Geographically Weighted Regression Method Research Articles

Remote and Proximal Sensors Data Fusion: Digital Twins in Irrigation Management Zoning.

The scientific field of precision agriculture employs increasingly innovative techniques to optimize inputs, maximize profitability, and reduce environmental impact. However, obtaining a high number of soil samples is challenging in order to make precision agriculture viable. There is a trade-off between the amount of data needed and the time and resources spent to obtain these data compared to the accuracy of the maps produced with more or fewer points. In the present study, the research was based on an exhaustive dataset of apparent electrical conductivity (aEC) containing 3906 points distributed along 26 transects with spacing between each of up to 40 m, measured by the proximal soil sensor EM38-MK2, for a grain-producing area of 72 ha in São Paulo, Brazil. A second sparse dataset was simulated, showing only four transects with a 400 m distance and, in the end, only 162 aEC points. The aEC map via ordinary kriging (OK) from the grid with 26 transects was considered the reference, and two other mapping approaches were used to map aEC via sparse grid: kriging with external drift (KED) and geographically weighted regression (GWR). These last two methods allow the increment of auxiliary variables, such as those obtained by remote sensors that present spatial resolution compatible with the pivot scale, such as data from the Landsat-8, Aster, and Sentinel-2 satellites, as well as ten terrain covariates derived from the Alos Palsar digital elevation model. The KED method, when used with the sparse dataset, showed a relatively good fit to the aEC data (R2 = 0.78), with moderate prediction accuracy (MAE = 1.26, RMSE = 1.62) and reasonable predictability (RPD = 1.76), outperforming the GWR method, which had the weakest performance (R2 = 0.57, MAE = 1.78, RMSE = 2.30, RPD = 0.81). The reference aEC map using the exhaustive dataset and OK showed the highest accuracy with an R2 of 0.97, no systematic bias (ME = 0), and excellent precision (RMSE = 0.56, RPD = 5.86). Management zones (MZs) derived from these maps were validated using soil texture data from clay samples measured at 0-10 cm depth in a grid of 72 points. The KED method demonstrated the highest potential for accurately defining MZs for irrigation, producing a map that closely resembled the reference MZ map, thereby providing reliable guidance for irrigation management.

Pemodelan Faktor-Faktor yang Mempengaruhi Kasus Stunting di Sulawesi Selatan Menggunakan Geographically Weighted Regression

One of the prevalent nutritional issues affecting toddlers worldwide is stunting. Several studies on stunting cases have been conducted in Indonesia. However, modeling using the Geographically Weighted Regression (GWR) method in South Sulawesi has not been carried out. This study aims to identify the variables that affect the incidence of stunting in each district in South Sulawesi based on spatial modeling using the GWR method. Data on the number of stunting cases, the pproportion of low-birth-weight infants, the percentage of under-five who are malnourished, the percentage of proper drinking water, and the percentage of poor people in South Sulawesi in 2020 were used. The results show that the GWR model has an value of 86.64%, which is higher than that of the global regression model. The factors that influence the percentage of stunting based on the GWR modeling results are the percentage of under-five who are malnourished and the percentage of proper drinking water. The findings of this study are anticipated to help the government address the issue of stunting in South Sulawesi. Early prevention may then be implemented.

Spatial Big Data Analytics of Inequity in Access to Live Music Among Disadvantaged Populations

In recent years, music cities around the world have developed various supportive policy frameworks ensuring live music is accessible to large populations. The question of whether live music is equitably distributed by socioeconomic status remains unanswered, however. This study investigated the accessibility of music events in socially and economically disadvantaged communities. The level of accessible concerts varies substantially across U.S. counties, revealing significant inequity in access to concerts. Almost 80 percent of concerts are located in 5 percent of counties. Ordinary least squares (OLS) regression, geographically weighted regression (GWR), and multiscale geographically weighted regression (MGWR) methods were then employed to explore associations between accessible concerts and the socioeconomic characteristics of communities where these concerts are located. The regression models revealed that areas with a higher proportion of residents without a high school degree, higher unemployment rate, and higher poverty rate were less likely to have access to concerts, yet positive associations were found between accessible concerts and mean household income. Local R 2 values further confirmed the robustness of regression results of both GWR and MGWR and showed significant spatial nonstationarity of model performance. GWR and MGWR methods improved model performance significantly over the OLS method and proved how local conditions influence the OLS regression. The results from this study can guide decision makers and stakeholders in making appropriate policies to achieve equitable access to music events, especially for disadvantaged communities.

