The Meteorological Observatory Lindenberg–Richard-Aßmann Observatory (MOL-RAO) is part of Deutscher Wetterdienst (DWD), the national meteorological service of Germany. The observatory is situated in the east of Germany, approximately 65 km to the southeast of the center of Berlin. MOL-RAO runs a comprehensive operational measurement program to characterize the physical structure and processes in the atmospheric column above Lindenberg. Measurements of ABL processes form an essential part of it; they are carried out at the boundary layer field site (in German: Grenzschichtmessfeld, GM) in Falkenberg, about 5 km to the south of the main observatory site. The GM Falkenberg is situated in a rural landscape dominated by forest, grassland, and agricultural fields (see Fig. ). A central measurement facility at the Falkenberg site is a 99 m tower, equipped with booms to carry sensors every 10 m.

Since 2014, MOL-RAO has been using a DWL “Stream Line” (Halo Photonics Ltd.) for boundary layer measurements. From that time the device has been extensively tested with respect to its operational use for wind and turbulence measurements. This included, for instance, tests of the technical robustness and data availability under all weather conditions, but also tests of different scanning strategies and retrieval methods for the 3D wind vector and for the TKE. The position of the DWL during a measurement period from 2 through 30 April 2019 was at the western edge of the field site at about 500 m of distance from the 99 m tower. It should be noted that there is a small patch of forest about 300 m to the W-NW of the lidar site. During this period the system continuously performed VAD scans with an elevation angle of 35.3∘, which will be analyzed for turbulence retrievals in this study.

Continuous turbulence measurements (20 Hz sampling frequency) using a sonic anemometer of type USA-1 (METEK GmbH) are performed at the 50 and 90 m levels on the tower and have been used for validation purposes. The instruments are mounted at the tip of the booms pointing towards south.

Within the scope of the CO2 and Methane (CoMet) mission that was conducted in spring 2018, three Doppler wind lidars of type Leosphere Windcube 200S (details see Table ) were installed in Upper Silesia (Poland) with the purpose of providing spatially distributed wind and turbulence measurements in the ABL. CoMet aims at a better understanding of the budgets of the two most important anthropogenic greenhouse gases (GHGs), CO2 and CH4. For this purpose, the research aircraft HALO (high altitude and long range) was taking remote sensing and in situ measurements over large parts of the European continent. A dedicated area of high interest was the region of Upper Silesia, where large amounts of methane are known to be released due to the intensive coal extraction activities in the coal basin. During the CoMet campaign, the DLR Cessna Grand Caravan 208B (D-FDLR) aircraft was equipped with in situ instruments to measure greenhouse gases and thermodynamic variables.

The DWL measurements are particularly helpful to support the CoMet measurements by providing wind information that is essential to derive emission flux estimates from passive remote sensing or in situ measurements of mass concentrations . The DWL wind information can also be used to validate modeled wind from the transport models for greenhouse gases. The lidars were remotely operated during the whole CoMet campaign period from 16 May to 17 June 2017 and were continuously measuring. The locations of the three lidars were planned to cover the whole region of interest and were finally chosen based on logistical constraints.

The lidars were operating in VAD modes with two different elevation angles. Since the focus for the CoMet campaign was on continuous wind profiling and a good height coverage was desired, the lidars were programmed to perform VADs with an elevation angle of 75∘ (see Table , VAD75) for a longer period, i.e., 24 scans (≈29 min), followed by only six scans (≈7 min) at a 35.3∘ elevation (VAD35) for turbulence retrievals.

As shown in Fig. , the three lidars were separated by several tens of kilometers and were located in different terrain types. While DWL no. 1 was in a mixed rural and urban area, DWL no. 2 was in a mostly forested environment, and DWL no. 3 was in close vicinity to the lake Goczałkowicki. The main wind direction during the campaign was from the east, with particularly strong winds during nighttime low-level jet (LLJ) events. In this study we analyze statistics of the whole campaign, as well as a case study on 5 June 2017, on which D-FDLR was performing long straight and level legs between 800 and 1600 m as indicated in the flight path in Fig. . Since the D-FDLR was focusing on GHG measurements at the hotspots of the Upper Silesian Coal Basin, there are no more straight and level flight paths that allow for turbulence retrieval. For this day, however, the research aircraft provides a unique possibility to validate lidar measurements with in situ measurements at higher altitudes that cannot be reached with sonic anemometers. The flow probe and inertial measurement unit on the D-FDLR are well-established instruments that allow for reliable measurements of the 3D wind vector and turbulence .

