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.

中文翻译：

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使用非平稳建模技术评估沙特阿拉伯比沙流域的NDVI与降雨关系

利用归一化植被指数（NDVI）和降雨数据对植被与降雨之间的空间关系进行建模。在以前的研究中，它们的相关性通常基于全局回归模型，该模型假定该相关性在整个空间中都是恒定的。另一方面，NDVI与降雨的关联在空间上是不稳定的，非线性的，与比例相关的，并且受局部因素（例如土壤背景）的影响。在这项研究中，在建模中使用了两种统计方法，即传统的普通最小二乘（OLS）回归和地理加权回归（GWR），以评估NDVI与降雨的关系。GWR是在2000年和2016年的生长季节中每年使用气候数据（归一化植被差异指数和降雨量）实施的。在所研究的比沙河流域（具有复杂景观的生态敏感区）中，NDVI与降雨的关系被发现具有约12 km的稳定运行规模。这些发现支持了以下假设：OLS模型的平均印象不能准确代表当地情况。通过解决空间非平稳性，GWR方法极大地提高了模型的准确性和预测能力。在分析NDVI模式与降雨之间的关系时，我们的研究表明，GWR优于全球OLS模型。这种优势主要源于对整个研究区域中关系的空间差异的考虑。诸如OLS之类的全局回归技术可以忽略局部细节，这意味着NDVI中的大部分方差无法解释。似乎降雨是决定这些地区植被分布的最重要因素。此外，降雨与主要位于湿地附近的地区之间的关系较弱，这表明需要其他因素来描述NDVI的变化。GWR方法在准确性，预测能力和减少的残留自相关方面表现更好。因此，当变量之间的关系受空间可变性影响时，建议使用GWR作为一种解释性和探索性技术。由于GWR是与当地条件相符的空间分析的一种局部形式，因此它有可能进行更准确的预测。但是，需要大量数据才能进行可靠的局部拟合。降雨与主要位于湿地附近的地区之间关系较弱，这表明需要其他因素来描述NDVI的变化。GWR方法在准确性，预测能力和减少的残留自相关方面表现更好。因此，当变量之间的关系受空间可变性影响时，建议使用GWR作为一种解释性和探索性技术。由于GWR是与当地条件相符的空间分析的一种局部形式，因此它有可能进行更准确的预测。但是，需要大量数据才能进行可靠的局部拟合。降雨与主要位于湿地附近的地区之间关系较弱，这表明需要其他因素来描述NDVI的变化。GWR方法在准确性，预测能力和减少的残留自相关方面表现更好。因此，当变量之间的关系受空间可变性影响时，建议使用GWR作为一种解释性和探索性技术。由于GWR是与当地条件相符的空间分析的一种局部形式，因此它有可能进行更准确的预测。但是，需要大量数据才能进行可靠的局部拟合。当变量之间的关系受空间可变性影响时，建议使用GWR作为一种解释性和探索性技术。由于GWR是与当地条件相符的空间分析的一种局部形式，因此它有可能进行更准确的预测。但是，需要大量数据才能进行可靠的局部拟合。当变量之间的关系受空间可变性影响时，建议使用GWR作为一种解释性和探索性技术。由于GWR是与当地条件相符的空间分析的一种局部形式，因此它有可能进行更准确的预测。但是，需要大量数据才能进行可靠的局部拟合。