Geographic Information System Mapping Risk Factors Stunting Using Methods Geographically Weighted Regression

Technological developments in this era of globalization are very rapid. This requires humans to enter life together with information and technology. Stunting as a chronic nutritional problem in children, continues to be a global challenge. Geographic Information Systems (GIS) have proven to be effective tools in spatial analysis and distribution mapping stunting. In this context, method Geographically Weighted Regression (GWR) has been used to model the spatial relationship between factors that contribute to stunting. This research will produce a Geographic Information System using the method Geographically Weighted Regression. With this Geographic Information System, it can display location points and affected information stunting. Because of this system, the Padang Lawas Utara District Health Office does not need to store location data stunting in archive form again but digitally. This study underscores the importance of using GIS with the GWR method in mapping patient locations stunting. Through the integration of geographic data and spatial analysis, we can generate a better understanding of the influencing factors stunting at the local level, which in turn can support prevention and response efforts stunting which is more effective.

Application of Geographically Weighted Regression Method on the Human Development Index of Central Java Province

Spatial data are data containing information on the location or geography of a region on the representation of objects on earth. Geographically Weighted Regression (GWR) is a development of the Ordinary Least Square (OLS) theory into a weighted regression model that considers spatial effects, resulting in a parameter estimation that can only be used to predict each location where the data are observed. The Human Development Index (HDI) is an essential indicator for measuring success in efforts to build human quality of life. HDI data regencies/cities in Central Java are interconnected, so it is said to be spatial data and there are spatial effects in it. Therefore, the GWR method was applied to obtain faculties affecting HDI in Central Java Province. The data used were secondary data in 2020. The determination coefficients of the GWR model ranged between 76.09% and 87.16%. If the variable values of population density and Gross Regional Domestic Product (GRDP) increase by one unit in each district/city in Central Java Province, the HDI variable value increases. These results were visualized on a dashboard providing information about the characteristics of HDI and independent variables, GWR parameter estimates, and the significance of independent variables in each regency/city.

Nickel Grade Inversion of Lateritic Nickel Ore Using WorldView-3 Data Incorporating Geospatial Location Information: A Case Study of North Konawe, Indonesia

The North Konawe region in Indonesia, known for its lateritic nickel (Ni) deposits, holds significant potential for obtaining Ni resources. However, the complex topographic conditions of this area pose challenges. Exploring the application of remote sensing technology to reveal the spectral response mechanism of Ni grade from high-precision multispectral data and inversion of Ni grade represents a novel direction in future Ni resource exploration. Traditional remote sensing inversion methods solely consider the spectral characteristics of sample data and ignore vital geospatial location information. As a result, efficiently obtaining regional details of target substance content over large areas has become challenging. The introduction of the geographically weighted regression (GWR) method offers an opportunity for fine-grained Ni grade inversion based on remote sensing. This study focused on the E and K blocks within the lateritic Ni mining area in North Konawe. Through utilizing the WordView-3 multispectral data which exhibits immense potential in quantitative remote sensing inversion studies, GWR was employed to integrate spectral features and spatial information. The goal was to reveal the correlation between multispectral remote sensing data and Ni grade. The obtained results were then compared and analyzed with multiple linear regression (MLR) and back propagation neural network (BPNN) models. The findings revealed that GWR achieved the highest coefficient of determination R2 of 0.96, surpassing MLR and BPNN values of 0.05 and 0.17, respectively. Additionally, GWR exhibited the lowest root mean square error of 0.04, which was lower than those of MLR and BPNN with the values of 0.25 and 0.23, respectively. These results confirmed the enhanced stability and accuracy of the GWR method compared to MLR and BPNN. Furthermore, GWR effectively mapped the spatial distribution trends of Ni grades in the study area, providing evidence of the method’s effectiveness in Ni grade inversion. The study also delved into the inversion effect of the GWR method in areas with varying weathering crust thickness and vegetation cover. The research revealed that higher values of weathering crust thickness negatively impacted the inversion effect. However, the influence mechanism of vegetation cover on Ni grade inversion necessitated further investigation. These results served as a significant demonstration of the remote sensing inversion of mineral resource grades in similar areas. They provided valuable insights for future exploration and decision-making processes.

