Wide Field Adaptive Optics (WFAO) systems are among the most sophisticated adaptive optics (AO) systems available today on large telescopes. Knowledge of the vertical spatio-temporal distribution of wind speed (WS) and direction (WD) is fundamental to optimize the performance of such systems. Previous studies already proved that the Gemini Multi-Conjugated AO system (GeMS) is able to retrieve measurements of the WS and WD stratification using the SLOpe Detection And Ranging (SLODAR) technique and to store measurements in the telemetry data. In order to assess the reliability of these estimates and of the SLODAR technique applied to such complex AO systems, in this study we compared WS and WD values retrieved from GeMS with those obtained with the atmospheric model Meso-NH on a rich statistical sample of nights. It has previously been proved that the latter technique provided excellent agreement with a large sample of radiosoundings, both in statistical terms and on individual flights. It can be considered, therefore, as an independent reference. The excellent agreement between GeMS measurements and the model that we find in this study proves the robustness of the SLODAR approach. To bypass the complex procedures necessary to achieve automatic measurements of the wind with GeMS, we propose a simple automatic method to monitor nightly WS and WD using Meso-NH model estimates. Such a method can be applied to whatever present or new-generation facilities are supported by WFAO systems. The interest of this study is, therefore, well beyond the optimization of GeMS performance.