Comparative Study on the Different Downscaling Methods for GPM Products in Complex Terrain Areas

Abstract

Fine spatial information of precipitation plays a significant role in regional eco-hydrological studies but remain challenging to derive from satellite observations, especially in complex terrain areas. Sichuan Province, located in the southwest of China, has a highly variable terrain, and the spatial distribution of precipitation exhibits extreme heterogeneity and strong autocorrelation. Multi-scale Geographically Weighted Regression (MGWR) and Random Forest (RF) were employed for downscaling the Global Precipitation Measurement Mission (GPM) products based on high spatial resolution terrain, vegetation, and meteorological data in Sichuan province, and their specific effects on gauged precipitation accuracy and spatial precipitation distributions have been analyzed based on the influences of environmental variables. Results show that the influence of each environmental factor on the distribution of precipitation at different scales was well represented in the MGWR model. The downscaled data showed good spatial sharpening effects; additionally, the biases in the overestimated region were well corrected after downscaling. However, when based on spatial autocorrelation and considering adjacent influences, the MGWR performed poorly in correcting outlier sites adjacent to the high–high clusters. Compared with MGWR, relying on independently constructed decision trees and powerful regression capabilities, superior correction for outlier sites has been achieved in RF. Nevertheless, the influence of environmental variables reflected in RF differs from actual conditions, and detailed characteristics of precipitation spatial distribution have been lost in the downscaled results. MGWR and RF demonstrate varying applicability when downscaling GPM products in complex terrain areas, as they both improve the ability to finely depict spatial information but differ in terms of texture property expression and precipitation bias correction.

1. Introduction

Precipitation plays an integral role in the water cycle, driving surface material circulation and energy exchange [1]. As a critical factor in climate change adaptation and ecological security, its spatiotemporal variability fundamentally constrains water resource management strategies. Traditional rain gauge observations, while valuable, are limited by factors such as station density and spatial representativeness, which hinder their ability to accurately capture precipitation distribution [2]. While weather radar offers the advantage of remote precipitation measurement within specific ranges, its capacity for continuous large-scale monitoring remains constrained. Particularly in mountainous regions, topographic variability can induce over 40% estimation bias in radar-derived precipitation [3]. The satellite remote sensing technology has revolutionized precipitation observation by enabling comprehensive, all-weather monitoring, and its precipitation products are indispensable for spatiotemporal analysis [4].

The Global Precipitation Measurement Mission (GPM), a successor to the Tropical Rainfall Measuring Mission (TRMM), enhances observational capabilities by accurately measuring light precipitation (less than 0.5 mm/h) and solid precipitation in mid- to high-latitude regions and represents an advancement in precipitation monitoring [5]. The Integrated Multi-satellite Retrievals for GPM (IMERG) algorithm is used to generate precipitation products with a spatial resolution of 0.1° and a temporal resolution of half an hour, thereby improving coverage and spatiotemporal precision. Although IMERG provides reliable global estimates, its resolution poses challenges in achieving detailed regional precipitation characterization [6].

Downscaling techniques enable the transformation of precipitation data from large-scale to small-scale resolutions, enhancing the representation of regional precipitation distributions with greater detail. Dynamic downscaling and statistical downscaling represent the two principal downscaling methodologies, where dynamic downscaling is physics-based and imposes greater demands on both parameterization and computational resources [7]. Statistical downscaling relies on the statistical principle of scale invariance, establishing relationships between low-resolution precipitation data and high-resolution environmental factors such as DEM (Digital Elevation Model) and NDVI (Normalized Difference Vegetation Index). Because of the advantages of computational efficiency, minimal data requirements, and adaptability [8], statistical downscaling has been widely applied. For instance, Jia et al. [9] developed a multiple linear regression model linking TRMM precipitation with DEM and NDVI, successfully upgrading the spatial resolution of TRMM data in the Qaidam Basin from 0.25° to 1 km. Furthermore, a comparative analysis in Inner Mongolia demonstrated the effectiveness of an exponential regression model in the context of TRMM downscaling [10].

