The Aeolus satellite has a weight of 1360kg, a launch configuration dimension of 4.6m×1.9m×2.0m, and a deployable solar array that provides a power of 2.4kW. Aeolus carries a single payload, ALADIN, which is a direct detection wind lidar operating at an ultraviolet wavelength of 354.8 nm. ALADIN emits short laser pulses (≈40 to 70mJ, 50.5Hz) down to the atmosphere, where a few of the photons are backscattered on air molecules, aerosols, and hydrometeors. The backscattered light is collected with a 1.5m diameter Cassegrain telescope and directed to the optical receiver that is used to detect the Doppler frequency shift of the backscattered light from which the wind velocity can be calculated in LOS direction at different altitudes. To do so, ALADIN is equipped with two different frequency discriminators, namely a Fizeau interferometer that analyzes the frequency shift of the narrowband particulate backscatter signal by means of the so-called fringe imaging technique  and two sequentially coupled Fabry–Pérot interferometers that analyze the frequency shift of the broadband molecular return signal by means of the so-called double-edge technique .

Both the Rayleigh and Mie channels sample the backscatter signal in a time-resolved manner, leading to 24 bins with a vertical resolution that can vary between 0.25 and 2.0km (see also Fig. ). Depending on the number of averaged measurements, which have a horizontal resolution of about 3km, the horizontal resolution of the wind observations is usually 90km for the Rayleigh channel (Rayleigh-clear winds) and 10km for the Mie channel (Mie-cloudy winds). Furthermore, due to the high-spectral-resolution receiver configuration, information on the vertical distribution of aerosol and cloud optical properties such as backscatter and extinction coefficients can be retrieved . Further information about the Aeolus satellite, the ALADIN instrument, and the retrieval algorithms can be found in other sources e.g.,.

The data of Aeolus are provided in different product levels containing different types of information e.g.,. The Level 0 data contain the raw data of ALADIN as well as the instrument housekeeping data and the housekeeping data of the satellite platform. The Level 1B (L1B) data provide processed ground echo data and preliminary horizontal LOS (HLOS) wind observations that have not been corrected for atmospheric temperature and pressure . The L2B data contain the time series of fully processed profiles of HLOS winds along the satellite orbit. L2B Rayleigh wind data are corrected for atmospheric temperature T and pressure p, which is needed to avoid systematic errors . As the Rayleigh–Brillouin spectrum of the molecular scattered light depends on T and p , any differences in either of the two quantities between the geographical location of the instrument response calibration and the one of the actual wind observation have to be taken into account. L2B data are used by the ECMWF for NWP  and for the validation by means of 2 µm DWL and Falcon in situ wind observations, as presented in Sect. . It is worth mentioning that the sign of the HLOS winds is defined such that it is positive for winds blowing away from the satellite LOS. For instance, for an ascending orbit, when the satellite moves from south to north and when the laser is pointing eastwards, westerly winds lead to positive HLOS winds. Furthermore, the L2B winds are classified by means of the optical properties of the atmosphere into Rayleigh-clear winds, indicating wind observations in aerosol-poor atmosphere, and Mie-cloudy winds, indicating winds acquired from particulate backscatter, predominately from clouds or ground returns. There are also Rayleigh-cloudy and Mie-clear winds available in the data product, which are not further discussed within this study.

Both the L1B and L2B processors are continuously updated, modified, and improved. Thus, data processed with different processor versions may result in different HLOS winds. In this study, the second reprocessed data set (processor baseline 11 – L2B processor version L2bP 3.40) is used for the AVATAR-I timeframe. For AVATAR-T, the near-real-time (NRT) data which are used in this study were processed with processor baseline 12 (L2bP 3.50). As only minor modifications have been applied between baseline 11 and 12, the different processor versions are not expected to have a significant impact on the results from the two different campaign data sets.

The 2 µm DWL has been operated by DLR for more than 20 years and has been deployed in several ground and airborne field campaigns for measuring, for instance, aircraft wake vortices , aerosol optical properties , horizontal wind speeds over the Atlantic Ocean as input data for assimilation experiments , and horizontal as well as vertical wind speeds to study the life cycle of gravity waves . In addition, the system was applied in several Aeolus pre-launch campaigns conducted within the last 10 years e.g.,.

The 2 µm DWL is a heterodyne-detection wind lidar system based on a Tm:LuAG laser operating at a wavelength of 2022.54 nm (vacuum), a laser pulse energy of 1 to 2mJ, and a pulse repetition rate of 500Hz, ensuring eye-safe operation. The system is composed of three main units, namely (1) a transceiver head containing the laser, an 11cm afocal telescope, receiver optics, detectors, and a double-wedge scanner, enabling the steering of the laser beam to any position within a 30∘ cone angle; (2) a power supply and the cooling unit of the laser, mounted in a separate rack; and (3) a rack containing the data acquisition unit and the control electronics. For a more detailed description of the 2 µm DWL, including a listing of the system specifications, refer to .

