Spatially Constrained Copula‐Based Clustering for Climate Zone Classification in Borneo

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Abstract
This study presents an advanced climate zone classification approach for Borneo using a spatially constrained copula‐based clustering framework. The methodology integrates copula theory for multivariate dependency modelling with fuzzy c‐means (FCM) clustering to capture uncertainty in regional climate classification, while spatial constraints enhance geographic coherence. Historical climate data from the Princeton Global Forcing dataset (1950–2014) were used, encompassing elevation, rainfall, average temperature (Tavg), minimum temperature (Tmin), maximum temperature (Tmax), diurnal temperature range (DTR) and relative humidity (RH). A total of 23 normalisation methods and 11 distance metrics were evaluated to optimize clustering performance. Clustering sensitivity was assessed using internal validation indices: Average Silhouette Width (ASW), Dunn Index (DI) and Calinski‐Harabasz Index (CHI). Results revealed that Yeo‐Johnson normalisation combined with Minkowski distance yielded the most robust performance (ASW = 0.3720, DI = 1.00EE‐04, CHI = 533.25). This configuration successfully delineated five distinct climate zones, Central‐North, East, West, Northeast and South, by achieving a high spatial coherence score (57.08) and establishing contiguous, topo‐climatologically meaningful regions. Central‐North emerged as the coolest and wettest, with the highest elevation, RH and DTR. East and South zones were the warmest, exhibiting the lowest RH and highest variability in DTR and rainfall. The Northeast showed the most pronounced seasonal and spatial temperature variation, while the West was marked by high rainfall and moderate DTR and RH. These zones reflect Borneo's climatic heterogeneity shaped by topographic and thermal‐hygrometric gradients. Spatial autocorrelation analysis using Moran's I confirmed clear spatial structures within clusters, with rainfall and RH showing the strongest spatial dependencies and Tmax the weakest. The West zone emerged as the most spatially homogeneous, while the South exhibited lower spatial dependence. This study advances regional climate classification by integrating statistical rigour, spatial consistency and multivariate climate behaviour, offering valuable insights for climate impact assessment, ecological planning and adaptive environmental management in tropical regions.

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