The laser transmitter of the A2D is based on a frequency-tripled Nd:YAG master oscillator power amplifier (MOPA) system, generating 20 ns pulses (full width at half maximum, FWHM) at 354.89 nm wavelength. The injection-seeded laser, which uses an active frequency stabilization technique, provides single-frequency UV pulses with energy of 60 mJ at 50 Hz repetition rate (3.0 W average power), while showing near-diffraction-limited beam quality. Concerning the spectral characteristics, the bandwidth of the transmitted UV laser pulses is 50 MHz (FWHM), while the pulse-to-pulse frequency stability is approximately 3 MHz (root mean square). A comprehensive description of the laser transmitter configuration and its performance is provided in Lemmerz et al. (2017) and Schröder et al. (2007).

In the last years, particular attention has been devoted to the cavity control mechanism which ensures high single-frequency operation stability even under vibration conditions. In addition to the strict requirements in terms of frequency stability, a further challenge is imposed by the necessity to trigger the receiver electronics about 60 µs before the laser pulse emission with an error of less than 100 ns. Therefore, a dedicated active frequency stabilization technique was developed which is based on the ramp–delay–fire method (Nicklaus et al., 2007). Fast detection of the master oscillator cavity resonances with the seed laser frequency enabled effective compensation of higher-frequency vibrations, while providing a sufficiently early trigger for the detector electronics with a timing stability of around 80 ns (Lemmerz et al., 2017). The long lead time of the detector electronics is due to an electronic preconditioning process of the accumulating charged-coupled device (ACCD) arrays described in Sect. 2.2. Although ACCDs of the same type are used for the satellite instrument, the preconditioning process is not an issue here, since the round-trip laser pulse travel time from the satellite to the first atmospheric range gate (≈ 2.5 ms) is sufficiently long.

Measurement of the transmitted laser frequency and calibration of the frequency-dependent transmission of the receiver spectrometers are prerequisite for accurate wind retrieval. Therefore, a small portion of the pulsed UV laser radiation, referred to as internal reference, is collected by an integrating sphere, coupled into a multi-mode fibre (200 µm core diameter) and guided to the receiver via the front optics, while allowing adjustable signal levels by using a variable fibre attenuator (not shown in Fig. 1). Another small fraction of the beam is directed to a wavelength meter (HighFinesse, WS Ultimate 2) with a relative accuracy of 10-8 in order to monitor the UV frequency of the outgoing laser pulse.

The spatial properties of the high-energy laser were characterized prior to the NAWDEX campaign according to the ISO 11146 standard (ISO, 2005), yielding a beam quality factor (M2) of 1.1 for both the major and minor beam axis. As a result, after passing through the beam expander, the collimated beam showed a full-angle divergence (±3σ, containing > 99 % of the energy) of 98 and 102 µrad at 4σ beam diameters of 7.3 and 7.1 mm for the two axes.

The UV laser is transmitted into the atmosphere via a piezo-electrically controlled mirror that is attached to the frame of a Cassegrain-type telescope, as shown in Fig. 1. In contrast to ALADIN that incorporates a 1.5 m diameter telescope and will operate at an off-nadir pointing angle of 35∘, the A2D employs a 0.2 m telescope which is oriented at an off-nadir angle of 20∘. The convex spherical secondary mirror of the telescope collects the backscattered light and guides it to the front optics of the A2D receiver assembly. The structural design of the telescope causes a range-dependent overlap function which has to be considered in the wind retrieval as it reduces the backscatter signal (Paffrath, 2006; Paffrath et al., 2009).