A New Algorithm for Large-Scale Geographically Weighted Regression with K-Nearest Neighbors

Geographically weighted regression (GWR) is a classical method for estimating nonstationary relationships. Notwithstanding the great potential of the model for processing geographic data, its large-scale application still faces the challenge of high computational costs. To solve this problem, we proposed a computationally efficient GWR method, called K-Nearest Neighbors Geographically weighted regression (KNN-GWR). First, it utilizes a k-dimensional tree (KD tree) strategy to improve the speed of finding observations around the regression points, and, to optimize the memory complexity, the submatrices of neighbors are extracted from the matrix of the sample dataset. Next, the optimal bandwidth is found by referring to the spatial clustering relationship explained by K-means. Finally, the performance and accuracy of the proposed KNN-GWR method was evaluated using a simulated dataset and a Chinese house price dataset. The results demonstrated that the KNN-GWR method achieved computational efficiency thousands of times faster than existing GWR algorithms, while ensuring accuracy and significantly improving memory optimization. To the best of our knowledge, this method was able to run hundreds of thousands or millions of data on a standard computer, which can inform improvement in the efficiency of local regression models.

PENERAPAN METODE GEOGRAPHICALLY WEIGHTED REGRESSION PADA TINGKAT PENCEMARAN AIR BERDASARKAN TOTAL COLIFORM DI PROVINSI JAMBI

The purpose of this study is to obtain a local estimation model formed by considering spatial factors on the level of water pollution based on total coliforms in Jambi Province and can determine the most dominant factors affecting the total coliform water of PDAM Districts / Municipalities in Jambi Province using Geographically Weighted Regression (GWR) analysis. The type of data used in this study is primary data in quantitative form. This primary data was obtained by taking PDAM water samples directly in 9 regencies/cities in Jambi Province. The results of GWR analysis show that the dominant factors affecting the total coliform of PDAM water in each district/city in Jambi Province vary with different estimated parameters. The best model formed is a model with the GWR method, the adaptive bisquare weighting function which is shown from the value of the model's goodness criteria, namely the smallest AIC value and the largest coefficient of determination

LULC changes to riverine flooding: A case study on the Jamuna River, Bangladesh using the multilayer perceptron model

In riverine nations like Bangladesh, floods are frequent, bringing disaster that impairs people's lives and the national economy. Due to climate change, uncontrolled growth, rapid urbanization, expansion of agriculture plantations, and other factors influence Land-Use-Land-Cover (LULC) changes which can make flooding conditions more unpredictable. The aim of this study is to examine the relationship between changes in LULC and floods in the Jamuna River over a 30-year period from 1990 to 2020 through a quantitative correlational approach. Due to spatial nonlinearity, the relationship between LULC changes and other flood-influencing factors of different areas may vary with flooding. As a result, applying a global regression model can produce biased results in certain locations. We employed the multilayer perceptron neural network and Geographically Weighted Regression (GWR) method to solve this issue. The GWR method applies local regression based on carefully chosen criteria to handle spatial variability. A multilayer perceptron neural network was used to determine the potential for riverine flooding. The study's findings revealed that LULC changes in the area far from the river had a significant impact on changes in riverine flooding, as shown by the fact that 29.71% of those locations had a Pearson coefficient greater than 0.75. In contrast, LULC changes near the river did not strongly correlate with changes in riverine flood potential because 19.83% of those locations had a very low Pearson coefficient of less than 0.75.

