Entropy-Based Analysis of Summer Heatwave Intensity Percentiles Using Parametric Functions across Iran

Global warming has contributed to an increase in both the intensity and frequency of extreme climatic events, including heat waves. The impacts of heatwaves are influenced by various parameters such as duration, frequency, intensity, magnitude and the spatial extent of the affected area. In this study, a nonlinear index was developed to quantify heatwave intensity, based on the probability distribution of daily temperatures in each region. The proposed Heatwave Intensity Index (HII) is derived using the concept of entropy and is proportional to the deviation from a temperature threshold. This threshold is determined from a parametric probability distribution function fitted to daily average temperature data for each region of Iran during the period 2011–2021. The index was evaluated in terms of intensity, duration, and spatial extent.
Daily average temperature data at a 2-meter height were employed over the entire area of Iran, with each grid cell treated as an individual study unit. A heatwave event was defined as a period of at least three consecutive days with daily average temperatures exceeding the 95th percentile of the warm-season (June–September) temperature distribution. The 95th percentile threshold for each region was derived from the best-fitting continuous parametric probability distribution function. Four distribution types were tested: normal, log-normal, Weibull, and gamma, and the one that best represented the observed data in each selected region.
The Weibull distribution provided the best fit for more than 85% of Iran’s territory. In contrast, less than 10% of the areas, primarily along the northern and southern coasts, as well as Ardabil and large parts of East Azerbaijan provinces, were best described by normal or log-normal distributions. The highest temperature thresholds, exceeding 43°C, were observed in southwestern Iran, particularly in Khuzestan, southern Ilam, and central regions of the Lut Desert. Given the geographical diversity and varying climatic conditions across Iran, applying a single, fixed temperature threshold for the entire country is not appropriate. Instead, region-specific thresholds should be used to accurately identify heatwave events. In areas with historically low heatwave frequency, return periods are estimated to range from 4 to 5 years, whereas regions with higher frequencies may experience heatwaves at least three times every two years. Except for southeastern Iran, the highest frequency and broadest spatial extent of heatwaves were observed in July. Except for one central region, the average heatwave duration in most areas did not exceed four days. In the years 2019 and 2021, the intensity and frequency of heatwave events were higher compared to other years. The results show that during the heatwave days in 2021, the heatwaves were more intense, and a larger area was affected by it than that in 2019. It can be said that, given the rising temperature trend in the later years of the study period, the magnitude of heatwave intensity has also increased. The geometric mean of the HII varied significantly across Iran, with the highest values exceeding 80 units recorded along the southern coastline. In recent years, both the spatial extent and the intensity of heatwave events have increased. The most expansive heatwaves primarily affected the central and eastern border regions of the country.