From the sonic anemometers on the meteorological mast, TKE and the TKE dissipation rate are calculated. TKE is calculated from the sum of variances ETKE=0.5σu2+σv2+σw2. The TKE dissipation rate ε is estimated through a fit of the theoretical longitudinal Kolmogorov structure function in the range τ1=0.1 s to τ2=2 s to the measured second-order structure function of horizontal velocity. showed that the structure function method is more robust than estimates from spectra. For this study, in order to have the best possible comparison to the lidar measurements the values for ε are calculated for 30 min intervals. The geometry of the sonic anemometer setup disturbs the measurements for wind directions from 330 to 50∘ (see also Appendix ). Data for these wind directions are removed from the analysis.

Methods to retrieve turbulence parameters from VAD scans are well-known and a variety of different methods exist. The method we refine in this study is based on the theory that was originally described by for lidar measurements. The variance of radial velocities σr2 depends on the range gate distance R, the azimuth angle θ, and the elevation angle φ. It is calculated from the measured radial velocities Vr: 1vr(R,θ,φ,t)=Vr(R,θ,φ,t)-〈Vr(R,θ,φ)〉,2σr2=〈vr(R,θ,φ,t)2〉.

From a partial Fourier decomposition (see Appendix ) and for the special case of φ=35.3∘, a simple equation for ETKE is derived: 3ETKE=32σ‾r2|φ=35.3∘. In this equation, σ‾r2 is the mean of the variance of radial velocities over all azimuth angles. In the following, we will refer to this method as E89 retrieval.

In order to retrieve estimations of the TKE dissipation rate ε from VAD scans, a similar approach to the method for sonic anemometers can be followed. A fit of the equation 4Dr(ψ)=(4/3)CK(εψR′)2/3 to the azimuth structure function yields an estimate for ε according to . In Eq. () Dr is the transverse structure function of radial velocities, CK the Kolmogorov constant, ψ the azimuth angle increment, and R′=Rcos⁡φ. We will refer to this method as S17A in the following.

Scanning with Doppler lidar in a classical VAD with continuous motion of the azimuth motor involves a volume averaging of radial velocities in the longitudinal (along the laser beam) and transverse (orthogonal to the beam) direction. The E89 and S17A methods do not consider this effect and will thus yield a systematic underestimation of TKE and ε. proposed a theory that considers the volume averaging and allows for the retrieval of ε from conical scans, independent of the elevation angle. In , this method has been combined with the E89 method to yield TKE, ε, and the momentum fluxes. It is based on the decomposition of radial velocity variance σr2 into its subcomponents, i.e., 5σL2=σa2+σe2,6σa2=σr2-σt2,7σr2=σL2+σt2-σe2, where σL2 is the lidar-measured variance, σa2 is the lidar-measured variance without instrumental error σe2, and σt2 is the turbulent broadening of the lidar measurement. In , all of these variances and structure functions are calculated for single azimuth angles and then averaged. We describe in Sect.  why we use the total variances and structure functions of all radial velocities.

The measured azimuth structure function Da(ψl) is a function of the separation angle ψl, where l is the index of the discrete separation angle of the scan. It can be decomposed into the lidar-measured structure function DL(ψl) and the instrumental error σe2: 8DL(ψl)=〈vr(θ)-vr(θ+ψl)2〉,9Da(ψl)=DL(ψl)-2σe2.

Combining Eq. () with Eq. () yields 10σr2=σL2+σt2-12DL(ψl)+12Da(ψl).