To measure the three-dimensional wind speed and direction, the velocity–azimuth display (VAD) scan technique is applied . That is, a conical step-and-stare scan around the vertical axes with an off-nadir angle of 20∘ is performed for 21 LOS positions, separated by 18∘ in azimuth direction. Considering a 1s averaging time for each LOS measurement and an additional second in order to change the laser beam pointing direction, one scanner revolution takes about 42s. By further taking into account the aircraft cruise speed of about 200 m s-1, the horizontal resolution of 2 µm DWL wind observations is about 8.4km, depending on the actual ground speed of the aircraft. The vertical resolution of the wind observations is determined by the laser pulse length and the averaging interval, which is set to be 100m.

To retrieve wind speed and wind direction profiles from the single LOS measurements performed during one scanner revolution, an algorithm based on a maximum function of accumulated spectra (MFAS) is used as baseline for the 2 µm DWL  . When using the MFAS algorithm, wind speed and wind direction are retrieved without estimating single LOS wind velocities and thus yields valid wind estimates, even in regions with a low signal-to-noise ratio (SNR). In particular, the spectra of all 21 LOS measurements are shifted to be proportional to their azimuth angle and an assumed wind vector and are accumulated afterwards. For a correctly assumed wind vector, the accumulated spectra have a maximum and thus indicate the prevailing wind vector. By applying the MFAS algorithm to one scanner revolution, the horizontal and vertical resolution of the retrieved wind vectors is about 8.4 km and 100 m, respectively. To additionally increase the coverage of 2 µm DWL measurements, the number of accumulated LOS measurements can be further increased at the expense of lower horizontal and/or vertical resolutions.

The suitability of the 2 µm DWL as a reference instrument for the Aeolus validation was demonstrated by means of dropsonde comparisons during several campaigns in the past. Based on these measurements, it was shown that single 2 µm DWL LOS measurements have a systematic error below 0.1 m s-1 and a random error of about 0.2 m s-1. The systematic error of horizontal wind speed is determined to be below 0.1 m s-1, and the corresponding random error varies between 0.9 and 1.5 m s-1, whereas these errors are composed of the contribution of the 2 µm DWL and the dropsondes as well as the corresponding representativeness errors . Thus, the random error of the 2 µm DWL can be considered to be of the order of 1 m s-1.

In addition to the 2 µm DWL observations, horizontal and vertical wind speed were measured in situ at flight level by the Falcon nose boom, which hosts a Rosemount model 858 flow angle sensor that is used together with a Honeywell Lasernav YG 1779 inertial reference system . Falcon nose boom observations provide a temporal resolution of 1Hz, which corresponds to a horizontal resolution of about 200m, considering the usual cruise speed of the Falcon aircraft of about 200 m s-1. The random error of the horizontal wind speed is specified to be 0.9 m s-1 and thus provides reference data at flight level that are suitable for Aeolus validation. Further details about the calibration method and retrieval algorithms of Falcon in situ winds are given by  and .

Due to the different horizontal and vertical sampling and resolution of 2 µm DWL measurements (≈8.4km, 100m for one scanner revolution) and Aeolus measurements (≈90km (Rayleigh) and ≈10km (Mie), 0.25 to 2km), special averaging procedures, as described in , are needed to compare respective wind observations. Furthermore, as Aeolus only provides HLOS winds, the 2 µm DWL measurements have to be projected onto the Aeolus HLOS direction. To this end, the wind speed and wind direction measured by the 2 µm DWL are averaged to the Aeolus grid by using the top and bottom altitudes as well as the start and stop latitudes given in the Aeolus L2B data product. As the 2 µm DWL does not provide full data coverage, a threshold for the number of available 2 µm DWL observations within an Aeolus grid cell has to be set. In this study, valid 2 µm DWL measurements need to be available to cover at least 50 % of the Aeolus bin to consider the averaged wind speed and wind direction for further comparison. Other more restrictive thresholds, for instance 75 % or 90 %, yield comparable systematic and random errors but with a significantly reduced number of data points that can be compared. For the Falcon in situ measurements, no such threshold is necessary because they have full horizontal coverage.

