-precipitation areas and the high-precipitation areas tended to stabilize. From 2012 to 2019, there was a significant shift in the spatial distribution of high-precipitation areas, while the low-precipitation areas changed relatively stably.

In conclusion, significant disparities were observed in the spatial distribution of monthly mean precipitation in Sichuan Province from 2001 to 2019. During the period from 2001 to 2008, there was a notable shift in the spatial distribution of areas with high-precipitation values, while no changes were observed in areas with low-precipitation values. From 2009 to 2011, substantial shifts occurred in the spatial distribution of low-value precipitation areas, whereas high-value areas exhibited relative stability. Between 2012 and 2019, there was considerable transfer of precipitation within high-value regions, while low-value areas remained relatively unchanged.

Overall, precipitation in high-precipitation areas in central Sichuan Province exhibited a decreasing trend, potentially attributed to the influence of the East Asian monsoon [41]. Conversely, the low-precipitation area in northwest Sichuan demonstrated an increasing trend, likely due to its location within the Hengduan Mountains. This region is not only influenced by the South Asian monsoon but also affected by the East Asian monsoon, Tibetan Plateau monsoon, and westerly winds. Furthermore, relevant studies have indicated that enhanced water vapor flux resulting from westerly wind circulation may contribute to increased precipitation in northwest Sichuan [42,43].

5. Conclusions

This paper integrated the NDVI, LST, DEM, and slope data to establish a GNNWR precipitation downscaling model that considers terrain and topography, seasonal changes, etc. The model can handle spatial heterogeneity and complex nonlinearities well. A deep learning optimization strategy was developed to improve optimization efficiency and problem-solving ability. The modeling accuracy and downscaling results were compared with three commonly used downscaling methods. Finally, the model was validated and evaluated using measured sites. The results show that the GNNWR precipitation downscaling model has the best fitting results, and better stability, and its maximum R² is 0.972, and the minimum RMSE is 3.551 mm. The GNNWR precipitation downscaling model has significant improvement over traditional downscaling models such as GWR and MGWR and has obvious advantages over typical machine learning algorithm downscaling models such as RF. The GNNWR model has a short training time and is highly operable. The GNNWR model’s downscaling results have a better correlation with the measured site data and higher data quality than other precipitation datasets of the same resolution. The GNNWR precipitation downscaling model has the best visual effect and is most consistent with the original product’s spatial precipitation distribution, with more reasonable local expressions than other downscaling models.

According to the GNNWR’s downscaled precipitation data from 2001 to 2019 in the Sichuan region, the spatiotemporal characteristics of precipitation changes in the study area were explored. The results indicate that there has been a significant overall increase in precipitation in Sichuan Province from 2001 to 2019, with the highest precipitation recorded in 2017 and the lowest in 2006. In terms of spatial distribution, the annual precipitation in Sichuan Province generally exhibits a pattern of low precipitation in the northwest and high precipitation in the southeast.

In summary, the downscaling method based on GNNWR proposed in this paper not only ensures spatial consistency but also enhances the downscaling accuracy and spatial texture information of the original low-spatial-resolution precipitation data. It provides a more convenient, rapid, and accurate approach for researchers in the field of precipitation-related studies to obtain high-resolution precipitation data.

Due to the limitation of objective factors, some contents can be further discussed in this study, mainly as follows: by comparing the four downscaling models, the GNNWR model has the highest accuracy and can accurately reflect the spatial distribution characteristics of precipitation, but the model only considers the surface factors, and the spatial distribution of precipitation is also affected by meteorological factors such as atmospheric circulation mode, wind direction, wind speed, and evapotranspiration [44].