In establishing statistical relationships between precipitation and environmental variables such as terrain and vegetation factors, traditional regression models often struggle due to the nonlinear interactions inherent in these relationships [11]. To address this limitation, machine learning models with robust regression capabilities have been increasingly adopted for downscaling remote sensing precipitation products, particularly given their ability to handle complex nonlinear patterns effectively. Shi et al. [12] demonstrated that the Random Forest (RF) model outperformed conventional methods such as multiple and exponential regressions in downscaling TRMM data across mainland China, showcasing superior performance and enhanced spatial representation of precipitation patterns. Sun et al. [13], leveraging Deep Convolutional Neural Networks (DCNN), applied similar techniques to TRMM and IMERG datasets in the complex precipitation environments of central Texas, USA. Their findings revealed that while DCNN excels at capturing fine-scale features, its effectiveness in improving precipitation accuracy is contingent upon extensive calibration with additional measurement data.

While traditional regression and machine learning approaches inherently assume spatial stationarity in precipitation-environment relationships [14], empirical evidence demonstrates significant geographical variations in these associations. For instance, the influence of elevation on precipitation intensity has been shown to vary by 600% across different topographic regimes [15]. Satellite-based analyses further confirm that over 50% of the variance in precipitation-vegetation relationships exhibits spatially non-stationary characteristics across continental scales [16]. To address how the relationship varies geographically, exhibiting significant spatial non-stationarity and scale-dependent effects, the Geographically Weighted Regression (GWR) model has been utilized in a downscaling study and confirms that GWR’s localized parameter estimation effectively captures the spatially varying relationships between precipitation and environmental drivers [17,18]. Building on this, Fotheringham et al. [19] introduced the Multi-scale Geographically Weighted Regression (MGWR) model to address the issue in GWR where scale differences in environmental variables’ effects are not accounted for. Li et al. [20] implemented MGWR between TRMM and environmental variables in the Weihe River Basin, achieving higher accuracy for 1 km spatial resolution precipitation products and better spatial detail representation. In a comparative study on IMERG downscaling in the Yellow River Basin, MGWR outperformed GWR in both spatial refinement of precipitation distribution and measurement accuracy [21].

Numerous studies have investigated TRMM/GPM downscaling techniques, and overall, as research on precipitation-environment interactions intensifies, the MGWR model, which better reflects the spatial heterogeneity of precipitation, has emerged as a promising approach [21,22]. Meanwhile, RF also demonstrates impressive performance in downscaling regression due to its thorough computational efficiency and insensitivity to feature selection [23,24]. Although both MGWR and RF have been widely applied across diverse regions, the understanding of downscaling effectiveness remains limited, and there is a lack of a reference basis for selecting appropriate models according to the regional precipitation characteristics. To comprehensively assess the applicability of the MGWR and RF models for downscaling GPM precipitation data in topographically complex regions, Sichuan Province was taken as a representative case in this study. Eight environmental covariates encompassing geomorphological constraints, vegetation dynamics, and meteorological parameters were selected for constructing the GPM downscaling model. By analyzing the effects of geographically weighted regression and decision tree-based regression algorithms on accuracy correction and spatial distribution optimization in downscaling outputs, this study evaluates model applicability for IMERG downscaling in topographically complex regions, thereby establishing evidence-based and statistically robust selection criteria for achieving high-resolution representation of regional precipitation.

2. Study Area and Dataset

2.1. Study Area

Sichuan Province (as illustrated in Figure 1), located in southwestern China, spans from 97°21′ E to 108°31′ E and 26°03′ N to 34°19′ N, covering a total area of 486,000 km². It serves as a transitional zone between the Qinghai–Tibet Plateau and the middle and lower reaches of the Yangtze Plain, with altitudes ranging from 7556 m to 188 m. The topography of Sichuan is complex, showing the overall change in terrain in the west and the east. Due to the special geographical location, Sichuan Province is affected not only by the East Asian monsoon and the Indian monsoon but also by the atmospheric circulation of the Qinghai–Tibet Plateau. At the same time, different topographic conditions such as plateaus, mountains, and basins also significantly shape the local climate, which together create complex precipitation patterns and distribution characteristics in Sichuan Province [25]. According to the result of climate zoning in China [26,27], Sichuan Province comprises three primary climate zones: Sichuan Basin, Southwest Sichuan mountains, and Northwest Sichuan Plateau (as illustrated in Figure 1), and their information has been listed in

Table 1. Climate zones and their characteristics in Sichuan province.

