On the variances of a spatial unit root model

The asymptotic properties of the variances of the spatial autoregressive model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\gamma X_{k-1,\ell-1}+\epsilon_{k,\ell}$ are investigated in the unit root case, that is when the parameters are on the boundary of domain of stability that forms a tetrahedron in $[-1,1]^3$. The limit of the variance of $n^{-\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces of the domain of stability $\varrho=1/4$, on the edges $\varrho =1/2$, while on the vertices $\varrho =1$

Calibration of wind speed ensemble forecasts for power generation

In the last decades wind power became the second largest energy source in the EU covering 16% of its electricity demand. However, due to its volatility, accurate short range wind power predictions are required for successful integration of wind energy into the electrical grid. Accurate predictions of wind power require accurate hub height wind speed forecasts, where the state of the art method is the probabilistic approach based on ensemble forecasts obtained from multiple runs of numerical weather prediction models. Nonetheless, ensemble forecasts are often uncalibrated and might also be biased, thus require some form of post-processing to improve their predictive performance. We propose a novel flexible machine learning approach for calibrating wind speed ensemble forecasts, which results in a truncated normal predictive distribution. In a case study based on 100m wind speed forecasts produced by the operational ensemble prediction system of the Hungarian Meteorological Service, the forecast skill of this method is compared with the predictive performance of three different ensemble model output statistics approaches and the raw ensemble forecasts. We show that compared with the raw ensemble, post-processing always improves the calibration of probabilistic and accuracy of point forecasts and from the four competing methods the novel machine learning based approach results in the best overall performance.Comment: 15 pages, 5 figure

Parametric model for post-processing visibility ensemble forecasts

Despite the continuous development of the different operational ensemble prediction systems over the past decades, ensemble forecasts still might suffer from lack of calibration and/or display systematic bias, thus require some post-processing to improve their forecast skill. Here we focus on visibility, which quantity plays a crucial role e.g. in aviation and road safety or in ship navigation, and propose a parametric model where the predictive distribution is a mixture of a gamma and a truncated normal distribution, both right censored at the maximal reported visibility value. The new model is evaluated in two case studies based on visibility ensemble forecasts of the European Centre for Medium-Range Weather Forecasts covering two distinct domains in Central and Western Europe and two different time periods. The results of the case studies indicate that climatology is substantially superior to the raw ensemble; nevertheless, the forecast skill can be further improved by post-processing, at least for short lead times. Moreover, the proposed mixture model consistently outperforms the Bayesian model averaging approach used as reference post-processing technique.Comment: 26 pages, 14 figures, 2 table

A two-step machine learning approach to statistical post-processing of weather forecasts for power generation

By the end of 2021, the renewable energy share of the global electricity capacity reached 38.3% and the new installations are dominated by wind and solar energy, showing global increases of 12.7% and 18.5%, respectively. However, both wind and photovoltaic energy sources are highly volatile making planning difficult for grid operators, so accurate forecasts of the corresponding weather variables are essential for reliable electricity predictions. The most advanced approach in weather prediction is the ensemble method, which opens the door for probabilistic forecasting; though ensemble forecast are often underdispersive and subject to systematic bias. Hence, they require some form of statistical post-processing, where parametric models provide full predictive distributions of the weather variables at hand. We propose a general two-step machine learning-based approach to calibrating ensemble weather forecasts, where in the first step improved point forecasts are generated, which are then together with various ensemble statistics serve as input features of the neural network estimating the parameters of the predictive distribution. In two case studies based of 100m wind speed and global horizontal irradiance forecasts of the operational ensemble pre diction system of the Hungarian Meteorological Service, the predictive performance of this novel method is compared with the forecast skill of the raw ensemble and the state-of-the-art parametric approaches. Both case studies confirm that at least up to 48h statistical post-processing substantially improves the predictive performance of the raw ensemble for all considered forecast horizons. The investigated variants of the proposed two-step method outperform in skill their competitors and the suggested new approach is well applicable for different weather quantities and for a fair range of predictive distributions.Comment: 25 pages, 12 figures, 4 table