Aside from a narrowband UV bandpass filter (FWHM: 1.0 nm) which blocks the broadband solar background spectrum, the front optics include an electro-optic modulator (EOM). The EOM is used to avoid saturation of the ACCD by shutting the atmospheric path for several µs after transmission of the laser pulse, thus preventing strong backscattered light produced close to the instrument (up to about 1 km) from being incident on the detectors. In this way, the EOM temporally separates the atmospheric signal from the internal reference signal. The latter is injected into the front optics assembly via the aforementioned multi-mode fibre, so that both signals enter the spectrometer optics on equal paths. In addition, active stabilization of the laser beam pointing is realized by a co-alignment control loop. For this purpose, a portion of the backscattered signal passing through the front optics is imaged onto a UV camera (SONY XC-EU50CE) to monitor the horizontal and vertical position of the centre of gravity (CoG) of the beam. A reference position (CoGX/CoGY) is defined and a feedback loop involving three piezo-actuators mounted on the last laser transmit mirror is applied to actively stabilize the co-alignment of the transmit and receive path of the laser beam. In this way, variations in the incidence angle of the atmospheric return signals on the receiver spectrometers are reduced. This is crucial for accurate wind measurements, especially for the Rayleigh channel, as angular variations of 1 µrad with respect to the 200 mm telescope diameter and a field of view (FOV) of 100 µrad introduce errors of the horizontal wind speeds of up to 0.4 m s-1, as derived from optical simulations and experiments (DLR, 2016). It should be noted that active stabilization of the transmit–receive co-alignment is not required for the satellite instrument, since the same telescope is used for transmission of the laser beam and reception of the backscattered signals.

The receiver optics of both the satellite instrument and the A2D are almost identical and consist of two different spectrometers, as shown on the right-hand side of Fig. 1. Two sequential Fabry–Pérot interferometers (FPIs) are employed for measuring the Doppler frequency shift of the broadband Rayleigh backscatter signal from molecules, whereas a Fizeau interferometer is used for determining the Doppler shift of the narrowband Mie signal originating from cloud and aerosol backscattering. Detection of the two signals is realized by using two ACCDs which allow for data acquisition in 24 range gates, where the vertical resolution within one profile can be varied from 296 m to about 2 km.

The wind measurement principle of the A2D wind lidar system is based on detecting frequency differences between the emitted and the backscattered laser pulses. Due to the Doppler effect, the frequency f0 of the outgoing pulse is shifted upon backscattering from particles (cloud droplets, aerosols) and molecules which move with the ambient wind. The frequency shift in the backscattered signal ΔfDoppler is proportional to the wind speed vLOS along the laser beam LOS: ΔfDoppler=2f0/c⋅vLOS, with c being the speed of light. For an emission frequency of f0 = 844.75 THz (354.89 nm vacuum wavelength), a LOS wind speed of 1 m s-1 translates to a frequency shift of 5.63 MHz which corresponds to a wavelength shift of 2.37 fm. The required accuracy of the frequency measurement is hence on the order of 10-8 to measure wind speeds with an accuracy of 1 m s-1. Owing to the large difference in spectral width of the Mie (∼ 50 MHz) and Rayleigh (∼ 3.8 GHz at 355 nm and 293 K) atmospheric backscatter signals, two different techniques are applied for deriving the Doppler frequency shift from the two spectral contributions separately.

The measurement principle of the Rayleigh channel relies on the double-edge technique (Chanin et al., 1989; Garnier and Chanin, 1992; Flesia and Korb, 1999; Gentry et al., 2000) and involves two bandpass filters (A and B) which are placed symmetrically around the frequency of the emitted laser pulse, as illustrated in Fig. 2a. The width and spacing of the filter transmission curves (free spectral range (FSR): 10.95 GHz, FWHM: 1.78 GHz, spacing: 6.18 GHz) is chosen such that the maxima are close to the inflexion points (edges) of the molecular line that is spectrally broadened by virtue of Rayleigh–Brillouin scattering (Witschas, 2011a, b, c). The transmitted signal through each filter is proportional to the convolution of the respective filter transmission function and the line shape function of the atmospheric backscatter signal. Consequently, the contrast between the return signals IA and IB transmitted through filters A and B represents a measure of the frequency shift between the emitted and backscattered laser pulse, thus defining the frequency-dependent Rayleigh response ΨRay as follows: ΨRayf=IAf-IBfIAf+IBf. Close to the filter cross point, where the transmission functions intersect, the relationship between Rayleigh response and frequency is approximately linear with a slope of about 5 × 10-4 MHz-1.