Afterwards, all valid averaged wind speeds (ws2µm) and directions (wd2µm) are projected onto the horizontal LOS of Aeolus (v2µmHLOS) by means of the range-dependent azimuth angle φAeolus that is provided in the Aeolus L2B data product according to 1v2µmHLOS=cos⁡φAeolus-wd2µm⋅ws2µm. In a next step, the Aeolus HLOS winds (Rayleigh-clear and Mie-cloudy) are extracted for areas of valid 2 µm DWL measurements. Beforehand, the data are filtered by means of an estimated error (EE) for the wind speeds given in the L2B data product, which is estimated based on the measured signal levels as well as the temperature and pressure sensitivity of the Rayleigh channel response . In this study, EE thresholds of 7.0 m s-1 (Rayleigh-clear) and 5.5 m s-1 (Mie-cloudy) are used for the AVATAR-I data set, and 8.5 m s-1 (Rayleigh-clear) and 5.0 m s-1 (Mie-cloudy) are used for the AVATAR-T data set. A discussion about the selection of EE thresholds is given in Sect.  as well as in a dedicated publication by . The Falcon wind measurements are treated in a similar way.

The explained averaging procedure is illustrated in Fig.  by means of the Aeolus underflight performed on 16 September 2019 during the AVATAR-I campaign, covering a flight distance of about 1000 km. The top panels show the measured 2 µm DWL wind speed (a) and direction (b). The corresponding projection onto the Aeolus HLOS direction using Eq. () is plotted in panel (c), and the actual Aeolus L2B Rayleigh-clear winds are indicated in panel (d). From the valid 6422 data points acquired by the 2 µm DWL along the underflight leg with its original resolution, only 163 data points remain for Rayleigh-clear wind comparison and 53 for Mie-cloudy (not shown) after being projected to the Aeolus grid. Thus, multiple underflights are needed to get enough data points for a statistically significant comparison.

To validate the quality of Aeolus HLOS observations (O), the HLOS wind velocity difference vdiff with respect to the corresponding reference or background data (B) from the 2 µm DWL or the Falcon nose boom, projected onto the Aeolus viewing direction, is calculated according to 2vdiff=OHLOS-BHLOS. The bias μ and standard deviation (SD) σ of vdiff are calculated by use of 3μ=1n∑i=1nvdiff and 4σ=1n-1∑i=1nvdiff-μ2, where n is the number of available data points. In addition to the standard deviation, the scaled median absolute deviation (scaled MAD) k is calculated according to 5k=1.4826×medianvdiff-medianvdiff. The scaled MAD has the advantage that it is less sensitive to single outliers, which may result in larger SD values. It is thus used as a measure of the random error of Aeolus HLOS winds. The scaled MAD is identical to the standard deviation (Eq. ) in the case that the analyzed data are normally distributed.

Furthermore, the uncertainty of the bias σμ is calculated according to 6σμ=kn.

Before performing a statistical comparison, an adequate quality control (QC) of Aeolus data is mandatory. The first parameter that is used for that purpose is the validity flag in the L2B wind product. Only winds with a validity flag that equals 1 are considered for further comparison. An additional parameter for QC is the estimated error (EE) which is reported in the L2B product. According to the Aeolus L2B Algorithm Theoretical Basis Document , the EE for the Rayleigh HLOS winds is computed from the uncertainty in the Rayleigh spectrometer response and is currently only dependent on the signal level (Poisson noise) and the solar background. Other quantities such as the dependency on atmospheric temperature and pressure, the contamination by Mie scattering, or the detector read-out noise are currently not considered for the EE calculation. On the other hand, the EE for Mie-cloudy winds is derived from the precision of the Mie response, which itself is dependent on the accuracy of the applied fit algorithm .

As the applied EE threshold impacts the determined statistical parameters such as the systematic and random error, a proper choice of the EE threshold is crucial; and as the EE varies over time and geographical location due to the different solar background and signal levels, the determination of a proper EE threshold gets even more difficult. Ideally, the EE thresholds are chosen such that the Aeolus wind errors with respect to the validation instrument (i.e., the 2 µm DWL or the Falcon in situ winds) are normally distributed, since the random error is defined as the standard deviation of a Gaussian distribution in the Aeolus mission requirements . While the comprehensive approach to determining the EE threshold is described separately by  , only a rough outline of the procedure is presented here.

