Airborne wind energy systems (AWESs) aim to operate at altitudes above conventional wind turbines where reliable high-resolution wind data are scarce. Wind light detection and ranging (lidar) measurements and mesoscale models both have their advantages and disadvantages when assessing the wind resource at such heights. This study investigates whether assimilating measurements into the mesoscale Weather Research and Forecasting (WRF) model using observation nudging generates a more accurate, complete data set. The impact of continuous observation nudging at multiple altitudes on simulated wind conditions is compared to an unnudged reference run and to the lidar measurements themselves. We compare the impact on wind speed and direction for individual days, average diurnal variability and long-term statistics. Finally, wind speed data are used to estimate the optimal traction power and operating altitudes of AWES. Observation nudging improves the WRF accuracy at the measurement location. Close to the surface the impact of nudging is limited as effects of the air–surface interaction dominate but becomes more prominent at mid-altitudes and decreases towards high altitudes. The wind speed frequency distribution shows a multi-modality caused by changing atmospheric stability conditions. Therefore, wind speed profiles are categorized into various stability conditions. Based on a simplified AWES model, the most probable optimal altitude is between 200 and 600 m. This wide range of heights emphasizes the benefit of such systems to dynamically adjust their operating altitude.

The prospects of higher energy potential, more consistent strong winds and less turbulence in comparison to near-surface winds has sparked interest in mid-altitude wind energy systems, with “mid-altitude” defined here as heights above 100 m and below 1500 m,. Airborne wind energy systems are a novel class of renewable energy technology that harvest stronger winds at altitudes which are unreachable by current wind turbines, at potentially significantly reduced capital cost

Developers and operators of large conventional wind turbines, AWES and drones require accurate wind data to estimate power output and mechanical loads.
They currently rely on oversimplified approximations such as the logarithmic wind profile

Recent advancements in wind lidar technology enable measurements at higher altitudes. This measurement technique, however, suffers from reduced data availability with increasing altitude caused by a decrease in aerosol density, which is needed for the backscattering of the lidar signal

This work is a continuation of a previous investigation of mid-altitude wind lidar measurements

Section

The lidar data used in this study

Topography map of all three WRF model domains

Lidar data availability highly depends on the applied carrier-to-noise ratio (CNR) filter and the aerosol content of the air as the wind speed is calculated based on the backscatter of the emitted laser beam. Most aerosols originate from the surface and are transported aloft. Particle density decreases with height and drops to almost zero within the free atmosphere above the ABL

To complement the 6-month lidar data set, two WRF 3.6.1 simulations using the Advanced Research Weather Research and Forecasting (ARW) model

This methodology uses the difference between the model and measurements to calculate a nonphysical forcing term which is added to the governing conservation equations of the simulation to gradually nudge the model towards the observation (see Eq.

EDDY: HPC cluster at the Carl von Ossietzky Universität Oldenburg; see

Observation nudging, also referred to as “dynamic analysis”, is a form of four-dimensional data assimilation (FDDA) whereby each grid point within the radius of influence and time window is nudged towards observations using a weighted average of differences between the model (

Vertical influence was set very small so that observations only affect their own

It is important to keep the differences in temporal and spatial resolution between lidar measurements and WRF simulations in mind. Furthermore, data availability highly influences the ability to nudge the simulation (see Sect.

To quantify the local effect of observation nudging, we investigate the cell closest to the lidar measurement location and compare measured and modeled horizontal wind speeds

Figure

Linear regression of lidar-measured wind speeds against NoOBS-modeled (WRF “baseline run” without observation nudging) wind speeds

The statistical analysis of the absolute difference between the WRF-simulated quantities at the measurement location and the lidar observations (

Statistical analysis of the bias between simulated and measured wind speed (

The simulation with observation nudging generally outperforms the unnudged simulation and is in better agreement with the measurements, particularly at the altitudes of interest to high-altitude wind energy systems. It furthermore reduces the spread of the bias, illustrated by the smaller whiskers and boxes. The root mean square error (RMSE)

The NoOBS shows an almost constant wind direction bias at all altitudes.
Observation nudging substantially reduces the directional bias

We compare 10 min mean horizontal wind speed for 24 h on 21 September 2015 in Fig.

