Multimodel Ensemble Methods for Prediction of Wake-Vortex Transport and Decay

Abstract

Several multimodel ensemble methods are selected and further developed to improve the deterministic and probabilistic prediction skills of individual wake-vortex transport and decay models. The different multimodel ensemble methods are introduced, and their suitability for wake applications is demonstrated. The selected methods include direct ensemble averaging, Bayesian model averaging, and Monte Carlo simulation. The different methodologies are evaluated employing data from wake-vortex field measurement campaigns conducted in the United States and Germany.= forecast of ith model g i yjf i = probability density function of forecast L = likelihood PB = probability that B occurs PBjA = probability that B occurs, given that A occurs py = probability density function of the y forecast

Multi-model ensemble wake vortex prediction

“…If the distributions of the deviations of the measurements from the deterministic predictions are unknown, normal distributions are a good estimate to generate the ensemble forecast [151]. However, it turns out that the unweighted mean model error distributions are rather leptokurtic as they exhibit higher peaks and fatter tails than Gaussian distributions, especially for the y-forecast ( Figure 5.13) [151]. This can be explained by the intermittent nature of wind [152], manifested in the form of gusts.…”

“…Not being resolved by the measurement-derived 10 minute wind averages that are employed as input data, gusts can cause large errors due to misjudged drifting velocities. Further, the wind measured by the instrumentation and the wind sensed by the vortices may deviate substantially depending on the spatial distance between measurement device and vortex [151]. As wind also affects the interaction of the vortices with the ground, the PDF of model deviations for the z * -forecast is non-Gaussian likewise.…”

“…As wind also affects the interaction of the vortices with the ground, the PDF of model deviations for the z * -forecast is non-Gaussian likewise. In addition, the model deviation PDFs turn out to be skewed and not to be centered at zero [151]. In order to enable the ensemble to achieve leptokurtic forecast distributions, the individual model PDFs that compose the ensemble forecast must be leptokurtic likewise.…”

“…It is important to mention that it is not intended to find a perfect fit here. Although sophisticated fits can be easily achieved by this technique by choosingμ 1 =μ 2 =μ 3 =μ 4 , the goal is rather to find a PDF that approximates the kurtosis [151]. The rest will be managed by the training described in Section 5.5.1, where the individual model forecasts are incorporated.…”

“…The rest will be managed by the training described in Section 5.5.1, where the individual model forecasts are incorporated. The resulting fits are depicted in Figure 5.13 for the WakeMUC/ WakeFRA/ WakeOP training sample [151]. Applying leptokurtic instead of Gaussian distributions eventually delivers better probabilistic prediction results as the tails of the PDFs are approximated more precisely [151].…”