Interactive comment on “ 3 D Water Vapor Field in the Atmospheric Boundary Layer Observed with Scanning Differential Absorption Lidar ” by F . Späth

Concerning the Rayleigh-Doppler correction and Eq. (4) and (5) and Fig. 2: Equation (4) gives the full DIAL equation including the Rayleigh-Doppler (RD) correction term (2nd term). Figure 2 shows the flow chart of the water vapor calculation with all needed parameters to compute the humidity data. This includes also βpar and βmol for the RD correction. If the RD effect is small we skip the additional effort (and related C1


Introduction
Water vapor (WV) is the most important greenhouse gas and plays a key role in Earth's weather and climate, from the surface to the troposphere to the stratosphere.Particularly important are exchange processes between the land surface and the atmospheric boundary layer (ABL) as well as between the ABL and the lower troposphere.For example, the diurnal cycles of evapotranspiration, the ABL moisture, and entrainment at the top of the ABL are the result of feedback processes in the land-atmosphere (LA) system (Seneviratne et al., 2010).However, generally the understanding of LA interaction has been based on model studies (e.g., Findell et al., 2003;Koster et al., 2006;van Heerwaarden et al., 2009;Santanello et al., 2013) and surface observations but not on suitable data sets including ABL WV fields.
Better parameterizations of land surface and turbulent transport processes in the ABL are essential for improved weather forecasts (e.g., Ek et al., 2003;Niu et al., 2011;Shin and Hong, 2011;Cohen et al., 2015) and regional climate projections (e.g., Warrach-Sagi et al., 2013;Milovac et al., 2016).These parameterizations were mainly derived by large eddy simulation (LES) models (e.g., Mellor and Yamada, 1982;Hong et al., 2006;Hong, 2007;Nakanishi and Niino, 2009;Shin and Hong, 2015) and only to a minor extent by observations.Vertical and horizontal moisture transports via mesoscale circulations and surface heterogeneities can result in convection initiation (CI) as well as the formation of clouds and precipitation (e.g., Behrendt et al., 2011; Published by Copernicus Publications on behalf of the European Geosciences Union.F. Späth et al.: 3-D water vapor field in the atmospheric boundary layer Corsmeier et al., 2011), which are very difficult to be observed from space (e.g., Aoshima et al., 2008).All these processes are interacting in a highly nonlinear way; therefore the three-dimensional (3-D) WV content needs to be represented very well in weather forecast models (Crook, 1996;Dierer et al., 2009), reanalyses (Bengtsson et al., 2004), and climate models (e.g., Kotlarski et al., 2014).
Models are only as good as the observations which were used for their parameterization and verification.Advanced observations of WV to study exchange, feedback, and mesoscale circulation processes require the observation of the 3-D WV field with a resolution permitting the simultaneous measurement of vertical gradients in the WV distribution in the surface layer, the mixed layer, and the entrainment layer at the top of the ABL.Only if these gradients are resolved, the corresponding transport processes can be studied and parameterized (Monin and Obukhov, 1954;Wulfmeyer et al., 2016).However, the distribution of ABL WV and its evolution in time is neither fully understood nor sufficiently observed.In consequence, it is not adequately reproduced in weather and climate forecasting models.A detailed overview about these processes and the requirements set to suitable observing systems is given by Wulfmeyer et al. (2015).
For WV measurements passive and active remote sensing instruments as well as in situ sensors are available.In situ sensors only deliver data from one location at one time; thus, remote sensing instruments are preferred for studying the vertical and horizontal WV structure in the ABL.However, many remote sensing systems only provide integrated WV (IWV) data which give no spatial information.Passive instruments like infrared (IR) spectrometers or microwave radiometers (MWRs) are able to retrieve WV profiles based on a first guess with temporal resolutions of 5-10 min.Their vertical range resolutions are 100 m for IR spectrometers or several 100 m for MWRs at the land surface and approximately 800 m for IR spectrometers and 2000 m for MWRs at the top of the ABL (Löhnert et al., 2009;Blumberg et al., 2015;Wulfmeyer et al., 2015).Due to these coarse vertical resolutions, fine structures and gradients cannot be resolved.A combination of several systems may be used to determine horizontal structures with the tomography technique.This was simulated for scanning MWRs (Steinke et al., 2014) but the vertical resolution still remains low due to the coarse resolution of the initial signals and inaccurate knowledge of initial fields.To analyze the aforementioned processes in the ABL, like LA feedback or CI, higher WV resolutions in time and space are needed.The corresponding requirements are summarized in Table 1 in Wulfmeyer et al. (2015).
