Statistical Modeling of Near-surface Wind Speed: A Case Study from Baden-Wuerttemberg (Southwest Germany)

Research Article

Austin J Earth Sci. 2015;2(1): 1006.

Statistical Modeling of Near-surface Wind Speed: A Case Study from Baden-Wuerttemberg (Southwest Germany)

Jung C and Schindler D*

Chair of Meteorology and Climatology, Albert-Ludwigs-University of Freiburg, Germany

*Corresponding author: : Schindler D, Chair of Meteorology and Climatology, Albert-Ludwigs-University of Freiburg, Werthmannstrasse 10, D-79085 Freiburg, Germany

Received: December 15, 2014; Accepted: January 29, 2015; Published: January 31, 2015


In this paper a methodology is presented that can be used to statistically model characteristics of near-surface wind speed in complex terrain at high spatial resolution. It was developed based on daily mean wind speed time series provided by the German Weather Service for 65 stations located in southwest Germany. After comprehensive preparation of the wind speed data that were measured in the period 1975 to 2010 including gap filling, homogenization, detrending and measurement height correction, 48 continuous distributions were fitted to the empirical distributions associated with the wind speed time series. The results of the evaluation of the goodness-of-fit demonstrate that the five-parameter Wakeby-distribution characterizes the statistical properties of measured wind speed better than all other tested distributions. Based on surface roughness, terrain-related parameters (curvature, topographic exposure) and ERA-Interim reanalysis wind speed data available for the 850 hPa pressure level, LSBoost-models were built to estimate station-specific Wakeby-parameters. The LSBoost-models were then used to model the Wakeby-parameters on a 50 m resolution grid in the entire study area as a function of the predictor variables. The area-wide availability of the Wakeby-parameters allows producing detailed wind speed quantile maps.

Keywords: Wind speed measurement; Ensemble methods; Wakebydistribution; Hellmann power law


A measure often used to quantify characteristics of near-surface wind fields is the absolute value of the horizontal wind vector commonly known as wind speed. While variations of wind speed at the earth surface are ubiquitous, there is often limited knowledge about the wind speed characteristics at a particular site. An inherent characteristic of wind speed is its high spatiotemporal variability [1,2]. Especially rough surfaces [3] and complex terrain [4] modify nearsurface wind fields. Unfortunately, there are often too few wind speed measuring stations in place although wind speed measurements made near the ground are strongly influenced by land cover and terrain at and around the measuring sites [5-7]. The lack of near-surface wind speed measurements often limits knowledge about statistical wind speed properties and thus about the local wind resource. the basis for the selection of most appropriate sites for wind turbines which offer great potential to reduce CO2-emissions [18].

There is ongoing debate whether there is a distribution function that describes empirical distributions of wind speed data best [19,20]. In many previous studies [1,2,4,6,19-29], the Weibull function was used to represent empirical wind speed distributions. However, results from other studies [30-33] demonstrate that wind speed distributions cannot always adequately be represented by the Weibull distribution, especially when wind speed strongly varies with wind direction [34].

Since the orography in the southwest of Germany is complex and the landscape is compartmentalized, the near-surface wind speed characteristics vary on small scales, i.e. from measuring station to measuring station. Thus, the goals of this study are (i) to evaluate which distribution function is most appropriate for describing the statistical properties of wind speed data measured near the ground in the southwestern German federal state Baden-Wuerttemberg, (ii) to develop a statistical model based on the best-fitting distribution that is able to provide reasonable estimates of near-surface wind speed quantiles in high spatial resolution (50 m resolution grid) in the study area.

Material and Methods

Study area

The study area is the German federal state of Baden-Wuerttemberg (southwest Germany). It has a surface area of 35752 km2. Its orography is complex and includes the low mountain ranges Black Forest (length ~150 km, width ~30-50 km, highest elevations > 1400 m) and Swabian Alb (length ~180 km, width ~35 km, highest elevations > 1000 m) as well as the broad, flat Rhine Valley, which borders on France in the west. The elevation (Φ) within the study area ranges from 85 m above sea level (a.s.l.) in the Rhine Valley to 1493 m a.s.l. at the top of the Feldberg, which is the highest mountain in Baden- Wuerttemberg. The Φ-values in the study area mainly vary between 200 m and 800 m a.s.l. (Figure 1a). The land cover types within the study area might change on small scales (< 1 km) and often create a compartmentalized landscape. The land cover types available from the Corine Land Cover (CLC) 2006 dataset for Germany [35] and the roughness length (z0) values associated with these land cover types are listed in Table 1. Rough surface types like urban areas and forests have higher z0-values (1.00 m and 0.80 m) than smoother surface types like agricultural areas (0.10 m) or natural grass land (0.03 m). The z0- values, which were interpolated from the original spatial resolution of the CLC-dataset of 100 m to a 50 m resolution grid, correspond to standard z0-values found in literature [36-38]. According to the CLCdata, the study area’s surface is mainly covered by agricultural areas (51%), forests (38%) and artificial surfaces like urban areas, airports, road networks and rail networks (9%). The corresponding bimodal z0-value distribution is displayed in Figure 1b.