3.2.1. First-Order Statistics of the Horizontal Wind Speed
For resource estimation in the wind industry, it is standard to use the scalar horizontal velocity (
). This approach is also followed here. Although in many remote sensing applications it is common practice to work with the vector average of the wind velocity, publications concerning the accuracy of lidars in complex terrain often use the scalar mean [4
]. While vector averaging produces slightly different numbers, the general patterns that can be observed remain the same and the differences are very small.
The comparison of
measurements of the ML combination using three lidars and the sonic reveals an excellent agreement between the two techniques as would be expected from the comparison of
a). Also, the ML technique using two lidars and neglecting the vertical component in the vector reconstruction only produces marginally different results for the scanner combination SE/SW (Figure 5
b). For the SW/EE combination, the scatter slightly increases and we can see a few points which significantly deviate from the linear relationship (Figure 5
d). The observed differences between the different dual-lidar configurations are likely to be at least partly caused by the setup of the instruments.
One characteristic which sets the different dual-lidar measurements apart is the difference in azimuth angle between the WindScanner beams. For SW/EE, the angle is smallest (43°) which causes the strongest error propagation from the radial wind speed onto the wind vector when solving Equation (3) (cf. [38
]). The angle for SE/EE is slightly larger (49°) and the SE/SW combination has an angle difference of 88°, which is close to the ideal 90°.
The DBS measurement with the Windcube v2 exhibits more scatter and the linear regression significantly deviates from 1:1 when compared to the sonic (Figure 5
e). Especially for low wind speeds, an overestimation of the
by the DBS lidar can be observed.
In general, the linear-regression statistics for the DBS lidar are similar to what has been reported at Rödeser Berg in earlier measurement campaigns [6
] and are similar to what has been reported from other lidar-mast inter-comparisons in complex terrain [39
] albeit significantly worse than in flat terrain (e.g., [1
]). In contrast, the statistics for the ML combinations are similar to the results which we regularly observe during DBS lidar calibrations in flat and homogeneous terrain. The “bump” in the DBS data at low wind speeds might be associated with turbulence effects which are more important for low wind speeds. Moreover, thermal effects on the flow might create increased vertical velocities (relative to the horizontal wind speed) which are likely to spatially vary in the complex surroundings at Rödeser Berg. In combination with the large scanning volume of the DBS lidar at 188 m this would introduce an increased complex terrain error.
To our knowledge no statistics from a comparably long-term data set for assessing the performance of ML measurements to derive the mean wind speeds have been published so far. Previously published results of mast-lidar inter-comparisons either focused on the evaluation of individual measurement periods [16
] or employed scanning strategies that focused more on assessing the spatial heterogeneity of the wind field than on evaluating ML measurements against a reference [17
]. The ML-mast inter-comparison in the latter two references is slightly worse, but due to the different focus of the scanning strategy, is likely to not be directly comparable. A recently published study by Newman only compares co-located DBS and ML measurements [19
]. The sonic anemometer used in this study only measures at significantly lower altitudes than the lidars and is only used to give an indication of the wind field below the lidar measurements. This precludes a quantification of the advantages of either of the techniques over the other in their study or a comparison to the results presented.
One of the typical observations for profiling lidars in complex terrain is that the deviation in
between the lidar and the mast measurements varies with the shape of the terrain and thus wind direction [4
]. This behaviour can also be observed for the DBS data collected during the Kassel Experiment 2014
). The pattern clearly reflects the shape of the terrain and is very similar to what has been observed in earlier inter-comparisons between cup anemometers and a DBS lidar at Rödeser Berg [6
]. If the flow is directed across the ridge of the hill (aprox. 50°–100° and 200°–270°), the DBS lidar underestimates
. This is a typical observation for convex flow as observed over e.g., ridges or hilltops [4
]. In contrast, the sectors showing an overestimation of
by the DBS lidar (approx. 290°–20° and 160°–180°) correspond to along the ridge flow. Here, the mast is located on the slope in front of/behind the highest point on the ridge and the terrain is slightly concave. This might also cause a concave flow pattern which results in an overestimation of the horizontal wind speed by the DBS lidar. Some evidence for this can be found in the change of sign of the flow angle measured by the sonic between 290°–20° and 160°–180°. Whereas for the first sector (mast in front of the hill top) the median flow angle is 1.7° (directed upwards), it is −2.2° (directed downwards) for the second sector (mast behind the hill top). It should be noted, however, that the real flow might be more complex than this simplified explanation. A more detailed discussion and modelling results of directional errors of DBS lidar measurements at Rödeser Berg can be found in [6
On average, the DBS-mast deviations are slightly shifted (1%–2%) towards an increased (relative to when compared to the earlier inter-comparison to cup anemometry. This might be caused by the different reference anemometers or the different DBS instruments used in the present study, although the reason could not be fully clarified.
The deviation between
for the ML measurements is smaller than for the DBS system for most sectors and WindScanner combinations (Figure 6
). Especially for the WindScanner combinations SW/SE/EE and SE/SW, the differences are small for all directions and only vary between approx. −2% and 2%. For the SE/EE combination, a relatively large positive deviation of the ML system in comparison to the sonic wind speed can be observed between approx. 350 and 25°, which even exceeds the DBS-sonic deviations. This is likely due to the fact that within this range, the angle between the mean wind direction and the beam directions of SE and EE are large and the difference in beam directions is small (cf. [38
]). This configuration leads to an increased error propagation in the estimation of
that largely dominates
—i.e., the azimuth angles and flow direction are unfavourable for the retrieval of
. For flow angles which are directed in a more parallel manner to the orientation of the lidar beams, the error propagation for
is expected to be large. The effect on
, however, is then much smaller.
