Modelling a multivariate distribution is a classical issue in statistics. Copula functions offer a useful solution to this issue by modelling the multivariate distribution as a function of its marginal distributions. They have been used in various problems in hydrology and water management such as flood frequency analysis and drought or rainfall intensity-duration frequency analysis. However, to the knowledge of the author, they have not been applied for stochastic simulation of hydrologic data. In this study we explore the applicability of the copula concept for stochastic streamflow simulation. Parametric and non-parametric functions are applied for fitting the distribution of the original observed data and the serial dependence structure is then modelled with alternative copula functions. The pros and cons of different copula models are investigated by comparing the statistics of the generated data. Two major features of the copula models include: (1) portraying the heteroscedasticity embedded in the serial correlation of the observed data and (2) the flexibility of applicable marginal distributions. The suggested copula models are applied to simulate synthetic annual streamflow data of the Nile River. The results showed that the benefits of using these copula models are somewhat marginal with respect to the well-known modelling procedures.

Time series forecasting of meteorological variables such as daily temperature has recently drawn considerable attention from researchers to address the limitations of traditional forecasting models. However, a middle-range (e.g., 5–20 days) forecasting is an extremely challenging task to get reliable forecasting results from a dynamical weather model. Nevertheless, it is challenging to develop and select an accurate time-series prediction model because it involves training various distinct models to find the best among them. In addition, selecting an optimum topology for the selected models is important too. The accurate forecasting of maximum temperature plays a vital role in human life as well as many sectors such as agriculture and industry. The increase in temperature will deteriorate the highland urban heat, especially in summer, and have a significant influence on people’s health. We applied meta-learning principles to optimize the deep learning network structure for hyperparameter optimization. In particular, the genetic algorithm (GA) for meta-learning was used to select the optimum architecture for the network used. The dataset was used to train and test three different models, namely the artificial neural network (ANN), recurrent neural network (RNN), and long short-term memory (LSTM). Our results demonstrate that the hybrid model of an LSTM network and GA outperforms other models for the long lead time forecasting. Specifically, LSTM forecasts have superiority over RNN and ANN for 15-day-ahead in summer with the root mean square error (RMSE) value of 2.719 (°C).