Geographically weighted regression based on a network weight matrix: a case study using urbanization driving force data in China

Geographically weighted regression (GWR) is a classical modeling method for dealing with spatial non-stationarity. It incorporates the distance decay effect in space to fit local regression models, where distance is defined as Euclidean distance. Although this definition has been expanded, it remains focused on physical distance. However, in the era of globalization and informatization, where the phenomenon of remotely close association is common, physical distance may not reflect real spatial proximity, and GWR based on physical distance has clear limitations. This paper proposes a geographically weighted regression based on a network weight matrix (NWM GWR) model. This does not rely on geographical location modeling; instead, it uses network distance to measure the proximity between two regions and weights observations by improving the kernel function to achieve distance attenuation. We adopt the population mobility network to establish a network weight matrix, modeling China’s urbanization and its multidimensional driving factors using network autocorrelation and NWM GWR methods. Results show that the NWM GWR model has more accurate fit and better stability than ordinary least squares and GWR models, and better reveals relationships between variables, which makes it suitable for modeling economic and social systems more broadly.

The thermal performance of urban form – An analysis on urban structure types in Berlin

Increasing urban heat issues induced by climatic changes and growing urban populations exacerbate the need for adaptation. The present study intends to foster the so far quite rarely realized transfer from research to real-world planning. Subject of investigation is the thermal performance and characterization of urban structure types (USTs) in Berlin, Germany. Applying Landsat 8 derived land surface temperatures (LSTs), we first determine differences in the temperature patterns of the regarded USTs. Second, after running correlation analyses with LST and potentially influencing factors (NDVI – normalized difference vegetation index, imperviousness, building ratio, and building height), we fit ordinary least square (OLS) and geographically weighted regression (GWR) models. Finally, we relate the GWR results to the USTs and determine the effect of each variable on the respective LST regime. We find significant differences in the thermal performance of USTs, strong correlations between explaining variables and LST, and a sophisticated picture concerning GWR coefficients at various locations. Quasi-global r2 for the GWR (0.83) improves the OLS model value (0.53) considerably. The spatially explicit GWR method in combination with results aggregated on the planning-relevant UST-level provides crucially important information for climate adaptation and planning while being adaptable and transferable to other urban areas.

Pemodelan Geographically Weighted Regression pada Kasus Stunting di Provinsi Nusa Tenggara Timur Tahun 2020

Stunting or short toddlers is one of the problems that Indonesia is currently facing. Based on data from the Indonesia Health Profile in 2020, the highest prevalence of stunting in Indonesia in 2020 was in the East Nusa Tenggara Province. The occurrence of stunting in each district/city has the possibility of having different characteristics from one region or another which is referred to as regional heterogeneity or spatial heterogeneity. This research was conducted to determine the factors that influence stunting cases in each district/city of East Nusa Tenggara Province. This research uses the Geographically Weighted Regression (GWR) method to model stunting cases in each district/city of East Nusa Tenggara Province. The factors that significantly affect stunting in districts/cities in East Nusa Tenggara Province spatially with α =10% percentage of infants receiving complete immunization, the percentage of poor people, the percentage of infants receiving exclusive breastfeeding, the percentage of women who have graduated from senior high school, and the percentage of women who have ever married underage. The modeling of stunting cases in East Nusa Tenggara Province using the GWR method obtained R2 of 99,25% larger than the OLS model of 52,1%, and the AIC of the GWR model of 59,8105 smaller than OLS model.

A physical method for downscaling land surface temperatures using surface energy balance theory