Climate Zone	Precipitation (mm/a)	Average Temperature (°C/a)	Climatic Characteristics
Sichuan Basin—tropical and humid zone	1000~1300	16~20	Warm and humid year-round, abundant rainfall, distinct seasons, high humidity
Southwest Sichuan Mountains—subtropical and subhumid zone	900~1200	14~18	Relatively high temperatures, indistinct seasons, obvious dry-wet season differences, abundant sunshine
Northwest Sichuan Plateau—cold alpine zone	500~900	4~10	Significant vertical climate variation, large diurnal temperature range, distinct seasons

. Considering the highly irregular and jagged configuration of Sichuan Province’s administrative boundaries, a 15 km outward buffer zone was established around the perimeter (Figure 1), and all data processing and analytical operations were confined to this buffered area to mitigate edge effects and ensure spatial continuity across jurisdictional transitions.

2.2. Dataset

2.2.1. Precipitation Data

This study investigates the performance of MGWR and RF models in refining the spatial representation of GPM precipitation products through downscaling. There is no requirement for the distribution of the time series. The GPM Level 3 IMERG Final Run Version 06B product covering Sichuan Province for two representative months—January (drought season) and August (monsoon season) of 2020—was selected.

The observed data from 40 meteorological stations distributed across the study area (Figure 1) were used to validate the accuracy of the downscaling results. Additionally, another reanalysis dataset was used for evaluation. This dataset [28] was constructed as a benchmark product through the ANUSPLIN method, based on the network data from over 2400 meteorological stations, for spatial-temporal interpolation.

2.2.2. Environmental Variable Data

(1) Geographical data

From a macroscale perspective, regions at higher longitudes exhibit increased precipitation probabilities due to reduced land–sea distance. Concurrently, lower latitude areas demonstrate enhanced precipitation attributable to relatively higher temperatures and humidity [29]. At the microscale level, topographic relief influences the convective activity of water vapor, which in turn affects local precipitation [30]. Therefore, elevation, slope, and aspect derived from DEM are commonly used for analyzing the impact on precipitation distribution.

In this study, considering Sichuan’s mountainous terrain and the fact that the water vapor brought by the monsoon is the primary source of precipitation, distinctly different precipitation patterns will occur on the windward and leeward regions. The relationship between the prevailing wind direction and aspect becomes a key factor affecting precipitation distribution [31]. Therefore, a novel index quantifying the angular relationship between predominant wind direction and aspect, windwardness, is taken as a critical factor. Its calculation formula is as follows:

$$\mathsf{\omega }=\mathrm{c}\mathrm{o}\mathrm{s}\left(\alpha -\beta \right)$$

(1)

In the formula, $\omega$ represents the windwardness, ranging from −1~1. When $\omega$ > 0, it refers to the windward; when $\omega$ < 0, it refers to the leeward. The larger the absolute value of $\left|\omega \right|$, the smaller the angle between the prevailing wind direction and aspect, indicating a stronger windward or leeward effect. $\alpha$ represents the predominant wind direction, and $\beta$ represents the aspect.

(2) Vegetation data

Vegetative growth is dominated by the regional precipitation and also impacted by the precipitation distribution through interception and transpiration. In such a feedback loop, reflecting time-dependent biogeochemical pathways involved in water absorption and biomass accumulation processes, the phenological response of vegetation quantified by NDVI exhibits an approximately 1-month temporal lag relative to precipitation [32]. Therefore, in this study, NDVI for February and September 2020 was selected as an influencing factor for the spatial distribution of precipitation in January and August.

(3) Meteorological data

Water vapor transport serves as a critical process in precipitation formation, and wind speed significantly influences this mechanism. Temperature can reflect precipitation distribution by affecting air humidity, so it is often used as an environmental variable, but the significant correlation between air temperature (AT) and elevation suggests a potential collinearity problem. For this reason, an alternative variable, diurnal land surface temperature range (DSTR), has been chosen, which reflects the dynamics of the land surface energy balance and is indicative of local climate conditions, also showing a strong association with precipitation [33]. DSTR can be calculated by the following equation in this study:

$${DSTR}_i={\displaystyle \frac{\sum _{j=1}^n\left({LST}_{max-j}-{LST}_{min-j}\right)}{n}}$$

In the formula, i represents the month; n represents the number of days in the given month; LST_max-j and LST_min-j correspond to the maximum and minimum land surface temperatures on the j-th day, respectively.

In summary, nine environmental variables, longitude (LON), latitude (LAT), elevation (ELE), slope (SLOP), windwardness (WWN), NDVI, wind speed (WS), AT, and DSTR are utilized as explanatory factors for downscaling IMERG data. The evaluation of downscaled results is conducted using observed precipitation data. Detailed information regarding the data sources and their characteristics is provided in

Table 2. Data sources and their basic information.