The determination of the Doppler shift from the narrowband Mie return signal is based on the fringe-imaging technique (McKay, 2002) involving the measurement of the spatial location of an interference pattern, as shown in Fig. 2b. For this purpose, a Fizeau interferometer is used consisting of two plane plates that are tilted by a small wedge angle of several µrad with respect to each other. Due to the wedge angle, the linear interference pattern (fringe) is produced at a distinct lateral position along the wedge where the condition for constructive interference is fulfilled. Hence, a Doppler frequency shift of the signal results in a spatial displacement of the fringe which is vertically imaged onto the ACCD detector, whereby the relationship between the Doppler shift and the centroid position of the fringe x is approximately linear (Δx≈k⋅ΔfDoppler), so that the Mie response reads ΨMief=xf=xf0+Δxf=x0+k⋅ΔfDoppler. Here, x0 represents the Mie fringe centroid position at the frequency f0 of the emitted laser pulse and is referred to as Mie centre. Δx is the shift of the Mie fringe centroid position with respect to the Mie centre and k denotes the proportionality factor between the Doppler frequency shift ΔfDoppler and the resulting shift of the Mie fringe Δx, thus describing the sensitivity of the Mie channel. The latter is on the order of k ≈ 100 MHz pixel-1. From the Fizeau FSR of 2.2 GHz, only a section of 1.6 GHz is recorded by the 16 pixel columns of the ACCD (imaged spectral range), resulting in an effective LOS wind measurement range of ±145 m s-1.

The thinned and back-side-illuminated ACCD with 16 × 16 pixels is optimized for operation in the UV showing a high quantum efficiency of 85 %, while cooling to -30 ∘C provides a low electronic noise level. The electronic charges generated in the imaging zone of the device are accumulated directly in a memory zone within the CCD chip, thus allowing for low readout noise (Reitebuch et al., 2009). For the ACCD used in the Mie channel, the electronic charges of all 16 rows are binned together to one row for each range gate of each laser pulse, resulting in 16 spectral channels of about 100 MHz width. For the Rayleigh channel, the two spots produced by the two FPIs are imaged onto the left and right half of a second ACCD of the same type, with the centres of the spots being separated by 8 pixels (see bottom right part of Fig. 1). As for the Mie channel, the electronic charges of all 16 rows are binned together to one row, whereas the signal of each Rayleigh filter is contained in 6 pixels that are summed up in the retrieval algorithms after digitization.

The memory zone of the ACCD contains 25 rows so that a maximum number of 25 range gates can be acquired, from which three range gates are used for detecting the background light, the detection chain offset (DCO) and the internal reference signal, while two range gates act as buffers for the internal reference. The DCO is a constant electric voltage at the analogue-to-digital converter. The atmospheric backscatter signals are collected in the remaining 20 (so-called atmospheric) range gates. The transfer time from the image to the memory zone limits the minimum temporal resolution of one range gate to 2.1 µs, which corresponds to a range resolution of 315 m and a height resolution of 296 m, taking account of the 20∘-off-nadir pointing of the instrument. The timing sequences of both ACCDs are programmable, providing flexible and independent vertical resolution for the Rayleigh and Mie wind profiles.

The horizontal resolution of the A2D is determined by the acquisition time of the detection unit. Here, the signals obtained from 20 laser pulses are accumulated to so-called measurements (duration 0.4 s), while the combination of the signals from 35 measurements (700 pulses) constitutes one observation (duration 14 s). Considering the time required for data read out and transfer (4 s), the separation time between two subsequent observations thus accounts for 18 s. For a typical ground speed of the Falcon aircraft of 200 m s-1, this results in a horizontal resolution of 3.6 km. Note that continuous data readout without gaps of 4 s is carried out for the satellite instrument on Aeolus, but the concept for on-chip averaging of multiple laser pulse returns to measurements is used as well. In the following, the terms observation and measurement are consistently used referring to the sampling of the A2D data.

Spectral response calibration of the A2D is a prerequisite for the wind retrieval, since the relationship between the Doppler frequency shift of the backscattered light, i.e. the wind speed, and the response of the two spectrometers has to be known for the wind retrieval. In particular, proper knowledge of the Rayleigh response for different altitudes is necessary, as the spectral shape of the Rayleigh–Brillouin backscatter signal significantly depends on temperature and pressure of the sampled atmospheric volume (Witschas et al., 2014) and thus varies along the laser beam path.

