Design of spatiotemporal variability index for climatic variables

Spatiotemporal signals are currently gaining wide popularity owing to their richness in terms of information content from both spatial and temporal aspects. Climatic studies involve the usage of such signals from different spatial locations to understand the climatic conditions, anomalies and for prediction of similar climatic zones. Measurement of the complex inter-relationships in the spatiotemporal processes is of vital importance in this regard. The predominant frequency components associated with annual, semi-annual, and quarterly seasonal variations exhibit interchangeability across spatial and temporal dimensions, thereby contributing significantly to the variability within the spatiotemporal region under investigation. Employing frequency domain analysis enables the examination of these crucial seasonal components, even amidst noise, provided effective frequency domain-based techniques are employed. This paper is based on the measurement of the variability of spatiotemporal climatic variables considered from different geographic zones using multivariate variational mode decomposition. The main advantage of the proposed index lies in the ability to measure the variability of the signals acquired from either spatially close or far-off locations on Earth. Also, the index harnesses the hidden frequency components in the spatiotemporal signals under test by comparing the aligned periodic components across different zones. The correctness of the proposed index is tested through exhaustive simulation studies and also against the weather measurements like the Earth skin temperature, humidity and precipitation acquired from spatially close and far-off locations over a period of 40 years.