Data Name	Time Scale	Spatial Resolution	Data Information	Data Source
GPM IMERG V06	Month	0.1°	Spatial distribution of precipitation	NASA (https://gpm.nasa.gov/) accessed on July 2022
SRTM3 DEM	--	90 m	Elevation, slope, aspect	National Earth System Science Data Center (http://www.geodata.cn/) accessed on July 2022
MOD13A3	Month	1 km	NDVI	NASA (https://search.earthdata.nasa.gov/) accessed on July 2022
China Near-Surface Average Temperature Dataset	Month	1 km	Near-surface temperature	National Earth System Science Data Center (http://www.geodata.cn/) accessed on July 2022
TRIMS LST [34]	daily	1 km	Maximum and minimum land surface temperature	National Tibetan Plateau Science Data Center (https://www.tpdc.ac.cn) accessed on July 2022
China Near-Surface Average Wind Speed Dataset	Month	1 km	Near-surface average wind speed	National Earth System Science Data Center (http://www.geodata.cn/) accessed on July 2022
China Surface Climate Standard Value Dataset	Month	Station	Observed precipitation and prevailing wind direction	National Meteorological Information Center (http://data.cma.cn/) accessed on July 2022
China Monthly reanalysis precipitation [28]	Month	1 km	Reanalysis Precipitation	China Scientific Data (www.csdata.org) accessed on July 2022

.

3. Methods

3.1. Downscaling Transformation

The hypothesis of “spatial scale invariance”, which posits that the regression relationship between target and environmental variables established at low spatial resolution persists at high spatial resolution [35], is a fundamental prerequisite for statistical downscaling. For precipitation, this invariance generally exists in monthly scale data [36]. This study employs MGWR and RF to conduct scale transformation on monthly IMERG data, so “spatial scale invariance” is tenable. The procedure comprises the following steps:

(1)

Data preparation. Based on Python programming 3.10, the IMERG data were subjected to format conversion, angle rotation, coordinate definition, and unit conversion to obtain the precipitation distribution data for Sichuan Province in January and August 2020, with a spatial resolution of 10 km. The DEM was resampled to 1 km and 10 km, and the corresponding elevation, slope, and aspect information were extracted at each resolution. Kriging interpolation was applied to the observed station data for predominant wind direction, and the data were sampled to 1 km and 10 km to calculate the corresponding WWN at each resolution. The MOD13A3, TRIMS LST, temperature, and wind speed data were synthesized monthly and then sampled to 1 km and 10 km by inverse distance weighting.

(2)

Factor testing. The spatial autocorrelation of the precipitation-dependent variables and the multicollinearity of the influencing factors were tested to analyze the precipitation distribution and select the explanatory factor for the regression model.

(3)

Establishing a regression model at 10 km low resolution. The MGWR and RF models were used to establish regression models between the IMERG data for Sichuan Province at a 10 km resolution and the environmental variables, thereby determining the regression relationship between the two.

(4)

Predicting precipitation distribution at 1 km high resolution. Based on the regression relationship established at 10 km low resolution, the environmental variables at 1 km high resolution were used to predict the precipitation distribution at 1 km resolution.

3.2. Regression Model

3.2.1. Multi-Scale Geographically Weighted Regression Model (MGWR)

MGWR establishes local regression equations at each spatial distribution regression point to explore the spatial heterogeneity of the dependent variable under the influence of explanatory factors. It overcomes the limitation in the GWR model where the same bandwidth is applied to all environmental variables and can reflect the differences in the scale of influence of different environmental variables on precipitation. This makes it suitable for regressing data such as precipitation, which has a high spatial distribution heterogeneity. The basic expression of MGWR is as follows [19]:

$$y_i={\beta }_0\left(u_i,v_i\right)+{\sum }_{j=1}^n{\beta }_j\left(u_i,v_i\right)x_{ij}+\epsilon \left(u_i,v_i\right)$$

(2)

In the formula ${\mathit{y}}_{\mathit{i}}$ is the precipitation at point i; ${\mathit{\beta }}_0\left({\mathit{u}}_{\mathit{i}},{\mathit{v}}_{\mathit{i}}\right)$ is the constant term of the regression at point i; $\left({\mathit{u}}_{\mathit{i}},{\mathit{v}}_{\mathit{i}}\right)$ are the coordinates of point i; n is the number of environmental variables; ${\mathit{\beta }}_{\mathit{j}}\left({\mathit{u}}_{\mathit{i}},{\mathit{v}}_{\mathit{i}}\right)$ is the regression coefficient of the j-th variable at point i; ${\mathit{x}}_{\mathit{i}\mathit{j}}$ is the value of the j-th variable at point i; $\mathit{\epsilon }\left({\mathit{u}}_{\mathit{i}},{\mathit{v}}_{\mathit{i}}\right)$ is the residual at point i.

