Probabilistic temperature forecasting based on an ensemble autoregressive modification

Abstract

To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts, the NWP model is run multiple times, each time with variations in the mathematical representations of the model and/or initial or boundary conditions. To correct for possible biases and dispersion errors in the ensemble, statistical postprocessing models are frequently employed. These statistical models yield full predictive probability distributions for a weather quantity of interest and thus allow for a more accurate representation of forecast uncertainty. This article proposes to combine the state-of-the-art Ensemble Model Output Statistics (EMOS) with an ensemble that is adjusted by an autoregressive process fitted to the respective error series by a spread-adjusted linear pool in the case of temperature forecasts. The basic ensemble modification technique we introduce may be used to simply adjust the ensemble itself as well as to obtain a full predictive distribution for the weather quantity. As demonstrated for temperature forecasts from the European Centre for Medium-Range Weather Forecasts ensemble, the proposed procedure gives rise to improved results over the basic (local) EMOS method.

Probabilistic temperature forecasting with a heteroscedastic autoregressive ensemble postprocessing model

“…Such an approach would yield a reduced number of parameters to estimate. This procedure, though perfectly applicable in accordance with our method described in sections 2.1 to 2.4, has already been found to be inferior with respect to evaluation measures for predictive performance in the earlier work by Möller and Groß (2016). Analysis of the data described in section 4 leads to the same conclusions, so that this approach is not further pursued here.…”

“…While in this work and in the original article by Möller and Groß () a univariate time series approach was employed, multivariate time‐series models, such as vector autoregressive (VAR) processes, may be investigated in future research. Possible multivariate settings of interest could for example involve modelling the forecast errors of each ensemble member jointly, modelling dependencies between ensemble forecasts and observations, or modelling dependencies between observation locations by spatial time‐series models, or in a more general setting, within the framework of space–time models.…”

“…Heteroscedastic autoregressive predictive distribution Möller and Groß (2016) assume the predictive distribution for Y (t) to be Gaussian, that is…”

“…The order p m is automatically selected by a modified Akaike information criterion (AIC) proceeding as if the required variance estimate were obtained by maximum likelihood; see function ar (R Core Team, 2019). This procedure is invoked with a default training length of 90 days, which has been found appropriate by Möller and Groß (2016).…”

“…The work presented here extends the AR‐EMOS model of Möller and Groß () to be of heteroscedastic (or “non‐homogeneous”) nature, meaning that the variance parameter of the model varies with the (empirical) ensemble spread. A postprocessing model using a heteroscedastic variance parameter accounts for the well‐known spread‐error correlation (Barker, ; Whitaker and Loughe, ) of forecast ensembles, stating that there is a positive association between the forecast error (or predictive skill) and the spread of the ensemble.…”