Demand for water resources has increased dramatically due to the global increase in consumption of water, which has resulted in water depletion. Additionally, global climate change has further resulted as an impediment to human survival. Moreover, Pakistan is among the countries that have already crossed the water scarcity line, experiencing drought in the water-stressed Thar desert. Drought mitigation actions can be effectively achieved by forecasting techniques. This research describes the application of a linear stochastic model, i.e., Autoregressive Integrated Moving Average (ARIMA), to predict the drought pattern. The Standardized Precipitation Evapotranspiration Index (SPEI) is calculated to develop ARIMA models to forecast drought in a hyper-arid environment. In this study, drought forecast is demonstrated by results achieved from ARIMA models for various time periods. Result shows that the values of p, d, and q (non-seasonal model parameter) and P, D, and Q (seasonal model parameter) for the same SPEI period in the proposed models are analogous where “p” is the order of autoregressive lags, q is the order of moving average lags and d is the order of integration. Additionally, these parameters show the strong likeness for Moving Average (M.A) and Autoregressive (A.R) parameter values. From the various developed models for the Thar region, it has been concluded that the model (0,1,0)(1,0,2) is the best ARIMA model at 24 SPEI and could be considered as a generalized model. In the (0,1,0) model, the A.R term is 0, the difference/order of integration is 1 and the moving average is 0, and in the model (1,0,2) whose A.R has the 1st lag, the difference/order of integration is 0 and the moving average has 2 lags. Larger values for R² greater than 0.9 and smaller values of Mean Error (ME), Mean Absolute Error (MAE), Mean Percentile Error (MPE), Mean Absolute Percentile Error (MAPE), and Mean Absolute Square Error (MASE) provide the acceptance of the generalized model. Consequently, this research suggests that drought forecasting can be effectively fulfilled by using ARIMA models, which can be assist policy planners of water resources to place safeguards keeping in view the future severity of the drought.

A meteorological drought study is performed using monthly time scale data from three separate locations in southern Sindh, Pakistan. Rainfall and temperature have been used to identify the drought. These data were transformed into drought indices known as the standardized precipitation evapotranspiration index (SPEI) and standardized precipitation index (SPI), which were derived using (the Hargreaves equation). In this study, two indices are compared for three separate meteorological stations Chhor, Mithi, and Badin where most socioeconomic livelihoods depend heavily on water. The SPEI is produced through a simple water balance combining precipitation and temperature, in distinction to the SPI, it just considers precipitation. In conclusion, our study showed that both indices were capable of detecting droughts that fluctuated in time across the reference period of 2004–2021. SPI and SPEI's direction of change was similar, however the impact on the drought condition varied. SPEI discovered more droughts with longer durations and greater with 13 moderate droughts at SPEI-3 for Chhor and Badin Station while Mithi indicated 8 moderate droughts during 2004-2021 and SPI-3 indicated 4 moderates for Chhor, Mithi and Badin indicated 6 moderate drought. Conversely, SPEI discovered more moderate-level droughts than SPI, however they were of shorter length and less frequent occurrence than the severe to moderate droughts. The findings imply that drought characteristics are significantly influenced by temperature variability.

The main theme of this research paper is to propose an explicit iterative numerical scheme over the modified Euler’s method (MEM) for solving initial value problems in ordinary differential equations. This iterative scheme has been proposed by changing the inner slope of the MEM by the mean of main slope of MEM and slope of explicit forward Euler’s method. The proposed iterative scheme has been tested for its performance by analyzing different numerical factors related to numerical algorithm and found it consistent, more accurate with the order of convergence 2 and it also shows greater stability region as compared to existing methods which are compared with proposed method.

The impact of nitrogen levels on the growth and yield of super basmati rice (Oryza sativa L