Visualization of modeled and measured 10 min mean wind speed and wind direction for 21 September 2015.

Even though observation nudging leads to statistical improvements in wind speed and wind direction prediction over the entire period (compare Sect.

The planetary boundary layer height (PBLH) (black line), which in the MYNN scheme is calculated from the profile of virtual potential temperature and from the profile of the TKE

Single-location observation nudging influences the area within the radius of influence (

Mean absolute wind speed difference

Average diurnal variation indicates typical wind speed variations for a given location and period. It further reinforces the benefit of dynamically adapting operating altitudes of AWES. The hourly average lidar wind speed depends on data availability, as described in Sect.

Figure

Hourly average diurnal variation of measured and modeled horizontal wind speed

The common way to approximate the probability distribution of the horizontal wind speed

Frequency of occurrence

All 6-month data sets show a high occurrence of low and high wind speeds, which indicates a multi-modal frequency distribution. This effect is most pronounced in the lidar data set. The comparison of wind speed frequency with the Weibull fit further emphasizes the multi-modality as a simple Weibull fit is not able to capture the higher probability at low and high wind speeds. These distinct flow situations further drift apart with increasing surface distance. As a result the Weibull distribution overestimates the occurrence of wind speeds between the two peaks. Both OBS and NoOBS slightly overestimate low-altitude wind speed (see Fig.

Weibull parameter trends over altitude and goodness of fit quantified by the Hellinger distance (right) over altitude for 6 months of lidar measurements (first row panels), the 6-month OBS model (second row panels), 6-month NoOBS model (third row panels) and the 12-month NoOBS model (fourth row panels).

Using the sign of the WRF-calculated SHF as a simple proxy to differentiate stable and unstable wind conditions similar to

Figure

The different trends under positive and negative SHF of both Weibull parameters visualize the existence of entirely different flow regimes.
The Hellinger distance between the Weibull fit and frequency distribution (negative SHF: blue, positive SHF: red), the total data and a simple fit (black), and between the total data and the weighted sum of both Weibull fits (green) is shown. All WRF models show an overall smaller

Even though the Hellinger distance of individual Weibull fits for times of positive or negative SHF is generally higher than the Weibull fit of the entire data set, the weighted sum of both individual fits yields the best result at all altitudes. The 12-month Weibull fit using the entire data set performs comparably to a weighted sum up to an altitude of about 250 m.

Atmospheric stability highly influences the shape of wind speed profiles, which is important for determining optimal operating conditions for an AWES (see Sect.

Wind speed

Stability classes according to Obukhov length calculated based on WRF results

In comparison with the unnudged simulation, OBS shows an increase in unstable and nearly unstable situations. Stable and nearly stable stratification seem almost unaffected by OBS nudging, while neutral and very stable stratification occur slightly less often. This might improve the overall predicting capabilities of WRF as the MYNN 2.5 boundary layer scheme overestimates the frequency of very stable conditions with an error of up to 9 %

Figure

Altitudes below 200 m are least affected by observation nudging as OBS remains almost unchanged from NoOBS (see Sect.

We estimate optimal operating altitude and traction power of a ground-generator AWES using a simple ground-generator (pumping-mode) AWES point-mass model adapted from

Figure

Frequency of optimal traction power over optimal operating altitude based on 6-month OBS

Figure

Optimal traction power per wing area

A full 6 months of lidar measurements up to 1100 m were assimilated into a mesoscale model using observation nudging. An unnudged reference model (NoOBS), the nudged model (OBS) outputs and lidar measurements were compared in terms of wind speed and direction statistics, as well as wind profile shape at the measurement site, and spatial differences were quantified. Observation nudging only has a marginal impact on simulated surface layer wind speeds as ground effects dominate the WRF model. Wind speeds between 300 and 500 m were most affected by observation nudging. Modeled wind speeds at these altitudes are statistically closest to the measurements, making this an adequate approach for resource assessment at mid-altitudes as measurement availability decreases. The impact of nudging weakens above these altitudes. Whether this is caused by lower measurement data availability or a generally better performance of the mesoscale model above the surface layer could not be determined. Observation nudging reduced the seemingly systematic wind direction bias between simulations and measurements at all altitudes. Due to the lack of high-resolution measurements at high altitudes, unnudged mesoscale model data are the best we have in terms of preliminary resource assessment.

