Identification of homogeneous rainfall regions in New South Wales, Australia

Identifying homogeneous regions based on spatial variables is vital for providing a certain and fixed region's spatial and temporal behavior. However, a significant problem of non-separation rises when the geographic coordinates are utilized for clustering, just because the Euclidean distance is not suitable for clustering when considering the geographic coordinates. Therefore, this study focuses on employing such methods where the non-separation is minimum for identifying homogenous regions. The average annual rainfall data of 226 meteorological monitoring stations for 1911–2018 of New South Wales (NSW), Australia, was considered for the current study. The data is standardized with zero mean and unit variance to remove the effect of different measurement scales. The geographical coordinates are then converted to rectangular coordinates by the Lambert projection method. Using the Partition Around Medoid (PAM) algorithm, also known as the k-medoid algorithm (which minimizes the sum of dissimilarities instead of the sum of squares of Euclidean distances) on rectangular Lambert projected coordinates, 10 well-separated clusters are obtained. The Mean Squared Prediction Error (MSPE) is comparatively smaller if the prediction of unobserved locations in cluster 3 is made. However, this error increases if the prediction is made for a complete monitoring network. The identified 10 homogeneous regions or clusters provide a good separation when the lambert coordinates are used instead of geographical coordinates.