Multivariate post-processing of temporal dependencies with autoregressive and LSTM neural networks

We consider the problem of post-processing forecasts for multiple lead times simultaneously. In particular, we focus on post-processing wind speed forecasts for consecutive lead times (0 - 48h ahead) from the deterministic HARMONIE-AROME NWP model. Given the strong temporal dependency between forecasts at consecutive lead times, it is essential to model the problem as a multivariate statistical post-processing problem in order to take this temporal correlation into account.

A standard procedure in multivariate statistical post-processing is to produce multiple probabilistic forecasts independently for each lead time and introduce the dependency between them at a later stage using an empirical copula. For our specific problem, a successful example of this approach is to use EMOS to fit truncated normal marginal distributions at each lead time and then model the joint distribution by drawing samples from these distributions and reconstructing the temporal dependencies using the Schaake Shuffle.

Our aim is to explore alternative methods that can model and exploit temporal dependencies more explicitly with the goal of improving forecast performance and moving away from sample based distribution modelling. We develop two new methods that produce multivariate truncated normal probabilistic forecasts for all lead times simultaneously, by combining elements from time series analysis and artificial neural networks.

In our first method, we exploit the autoregressive dependencies in the residuals of the NWP wind speed forecasts to deduce an explicit multivariate model. By using a neural network to determine the parameters of this model, we arrive at our first method, which we coin ARMOSnet.

In our second method, we apply Long Short-Term Memory networks, which rank among the state-of-the-art tools for the forecasting of time series. We adapt the LSTM architecture to output a multivariate density that models the temporal dependencies between the consecutive lead times.

We compare our two methods to EMOS combined with the Schaake Shuffle for post-processing wind speed forecasts from the HARMONIE-AROME NWP model. Our new methods both outperform the EMOS-Schaake Shuffle approach in terms of the logarithmic, energy, and variogram scores. Among the two new methods, ARMOSnet exhibits the best performance.