Predicting the state of the weather, from tracking hurricanes and thunderstorms to assessing daily temperatures, is of crucial importance. Over the past decades, these predictions have relied on solving complex sets of partial differential equations and closure models spanning multiple temporal and spatial scales. Recently, advances in machine-learning technologies have given rise to data-driven weather emulators that are able to perform skillful predictions at a lower computational cost. However, these data-driven weather models predict only a limited subset of meteorological variables. The objective of this work is to complete AI-based weather models by predicting some secondary meteorological variables of interest. We adopt a data-driven approach in which the models considered consist of neural networks, with several simplifying hypotheses regarding spatial and temporal dependence. The capability of the model to generalize in time and space is assessed using two metrics: a weighted mean squared error and the Structural Similarity Index Measure. The model errors are further investigated by computing their spatial and temporal correlations. A spectral analysis of the model's predictions is also performed. Finally, we carry out a sensitivity analysis to identify the relevant parameters of the model.