Fine-resolution land surface temperature (LST) derived from thermal infrared remote sensing images is a good indicator of surface water status and plays an essential role in the exchange of energy and water between land and atmosphere. A physical surface energy balance (SEB)-based LST downscaling method (DTsEB) is developed to downscale coarse remotely sensed thermal infrared LST products with fine-resolution visible and near-infrared data. The DTsEB method is advantageous for its ability to mechanically interrelate surface variables contributing to the spatial variation of LST, to quantitatively weigh the contributions of each related variable within a physical framework, and to efficaciously avoid the subjective selection of scaling factors and the establishment of statistical regression relationships. The applicability of the DTsEB method was tested by downscaling 12 scenes of 990 m Moderate Resolution Imaging Spectroradiometer (MODIS) and aggregated Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) LST products to 90 m resolution at six overpass times between 2005 and 2015 over three 9.9 km by 9.9 km cropland (mixed by grass, tree, and built-up land) study areas. Three typical LST downscaling methods, namely the widely applied TsHARP, the later developed least median square regression downscaling (LMS) and the geographically weighted regression (GWR), were introduced for intercomparison. The results showed that the DTsEB method could more effectively reconstruct the subpixel spatial variations in LST within the coarse-resolution pixels and achieve a better downscaling accuracy than the TsHARP, LMS and GWR methods. The DTsEB method yielded, on average, root mean square errors (RMSEs) of 2.01 K and 1.42 K when applied to the MODIS datasets and aggregated ASTER datasets, respectively, which were lower than those obtained with the TsHARP method, with average RMSEs of 2.41 K and 1.71 K, the LMS method, with average RMSEs of 2.35 K and 1.63 K, and the GWR method, with average RMSEs of 2.38 K and 1.64 K, respectively. The contributions of the related surface variables to the subpixel spatial variation in the LST varied both spatially and temporally and were different from each other. In summary, the DTsEB method was demonstrated to outperform the TsHARP, LMS, and GWR methods and could be used as a good alternative for downscaling LST products from coarse to fine resolution with high robustness and accuracy.

Geographically Weighted Regression dalam Menganalisis Faktor-Faktor yang Mempengaruhi Kasus Tuberkulosis di Sumatera Utara

Geographically Weighted Regression (GWR) is a method used to analyze a case by considering spatial effects. Spatial effects indicate differences in environmental characteristics between regions. A spatial effect can be seen from the violation of the assumption of the multiple linear regression homoscedasticity test. Research in the health sector often shows that the spread of disease, especially infectious diseases, is influenced by spatial effects, one of which is tuberculosis. In 2020, North Sumatra will become one of the areas with high tuberculosis cases, so it is necessary to study tuberculosis cases and determine the factors that influence it by involving spatial effects. This study aims to model tuberculosis cases and analyze the ten factors thought to influence it using the GWR method with the adaptive kernel bi-square weighting function. The results showed that 23 regencies/cities had local GWR models and different factors influencing tuberculosis cases for each region, and ten other regencies/cities were influenced by other factors outside the variables studied. Based on the variables that affect it, 13 regional groups are formed. Modeling with the GWR method can explain tuberculosis cases in North Sumatra by 99.4%, and other predictor variables influence the rest.

Estimation of the soil arsenic concentration using a geographically weighted XGBoost model based on hyperspectral data

Considering the high toxicity of arsenic (As), its contamination of soil represents an alarming environmental and public health issue. Existing soil heavy metal concentration estimation models based on hyperspectral data ignore the spatial nonstationarity of the relationship between the soil spectrum and heavy metal concentration. A novel model (geographically weighted eXtreme gradient boosting or GW-XGBoost model) combining geographically weighted regression (GWR) method with XGBoost algorithm was proposed. The northeast district of Beijing, China, was chosen as a case study area to assess the effectiveness of the proposed model. The GW-XGBoost model was established to estimate the As concentration based on the typical spectrum of As and the spatial correlation between the spectrum and As concentration obtained using the GWR method, and the result was compared to that obtained with the XGBoost and GWR models. The accuracy of the GW-XGBoost model was obviously better than that of the other models (R2GW-XGBoost = 0.90, R2XGBoost = 0.48, and R2GWR = 0.74). Therefore, the proposed model is reliable, as it considers the spatial correlation between the spectrum and As concentration.

