Spatio-temporal patterns of diurnal temperature: a random matrix approach I-case of India

We consider the spatio-temporal gridded daily diurnal temperature range (DTR) data across India during the 72-year period 1951--2022. We augment this data with information on the El Nino-Southern Oscillation (ENSO) and on the climatic regions (Stamp's and Koeppen's classification) and four seasons of India. We use various matrix theory approaches to trim out strong but routine signals, random matrix theory to remove noise, and novel empirical generalised singular-value distributions to establish retention of essential signals in the trimmed data. We make use of the spatial Bergsma statistics to measure spatial association and identify temporal change points in the spatial-association. In particular, our investigation captures a yet unknown change-point over the 72 years under study with drastic changes in spatial-association of DTR in India. It also brings out changes in spatial association with regard to ENSO. We conclude that while studying/modelling Indian DTR data, due consideration should be granted to the strong spatial association that is being persistently exhibited over decades, and provision should be kept for potential change points in the temporal behaviour, which in turn can bring moderate to dramatic changes in the spatial association pattern. Some of our analysis also reaffirms the conclusions made by other authors, regarding spatial and temporal behavior of DTR, adding our own insights. We consider the data from the yearly, seasonal and climatic zones points of view, and discover several new and interesting statistical structures which should be of interest, especially to climatologists and statisticians. Our methods are not country specific and could be used profitably for DTR data from other geographical areas.