This study establishes the MGWR model based on MGWR2.2 [37] developed by the Spatial Analysis Research Center at Arizona State University (https://sgsup.asu.edu/SPARC), accessed on 1 January 2022. The kernel function of the model is set to a quadratic kernel, with the corrected Akaike Information Criterion (AICc) chosen as the bandwidth selection criterion, and the optimal bandwidth search type set to the Golden Section algorithm.

3.2.2. Random Forest Model (RF)

RF is an ensemble learning-based algorithm that establishes a regression relationship by integrating the prediction results of multiple decision trees [38]. It does not have specific requirements regarding data distribution or the linear relationships between factors. In RF regression, each decision tree is trained independently and randomly selects sub-samples, which gives it good generalization ability and helps reduce the risk of overfitting. This makes it suitable for data with complex nonlinear relationships, such as the one between precipitation and environmental variables. In this study, the Random Forest model between precipitation and environmental variables was built using the sklearn library in Python. The samples were divided into training and validation sets with an 80% and 20% split, respectively. Two important parameters in the model—number of decision trees and number of variables—were optimized by selecting the parameters that minimized the error through a grid search. The number of decision trees was varied in steps of 50, from 200 to 500, and the number of variables was varied in steps of 1, from 1 to the total number of environmental variables.

3.3. Evaluation Indicators

For the precipitation evaluation, while object-based assessment methods provide a novel perspective on the overall performance of regional precipitation [39,40], it is necessary to better reflect the spatial distribution characteristics of downscaling results. The regression accuracy of MGWR and RF, as well as the accuracy of IMERG precipitation data before and after downscaling, were evaluated at the station scale using three indicators: the coefficient of determination (R²) [41], relative bias (BIAS), and root mean square error (RMSE) [42]. The calculation formulas for these three indicators are as follows:

$$R^2={\displaystyle \frac{{\left[{\sum }_{i=1}^n\left(G_i-\overline{G}\right)\left(P_i-\overline{P}\right)\right]}^2}{{\sum }_{i=1}^n{\left(G_i-\overline{G}\right)}^2{\left(P_i-\overline{P}\right)}^2}}$$

(3)

$$BIAS={\displaystyle \frac{{\sum }_{i=1}^n\left(G_i-P_i\right)}{{\sum }_{i=1}^n{P}_i}}\ast 100\%$$

(4)

$$RMSE=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(G_i-P_i\right)}^2}{n}}}$$

(5)

In the formula ${\mathit{G}}_{\mathit{i}}$ is the precipitation at point i for IMERG, in mm; $\overline{G}$ is the average precipitation of IMERG, in mm; ${\mathit{P}}_{\mathit{i}}$ is the reference precipitation at point i, in mm; $\overline{\mathit{P}}$ is the average reference precipitation, in mm; n is the sample size, and i is the index of sample number.

4. Results and Analysis

4.1. Environmental Variables Correlation

RF does not impose specific requirements on environmental variables. However, multicollinearity among these factors can impair the MGWR model’s ability to detect spatial non-stationarity, which increases model uncertainty and leads to unreliable regression results. Among the selected nine environmental variables, latitude and longitude coordinates were utilized for geographic positioning without direct involvement in regression analysis in MGWR, so the multicollinearity diagnostic test was performed on the remaining seven variables. The findings revealed a high linear correlation between air temperature and elevation. At a 0.05 significance level, the correlation coefficients for January and August were −0.8 and −0.95, respectively (as illustrated in Figure 2). Furthermore, the Variance Inflation Factor (VIF) values exceeded 5 and 12, respectively (as shown in Figure 3), indicating significant multicollinearity between these two factors.

Considering the stronger correlation between elevation and IMERG precipitation, air temperature was excluded. Consequently, ELE, SLOP, WWN, NDVI, WS, and DSTR were selected as the factors influencing the spatial distribution of precipitation. Upon re-evaluation, all VIF values for these environmental variables were found to be below 3 at a significance level of 0.05, confirming no multicollinearity issues.