For deriving the frequency dependency of the Rayleigh and Mie channel spectral response, a frequency scan of the laser transmitter is carried out, thus simulating well-defined Doppler shifts of the radiation backscattered from the atmosphere within the limits of the laser frequency stability. During the calibration, the contribution of (real) wind related to molecular or particular motion along the instruments' LOS has to be eliminated, i.e. the LOS wind speed vLOS needs to be zero. In practice, this is accomplished by flying curves at a roll angle of the Falcon aircraft of 20∘, resulting in approximate nadir pointing of the instrument and hence vLOS ≈ 0, while assuming that the vertical wind is negligible. Consequently, regions with expectable non-zero vertical winds, e.g. introduced by gravity waves or convection, are avoided in this procedure. Nadir pointing leads to a circular flight pattern of the aircraft which is preferably located over areas with high surface albedo in the UV spectral region (e.g. over ice), hence enabling strong ground return intensities and, in turn, high SNR. In the course of the calibration procedure, which takes about 24 min, highest attention has to be paid to the minimization of all unknown contributions to the Rayleigh and Mie response such as biases resulting from inaccurate co-alignment of the transmit and receive path, temperature variations of the spectrometers or frequency fluctuations of the laser transmitter.

During NAWDEX, six response calibrations have been carried out over Iceland, four over the Vatnajökull glacier and two over ice-free land in the north of the island. During each calibration, the laser frequency was tuned in steps of 26 MHz (corresponding to 4.5 m s-1) over a 1.4 GHz interval (±125 m s-1) and the Rayleigh and Mie responses were determined after averaging over 700 pulses (1 observation) per frequency step. While the Rayleigh response is given by the intensity contrast function of filters A and B according to Eq. (1), the Mie response is described by the centroid position of the Fizeau fringe according to Eq. (2). Polynomial fitting is then performed for each individual range gate to derive polynomial coefficients that are later fed into the wind retrieval algorithm (Marksteiner, 2013). Here, a fifth-order polynomial was empirically chosen for fitting the Rayleigh response curves, whereas a linear fit is applied for the Mie response function: ΨRayf=∑i=05cifi,ΨMief=C0+C1f. The determined polynomial coefficients for each range gate are then used for the calculation of the Doppler frequency shift from the Rayleigh and Mie responses obtained for each wind observation. Since both the range gate setting and the flight altitude generally differ between the calibration flight and the actual wind scene, a linear interpolation is performed between the coefficients deduced from the calibration in order to obtain the response function for the respective bin altitudes of the wind observation.

For the satellite instrument, the atmospheric Rayleigh response function is derived after adding the return signals obtained from a number of range gates in the upper troposphere (e.g. between 6 and 16 km) in order to increase the SNR. The selection of the appropriate range for averaging is performed during on-ground processing and the information for each single range gate is still included in the downlinked raw data. In the satellite wind retrieval for the L2B product, a Rayleigh–Brillouin line shape model is used in combination with atmospheric temperature and pressure profiles from a NWP model (e.g. from ECWMF) to account for the altitude-dependence of the Rayleigh response over the entire vertical measurement range from ground to the lower stratosphere (Dabas et al., 2008; Tan et al., 2016).

Unlike for molecular scattering, the backscattering of the laser radiation from aerosols, cloud particles or hard targets does not induce a significant spectral broadening, so that the altitude-dependent variations in temperature and pressure have a negligible impact on the Mie response. Therefore, in contrast to the Rayleigh response calibration, the Mie response function determined for the ground return is sufficient for the wind retrieval and used for all the atmospheric range gates. Due to this fact, precise determination of the coefficients {C0,C1} for the ground is of utmost importance for an accurate Mie wind retrieval. A detailed study on A2D response calibrations and the various influencing factors that affect their quality will be provided in a forthcoming publication. Based on a set of criteria which have been defined over the last years, out of the six available from 2016 one particular calibration, i.e. set of response coefficients {ci} (i = 1, …, 5) and {C0,C1}, was determined as the baseline for the subsequent Rayleigh and Mie wind retrieval.