PEMODELAN MIXED GEOGRAPHICALLY WEIGHTED REGRESSION DENGAN ADAPTIVE BANDWIDTH UNTUK ANGKA HARAPAN HIDUP (Studi Kasus : Angka Harapan Hidup di Jawa Tengah)

Life expectancy at birth (AHH) is an estimate of the years a person will take from birth. AHH is used as an indicator of public health and welfare. These two indicators are of concern to the government in relation to human development. It is hoped that the AHH value will continue to increase so that the quality of human development will also increase. Modeling of the factors that influence AHH needs to be done so that efforts to increase AHH become more effective.The AHH value for Central Java (Central Java) in 2020 is 74.37. Factors thought to influence AHH in Central Java are the percentage of poor people (X1), the percentage of households with proper sanitation (X2), the percentage of children under five who are fully immunized (X3) and the open unemployment rate (X4). The assumption of homoscedasticity in AHH modeling in Central Java using linear regression was not fulfilled, meaning that there was spatial heterogeneity between districts/cities, so the Geographically Weighted Regression (GWR) method was used. The weighting function used is the Bisquare and Tricube kernels with adaptive bandwidth. The GWR method will encounter problems if not all independent variables are local, so the Mixed Geographically Weighted Regression (MGWR) method is used. The results of the GWR analysis for the two weighting functions are that the X1 variable is not local, so the MGWR method is used. The results of MGWR modeling for the two weighting functions are that local variables and global variables have a significant effect. The best model is the MGWR model with Kernel Tricube weighting because it has the smallest AICc value. Keyword : AHH, GWR, MGWR, Adaptive Kernel Bisquare, Adaptive Kernel Tricube, AICc

A GWR downscaling method to reconstruct high-resolution precipitation dataset based on GSMaP-Gauge data: A case study in the Qilian Mountains, Northwest China

Accurate precipitation data are crucial for hydrological, meteorological, and ecological research. However, it is difficult to obtain high-precision and high-resolution spatiotemporal distributions of precipitation in remote mountain regions with complex topography and sparse rain gauges. In addition, the spatial resolutions of existing satellite precipitation products are too coarse to apply them in the mountain regions with great spatiotemporal heterogeneity. To overcome the disadvantage, downscaling satellite precipitation products has been an effectively method to develop high-resolution precipitation data. In this study, a geographically weighted regression (GWR) model, coupling with topographical and water vapor source variables filtered by stepwise regression analysis (SRA), is applied to downscale the GSMaP-Gauge precipitation products (0.1° × 0.1°) to obtain high-resolution (1 km × 1 km) precipitation from 2000 to 2020 at annual, seasonal, and monthly scales over the Qilian Mountains. Besides, the accuracy of the downscaled precipitation based on all meteorological stations and the stations at high altitude (i.e., over 3000 m) are validated. Furtherly, the spatiotemporal variations of precipitation are analyzed. The results show that: (1) the accuracy after downscaling has been improved comparing with that of the original data. The accuracy of precipitation simulated at high-altitude stations is lower than that at all stations; (2) The trend of precipitation before and after downscaling is consistent in space. The spatial distributions of precipitation at annual, spring, summer, autumn, and months from March to November are decreased from the southeast to the northwest; (3) The spatial variations of precipitation show an increasing trend in most areas (>50%) at different time scales, except for March and September. Along with the time, the annual precipitation shows an increasing trend with a slope of 3.83 over the last 20 years. These findings suggest that the GWR method can be applied effectively to downscale annual, seasonal, and monthly precipitation of GSMaP-Gauge products in the Qilian Mountains.

Estimation of air temperature and the mountain-mass effect in the Yellow River Basin using multi-source data.

Quantitative studies of the multiple factors influencing the mountain-mass effect, which causes higher temperatures in mountainous than non-mountainous regions, remain insufficient. This study estimated the air temperature in the Yellow River Basin, which spans three different elevation ranges, using multi-source data to address the uneven distribution of regional meteorological stations. The differences in mountain-mass effect for different geomorphic regions at the same altitude were then compared. The Manner–Kendall nonparametric test was used to analyse time series changes in temperature. Moreover, we employed the geographically weighted regression (GWR) model, with MODIS land-surface and air-temperature data, station-based meteorological data, vertical temperature gradients corresponding to the 2000–2015 period, and elevation data, to estimate the correlation between monthly mean surface temperature and air temperature in the Yellow River Basin. The following major results were obtained. (1) The GWR method and ground station-based observations enhanced the accuracy of air-temperature estimates with an error of only ± 0.74°C. (2) The estimated annual variations in the spatial distributions of 12-month average temperatures showed that the upper Tibetan Plateau is characterised by low annual air temperatures with a narrow spatial distribution, whereas north-eastern areas upstream of the Inner Mongolia Plateau are characterised by higher air temperatures. Changes in the average monthly air temperature were also high in the middle and lower reaches, with a narrow spatial distribution. (3) Considering the seasonal variation in the temperature lapse rate, the mountain-mass effect in the Yellow River Basin was very high. In the middle of each season, the variation of air temperature at a given altitude over the Tibetan Plateau was higher than that over the Loess Plateau and Jinji Mountain. The results of this study reveal the unique temperature characteristics of the Yellow River Basin according to its geomorphology. Furthermore, this research contributes to quantifying mountain-mass effects.