4.2. IMERG Precipitation Validation

4.2.1. Spatial Distribution

MGWR is a spatial regression method for estimating local parameters, where spatial heterogeneity is considered a prerequisite for local statistics, and spatial autocorrelation is regarded as the foundation of spatial regression [43]. From the spatial distribution of IMERG precipitation in Sichuan Province (as shown in Figure 4), it can be observed that both January and August exhibit extremely strong spatial heterogeneity. Additionally, the northwestern Sichuan Plateau displays a discrete spatial variation with distinct grid boundaries in January. The spatial autocorrelation analysis using the Global Moran’s I index indicates significant spatial positive correlations for IMERG precipitation, with values of 0.95 (January) and 0.97 (August) at a significance level of 0.05. Further cluster detection via Local Moran’s I reveals that in January, high–high clusters (approximately 70 mm monthly precipitation) are concentrated in the central Sichuan Basin, while low-low clusters (around 5 mm) dominate the eastern northwestern Sichuan Plateau and the northern regions adjacent to the Sichuan Basin. In August, precipitation clusters are characterized by high–high clusters in the Sichuan Basin and low-low clusters in the northwestern Sichuan Plateau.

Cross-validation between IMERG and reanalysis precipitation data demonstrated their strong spatial consistency, with determination coefficients reaching 0.62 and 0.85 in January and August, respectively, indicating that IMERG can effectively capture the overall distribution characteristics of precipitation in Sichuan. The spatial distribution of precipitation in Sichuan Province exhibits distinct spatial heterogeneity and significant positive spatial autocorrelation, providing a solid foundation for conducting MGWR.

4.2.2. Accuracy

The accuracy of IMERG precipitation was analyzed based on observed precipitation from 40 meteorological stations across Sichuan Province, with results shown in Figure 5. IMERG exhibited weak detection capability for January dry season precipitation, with a correlation coefficient of only 0.39 compared to observed data. In addition to a systematic overestimation of precipitation at stations with approximately 10 mm of precipitation, two notable outliers were observed: the Leshan and Mianyang stations. Two stations are located on the edges of two high–high clusters in the central Sichuan Basin (Figure 2), with observed precipitations of 17.4 mm and 3.6 mm, respectively, significantly lower than the cluster average precipitation of 51.6 mm.

In August, during the monsoon season, IMERG performed well overall, achieving a correlation coefficient of 0.76 with observed data. However, overestimation issues persisted in low-precipitation regions. Similarly, at Doujiangyan Station on the edge of the high–high cluster in the central Sichuan Basin, there was a severe deviation from the regression line, with an observed precipitation of 1080 mm, far exceeding the cluster average of around 700 mm.

For both the dry season (January) and wet season (August), IMERG systematically overestimates low-precipitation areas in Sichuan, exhibiting significantly lower accuracy in these regions compared to high-precipitation zones. Furthermore, IMERG fails to capture precipitation patterns at outlier stations adjacent to spatial clusters accurately, resulting in severe overestimation of anomalously low precipitation and underestimation of anomalously high precipitation. These limitations collectively contribute to a substantial degradation in the overall accuracy performance of IMERG estimates.

4.3. Downscaling Results

4.3.1. Changes in Precipitation Spatial Distribution

Figure 6 illustrates the downscaled IMERG precipitation distributions over Sichuan Province for January and August. Both the MGWR and Random Forest (RF) models improved the spatial resolution of IMERG precipitation data from 10 km to 1 km, enhancing overall spatial clarity. However, when examining local details, there were distinct differences between the two models. In regions influenced by transitional changes in precipitation clusters (e.g., areas shifting from high–high clusters to non-significant clusters in panels a and c) or abrupt variations in explanatory factors (e.g., terrain-driven fluctuations in panels b and d), the RF-downscaled precipitation exhibits a distinct stair-stepping pattern, whereas MGWR produces a gradual and continuous spatial transition, demonstrating superior spatial degradation performance.

This divergence stems from fundamental differences in regression methodologies. RF constructs independent decision trees for each regression point, with predicted values based on the training outcomes of these trees, without directly being influenced by neighboring regression points. Consequently, it introduces a “fragmented patch” texture in visual outputs. In contrast, MGWR leverages spatial autocorrelation to establish local regression relationships that reflect the cumulative effects of various explanatory factors within a specific scale range on the regression point. As a result, it presents smoother texture degradation effects, better capturing the continuous spatial variations in precipitation distribution based on spatial autocorrelation.