One fundamental aspect when defining an EE threshold is to discard observations that suspiciously deviate from the expectations (outliers). To screen a data set for outliers, it is common to use the so-called Z score, which describes the distance from the bias μ in units of the standard deviation σ according to 7Zi=vdiffi-μσ. However, as shown, for instance, by , Z scores are not satisfactory, especially for small data sets, as they are available from airborne campaigns. The problem when using the Z score is that the mean and standard deviation used for Z-score calculation can be greatly affected by single outliers. To solve this problem, it is useful to apply the modified Z score instead, which is defined as 8Zm,i=vdiffi-median(vdiff)k. Hence, compared to the Z score, the mean is replaced by the median, and the standard deviation is replaced by the scaled MAD, making the modified Z score more robust with respect to outliers and to the sample size. In this study, a modified Z-score threshold of Zm>3 is used to define outliers.

For the definition of a suitable EE threshold, it turned out that it is useful to perform a statistical analysis of systematic and random errors and the data coverage depending on the EE threshold. Fig.  illustrates the results from the statistical comparison of Aeolus L2B Mie-cloudy (a, c) and Rayleigh-clear winds (b, d) against 2 µm DWL data (one scan accumulation) from the 10 underflights of the AVATAR-I campaign (top) and the 11 underflights of the AVATAR-T campaign (bottom), depending on the EE threshold without and with outlier removal based on the modified Z score. The bar plots depict the percentage of filtered winds after QC (Zm<3, green and blue bars) and outliers (Zm>3, red bars) from all wind results that are flagged as valid in the L2B product (left y axes). The percentage of outliers is indicated above the bars. The lines and symbols refer to the statistical results (mean bias μ, Eq. ; standard deviation σ, Eq. ; and scaled MAD k, Eq. ) without removing the gross errors from the data sets (gray, light blue, magenta), while the black, blue, and red lines represent the statistical parameters after QC based on the modified Z score (right y axes). The EE thresholds that are deemed reasonable to provide robust statistical results are highlighted by orange frames.

As expected, the number of available valid data points increases when increasing the EE threshold. This is true for both Rayleigh-clear (green bars) and Mie-cloudy winds (blue bars) and for both campaign data sets. At the same time, the number of outliers in the data set also increases. Additionally, it can be seen that the mean bias (black without and gray with outliers), the standard deviation (dark blue without and light blue with outliers), and the scaled MAD (red without and magenta with outliers) are dependent on the EE threshold. This further demonstrates that the EE threshold can significantly impact the results of the statistical comparison.

In the following, several subjectively selected quality criteria are used to define a suitable EE threshold. For instance, it is checked for which EE threshold the SD starts to deviate from the scaled MAD, as this marks the point where the data set starts to deviate from a normal distribution. Furthermore, the number of available data points and determined outliers is analyzed. If too many outliers are determined, the QC can be considered too strict. Additionally, it is checked if the respective statistical quantities differ significantly when being calculated from the data set with and without outliers.

For the Rayleigh-clear winds of the AVATAR-I data set (Fig. b), for instance, the number of available data points increases quickly with increasing EE threshold. For an EE threshold of 4.5 m s-1, 80 % of all data points are already included, and only 0.4 % outliers are detected. Furthermore, for this threshold, the SD and the scaled MAD are almost similar for both cases calculated with and without outliers. Between an EE threshold of 6.0 and 6.5 m s-1, the SD calculated including outliers makes a jump of about 1 m s-1, whereas the other quantities remain rather constant. For an EE threshold larger than 7.0 m s-1, mainly outliers are added to the data set. Thus, 7.0 m s-1 is considered the optimum EE threshold for Rayleigh-clear winds of the AVATAR-I data set.

For the Rayleigh-clear winds of the AVATAR-T data set, which was acquired almost 2 years later in a different geographical region and at decreased ALADIN signal performance, the distribution looks different (Fig. d). The number of valid data points increases much slower compared to the AVATAR-I case. For an EE threshold of 7.0 m s-1, the SD is still rather close to the scaled MAD; however, only 65 % of the data points are included. By further increasing the EE threshold to 8.5 m s-1, the number of data points used increases to 78 %. For even larger EE thresholds, the difference of the scaled MAD calculated without (red) and with (magenta) outliers starts to increase, indicating that the outliers start to have an impact on the calculated statistical parameters. Thus, an EE threshold of 8.5 m s-1 seems to be a good compromise for the Rayleigh-clear winds of the AVATAR-T data set.

For the Mie-cloudy data set, the distribution of statistical parameters is even more sensitive to the EE threshold. It can be seen that Mie-cloudy winds in general contain more outliers. This also confirms that the QC by means of the validity flag and the EE threshold is not sufficient and that an additional QC by means of the modified Z score is needed, especially for the Mie-cloudy winds . Following the same logic as for the Rayleigh-clear winds, an optimal EE threshold of 5.5 m s-1 is determined for the Mie-cloudy winds of the AVATAR-I data set and 5.0 m s-1 for the Mie-cloudy winds of the AVATAR-T data set. It is worth mentioning that the statistical comparison of AVATAR-T Mie-cloudy winds is not very sensitive to the actual EE threshold. For instance, an EE threshold of up to 7.0 m s-1 would yield similar results.