Evaluating the NDVI–Rainfall Relationship in Bisha Watershed, Saudi Arabia Using Non-Stationary Modeling Technique

The Normalized Difference Vegetation Index (NDVI) and rainfall data were used to model the spatial relationship between vegetation and rainfall. Their correlation in previous studies was typically based on a global regression model, which assumed that the correlation was constant across space. The NDVI–rainfall association, on the other hand, is spatially non-stationary, non-linear, scale-dependent, and influenced by local factors (e.g., soil background). In this study, two statistical methods are used in the modeling, i.e., traditional ordinary least squares (OLS) regression and geographically weighted regression (GWR), to evaluate the NDVI–rainfall relationship. The GWR was implemented annually in the growing seasons of 2000 and 2016, using climate data (Normalized Vegetation Difference Index and rainfall). The NDVI–rainfall relationship in the studied Bisha watershed (an eco-sensitive zone with a complex landscape) was found to have a stable operating scale of around 12 km. The findings support the hypothesis that the OLS model’s average impression could not accurately represent local conditions. By addressing spatial non-stationarity, the GWR approach greatly improves the model’s accuracy and predictive ability. In analyzing the relationship between NDVI patterns and rainfall, our research has shown that GWR outperforms a global OLS model. This superiority stems primarily from the consideration of the relationship’s spatial variance across the study area. Global regression techniques such as OLS can overlook local details, implying that a large portion of the variance in NDVI is unexplained. It appears that rainfall is the most significant factor in deciding the distribution of vegetation in these regions. Furthermore, rainfall had weak relationships with areas predominantly located around wetlands, suggesting the need for additional factors to describe NDVI variations. The GWR method performed better in terms of accuracy, predictive power, and reduced residual autocorrelation. Thus, GWR is recommended as an explanatory and exploratory technique when relations between variables are subject to spatial variability. Since the GWR is a local form of spatial analysis that aligned to local conditions, it has the potential for more accurate prediction; however, a larger amount of data is needed to allow a reliable local fitting.

Spatial prediction of soil calcium carbonate content based on Bayesian maximum entropy using environmental variables

Soil calcium carbonate (CaCO3) content is an important soil property. The prediction of soil CaCO3 content is necessary for the sustainable management of soil fertility. In this work, we attempted to incorporate environmental variables directly and through regression models into the framework of Bayesian maximum entropy (BME) to predict CaCO3 content. Firstly, multiple linear regression (MLR) and geographically weighted regression (GWR) were used to establish a relationship between sampling data and environmental variables, including Digital Elevation Model, pH, temperature, rainfall, and fluvo-aquic soils. Prediction results of MLR and GWR served as soft data and were incorporated into the framework of BME to estimate the CaCO3 content. Secondly, soil samples and environmental variables were combined to generate probability distributions of CaCO3 at unsampled points. These probability distributions were used as soft data for the BME to predict the CaCO3 content. The results showed that the GWR method (r = 0.84, RMSE = 24.0 g kg−1) performed better than the MLR method (r = 0.73, RMSE = 30.1 g kg−1). The BME-GWR method outperformed the BME-EV and BME-MLR methods. The r values of BME-GWR, BME-EV, and BME-MLR methods were 0.87, 0.86, and 0.82, respectively, and the RMSEs of the three methods were 22.2, 23.9, and 25.2 g kg−1, respectively. The spatial distribution of CaCO3 content predicted by the above methods was similar and significantly higher in the southwest than in the northeast.