Modelling and forecasting of monthly extreme temperature using MLE and L-moment estimation methods: Khyber Pakhtunkhwa, Pakistan

Extreme Events Analysis (EEA) is an essential tool for the designing and policy-making of rare events occurrence and infrastructure epically in Climate Change (CC). The results of EEA can be used to predict the magnitude and frequency of extreme environmental events in the future like temperature, droughts, rainfalls, floods, high winds and storms etc. EEA of extreme temperature based on Maximum Likelihood Estimation (MLE) and L-MOM Estimation Method has been carried out in this study. Both methods are used on two sets of data, collected from (Peshawar and Risalpur) of monthly mean (minimum) temperature data, maintained by Pakistan Metrological Office, Islamabad from the period of 1951 to 2018 and 1954 to 2018 respectively. Numerous tests are applied for initial fundamental assumptions i.e. stationarity, randomness, independence and homogeneity. Data from both the sites satisfied the said tests. For best fitted and robust estimation of parameters of the distribution, well-known goodness of fit tests i.e. Chi-square fit, Anderson-Darling test and Kolmogorov Smirnov method are used. Model is based on the model selection, the Generalized Extreme Value (GEV) distribution appeared to provide better results than other models used for the same purpose. In this study, quantile estimates for return ranging from 5 to 100 years have also been examined. Return periods and non-exceedance probabilities are used to generate quantitative estimations. The investigation shows that quantitative estimates or design prices based on the L - MOM estimating approach are lower than those based on maximum likelihood estimation (MLE) with equal return durations and non-exceedance probabilities. In such cases, Maximum Likelihood Estimation (MLE) is applied. As a result, it may be advised that the data produced from various methods and procedures should be compared during the design and policy planning phase for extreme temperature events. Furthermore, the results of such investigations can be utilized to choose improved design criteria for temperature policy management, notable measures for the prevention of extreme temperature events.