Precise identification of the ground return signals is crucial for exploiting the information included therein. Systematic wind errors which can be caused by changes in the alignment of the transmit–receive path or inaccuracies in the aircraft attitude data can be reduced by applying ZWC. Regarding the aircraft speed of the Falcon, the specification of the incorporated GPS receiver assures an accuracy of better than 0.1 m s-1 (Weissmann et al., 2005). Due to the coarse vertical resolution (hundreds of metres) of the A2D and ALADIN, ZWC based on ground return signals is rather challenging, as the ground bin is very likely to be contaminated by atmospheric signals. For the Mie channel, strong aerosol backscatter close to the ground can influence the ground speed measurement, while the SNR of the ground measurement for the Rayleigh channel is diminished by the broad bandwidth molecular return collected from near the ground surface. Moreover, both channels are potentially affected by surface winds, which introduce systematic errors in the measurement of the ground speed or sea surface with non-zero ground speed (Li et al., 2010). This situation is aggravated by the fact that the ground signals can be distributed over multiple range bins. First, this is due to the charge transfer process of the ACCD, which leads to a temporal overlap in the acquisition of two subsequent range gates of about 1 µs. Laser timing fluctuations in combination with charge transfer inefficiency during the readout of the ACCD, especially occurring at high signal intensities, can cause a signal spread over even more than two range gates within a measurement and observation. Second, varying ground elevations during the duration of one measurement (0.4 s, 20 pulses at 50 Hz repetition rate) and laser pointing fluctuations can lead to the detection of ground signals in multiple range gates, taking into account that the laser pulses cover a distance of 80 m along track on the ground at an aircraft speed of 200 m s-1. Figure 3 illustrates this circumstance for two cases; one with ground signals completely contained in one range gate (a) and another with ground signals distributed over two range gates (b). The height difference between a reference ground elevation during one measurement and the upper bin border of the highest (or first) range gate that contains ground signals is denoted by ΔH and represents a measure of the atmospheric contribution to the ground signal detected by the A2D. The reference ground elevation per measurement is derived from the DEM ACE2, providing elevation data at a resolution of 9 arcsec (300 m × 300 m at the Equator) (Berry et al., 2010).

In previous A2D studies, ground detection for the calibration mode was based on an analysis of the curtain plot depicting the Rayleigh and Mie signal intensities after range correction and normalization to the integration time of each range gate (see Fig. 4a and b). Here, high signal intensities related to strong ground return become visible as white bins, as the intensity exceeds the maximum of the respective colour scale. Ground range gates were then specified per flight leg and the corresponding signal intensities in the identified range gates were summed up (Marksteiner et al., 2013). For the example shown in Fig. 4, range gates 21 to 23 would be subjectively selected as ground range gates in the old scheme (by visual inspection by an experienced data analyst), since most of the white bins are found therein. This approach leads to an underestimation of the actual ground signal which might also be contained in adjacent range gates as well as to an additional summation of atmospheric signal causing error-prone ground data, especially for varying terrain during the flight leg. The imperfect differentiation between atmospheric and ground return signals thus introduces systematic errors in the ground response functions of both detection channels. Concerning the Mie channel, this affects the entire wind profile, as the ground response is used for the wind retrieval in all atmospheric range gates as mentioned above. The old ground detection scheme was acceptable in previous airborne campaigns where the response calibrations were performed over flat terrain, e.g. sea ice, so that ground signals were almost completely contained in only one range gate. However, since complex terrain scenes were encountered in the response calibrations during NAWDEX, the ground detection scheme was refined as explained in the following.

In order to derive more accurate ground speeds, a trade-off has to be found between summing up as much ground signal as possible and minimizing the atmospheric portion in the ground bins. For this purpose, a ground detection algorithm on measurement level was developed (Weiler, 2017). Similar to the wind retrieval algorithm employed for Aeolus (Reitebuch et al., 2017, 2018), it is based on a signal-gradient approach to estimate ground bin candidates within a predefined range around the ground level which is given by the DEM. In a range of ±3 bins around the expected ground level according to the DEM, the signal gradients of two adjacent bins are calculated for each measurement and per range gate i: ΔIiΔRi=Ii+1-IiRi+1-Ri. Here, I denotes integrated signal intensity per measurement, while R is the range from the instrument to the bin centre which can be calculated from the respective range gate integration time. In a next step, gradient thresholds are introduced to identify the uppermost and lowermost ground bin. For the analysed flights, thresholds of TGR,high = 0.015 arb. units km-1 and TGR,low = -0.015 arb. units km-1 (arbitrary units is abbreviated arb. units) have been empirically found to yield consistent results for both the Rayleigh and Mie channel. In order to avoid large atmospheric contribution to the ground signal, another threshold TGR;DEM+1 has been implemented which analyses the signal level of the range gate just above the DEM bin covering the reference ground elevation. If the intensity in this bin does not make up more than five percent of the total summed ground signal, it is not considered for the ground signal summation. Careful analysis has shown that ground intensities falling below that threshold have negligible influence on the accuracy of ground response calibration curves or ground wind speeds and thus can be omitted for the ground signal summation (Weiler, 2017). Using this approach, ΔH and hence the atmospheric portion of the ground signal can be significantly diminished. The ground detection method has been employed for the analysis of the Mie and Rayleigh response calibration data obtained in the NAWDEX campaign and formed the basis for the ZWC applied for the wind scenes on 4 October 2016 discussed in Sect. 4.2. Moreover, the comparison between refined ground detection and the previous scheme allows for the characterization of the influence of the atmospheric contamination of the ground calibration parameters.