The mean systematic error of the Aeolus wind data and its corresponding uncertainty are calculated according to Eqs. () and (), respectively. It yields values of (-0.8±0.2) m s-1 (Rayleigh-clear) and (-0.9±0.1) m s-1 (Mie-cloudy) for the AVATAR-I data set and (-0.1±0.3) m s-1 (Rayleigh-clear) and (-0.7±0.2) m s-1 (Mie-cloudy) for the AVATAR-T data set, respectively. Hence, the systematic errors for both wind products and both campaign periods are close to the specified mission requirement of 0.7 m s-1 for Aeolus HLOS winds . Compared to the previous campaign results where the systematic error was determined to be (2.1±0.3) m s-1 (Rayleigh-clear) and (2.3±0.2) m s-1 (Mie-cloudy) for the WindVal III data set and (-4.6±0.2) m s-1 (Rayleigh-clear) and (-0.2±0.1) m s-1 (Mie-cloudy) for AVATAR-E, a significant decrease in the systematic error can be observed (see also Table ), which is due to the implementation of correction schemes for the hot pixels and the thermal fluctuations on the telescope mirror in the Aeolus processor that were not available in the early phase of the mission. It is worth mentioning that, for the analysis of the AVATAR-I campaign, which was performed in fall 2019, the second reprocessed Aeolus data set is used (B11) and hence also contains the correction scheme for the telescope temperature fluctuations. The Aeolus processor versions used for the analysis of the respective campaign data sets are also given in Table . Furthermore it has to be pointed out the results from the different campaign data sets are not necessarily comparable, as they are dependent on the applied QC procedure, as discussed in Sect. .

The random error of the Aeolus wind is represented by the scaled MAD according to Eq. (). It is determined to be 5.5 m s-1 (Rayleigh-clear) and 2.7 m s-1 (Mie-cloudy) for the AVATAR-I data set and 7.1 m s-1 (Rayleigh-clear) and 2.9 m s-1 (Mie-cloudy) for the AVATAR-T. The impact of the 2 µm DWL uncertainty of about 1 m s-1 (see also ) on the determined random error is only marginal. It can be recognized that the mean random error of Rayleigh-clear winds is significantly larger than the 2.5 m s-1 originally specified for Aeolus HLOS winds at altitudes between 2 and 16 km . The main reason for this is the lower signal levels of the backscattered light from the atmosphere, which are indicated to be caused by a combination of instrumental misalignment, the wavefront error of the 1.5m telescope, and laser-induced contamination (LIC) within the system.

Furthermore, it can be seen that the Rayleigh-clear random error increased by about 30 % between the AVATAR-I and the AVATAR-T campaigns, although the actual laser UV energy was 20 % larger during the AVATAR-T campaign. However, the atmospheric signal level itself was about 50 % smaller due to the aforementioned degradation. This signal decrease was partly compensated for by enlarging the Aeolus range bins during the AVATAR-T campaign, which were 750 m instead of 500 m, as applied during AVATAR-I. Additionally, the solar background signal was smaller by about a factor of 3 during AVATAR-T, which also partly compensates for the overall signal decrease. The mean useful signal – which denotes the average signal level per observation in LSB (least significant bit) after being corrected for the detection chain offset (DCO), the solar background, and the dark current – is determined to be (247±1)LSB for Rayleigh signals during AVATAR-I and (175±3)LSB for AVATAR-T. Considering just Poisson noise in the measured data set, the random error can be considered to be proportional to N-1/2, where N is the signal level. Hence, by using the random error determined from AVATAR-I and considering the mean useful signal levels of both campaign data sets, the random error for AVATAR-T would be expected to be (247/175)1/2×5.5ms-1=6.5 m s-1, which is close to the measured value of 7.1 m s-1. It should also be mentioned that the error calculation based on signal levels is only a rough approximation, as valid Rayleigh-clear winds are also available in aerosol-loaded areas with a scattering ratio larger than 2 or 3. Hence, the signal does not necessarily originate from backscattering on molecules, which would distort the random error calculation of the Rayleigh-clear winds.

