In the context of ''TO CHAIR'' project, this work aims to improve the accuracy of short-term forecasts of maximum air temperature obtained from the https://weatherstack.com/ website. The proposed methodology is based on a state-space representation that incorporates the latent process, the state, which is estimated recursively using the Kalman filter. The proposed model linearly and stochastically relates the forecasts from the website (as a covariate) to the observations of the maximum temperature recorded at the study site. The specification of the state-space model is performed using the maximum likelihood method under the assumption of normality of errors, where empirical confidence intervals are presented. In addition, this work also presents a treatment of outliers based on the ratios between the observed maximum temperature and the website forecasts.

Within the scope of the TO CHAIR project, a state space modeling approach is proposed in order to improve accuracy obtained from the weatherstack.com website with a dataset of real observations. The proposed model establishes a stochastic linear relationship between the maximum temperature observed and the h-step-ahead forecast produced from the website. This relation is modeled in a state space framework associated to the Kalman filter predictors. Since normality of disturbances was not a good assumption for this dataset, alternative Generalized Method of Moments (GMM) estimators were considered in the models parameters estimation. The results show that this approach allows reducing the RMSE of the uncorrected forecasts in 16.90% considering the 6-step-ahead forecasts and in 60.45% considering the 1-step-ahead forecasts, compared with the initial RMSE. Additionally, empirical confidence intervals at the 95% level have a coverage rate similar to this confidence level. So, this approach has proven suitable for this type of forecasts correction since it considers a stochastic calibration factor in order to model time correlation of this type of variable.

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Increasingly, reduction of water availability has been a reality, and population growth, pollution, and climate change have contributed to exacerbating this problem. Dry periods, which occur when precipitation is lower than expected in a given territory, have become more frequent and prolonged, and therefore it is crucial to efficiently manage water use in response to environmental concerns. The main challenge in this work is to present the irrigation problem as an optimal control problem along with the presentation of preliminary results based on an exploratory statistical and critical analysis of daily meteorological variables. The variables considered are: maximum air temperature, minimum air temperature, and total precipitation recorded during the last ten years (2010-2019). The methodology followed, based on state-space models, shows flexibility to allow the integration of new data, updating in real time the model, and the incorporation of covariates that are important to explain the process in analysis.