For WV profiling with lidar, the Raman technique (e.g., Melfi et al., 1969;Whiteman et al., 1992;Behrendt et al., 2002;Hammann et al., 2015, Wulfmeyer et al., 2010) or the WV differential absorption lidar (WVDIAL) technique (Schotland, 1966;Browell et al., 1979;Bösenberg, 1998;Wulfmeyer and Bösenberg, 1998) can be applied.An overview of the performance of these techniques is given in Behrendt et al. (2007) and Bhawar et al. (2011).It was shown that WVDIAL has a better spatial/temporal resolution in the lower troposphere than WV Raman lidar (WVRL) during daytime (Wulfmeyer and Bösenberg, 1998).The WV-DIAL technique uses two elastic backscatter signals at wavelengths with high and low absorption of WV.In contrast to WVRL, the WVDIAL technique is self-calibrating and needs no further information than the absorption cross section at the wavelengths used (Browell et al., 1979).Due to the elastic backscatter signals, the signal-to-noise ratio (SNR) is much higher for the detected signals than using inelastic Raman scattered signals.This also helps to reach a larger range during daytime and allows integration times to be kept short.The horizontal variations of the moisture fields can be detected with scanning lidar.Scanning WVRL measurements were used, for example, to observe the WV structures in the ABL (Goldsmith et al., 1998;Eichinger et al., 1999;Whiteman et al., 2006;Froidevaux et al., 2013;Matsuda, 2013) or to estimate latent heat fluxes at the surface (Eichinger et al., 2000).However, the SNR is still limited during daytime (Turner at al., 2002), making high-resolution scans under daylight conditions more difficult than with WVDIAL; and 3-D measurements of WVRL have not been demonstrated yet.
Therefore, we focused on the WVDIAL technique and developed a scanning system permitting high-resolution scans of the WV field even during daytime.The University of Hohenheim (UHOH) WVDIAL is a ground-based mobile instrument which has already demonstrated vertical measurements in the ABL with high resolution and accuracy (Bhawar et al., 2011;Muppa et al., 2016;Wulfmeyer et al., 2016).Here, we present different types of scanning measurements of this system and discuss the measurement uncertainties.Particularly, we demonstrate the measurement of a 3-D water vapor field, which to our knowledge was achieved for the first time with a lidar.
We focus on three different scan strategies.
1.With range-height indicator (RHI) scanning measurements, the vertical WV structure over a certain horizontal range can be observed.We present a new technique to determine the corresponding 2-D error field and discuss the measurement performance in this configuration.This is essential to find the best compromise between scan speed and temporal and range resolution in order to detect the fine structure of the WV field with high confidence.
2. Conical scans can be performed to study the humidity variations from the mixed layer throughout the top of the ABL.Combining several of such scans with different elevations yields a 3-D image of the ABL moisture field.We discuss a corresponding first measurement and derive the error statistics in order to characterize fine structures in the WV field.3. Low-elevation scans close to the surface can be used to study LA feedback processes.The applied elevation angle range was 0 to 12 • and because of overlap effects, the measurement range started at 300 m.Also here, the error statistics are derived in order to investigate how accurately the small-scale variability of the ABL WV field from the surface to the mixed layer can be derived.
The UHOH DIAL system is introduced in Sect. 2. The DIAL technique and the data analysis procedure are presented in Sect.3. The three different scanning strategies are discussed in Sects.4-6.Finally, results are summarized and an outlook is given in Sect.7.