In addition to 2 µm DWL observations, in situ measurements performed on board the Falcon aircraft were statistically analyzed, as demonstrated by the scatter plot shown in Fig. . Here, the Aeolus HLOS Rayleigh-clear wind speeds are plotted versus Falcon in situ data for the AVATAR-I data set (blue dots) as well as for the AVATAR-T data set (green dots). Line fits to the data are depicted by the dark blue and green lines, and the x=y line is represented by the gray dashed line. The Falcon measurements are mainly taken at altitudes between 10 and 11km and have a random error of 0.9 m s-1, with a temporal resolution of 1s, hence providing very good reference data. It is only the representativeness error that is difficult to assess, as it is dependent on the vertical homogeneity of the atmosphere in the vicinity of the performed observations. Furthermore, as no Mie-cloudy winds were present at flight level, only Rayleigh-clear winds could be analyzed.

The mean systematic error is determined to be (-0.3±0.5) m s-1 (AVATAR-I) and (-0.2±0.4) m s-1 (AVATAR-T) and hence confirms the results obtained from the 2 µm DWL analysis and that the Aeolus Rayleigh-clear winds meet the mission requirement of a systematic error smaller than 0.7 m s-1.

The corresponding random errors yield values of 5.0 m s-1 (AVATAR-I) and 4.6 m s-1 (AVATAR-T). Thus, for the AVATAR-I data set, the random error is comparable to the one determined from the 2 µm DWL (5.5 m s-1) but differs significantly for the AVATAR-T data set, where the 2 µm DWL analysis yields a random error of 7.1 m s-1. This is explained by the fact that the Rayleigh-clear random error depends on the signal level, which is lower at lower altitudes (see also Sect. ). For the AVATAR-T campaign, lower signal levels in the SAL due to the extinction induced by aerosols cause the random error of Rayleigh-clear winds to increase in this region. Hence, the mean random error is larger in lower altitudes compared to the one at flight level.

In Fig. , the dependency of the Aeolus Rayleigh-clear HLOS wind speed error with respect to the 2 µm DWL (Eq. ) on the 2 µm DWL-measured wind speed (a), on the latitude (b), on the time difference between Aeolus and 2 µm DWL observation (c), and on scattering ratio (d) is shown. The data from AVATAR-I are indicated in blue and from AVATAR-T in orange. The solid lines denote the median value for certain intervals, and the shaded area represents the median plus–minus the scaled MAD. To have enough data points and hence a reliable value for the mean and the scaled MAD, the averaging intervals Δ for the AVATAR-I and AVATAR-T data sets are chosen to be Δ=(5.8and1.7) m s-1 (2 µm DWL wind speed), Δ=(0.44and0.67)∘ (latitude), Δ=(296and342)s (time difference), and Δ=0.95 and 0.98 (scattering ratio), respectively.

From Fig. a, it is obvious that the Aeolus wind speed error has no significant dependency on the actual wind speed which is represented by the 2 µm DWL. Both the median (systematic error) and the scaled MAD (random error) are nearly constant for all wind speeds and both campaign data sets. Please note that the median is used instead of the mean to be insensitive to single outliers of the small number of data for each averaging interval. Still, single outliers for very high wind speeds during the AVATAR-I campaign are an artifact caused by a lack of sufficient data points. Furthermore, especially for the AVATAR-I data set, it is evident that there are more outliers with a positive error than with a negative one. A potential explanation for this behavior is not available so far.

In Fig. b, the error is plotted against the latitude. As both campaign sites were at different latitudes, the x axis has a break between 22 and 59∘ N, but both sides cover the same range of 13∘. As for the wind speed, no significant dependency of the systematic and random error on the latitude can be recognized. It is probable that the usual range covered during Falcon campaigns (≈10∘) is not enough to resolve any geolocation dependency of the Aeolus errors.

In addition, it is investigated whether the time difference between the Aeolus overpass and the actual 2 µm DWL observation on the track has an impact on the determined wind speed error (Fig. c). It can be seen that the maximum temporal discrepancy between the Aeolus overpass and the 2 µm DWL observation is always smaller than 1 h and that neither the systematic nor the random error is significantly dependent on this time difference.

The dependency of the Aeolus errors on the scattering ratio is shown in Fig. d. It is obvious that Rayleigh-clear winds are even available for scattering ratios of 10 and larger. However, as mentioned before, it cannot be guaranteed that the scattering ratio data represent the actual atmospheric composition of the volume from which the Rayleigh-clear wind was retrieved. Still, for the given data, no dependency of the systematic error on the scattering ratio can be observed. In addition, it can be seen that outliers, determined by the modified Z-score threshold of 3, appear for low as well as for high backscatter ratios.

