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This article presents a method for incorporating the effect on expected annual energy production of a wind farm caused by asymmetric uncertainty distributions of the applied losses and the nonlinear response in turbine production. The necessity for such a correction is best illustrated by considering the effect of uncertainty in the oncoming wind speed distribution on the production of a wind turbine. Due to the shape of the power curve, variations in wind speed will result in a skewed response in annual energy production. For a site where the mean wind speed is higher than 50% of the rated wind speed of the turbine (in practice all sites with sufficiently high wind speed to motivate the establishment of a wind farm), a reduction in mean wind will cause a larger reduction in annual energy production than a corresponding increase in mean wind would increase the annual energy production. Consequently, the expected annual energy production response when considering the uncertainty of the wind will be lower than the expected annual energy production based on the most probable incoming wind. This difference is due to a statistical bias in the industry standard methods to calculate expected annual energy production of a wind farm, as implemented in tools in common use in the industry. A method based on a general Monte Carlo approach is proposed to calculate and correct for this bias. A sensitivity study shows that the bias due to wind speed uncertainty and nonlinear turbine response will be on the order of 0.5%-1.5% of expected annual energy production. Furthermore, the effect on expected annual energy production due to asymmetrical distributions of site specific losses, for example, loss of production due to ice, can constitute additional losses of several percent.

Environmental problems are receiving increasing attention in socioeconomic and health studies. This in turn fosters advances in recording and data collection of many related real-life processes. Available tools for data processing are often found too restrictive as they do not account for the rich nature of such data sets. In this paper, we propose a new statistical perspective on forecasting spatial environmental data collected sequentially over time. We treat this data set as a surface (functional) time series with a possibly complicated geographical domain. By employing novel techniques from functional data analysis we develop a new forecasting methodology. Our approach consists of two steps. In the first step, time series of surfaces are reconstructed from measurements sampled over some spatial domain using a finite element spline smoother. In the second step, we adapt the dynamic functional factor model to forecast a surface time series. The advantage of this approach is that we can account for and explore simultaneously spatial as well as temporal dependencies in the data. A forecasting study of ground-level ozone concentration over the geographical domain of Germany demonstrates the practical value of this new perspective, where we compare our approach with standard functional benchmark models.1. Introduction. Studies on the prediction of environmental data sampled across time and over geographical areas/regions have received wide attention across many fields. Examples of such studies include air quality control (see, e.g.,