It shows that since the instrumental error σe2 is assumed to be a constant offset of azimuth structure function Da(ψl) and the lidar measurement DL(ψl), l can be chosen arbitrarily here. It is set to l=1 because potential random errors like nonstationary flow will be smaller for small separation angles. Using Eqs. () and () (see Sect. ), TKE can be redefined as a function of the measured line-of-sight variances σL2, the measured lidar azimuth structure function of radial velocities DL(ψ1), and a residual term G, which includes the two unknowns, σt2 and Da(ψ1): 11ETKE=32σL2-DL(ψ1)2+G,12G=σt2+12Da(ψ1).

In , a relationship between the two unknowns and the TKE dissipation rate is theoretically derived from the two-dimensional Kolmogorov–Obukhov spectrum as 13σt=ε2/3F(Δy),14Da(ψl)=ε2/3A(lΔy), where F(Δy) and A(lΔy) are model functions that include the lidar filter functions (see Appendix ). The lidar filter functions in the longitudinal direction depend on the pulse width of the laser beam Δp and the time window Tw of the data acquisition. The transverse filter function is defined by Δy=RΔθcos⁡φ, which is the distance the lidar beam moves along the cone during one accumulation period. The parameters for the lidars in this study are provided in Table  and are calculated from information given by the manufacturer for the specific lidar type. Hence, G depends on the turbulence dissipation rate ε: 15G=ε2/3F(Δy)+A(Δy)2.

Using Eqs. () and (), ε can be retrieved from Da(ψl)-Da(ψ1): 16ε=DL(ψl)-DL(ψ1)A(lΔy)-A(Δy)3/2. This equation does not depend on the elevation angle so that the method allows for the retrieval of ε from VAD scans with elevation angles different from 35.3∘ as well. Figure  gives an example of the different structure functions that are calculated in this method (i.e., DL, Da, and A) and also gives a comparison to the structure function Ds as calculated from sonic anemometer measurements. found a separation angle of lΔθ=9∘ to be an appropriate value for ABL measurements. In this study, all VAD scans are performed with a resolution of Δθ=1∘ so that l=9. In Fig.  the range that is thus used for the structure function fit is indicated by the bold black line.

The retrieval method for ε using Eq. () and TKE using Eq. () will be referred to as S17 in the following.

The estimation of turbulence parameters from the wind measurement system on the DLR Cessna Grand Caravan 208B is done very similarly to the in situ estimations from the sonic anemometer. TKE is calculated from the sum of variances as described in Sect. . The dissipation rate is also calculated from the second-order structure function but with different bounds for the time lag. For the flight data we use τ1=0.2 s and τ2=2 s, corresponding to approximately 13–130 m lag at 65 m s-1 mean airspeed.

To evaluate the heterogeneity of turbulence due to changing land use along the flight legs of more than 50 km length, we divided the legs into sub-legs of 6.5 km (i.e., 100 s averaging time) and calculated turbulence for each leg individually. The location of the legs and the sub-legs is shown in Fig. .

The best possible validation of the methods introduced in Sect.  can be performed with the lidar in close proximity to the meteorological mast such as at the measurement site at MOL-RAO. The sonic anemometers at 50 and 90 m on the mast almost coincide with the measurement levels of the lidar at 52 and 93.6 m, respectively. Since the VAD retrieval with an elevation angle of 35.3∘ yields TKE and its dissipation rate, both turbulence parameters can be compared to values obtained from the sonic anemometers. In this section we will evaluate the methods described in Sect. , in particular the validity of the assumptions made in Sect.  and the efficiency of the advection correction described in Sect. .

