Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

Comparison of aerosol optical properties above clouds between POLDER and AeroCom models over the South East Atlantic Ocean during the fire season

Aerosol properties above clouds have been retrieved over the South East Atlantic Ocean during the fire season 2006 using satellite observations from POLDER (Polarization and Directionality of Earth Reflectances). From June to October, POLDER has observed a mean Above-Cloud Aerosol Optical Thickness (ACAOT) of 0.28 and a mean Above-Clouds Single Scattering Albedo (ACSSA) of 0.87 at 550 nm. These results have been used to evaluate the simulation of aerosols above clouds in 5 AeroCom (Aerosol Comparisons between Observations and Models) models (GOCART, HadGEM3, ECHAM5-HAM2, OsloCTM2 and SPRINTARS). Most models do not reproduce the observed large aerosol load episodes. The comparison highlights the importance of the injection height and the vertical transport parameterizations to simulate the large ACAOT observed by POLDER. Furthermore, POLDER ACSSA is best reproduced by models with a high imaginary part of black carbon refractive index, in accordance with recent recommendations.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.