The largest influence of the refined scheme on the calibration parameters compared to the former approach was obtained for the sixth response calibration procedure performed during NAWDEX on 15 October 2016 between 17:24 and 17:48 UTC. The Rayleigh and Mie signal intensities measured during the calibration are shown in Fig. 4a and b, respectively. The calibration flight was carried out in the region around 65.5∘ N and 17.8∘ W, which is characterized by a mountainous and ice-free terrain with ground elevations ranging from about 200 to 1200 m. Consequently, ground signals were detected in four different range gates (20 to 23) during the calibration procedure, as the Falcon aircraft flew circular patterns over this region. While the ground response calibration based on the old ground detection method would have summed up all the signals contained in these four range gates for each observation, i.e. frequency step of the calibration, the refined method only considers those bins per measurement that fulfil the threshold conditions as explained above. The corresponding Rayleigh and Mie ground masks illustrating the range bins that were identified as ground bins for each measurement are depicted in Fig. 4c and d. Due to the different sensitivities of the two receiver channels, and thus different measured signal intensities, the two masks are not fully identical.

For both channels, the atmospheric contribution is drastically reduced resulting in more accurate response values. While the mean value of ΔH over all measurements of calibration 6 is 454 and 505 m for the Rayleigh and Mie channel when the old ground detection technique is applied, it is only 207 and 249 m for the new method, respectively. An overview of the atmospheric contributions (mean ΔH) for all the six Rayleigh and Mie response calibrations (RRC and MRC) using the two different ground detection schemes is given in Tables 2 and 3. The tables also summarize the zero- and first-order polynomial coefficients {c0,c1} and {C0,C1} (referred to as intercept and slope) obtained from fitting of the response curves according to Eqs. (3a) and (3b). The second- and higher-order coefficients {ci} (i = 2, 3, 4, 5) of the Rayleigh response function are not given. Since calibration 1 was carried out using a different setting of the co-alignment loop reference position (CoGX/CoGY) (see Sect. 2.1) affecting the incidence angle of the backscattered signals on the Rayleigh and Mie spectrometer, the resulting calibration parameters were disregarded in the statistical calculations leading to the values provided in Tables 2 and 3.

In general, larger deviations in the slope and intercept values between the two methods are present for the Rayleigh channel. This can be explained by the fact that the broadband Rayleigh channel is more sensitive to the broadband atmospheric molecular background signal than the narrowband Mie channel where the broadband atmospheric contribution leads to a nearly constant intensity offset to the narrowband ground signals. The impact on the Rayleigh channel is especially large in cases of low-albedo surfaces where the atmospheric contribution to the weaker ground signals is more pronounced. As a result, large discrepancies between the calibration parameters obtained with the old and new method are observed for the two last calibrations that were performed over ice-free land with low albedo in the UV. In particular, the intercept values derived for the RRC 6 discussed before differ by as much as 1.24 × 10-2. Using a typical Rayleigh response slope value of 4.6 × 10-4 MHz-1 (Table 2) and the conversion between Doppler frequency shift and LOS wind speed (1 m s-1 =^ 5.63 MHz) introduced in Sect. 2.2, this difference in intercept translates to a wind speed difference of 4.8 m s-1. That means that ground speed values determined from RRC 6 using either the old or the new ground detection method would differ by that value. With a view to ZWC, the large discrepancy in the ground speed values underlines the relevance of proper ground detection for the wind retrieval, as the ground speeds are used as zero reference for the derived wind speeds. Likewise, using the refined ground detection method for the analysis of MRC 6 results in a change in the Mie intercept values by 11.7 × 10-3 pixel which corresponds to a wind speed difference of 0.2 m s-1, considering a typical Mie response slope of about 100 MHz pixel-1 (Table 3).

