A New Class of Metrics for Quantifying the Intensity of Heat Waves Based on Relative Entropy

Among the challenges in studying the statistics and physics of extreme heat events is the quantification of their intensity. There is a plethora of definitions based on (1) thresholds of absolute values of measures of heat discomfort, e.g., the heat index, and (2) the difference between a three-day average temperature (maximum daily temperature or averaged daily temperature) and a specific quantile of daily temperature, typically the 95th percentile. The proliferation of heat wave indices stems from the nature of the problem, which includes human perception. Additional complexity arises due to the difficulty of directly linking meteorological variables and mortality because of early warnings and the use of air conditioning. In this paper, we address the human perception issue by using excessive heat warnings issued by the NWS Weather Forecasting Offices (WFO). Despite following precise criteria, these alerts also contain adjustments based on knowledge of local conditions by the forecaster. Once a WFO issues a heat wave, we consider hourly meteorological variables from ERA5 for all grid points within its area and compare the resulting distribution with the distribution of the same variable during non-warning periods. The comparison is done using the Kullback-Leibler divergence. This presentation demonstrates the utility of the approach by focusing on specific heat events from 2006 to 2023 over the CONUS.