Applying Extreme Value Analysis (EVA) to Daily and Monthly Precipitation in Iraq

Extreme value analysis (EVA) is a branch of statistics focused on assessing the probability of extreme events. Unlike typical statistical methods that focus on average or common events, EVA is concerned with the tails of probability distributions, those rare but impactful occurrences that can have significant consequences. When analyzing extreme values, especially when there are multiple high values in a single block (hourly, daily, monthly, yearly), we normally consider two approaches to estimate extreme values for different return periods: Block Maxima (BM) Method and Peak Over threshold (POT) Method. Both methods, BM and POT are powerful tools in extreme value analysis but are suited to different types of data and research questions. POT is more flexible and detailed for rare events, while BM offers simplicity and ease of interpretation. The choice between them depends on the nature of the data, the research objectives, and practical considerations. In many cases, both methods are used to improve the reliability of the results. In the analysis of monthly precipitation in the four selected locations in Iraq (Baghdad, Mosul, Rutba and Basrah), we observed that the dry season extends from June to September, while in Baghdad, on a daily scale, it extends from late May to late October. Monthly precipitation data follows different distributions: Gamma in Mosul, Rutba, and Basrah, Chi-squared in Baghdad, and an exponential distribution for daily data in Baghdad. The study indicates a decreasing trend in the monthly precipitation data for Mosul and Rutba, while Baghdad and Basrah do not exhibit such trends. For the 100-year return period, the daily precipitation in Baghdad is estimated to be 140 mm, with monthly return values ranging from 154 to 162 mm. In Mosul, the monthly return values range from 207 to 220 mm; in Rutba, from 138 to 145 mm; and in Basrah, from 129 to 134 mm. The results from the HEC-SSP model and a Python script for Block Maxima (BM) analyses are consistent. Additionally, the Peak Over Threshold (POT) method applied to the short data series in Baghdad's daily analysis shows a notable improvement in reducing the confidence interval size compared to BM. Monthly analyses using both POT and BM methods yielded similar results, demonstrating the reliability of the substantial 86-year dataset and the analyses performed.