Climate time series variability analysis of Islamabad Capital Territory using fractal dimension and Hurst exponent methods

This study is an attempt to examine variability of climatic parameters at local scale, Islamabad Capital Territory (ICT). Climate change can affect temperature trends and precipitation patterns, horticultural activity, agricultural productivity, underground water level, portable water availability, and infrastructure.To assess the impact of climate change of Islamabad Capital Territory, the data of precipitation, minimum and maximum temperatures were obtained for the period from 1983 to 2022 from Pakistan Metrological Department (PMD). Fractal dimension D and Hurt exponent H methods were employed to estimate the monthly maximum and minimum temperatures, and precipitation of the study area. The data was portioned into 4 subsets. Rescaled range analysis method was applied on the datasets to compute values of Hurst exponent and fractal dimension. The results obtained show Brownian random and persistent tendencies, correspondingly. On the other hand, the period from 2013 to 2022 shows anti-persistent trend for H and random trend during (2013-2022) for D, respectively. The time series showing persistent results contain the long-term memory. When a time series shows random Brownian behaviour, thenthere will be no any extended long-term memory. Rescaled range analysis (R/S)method was employed to compute fractal dimensions show consistent outcomes, reveal small fluctuation in the local behaviour of minimum temperatures.Whereas, Hurst exponent values of maximum temperatures show random behavior i.e. there exists no correlation. The Hurst exponents computed confirm persistent results for precipitation pattern. Likewise, the computed values of fractal dimensions also show persistent results. Thus, the precipitation pattern shows cyclic behaviour, i.e. the precipitation time series retain long-run memory. Finally, from the persistent behavior of time series, one would infer that there will bean extended time effect on the local precipitation pattern. Python software was used to perform computations.