4.3.2. Changes in Precipitation Accuracy

As shown in Figure 6, after MGWR downscaling, precipitation in overestimated low-value regions has been reduced, while high-value regions remained largely unchanged. In contrast, RF downscaling reduced precipitation in high-value regions but made little change to the overestimated low-value regions. Furthermore, the accuracy of downscaled IMERG precipitation was re-evaluated against in situ measurements from 40 meteorological stations, as summarized in Figure 7. Compared to the original IMERG performance (Figure 5), both MGWR and RF downscaling improve the accuracy of January and August precipitation estimates to varying degrees. However, quantitative evaluation metrics indicate that the RF model achieves superior overall accuracy performance.

Firstly, the overestimation phenomenon in the original IMERG data for low-precipitation regions of northwestern Sichuan was notably improved by the MGWR downscaling. Among 18 in situ stations within these regions, the correlation coefficients for January and August increased from 0.21 and 0.46 (original IMERG) to 0.24 and 0.52 (MGWR), respectively. In contrast, the RF model yielded lower correlations of 0.20 and 0.48 for the same periods. Additionally, as shown in

Table 3. Correction of IMERG to “near-heterogeneous” outliers after downscaling by MGWR and RF.

Outlier Stations	Observation (mm)	Original GPM (mm)	MGWR Result (mm)	RF Result (mm)
Leshan (January)	17.8	52.6	50.1	42.7
Mianyang (January)	3.6	38.8	27.5	21.4
Doujiangyan (August)	1080	545.7	548.9	628.9

, it is particularly notable that the precipitation changes at three outlier stations (Leshan, Mianyang, and Doujiangyan). Since all three stations are located on the edges of high-precipitation clusters in the Sichuan Basin, MGWR, which relies on spatial autocorrelation, considers the influence of nearby regression points during correction. Consequently, its correction for these outlier stations was limited. For these sites, relative errors decreased from 196%, 978%, and −49% to 181%, 664%, and −49%, respectively, before and after downscaling. In contrast, RF employs independent decision trees with stronger regression capabilities, effectively correcting the station’s biases and reducing the relative errors to 140%, 494%, and −42% after downscaling, respectively. This superior handling of cluster-adjacent outliers is identified as the primary reason for RF’s overall accuracy advantage over MGWR.

5. Discussion

This study performed downscaling of IMERG based on the fundamental hypothesis of “spatial scale invariance”. By establishing statistical regression relationships between low-resolution precipitation and environmental variables, higher-resolution environmental variables were utilized to predict precipitation at finer spatial scales. The primary objective of downscaling is to achieve enhanced spatial characterization, which necessitates that the statistical relationships between precipitation and environmental variables encompass two fundamental requirements. First, the regression accuracy must be ensured, as this forms the foundation for high-resolution precipitation prediction. Second, the relationships should reflect the actual physical influences of environmental variables on precipitation. This ensures that the fine-scale spatial distribution information from high-resolution environmental variables is incorporated into the precipitation data [44], thereby improving data accuracy while reducing spatial scale dependency.

In this study, the relationships between the selected environmental variables and precipitation have been widely validated by numerous prior studies. However, in Sichuan Province, precipitation distribution is shaped under the influence of East Asian monsoons, Indian monsoons, and Tibetan Plateau atmospheric circulations, combined with the region’s diverse topography (encompassing plateaus, mountains, and basins) [25]; consequently, the conditions forming precipitation distributions are more complex. As demonstrated in earlier analyses, Sichuan’s precipitation exhibits strong heterogeneity and significant autocorrelation (Figure 4), alongside extreme outlier sites adjacent to precipitation clusters. Therefore, from the perspective of downscaling objectives, the performance of regression models and their applicability in such complex regions as Sichuan warrant further investigation.

From the regression results of IMERG data by MGWR and RF (as shown in Figure 8), three evaluation metrics indicate that both models achieved well-maintained regression accuracy, with overall regression errors controlled near zero. Additionally, the correlation coefficients are close to 1 for both models, suggesting a consistent trend between predicted and observed values. However, residual distributions reveal distinct methodological differences. The RF model, leveraging the ensemble learning capability of multiple decision trees, consistently produced smaller residuals across all regression points compared to MGWR, particularly in both January (dry season) and August (wet season).