Another aspect that becomes obvious from Tables 2 and 3 is that the spread of intercept values between the different Rayleigh response calibrations is reduced when applying the new ground detection method. The standard deviation over the five RRCs 2 to 6 is 1.02 × 10-2, whereas it is 0.68 × 10-2 for the new method. Hence, depending on the calibration used for the wind retrieval, the Rayleigh ground wind speed varies by 3.9 m s-1 if the old technique is applied. This value is reduced by more than 30 % to 2.6 m s-1 with the new scheme, which is still unsatisfactorily large regarding the consistency of Rayleigh response calibrations. For the Mie channel, no change in the spread of the calibration parameters is evident. Nevertheless, the new ground detection approach provides a considerable improvement in the accuracy of the ground calibration parameters and, in turn, of the derived ground wind speeds. With a view to the Aeolus mission, it can be concluded that calibrations should be performed over surfaces with high albedo, like ice surfaces, in order to minimize the impact of the atmospheric contamination. Furthermore, the quantity ΔH could be considered as a quality parameter for evaluating the quality of response calibrations or even to correct calibrations for the atmospheric contribution.

While the instrument response calibrations were performed during two dedicated flights over Iceland, the other 12 research flights within the NAWDEX campaign were devoted to wind observations over the North Atlantic region. Here, sampling of the jet stream was of particular interest with regards to both the pre-launch activities of Aeolus and the scientific objectives related to atmospheric dynamics. The observation of high horizontal wind speeds and large wind gradients occurring in relation to the jet provided an extensive characterization of the instrument over a large operating range and accurate wind profiles for the NAWDEX science objectives. In the context of the fourth NAWDEX intensive observation period, the goal of the flight carried out on 27 September 2016 was to observe very high jet stream wind speeds related to the former tropical cyclone Karl. As Karl moved towards the mid-latitudes, it merged with an initially weak downstream cyclone and strongly intensified. Later, at the time of the flight, the already weakened cyclone was located between Iceland and Scotland and the zonally oriented jet stream extended towards Scotland with horizontal wind speeds exceeding 80 m s-1 at altitudes of 9 to 10 km (see Fig. 5 and for a detailed description of the meteorological situation refer to Schäfler et al., 2018). To observe the high wind speeds, the Falcon aircraft flew towards the Faroe Islands and the Outer Hebrides right into the centre of the jet stream at a flight altitude of 11.5 km before returning to the air base in Keflavík. The satellite image taken from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard NASA's Terra satellite (MODIS, 2017a), shown in Fig. 5a, depicts increased cloud coverage along the flight track crossing the cyclone. From the total flight duration of 3 h and 56 min (09:28 to 13:24 UTC), wind observations were conducted in the period between 10:28 and 12:36 UTC, split into two scenes of about 1 h each.

The wind scene on 27 September 2016 presented in the previous sections was characterized by optically dense clouds at different altitudes. As a consequence, the ground return signals detected during the scene were too weak for reliable determination of the ground speed which could be used for ZWC. Consequently, for this particular research flight, the refined ground detection scheme could not be exploited for reducing the systematic error of the Mie and Rayleigh wind speeds. Unfortunately, this circumstance holds true for most of the flights conducted in the context of NAWDEX, since the flight planning was primarily driven by the atmospheric science objectives of the campaign, resulting in complex atmospheric conditions with rather dense cloud coverage. One exception is the flight performed on 4 October 2016, which was dedicated to the investigation of the jet stream east of Iceland. For this purpose, the Falcon aircraft crossed the jet stream with increased wind speeds twice, as it flew two legs back and forth between the way points located at 66.0∘ N, 17.5∘ W and 64.0∘ N, 7.0∘ W (see Fig. 10). To the west of the jet axis cloud-free conditions prevailed over the northeast of Iceland. Hence, high ground visibility was obtained at the beginning of the first leg and at the end of the second leg, as can be seen by the visible satellite image (MODIS, 2017b) a few hours after the flight depicted in Fig. 10a together with the flight track of the Falcon. The A2D measured wind profiles during the periods from 09:00 to 09:44 and from 09:54 to 10:30 UTC (see also Table 1). The figure reveals the contrasting atmospheric circumstances experienced during the flight which were characterized by highly variable cloud cover along the flight path.