A second effect which can affect the quality of the measurements of SE/EE combination is the relatively large elevation angle of the EE system compared to the other systems (Table 1
). The assumption,
, thus results in a contamination of
. Due to the low availability, an inclusion of the MA system which could correct for the influence of
in the directional analysis was not possible. Therefore, a direction-dependent correction factor was calculated using
. Equation (3) is first solved using
. In a second step, (3) is solved only using
. The ratio of the two results is then applied as a correction factor to
. The correction reduces the deviations in the 350°–25° sector. The effect is, however, relatively small. Therefore, the assumption
does not seem to be the main cause of the observed deviations. Some of the deviations between the sonic and the lidar measurements might also be caused by the flow distortion of the mast. However, we estimate this effect to be small (c.f. Section 2.4
3.2.2. Second-Order Statistics of the Horizontal Wind Vector Components
This section presents the second-order statistics (variances and spectra) of the horizontal wind components
. The second-order statics for the
component can be found in Section 3.1.2.
(MA WindScanner). Figure 7
displays the scatter plots and linear-regression statistics for the different ML combinations and the DBS lidar when compared to the sonic measurements. The differences between the DBS and ML, but also among the different ML combinations, are quite large. Almost identical linear-regression statistics can be observed for the SW/SE/EE and SW/SE combinations (Figure 7
a,b). The R2
values of the linear regression for
are similar to the statistics of
and Figure 3
). Also the slope indicates a similar underestimation of
) of about 20%. Looking at the spectra of SW/SE/EE and SW/SE, one can clearly see the effects of line averaging which causes the reduction in
a,b). As for
, an attenuation in the spectral density from approx.
can be observed. The line averaging effect thus also causes the reduced
in SW/SE/EE and SW/SE.
The scatter in the inter-comparison between the SW/EE and SE/EE is larger than for SW/SE/EE and SW/SE and the slope of the linear regression shifts close to 1. One of the reasons for the increased scatter in the ML combinations using two WindScanners including the EE system might be that the EE system has an inclination angle which is not close to 0°. In the wind-vector reconstruction for two scanners, the
component is assumed to be 0 m·s−1
. Some of
will thus contaminate the measurement of
. Moreover, as discussed earlier, the direction of the flow in relation to the beam directions will also influence the error propagation for the individual components, especially if the angle between the beams is small [38
]. In the experimental setup it is, however, difficult to separate these effects as they are likely to be correlated.
This observation suggests that for the ML method, an adequate positioning of the lidar devices is even more important for measuring turbulence quantities than for the mean wind speed.
In general, random measurement errors in the time series will always lead to an increased variance. Therefore, both the contamination by the component and the unfavourable angles in the lidar combination lead to increased and in the lidar measurement. The slope values close to the 1:1 line are thus likely a result of the combination of these measurement errors and the line averaging, which act in opposing directions.
The comparison between the DBS system and the sonic indicates a clear overestimation of
by the DBS system (Figure 7
e and Table 3
). Also, the R2
values are lower than for all ML combinations. The spectra of the DBS system show a significant contamination of the variance measurements across almost the whole wavenumber range. Only for very large
are the spectra for the
component of the DBS lidar and the sonic close together. For the
component, a local maximum can be observed around approx.
spectrum of the DBS lidar is higher than the sonic spectrum for the whole wave number range and a (smaller) second maximum can be observed around
. For higher wave numbers, the spectra then quickly drop off.
The exact shape of the measured spectra of a Windcube does not only depend on the atmospheric conditions and measurement heights, but will also vary with the flow direction towards the scanning geometry of the Windcube [10
]. It is thus difficult to explain all features of the measured spectra.
The strong positive deviations from the sonic spectra in this range are likely to be caused by the cross-contamination effects between
and especially by the contamination of the horizontal variances by
. The short region where the spectra are almost horizontal at the high wavenumber end is likely to be caused by the algorithm which derives the wind vector from the measurements of
. In analogy with the internal software of the Windcube v2, in this paper the wind vector was calculated whenever a new measurement of
was available—i.e., at a frequency of approx. 0.89 Hz. One full rotation, however, takes five measurements of
and thus acts similarly to a moving average filter [41
The relatively strong overestimation in the measured variances by the Windcube compared to some other studies using similar instruments (Windcube v1 and v2) [9
] is likely to be related to the great measurement height (188 m) and thus the large distance between the different beams. In parts, it might also be caused by a dominance of unstable conditions which are more frequent during the summer season and the inhomogeneous flow caused by the terrain complexity.
In Table 3
, we also provide the statistics for periods when
, as this filter criterion is often used in applications and studies in the wind-energy sector, thereby allowing a more direct comparison to other experiments. For the ML combinations SW/SE/EE, SW/SE and SE/EE, there is only a small change in the linear-regression statistics. For the Windcube v2 and the SW/EE, which have lower R2
significantly improves after the application of the