More importantly, regarding the environmental variable effects captured by the models, Figure 9 illustrates the variable importance in the RF model. Longitude, latitude, and elevation emerge as the three most influential factors, collectively contributing over 90% to regression accuracy, while the remaining five environmental variables account for less than 10%. Longitude and latitude, as macro-level factors, have a substantial influence on precipitation distribution at global scales. However, in the context of Sichuan Province’s regional scale, micro-geographical factors play a more prominent role [45]. In January, precipitation in the northwestern plateau of Sichuan occurs only when strong warm and humid air masses arrive. In contrast, within the Sichuan Basin, where airflow impacts are relatively minor, precipitation primarily results from water vapor accumulating in the basin and forming air convection. During August (monsoon season), moisture-laden airflows interact with heterogeneous terrain (plateaus, mountains, basins) to generate spatially diverse precipitation regimes [46].

A significant discrepancy exists between the feature importance rankings in RF and empirical observations. This phenomenon can be primarily attributed to RF’s feature importance quantification method that employs mean decrease in impurity. During node splitting in decision trees, variables with higher impurity levels indicate greater sample heterogeneity, which adversely impacts predictive performance. In this downscaling regression framework, longitude, latitude, and elevation exhibit spatially continuous and patterned distributions, and these spatial characteristics likely enhance their capacity to reduce impurity during node splitting in decision trees. Consequently, these geospatial predictors demonstrate heightened importance metrics and make greater contributions to regression model accuracy.

Compared to RF, which focuses on mathematical computations, the MGWR model incorporates local adaptability by accounting for spatial heterogeneity in precipitation distribution, utilizing bandwidth optimization to reflect scale-dependent relationships between environmental variables and precipitation [19,47]. The spatial scales of influence and significant impact areas for environmental variables in the MGWR model are presented in

Table 4. Spatial scales of each explaining variable in the MGWR model.

Variable	ELE	SLOP	WWD	NDVI	DSTR	WS
January	44	5249	5249	44	44	44
August	44	2161	4759	46	46	44

and Figure 10, respectively. Slope and windwardness, as micro-scale topographic factors, exhibit irregular and discrete heterogeneity across Sichuan. However, since MGWR is grounded in spatial autocorrelation principles, these factors operate at relatively large spatial scales. In January, they function as global variables (spanning the entire region with 5431 regression points) without statistically significant impacts on precipitation. During August, they transition to regional variables, demonstrating significant influence in the northwestern Sichuan Plateau. The remaining four environmental variables act as local variables in both January and August, but their significant impact zones differ markedly. In August, however, the IMERG precipitation distribution is continuous, resulting in contiguous significant influence zones; these zones break at the edge of high–high clusters in the Sichuan Basin. This discontinuity arises because MGWR is based on the assumption of “spatial proximity correlation” and lacks effective detection for “proximity anomalies,” as previously analyzed [48,49]. Consequently, this limitation also explains why MGWR fails to correct three atypical deviation points effectively.

6. Conclusions

Precipitation distribution in the topographically complex Sichuan region exhibits extreme spatial heterogeneity and significant positive spatial autocorrelation. While IMERG demonstrates reasonable accuracy in high-precipitation regions, it systematically overestimates low-precipitation areas. Additionally, IMERG fails to adequately detect extreme rainfall anomalies along the periphery of high-aggregation zones in the Sichuan Basin. Topographic, meteorological, and vegetational factors that accurately characterize regional spatial precipitation distribution were employed to construct the downscaled models, RF and MGWR. Generally, both models achieve partial success in refining spatial precipitation information for satellite-based precipitation products over topographically complex regions. However, the two models exhibit distinct strengths. MGWR, through bandwidth-optimized local regression, effectively captures the scale-dependent relationships between environmental variables and the spatial heterogeneity of precipitation. The results of downscaling demonstrate better spatial sharpening effects, accurately capturing the fine-scale characteristics of spatial precipitation while also improving corrections for overestimations in low-value regions. The RF demonstrates robust regression capabilities by constructing independent decision trees for each regression point and employing ensemble learning, which effectively corrects anomalous values around high-aggregation zones. Due to the distinct algorithmic frameworks between MGWR and RF, these two models exhibit different advantages, allowing selective application based on regional precipitation characteristics during downscaling. Leveraging their complementary strengths, developing hybrid algorithms constitutes a promising research direction for comprehensively improving satellite precipitation downscaling performance in topographically complex regions.