Drought trends projection under future climate change scenarios for Iran region

parameter log-logistic is needed to calculate the SPEI as the following [7]: f x ð Þ ¼ b a x g a Þb 1 1 þ x b a � �b " # 2 ð2Þ where α, β and γ are scale, shape, and origin parameters, respectively, for D values (γ�D�1). The probability distribution function of the D series, according to the log-logistic distribu- tion, is given by: F x ð Þ ¼ 1 þ a x g � �b " # 1 ð3Þ The F(x), values for the D series at different time scales adapt very well to the empirical F(x) values at the different observatories, independent to the climate characteristics and the time scale of the analysis. With F(x), the SPEI can easily be obtained as the standardized values of F(x). For example, following the classical approximation of [31]: SPEI ¼ W 2:515517 0:802853W þ 0:010328W2 1 þ 1:432788W þ 0:189269W2 þ 0:001308W3 ð4Þ where; W ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 lnðpÞ p for p � 0:5 ð5Þ P presents the computed D value exceeding probability. P = 1-F(x). if >0.5, then P is substi- tuted by (1-p) and the sign of the resultant SPEI is reversed. The SPEI mean and standard deviation values are zero and one, respectively. SPEI is an indication for standardized variable and thus it is comparable with other SPEI magnitudes over time and space. An SPEI of 0 signifies a corresponding value to 50% of the cumulative probability of D, this is according to a log-logistic distribution [32]. In the present investiga- tion, the SPEI was run on package of the R 3.63 software. Since the definition and conception of SPI is applied in the development of SPEI, different

classes of drought intensity are based on recommended values by [33]. Table 1 reveals the clas- sification of the drought categories with respect to SPEI. For describing and analyzing the drought characteristics, the Run theory was used. In this theory, severity, duration, and intensity are considered as three important characteristics of drought. Fig 2 depicts these traits with X0 as threshold of Xt [34]. First, the climatic variables were computed by LARS-WG for the future period as this is needed for the calculation of future PET. LARS-WG was calibrated using maximum and mini- mum temperatures (Tmax and Tmin) and precipitation during base period of 1992–2012 for Table 1. Different classes of drought intensity dependent on SPEI (Edwards and McKee, 1997). Drought classes Index value Extreme wet Index �.2 Severe wet 1.5�index<2.0 Modest wet 1.0�index<1.5 Normal -0.99�index<0.99 Moderate drought -1.5<index�1.0 Severe drought -2.0<index�-1.5 Extreme drought index�-2.0 https://doi.org/10.1371/journal.pone.0290698.t001 PLOS ONE Drought trends projection under future climate change scenarios for Iran region PLOS ONE | https://doi.org/10.1371/journal.pone.0290698 November 9, 2023 5 / 24