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Extreme rainfall is the most common cause of flooding and likelihood of such events is found to increase in recent studies. Large scale natural variability, human induced global warming and local atmospheric warming are important drivers of extreme rainfall. Understanding the association of these drivers with extreme rainfall and finding out the most significant physical driver will provide a foundation for risk assessment. This study presents a methodology to investigate the association of extreme rainfall events with physical drivers and to model their dependence structure. The methodology is demonstrated with application to Mahanadi River basin, India. Non-stationary extreme value models with multivariate ENSO index, global average temperature anomalies and local mean temperature anomalies as covariates are fitted at non-stationary rainfall grids of the basin. Statistical modelling confirms localized temperature to be the main driver influencing rainfall extremes. Clausius-Clapeyron (CC) scaling curves relating daily rainfall extremes and local mean temperature are developed at all the grids to obtain insights into warming induced changes in rainfall extremes. Significant deviations from the expected CC scaling behaviour are observed. Daily rainfall extremes show peaks at low (25 degrees C) to medium (30 degrees C) range of temperature, but exhibit a decrease at high temperatures for most of the grids. No change in this pattern of relationship is observed when the extreme rainfall is lagged by 1-9 days with temperature. This time lag is selected based on the concept of residence time of water in the atmosphere. The Copula theory is applied to capture the dependence of annual maximum daily rainfall and temperature extremes. Conditional probabilities of extreme rainfall are estimated by conditioning on local mean temperature values of strongest extreme rainfall events. Comparison of conditional probabilities suggests that stronger rainfall events are occurring at 30 degrees C. This study emphasizes the necessity of understanding the dependence structure of extreme rainfall and local mean temperature.