Using the same Rayleigh and Mie response calibrations as for the flight on 27 September 2016, the results of the wind retrieval are displayed in Fig. 11. While the Rayleigh wind curtain shows good coverage at the beginning and the end of the period (Fig. 11a), valid Mie winds were primarily obtained in the vicinity of the jet stream centre, which was sampled in the middle of the flight (Fig. 11b). This again underlines the complementarity of the two channels which allows for excellent data coverage despite strongly diverse atmospheric conditions. Since the direction of the wind was towards the A2D LOS on the first leg, positive LOS wind speeds of up to 25 m s-1 (HLOS: 73 m s-1) were measured, whereas negative winds of the same magnitude were detected on the flight leg back to Iceland.

The systematic and random errors for the Rayleigh and Mie winds were determined from a statistical comparison with the 2 µm reference wind lidar data. The resulting scatterplots and PDFs are shown in Fig. 12, while the statistical parameters are given in Table 5. Due to the poor overlap of the A2D Rayleigh wind data with the 2 µm wind curtain (see Fig. 11d), only a small number of data points (168) entered the comparison despite a low coverage ratio threshold of 25 %. Consequently, the calculated mean bias (1.54 m s-1) and scaled MAD (2.7 m s-1) lack statistical significance. This also becomes obvious from the shape of the histogram illustrating the distribution of the Rayleigh wind errors (Fig. 12b), which strongly deviates from a Gaussian distribution. For this reason, the following discussion concentrates on the Mie channel. Here, a scaled MAD of 2.0 m s-1 was derived from the comparison with the reference lidar, which showed large data overlap with the Mie channel, resulting in 1246 compared bins. The mean bias of 0.57 m s-1 is considerably larger than the value obtained for the flight on 27 September 2016. The increase in systematic error might result from changes in the alignment of the transmit–receive path, which can slightly vary from flight to flight. In combination with potential inaccuracies in the aircraft attitude data, this leads to unknown contributions to the retrieved LOS wind speed which are not considered in the retrieval algorithm.

The wind speed offset can, however, be reduced by ZWC based on the developed ground detection scheme. Any deviation from zero is interpreted as systematic error in the wind speed retrieval and hence subtracted from the measured wind speed. The ground speed (or ZWC) values obtained for the Mie channel during the two wind scenes on 4 October 2016 are plotted in Fig. 11c. From a total number of 268 observations, 59 observations included valid ZWC values in the ground range gates which were identified by the algorithm explained in Sect. 3.2. The respective observations are indicated as grey boxes in the Mie wind curtain. Thanks to the refined ground detection on measurement level, atmospheric contamination of the ground signals was minimized, thus ensuring that the detrimental influence of near-surface winds on the ZWC values was diminished. The mean of the ZWC values was determined to be 0.53 m s-1 with a standard deviation of 1.2 m s-1. The variation around the mean, which is also observed as random error in the atmospheric Mie wind speeds, can again be traced back to fluctuations in the Mie response measured for the internal reference. In order to confirm the correlation between the variability of the ZWC values and the internal reference variations, the Mie responses of the internal reference were converted to relative (laser) frequencies using the Mie response calibration. The obtained frequencies were compared to the frequencies measured with the high-precision wavemeter which tracked the absolute wavelength of the laser pulses emitted during the flight. The frequency difference (Mie response minus wavemeter) was finally translated into wind speed differences (1 m s-1=^ 5.63 MHz), resulting in the dashed line plotted in Fig. 11c. The course of the curve is obviously correlated to the progression of the ZWC values, thus verifying that the noise in the internal reference considerably affects the measured ground speeds. As mentioned in the previous section, speckle noise is responsible for Mie response variations on the order of σ = 0.7 m s-1. Nevertheless, the mean value was used for correcting the Mie wind speeds, leading to the scatterplot depicted in Fig. 12a. The statistical parameters after ZWC are given in the right column Table 5. Subtraction of the mean ZWC value reduces the mean bias to 0.04 m s-1, which is comparable to the result obtained for the flight on 27 September 2016. Hence, ZWC in combination with the refined ground detection scheme improves the accuracy of the A2D remarkably for the discussed flight.