Hence, the Aeolus mean systematic and random errors are neither significantly dependent on the wind speed nor on the latitude, the time difference, and the scattering ratio, confirming that the Aeolus calibration is working properly. It has to be mentioned that these results are restricted to certain geographical regions, certain time periods, and a limited number of data points. Thus, it is probable that not all error contributions can be detected in this analysis, especially if those are related to strong non-periodic sources like strong deviations from the atmospheric temperature profile or orbital variations. For an even more conclusive error characterization, data from other CalVal teams as well as model data are needed.

In Fig. , the altitude dependency of the mean useful signal (a), the estimated error (b), the Aeolus error with respect to the 2 µm DWL observations (c), the scattering ratio (d), and the HLOS wind velocity derived from 2 µm DWL measurements (e) for Rayleigh-clear wind observations available for the AVATAR-I data set (blue) and the AVATAR-T data set (orange) is shown. The mean useful signal denotes the mean signal level per observation and the range bin in LSB after being corrected for the detection DCO, the solar background, and the dark current. The actual valid data points are indicated by the small dots, and corresponding outliers, defined by a modified Z-score threshold of 3, are plotted by larger dots. The median value per each range gate is indicated by the solid line, and the shaded area indicates the median plus–minus the scaled MAD for each range bin.

By analyzing the altitude dependency of the mean useful signal (Fig. a), it can be seen that the two data sets differ. For AVATAR-I (blue), the signal levels are rather constant at about 240LSB. Only at altitudes of about 10.5km is the signal level twice as high due to the larger range bin size at this altitude (see also Fig. ). On the contrary, the mean signal level for the AVATAR-T data shows a remarkable decrease between about 4.5km and the ground, which is due to the signal extinction caused by the aerosols that are prominent in the SAL. Even at altitudes above 4.5km, the signal levels for AVATAR-T data were lower than for AVATAR-I, although the range bins were already increased to 750m. This additionally confirms that the decreasing Aeolus performance leads to lower (Rayleigh-clear) signal levels at all altitudes. Furthermore, it can be observed that outliers appear in all altitudes and were successfully determined by the applied Z-score threshold.

The altitude dependency of the EE is plotted in Fig. b. It can be seen that it is indirectly proportional to the signal levels shown in panel (a). All regions of smaller signal levels correspond to a larger EE (as expected). For AVATAR-I, the EE is about 4 m s-1 at all altitudes, except for the highest range bin at about 10.5km, where it goes down to 2.5 m s-1 due to the larger range bin size. At lower altitudes, it goes up to 5 m s-1 due to the lower signal levels in this region. For the AVATAR-T data set, the EE is about 4to4.5 m s-1 between 4.5 and 10.5km altitude and increases up to 7.5 m s-1 below due the low signal levels in this region. This also explains why the random error retrieved from the Falcon observations at about 10.5km altitude (5.0 m s-1) is significantly lower than the mean random error derived from all 2 µm DWL observations (7.1 m s-1).

In Fig. c, the Aeolus error with respect to the 2 µm DWL is shown. It can be observed that the mean bias does not show any height dependency for both data sets. The outlier at 7.5km of the AVATAR-T data set is a result of an insufficient number of data points. Furthermore, it can be seen that the random error follows the EE (Fig. b) rather well. In particular, the random error increase for AVATAR-T in the SAL is predicted well by the EE.

The height dependency of the scattering ratio is depicted in Fig. d. It can be realized that Rayleigh-clear winds are available even for scattering ratios up to 10 and larger and that these scattering ratios occur at all altitudes. However, as mentioned above, these data have to be treated with caution. The mean scattering ratio is below 1.5 for both data sets and all altitudes.

In Fig. e, the 2 µm DWL winds are shown to be range resolved, demonstrating that much higher wind speeds between -60and55 m s-1 were measured during AVATAR-I (blue) and mainly at altitudes between 6 and 10km in the vicinity of the North Atlantic jet stream. During AVATAR-T, the measured wind speeds were much lower, varying between -20 and 18 m s-1, and had their maximum between 3 and 6km, which is most probably related to the African easterly jet.

A similar analysis as shown for Rayleigh-clear winds in Fig.  is done for Mie-cloudy winds, as presented in Fig. . Since fewer data points are available for Mie-cloudy winds, the averaging intervals Δ for the AVATAR-I and AVATAR-T data sets had to be enlarged to Δ=(10.5and4.3) m s-1 (2 µm DWL wind speed), Δ=(1.2and1.6)∘ (latitude), Δ=(604and677)s (time difference), and Δ=6.9 and 7.4 (scattering ratio), respectively.

