Climate change and spatio-temporal trend analysis of climate extremes in the homogeneous climatic zones of Pakistan during 1962-2019

maximum rainfall during the monsoon season. Zone 3 is the south-western part of the country and has least rainfall in a year as compared to the other regions of the country. Zone 4 includes the south-eastern and coastal areas in the south of the country. Zone 5 is the central-eastern part of the country and due to its fertile land, it is considering the food basket of the country. Observed daily climate data (maximum, minimum temperature and precipitation) for the period of 1962–2019 was acquired from Pakistan Meteorological Department (PMD) for fifty- four (54) meteorological stations across the country. The spatial distribution of meteorological stations is shown in Fig 1. The data was divided into two independent climatic periods (1962– 1990 and 1991–2019) for the assessment of climate change and extremes analysis over Pakistan. 3. Methodology 3.1. Inconsistencies in the data There were some missing values in the maximum, minimum temperature and precipitation par- ticularly at the stations situated at high elevation. There are various statistical methods available to address the issue of missing values, for instance, multivariate regression, interpolation, imputation etc. In this study, imputation method (a regression-based approach) is used at multiple stations to preserve the spatial dependence structure. Multiple chains have been run and the convergence is assessed in each chain after a specified number of iterations. The number of iterations depend on researcher and the nature of the study [52]. However, the convergence of the process can be

assessed at each iteration. The process can be stopped if there are no significant changes during the successive iterations. It is important to note that the inhomogeneous data need to be homoge- nized before the start of further analysis [53]. Inhomogeneities in data may occur due to breaks, changes or disorder in measuring instruments, observing practices of enumerators, location, and environment of the stations. The standard normal homogeneity tests (SNHT) are useful tools to assess the homogeneity, consistency and to detect the spikes and outliers in daily time series [54– 57]. The commonly used SNHT for testing the homogeneity of data include Buishand Range test, Pettitt test, and Von Neumann Ratio test. In this study we have used Buishand Range test for test- ing the homogeneity of the data which can identify the month/year where the gap occurs. For fur- ther details about the above-mentioned homogeneity tests, we refer to [58]. 3.2. Climate change assessment For climate change assessment, the average differences between the two time slices are tested for possible statistical significance at a 5% level of significance. This is carried out under the hypothesis testing procedures of the student t-test. Under this procedures, the null hypothesis states that there is no difference between the average climatology of two-time slices where the alternative hypothesis states opposite to the null hypothesis. The hypothesis under the student t-test can be formulated as: H0 : on the average there is no change in the climatology of both time slices Vs

HA : on the average there is change in the climatology of both time slices Alternatively, it can be written as: Ho : m1991 2019 m1962 1990 ¼ 0 Vs HA : m1991 2019 m1962 1990 6 ¼ 0 PLOS ONE Climate change and extremes analysis using observed data (1962-2019) over Pakistan PLOS ONE | https://doi.org/10.1371/journal.pone.0271626 July 27, 2022 5 / 27