BackgroundInvestigation of global clustering patterns across regions is very important in spatial data analysis. Moran's I is a widely used spatial statistic for detecting global spatial patterns such as an east-west trend or an unusually large cluster. Here, we intend to improve Moran's I for evaluating global clustering patterns by including the weight function in the variance, introducing a population density (PD) weight function in the statistics, and conducting Monte Carlo simulation for testing. We compare our modified Moran's I with Oden's I*pop for simulated data with homogeneous populations. The proposed method is applied to a census tract data set.MethodsWe present a modified version of Moran's I which includes information about the strength of the neighboring association when estimating the variance for the statistic. We provide a power analysis on Moran's I, a modified version of Moran's I, and I*pop in a simulation study. Data were simulated under two common spatial correlation scenarios of local and global clustering.ResultsFor simulated data with a large cluster pattern, the modified Moran's I has the highest power (43.4%) compared to Moran's I (39.9%) and I*pop (12.4%) when the adjacent weight function is used with 5%, 10%, 15%, 20%, or 30% of the total population as the geographic range for the cluster.For two global clustering patterns, the modified Moran's I (power > 25.3%) performed better than both Moran's I (> 24.6%) and I*pop (> 7.9%) with the adjacent weight function. With the population density weight function, all methods performed equally well.In the real data example, all statistics indicate the existence of a global clustering pattern in a leukemia data set. The modified Moran's I has the lowest p-value (.0014) followed by Moran's I (.0156) and I*pop (.011).ConclusionsOur power analysis and simulation study show that the modified Moran's I achieved higher power than Moran's I and I*pop for evaluating global and local clustering patterns on geographic data with homogeneous populations. The inclusion of the PD weight function which in turn redefines the neighbors seems to have a large impact on the power of detecting global clustering patterns. Our methods to improve the original version of Moran's I for homogeneous populations can also be extended to some alternative versions of Moran's I methods developed for heterogeneous populations.

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As regulated by the ‘fire environment triangle’, three major forces are essential for understanding wildfire danger: (1) topography, (2) weather and (3) fuel. Within this concept, this study aimed to assess the wildfire danger for China based on a set of topography, weather and fuel variables. Among these variables, two remotely sensed key fuel variables, fuel moisture content (FMC) and foliage fuel load (FFL), were integrated into the assessment. These fuel variables were retrieved using radiative transfer models from the MODIS reflectance products. The random forest model identified the relationships between these variables and historical wildfires and then produced a daily updated and moderate-high spatial resolution (500 m) dataset of wildfire danger for China from 2001 to 2020. Results showed that this dataset performed well in assessing wildfire danger for China in terms of the ‘Area Under the Curve’ value, the fire density within each wildfire danger level, and the visualisation of spatial patterns. Further analysis showed that when the FMC and FFL were excluded from the assessment, the accuracy decreased, revealing the reasonability of the remotely sensed FMC and FFL in the assessment.

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