Filtering the mesoscale model data according to lidar data availability yields similar diurnal variation, with OBS being closer to measurements. Comparing the diurnal variation of the unfiltered model wind speeds to measurements shows a significant deviation, which is likely caused by insufficient lidar data availability at higher altitudes. The bias between real and lidar-measured wind speed, which depends on the applied CNR threshold and data availability, can result in a misrepresentation of the actual wind conditions, especially at higher altitudes. Mesoscale models, particularly with observation nudging, can be used to account for this error. Lidar measurements seem to be biased towards high wind speeds as measured winds are generally higher than the unfiltered mesoscale model data. The impact of observation nudging on the wind profiles in the case of an unstably stratified boundary layer is relatively low, while wind speed profiles under stable stratification are significantly affected. At the measurement location OBS is overall closer to measurements, especially between 200 and 600 m. Variations of stratification, primarily those associated with the diurnal cycle, lead to a multi-modal wind speed frequency distribution which is better represented by the weighted sum of two Weibull fits than by a single Weibull fit. Obukhov-length-categorized wind speed profiles, especially during neutral and stable conditions close to the surface, show a divergence with height. This indicates inhomogeneous atmospheric stability and suggests that surface-based stability categorization is insufficient for higher altitudes.

Optimal AWES operating altitudes and power output per wing area were estimated based on a simplified model for 6 months of OBS and 12 months of NoOBS. The model neglects kite and tether weight as well as tether drag. Accounting for these losses, which are proportional to tether length, will reduce the performance of the AWES. Results for both wind speed data sets show the highest potential at an altitude between 200 and 600 m above which the losses associated with the elevation angle are too high. A comparison of different tether lengths under average wind speeds associated with different atmospheric stability conditions shows diminishing returns in terms of power output for tether lengths longer than 1500 m. While higher altitudes can potentially be reached, the optimal operating altitude remains almost unchanged. The highest energy potential and operating altitude is associated with neutral and stable stratification. Unstable conditions result in significantly lower energy potential due to lower, almost altitude-independent average wind speeds.

Future studies will include using the enhanced mesoscale model output to drive large-eddy simulations to provide better insight into mid-altitude turbulence. The resulting data set will lead to the development of a mid-altitude engineering wind model which can be used for the design, load estimation, control and optimization of airborne wind energy systems. Mesoscale model data will be implemented into an AWES optimization framework to quantify the impact of various wind speed profiles on power production, optimal trajectory and system size. Furthermore, the possibility of merging the mesoscale output with lidar measurements to fill gaps in the measurement data set to reduce the wind speed bias introduced by lidar availability is being investigated.

The data are not publicly available because they are subject to an NDA with the Fraunhofer IWES. Furthermore, the overall WRF data size makes up multiple terabytes.

MD and GS helped set up the numerical simulation and contributed to the meteorological evaluation of the data. MS evaluated the data and wrote the paper in consultation with and under the supervision of CC.

The corresponding author (Markus Sommerfeld) confirms on behalf of all authors that there have been no involvements that might raise the question of bias in the work reported or in the conclusions, implications or opinions stated.

The authors thank the Federal Ministry for Economic Affairs and Energy (BMWi) for funding of the OnKites I and OnKites II project (grant number 0325394A) on the basis of a decision by the German Bundestag and project management by Projektträger Jülich. The simulations were performed at the HPC Cluster EDDY, located at the University of Oldenburg (Germany), and funded by the Federal Ministry for Economic Affairs and Energy (BMWi) under grant number 0324005. We thank the PICS and the DAAD for their funding. We further thank all the technicians and staff at the Fraunhofer Institute for Wind Energy Systems (IWES) for carrying out the measurement campaign at Pritzwalk and their support in evaluating the data.

This research has been supported by the Federal Ministry of Economics and Technology (Germany) (grant no. 0325394A), the Federal Ministry for Economic Affairs and Energy (BMWi) (grant no. 0324005), and the Pacific Institute for Climate Solutions (PICS) (student scholarship project).

This paper was edited by Jakob Mann and reviewed by Roland Schmehl and Rogier Floors.