Uncertainty Reduction in the Neural Network’s Weather Forecast for the Andean City of Quito Through the Adjustment of the Posterior Predictive Distribution Based on Estimators

Abstract

The weather forecast in cities as Quito is highly complicated due to its proximity to Latitude 0° and because it is located in the Andes mountains range. A statistical post-processing is compulsory in order to improve the output from the physical model and to improve the weather forecast in the city. A neural network can be applied in order to carry out this task but it is necessary first to reduce its uncertainty. The Bayesian Neural Networks (BNN) have been studied deeply thanks to its probability analysis, the uncertainty can be approximated. In this paper an analysis founded on the adjustment of the posterior predictive distribution based on estimators is carried out in order to reduce the prediction error variation (implicitly the uncertainty) in a Short-Term Weather Forecast for the Andean city of Quito. From the analysis it is obtained a maximum error forecast of 12% and it is proven that for Long Short Term Memory (LSTM) structures, the variation of the error reduces almost to the half with weight-decays of $2.04 \times 10^{ - 7}$ and $2.23 \times 10^{ - 7}$.