Analysis and prediction of climate forecasts in Northern Morocco: application of multilevel linear mixed effects models using R software.

For many years, the application of mixed-effects modeling has received much attention for predicting scenarios in the fields of theoretical and applied sciences. In this study, a "new" Multilevel Linear Mixed-Effects (LME) model is proposed to analyze and predict multiply-nested and hierarchical data. Temperature and rainfall observation were carried out successively between 1979-2014 and 1984-2018; and the data input was organized on monthly basis for each year. Besides, a daily observation was made for "Dar Chaoui" zone of Northern Morocco. However, we chose in the first time a simple linear regression model, but the estimation has been just for fixed effects and ignoring the random effect. On the other hand, in multilevel linear mixed effects models, once the model has been formulated, methods are needed to estimate the model parameters. In this section, we first deal with the joint estimation of the fixed effects (β), random effects (ui) and then with estimation of the variance parameters (γ, ρ and σ). The study revealed that the predicted values are very close to the real value. Besides, this model is capable of modelling the error, fixed and random parts of the sample. Moreover, in this range, the results showed that there is three standard deviations measures for fixed and random effects, also the variance measure, which demonstrate us a great prediction. In conclusion, this model gives a decisive precision of results that can be exploited in studies for forecast of water balance and/or soil erosion. These results can also be used to inhibit the risk of erosion with possible arrangements for the environment and human security.