The dependency of the Aeolus wind error on the actual wind speed represented by the 2 µm DWL is shown in Fig. a. For the AVATAR-I data set, it can be recognized that there are regions where the error is negative – as, for instance, for a 2 µm DWL-measured wind speed around 15 m s-1, where the systematic error is about -2 m s-1. As this is also the region with the most data points, this explains the overall negative systematic error of -0.9 m s-1 retrieved from the statistical comparison. Furthermore, it can be seen that there are remarkably more outliers towards positive errors. This was already true for Rayleigh-clear winds; however, it cannot be concluded that this is due to the same root cause, which is essentially unknown and a topic for further investigations.

The dependency of the Aeolus Mie-cloudy wind speed error on latitude is indicated in Fig. b. For the AVATAR-I data set (blue), it can be seen that the median is negative for all latitudes, varying between 0 and -2 m s-1. The modulation of the median is not meaningful due to a lack of sufficient data points. This is even more true for the AVATAR-T data set, where no conclusion can be drawn from the latitude-averaged data set.

In Fig. c, the Aeolus Mie-cloudy error is plotted with respect to the time difference between Aeolus overpass and 2 µm DWL observation. As for the Rayleigh-clear winds, no significant dependency can be observed for either data set. Thus, even Mie-cloudy winds seem to change only marginally within a ±1h timeframe (on average), although Mie-cloudy winds are expected to have a higher variability compared to Rayleigh-clear winds.

Fig. d depicts the Aeolus error depending on the scattering ratio. From the AVATAR-I data set, it can be seen that the scattering ratio extends to values of up to 100 and that the median drifts to negative values for larger scattering ratios. Also, the random error is significantly reduced from about ≈±4 m s-1 for lower scattering ratios (0–10) to ≈±2 m s-1 for larger backscattering ratios (20–100). Hence, it can be concluded that the accuracy and precision of Mie-cloudy winds are dependent on the scattering ratio. In particular, observations with a higher backscatter ratio and, thus, a better SNR provide more accurate Mie-cloudy winds; however, they also present a different bias, a topic which has to be investigated in the future. A similar behavior can be seen from the AVATAR-T data set, although it is less conclusive due to the lower number of available data points.

Furthermore, similar to the Rayleigh-clear wind analysis, the altitude dependency of the mean useful signal (a), the estimated error (b), the Aeolus error with respect to the 2 µm DWL observations (c), the scattering ratio (d), and the HLOS wind velocity derived from 2 µm DWL measurements (e) is investigated for Mie-cloudy winds from the AVATAR-I data set (blue) and the AVATAR-T data set (orange), as shown in Fig. .

From Fig.a, it can be seen that the mean useful signal varies much more than for Rayleigh-clear winds from almost 0 up to about 1600LSB for the AVATAR-I data set at about 7km altitude. The mean signal levels range from about 100 to 500LSB for both data sets. Furthermore, it is interesting to realize that no Mie-cloudy winds are available for the AVATAR-T data set between 1 and 4.5km altitude, which represents the dust-laden SAL. Thus, Mie-cloudy winds are indeed just retrieved from cloud returns and not from aerosol-rich regions. This is a known issue and is related to the scattering ratio thresholds and grouping schemes that are currently used in the Aeolus processor. Outliers appear in all altitudes but mainly for low signal levels.

The altitude-dependent EE is depicted in Fig. b. In general, as for Rayleigh-clear winds, the EE is smaller in regions of larger signal levels. However, as the Mie-cloudy EE does not directly depend on the signal level but on the accuracy of the actual fit routine, this behavior is less pronounced. The mean EE ranges from about 1 to 3 m s-1 for both data sets.

The altitude-dependent Aeolus error with respect to the 2 µm DWL observations is shown in Fig. c. From the AVATAR-I data, it can be seen that the mean error is obviously negative (≈-2.5 m s-1) for altitudes between 4.5km and the ground, where the random error is relatively small. This is also the region with larger scattering ratios, as they are shown in Fig. d, and thus confirms that the accuracy and precision of Mie-cloudy winds depend on the scattering ratio (see also Fig. d). The AVATAR-T data set does not provide enough data points to draw a similar conclusion. The scattering ratio, in general, varies from close to 1 up to 100, whereas the mean scattering ratio varies from close to 1 up to 30 for both data sets. For the AVATAR-I data set, larger scattering ratio values up to 30 are prominent at altitudes from the ground up to 4.5km, which is also the region that shows an enhanced negative systematic error.

The altitude dependency of the measured 2 µm DWL winds is shown in Fig. e. The wind speed range is much smaller than for Rayleigh-clear winds and varies from about -30 to 50 m s-1 for AVATAR-I and from about -20 to 15 m s-1 for AVATAR-T. As for Rayleigh-clear winds, the highest wind speeds are found in the vicinity of the jet stream in the AVATAR-I data set.