VAD scans with 35.3∘ allow for the retrieval of TKE and momentum fluxes using the methods described in Sect. . The disadvantage compared to VAD scans with larger elevation angles is that at the same range of the lidar line-of-sight measurement, lower altitudes are reached. If the limit of range is not given by the ABL height in any case, this can lead to significantly lower data availability at the ABL top. Another advantage of greater elevation angles is that the horizontal area that is covered with the VAD, and thus the footprint of the measurement, is much smaller than with low elevation angles. From the theory derived in Sect. , we see that the dissipation rate retrieval does not depend on the elevation angle and can thus also be obtained from VAD scans with a 75∘ elevation angle if the assumptions of isotropy and homogeneity hold. However, since the VAD at 75∘ has the more narrow cone, the separation distances Δy at respective measurement heights are smaller, and thus the sensitivity to advection errors is expected to be larger. The measurements with two different elevation angles during the CoMet campaign allow us to compare dissipation rate retrievals for both kinds of VAD scans with the restriction that they are not simultaneous but sequential.

Figure  shows the comparison of both types of VADs in scatterplots of three measurement heights for the whole campaign period and DWL no. 1. In general, a large scatter is found between the two types of VAD that can be attributed to the different measurement times, different footprint, and heterogeneous terrain. Applying a filter for significant advection as described in Sect.  removes most of the measurement points at the 100 m level in the 75∘ VAD. Without the filter (grey and red points), large systematic overestimation against the VAD at 35.3∘ is found, which can still be seen at 500 m but is no longer found at 1000 m. With the advection correction of W20, the systematic error is reduced, but the random errors remain.

As for the comparison with the sonic anemometer, we evaluate the error as a function of wind speed by binning the data in wind speeds between 0 and 10 m s-1 (see Fig. ). A clear trend is found for the 100 m level, which can be significantly reduced with the W20 method. A very small difference between the two elevation angles at the 500 m level is only reduced very little in the W20 method.

During CoMet, no meteorological tower with sonic anemometers at levels that could be compared to the Doppler lidars was available. Instead, the aircraft D-FDLR was operating with a turbulence probe and provided in situ turbulence data. On 5 June 2018, the aircraft was flying a so-called “wall” pattern, with long, straight, and level legs at five altitudes (800, 1000, 1100, 1300, and 1600 m). At least the lowest three levels of this flight allow for a comparison to the measurement levels of the top levels of lidar measurements on this day. Figure  shows the measured TKE of D-FDLR at the five flight levels. Only at the lowest two light levels (i.e., 800 and 1000 m) is significant turbulence measured, with strong variations along the flight path.

Figure  shows the measurements from D-FDLR and the lidars DWL no. 1 and DWL no. 3 that were taken between 14:00 and 15:30 UTC as vertical profiles. The solid red line gives the average of all sub-legs along the 50 km flight of D-FDLR, and the shaded areas give the range between the minimum and the maximum at each height. It nicely shows how the measurements of turbulence at the DWL no. 3 site are significantly lower than at DWL no. 1, which we attribute to the lake fetch. The D-FDLR measurements of TKE almost match the DWL no. 1 site and are all higher than at the DWL no. 3 site, which makes sense given the environmental conditions of heterogeneous land use. Figure a also gives a comparison between E89, S17, and W20 estimates from the same dataset. Here, it shows that the difference between S17 and W20 only occurs at the very lowest level, but the underestimation of the E89 method is found up to 750 m. In dissipation rate estimates, the DWL no. 1 measurements are at the low end of the range that was measured with D-FDLR, and the lake-site measurements are even smaller. The estimates from 35.3∘ scans and 75∘ scans agree very well, especially at the higher levels, which shows that the assumption of isotropy and homogeneity seems to hold. The presumed underestimation of the ε of lidar retrievals compared to in situ measurements at absolute values of 10-3 m2 s-3 is consistent with what was found for the comparison to sonic anemometer measurements. This single case of airborne measurements compared to lidar retrievals at higher altitudes cannot, however, provide any statistical validation.

Figure  shows measurements of ε retrieved with the W20 method for the VAD scans with 75∘ elevation and all three lidars. It shows that the growth of the boundary layer with its increased turbulence can be nicely captured by the lidars. There are some differences between the three locations, especially lower turbulence close to the ground at the DWL no. 3 location and a higher boundary layer at the DWL no. 2 location. More studies will be necessary in the future, analyzing the data from the whole campaign, to improve the understanding of land–atmosphere interaction in this case.