This study aimed to conduct a drought trend analysis using the standardized precipitation evapotranspiration index (SPEI) in two mountainous and cold-climate regions in Iran and the United States (US). The Mann–Kendall test was employed to assess the trend in the Upper Colorado River Basin (UCRB) in the US and Lorestan province. The results reveal a predominantly decreasing trend in drought occurrences across Lorestan, especially in southern and southwestern areas with lower elevations. In contrast, the UCRB showed a positive trend, indicating a wet period. The western parts of the UCRB were predominantly affected by droughts. Among the stations, the Khorram Abad station exhibited the most statistically significant trend at the 99% confidence level (Z > 2.57). A temporal trend analysis of droughts revealed more positive and negative abrupt changes in the UCRB than in Lorestan. This indicates a higher degree of small-scale variability in the UCRB compared to Lorestan. This study indicates that factors such as elevation, land use changes, and proximity to water sources may contribute to the observed variations in drought trends. Additionally, the findings highlight that rising temperatures have a significantly greater impact on drought severity than reductions in precipitation. This study provides a temperature-responsive method for drought assessments, supporting the development of adaptive strategies that address snowmelt variability, seasonal water availability, and shifting drought patterns in cold regions.

Hydrometric stations are important in most countries because of the application and importance of the data obtained from these stations. It is necessary to choose the best place for their establishment according to the cost of constructing hydrometric stations. The aim and innovation of this research are to optimize the location of hydrometric stations using Bat's meta-heuristic algorithm and interpolation methods, which information transfer entropy theory and Bat's algorithm were used to maximize the average amount of information transfer entropy. For this purpose, the data of 43 hydrometric stations of Karkheh basin in western Iran in period of 1991–2015 were used. In this research, two scenarios were investigated in order to improve the entropy of information transmission between stations. In the first scenario, using the kriging method to prepare the flow distribution map in the region and choosing normal kriging with spherical variogram as the best model to fit the average annual flow data and using the Bat algorithm to increase the correlation coefficient between the data and assuming no none of the available stations, 43 points were used to redeploy stations with higher average entropy in the region. The results of this scenario showed the concentration of new stations in the central and eastern areas of the basin. In the second scenario, the amount of entropy of information transfer at the regional level was calculated and 18 potential points were recommended for the establishment of new stations. The obtained variogram for the discharge of the basin showed that the range of influence is low and it is necessary to establish the stations at a close distance.

This study aims to investigate the capability of the SWAT (Soil and Water Assessment Tool) model in hydrologic simulation of a cold and mountainous climate, the Azna–Aligoudarz Basin, Iran. For this purpose, daily climatic data from the Aligoudarz synoptic station, discharge data from the Marbare hydrometric station, soil and land use maps, and a 10 m digital elevation model of the study area were used. The results demonstrated that the model exhibited poor performance due to poor simulation of runoff generated from snowmelt. To enhance the model’s performance, the calibration period was split into warm and cold seasons using a temperature threshold of 3.6 °C. As a result, the model’s performance improved, with the Nash–Sutcliffe Efficiency (NSE) increasing from 0.28 to 0.60 and R² rising from 0.32 to 0.61. The research indicated that refining the conceptual and theoretical framework of the SWAT model is essential to reduce uncertainty and achieve reliable accuracy, particularly in snow-dominated and mountainous areas.

FAO model is used as a reference to estimate reference evapotranspiration. In this method, a lot of input information is needed to estimate evapotranspiration, which is difficult to collect this data in many cases, so, the need to replace simpler models with low inputs and proper accuracy is felt. Therefore, this research aims to investigate the capability of models based on wavelet neural networks and Group Method of Data Handling, along with empirical models of reference evapotranspiration estimation, which require less data, compared to the FAO–Penman–Mantith model under urban climatic conditions. Various monthly meteorological data were used in the period of 1982–2017. Based on the correlation between input and output parameters, six input patterns were determined for modeling and Tmax was the most effective parameter on ET. Experimental ET analysis showed that Kimberly Penman has the best accuracy with RMSE = 0.39 and R = 0.98. The results of the analysis of the models showed that the combined models have a good performance in estimating evapotranspiration. The results of the evaluation criteria showed that the wavelet neural network model with the average absolute value of relative error of 0.0524 and the mean ratio of 1.001 had a better performance in estimating reference evaporation and transpiration.

Reference evapotranspiration, which includes the contribution of climatic conditions in potential evapotranspiration, is considered as an important and strategic criterion in water resources management and irrigation designs. Therefore, it is necessary to determine and predict its changes in each region. In this study, using copula functions, the behavior and changes of this component were investigated in the west of Iran. For this purpose, the meteorological information of nine synoptic stations including Tmax, Tmin, WS, Rs, RHmax, and RHmin were used. This research aims to explore multivariate simulation based on vine tree sequences. Among these parameters, wind speed had the least effect on ET₀, and in all the studied stations, there was the highest correlation between ET₀-Tmax pair variable, which was equal to 0.90, 0.87, 0.89, 0.88, 0.86, 0.85, 0.88, and 0.81 in Aligudarz, Azna, Borujerd, Dorud, Khorramabad, Kuhdasht, Nurabad, and Poldakhter stations, respectively, based on Kendall's Tau statistics. The tree sequence of vine copulas including C-, D-, and R-vine was examined according to the input variables based on AIC and logarithm of likelihood evaluation criteria. According to the results, it was found that based on the evaluation criteria, the D-vine tree sequence has the best performance in the joint probability analysis of the studied variables. In addition, the results showed that the D-vine tree sequence, unlike the two R and C type sequences, has maintained the correlation between the studied pair variables until the last tree. The results of this study showed that copula functions could analyze evapotranspiration in different climates with high capability, which can be used in predicting the behavior of non-linear variables.