University of Hohenheim water vapor DIAL system
The laser transmitter of the UHOH DIAL (Fig. 1) is based on a Ti:sapphire ring laser (Schiller, 2009;Wagner et al., 2011Wagner et al., , 2013) ) which is end-pumped with the frequency-doubled radiation of a pulsed diode-pumped Nd:YAG laser (Ostermeyer et al., 2005).Frequency control is realized with the injection seeding technique (Barnes et al., 1993a, b) in combination with a resonance frequency control (e.g., Wulfmeyer and Bösenberg, 1996).For the measurements described in this paper, the previous transmitter configuration (Wagner et al., 2013) was modified by the following aspects.The pump laser has undergone a full redesign and consists now of an unidirectional ring oscillator in triangle configuration.The resonator of the Ti:sapphire laser has also been changed.Now, four resonator mirrors form a dynamically stable ring resonator in bow-tie configuration (Metzendorf et al., 2012).A new seed laser system with two frequencystabilized distributed feedback (DFB) laser diodes as in-jection seeders (Späth et al., 2013) was operated for the first time as part of the transmitter during the High Definition of Clouds and Precipitation for advancing Climate Prediction (HD(CP) 2 ) Observational Prototype Experiment (HOPE).For the Surface Atmosphere Boundary Layer Exchange (SABLE) campaign, the online DFB laser was later replaced by an external cavity diode laser (ECDL) with excellent passive frequency stability (Metzendorf et al., 2015) combined with the Drever-Hall-Wulfmeyer frequency control technique for pulsed, injection-seeded laser (US patent no.6,633,596, Wulfmeyer et al., 2000).
The UHOH DIAL has two configurations for transmitting the laser pulses to the atmosphere and receiving the backscattered lidar signals: one for vertical pointing measurements and one for scanning measurements.In the scanning configuration (the only one shown in Fig. 1b), the laser pulses are coupled into an optical fiber and transmitted to the atmosphere via a 20 cm telescope.The laser output power is currently restricted to 2 W in this configuration because experiments showed that this type of fiber accepts only up to this power level before being damaged.Due to losses when coupling the light into the fiber and out as well as due to the transmitting telescope optics, the power transmitted into the atmosphere is then 1.6 W. The backscattered photons are collected with an 80 cm diameter telescope with a focal length of 10 m.The transmitting and receiving telescopes are mounted together on the scanner unit using a receiver in Coudé configuration with excellent pointing stability on the detector, which allows for 3-D observations.The scanner unit can be operated with speeds between 0.1 and 6 • s −1 .The control software of the scanner unit offers predefined modes like range-height indicator (RHI -varying elevation angle  Together with the lidar signals, elevation and azimuth angles of the telescope are recorded with each pulse.For the WV calculation, the raw data are typically averaged over 1 s to 1 min in time for the online and offline data.Range averaging is applied within the WV derivation (so-called Savitzky-Golay derivation).The system specifications of the UHOH DIAL are summarized in Table 1.
In recent years, the performance of the UHOH DIAL system was investigated within several intercomparison campaigns.Bhawar et al. (2011) performed an extensive comparison study between the UHOH DIAL and six other WV lidar systems during the Convective and Orographically-induced Precipitation Study (COPS) in 2007 (Wulfmeyer et al., 2011;Behrendt et al., 2013).They found a bias of only −1.43 % for the UHOH DIAL relative to the mean of all measurements.In 2013, in Hohenheim, Stuttgart (Germany), a further comparison study with Vaisala RS-92 radiosondes was performed and resulted in a mean bias of −1.0 % ± 2.6 % (Späth et al., 2014).Following the method of Lenschow et al. (2000) and Wulfmeyer et al. (2016), an analysis of the autocovariance function of the WV time series at each height is used to distinguish between instrumental noise and atmospheric vari-ances.This technique yielded a noise error of < 5 % up to 2 km using a time resolution of 1-10 s (Muppa et al., 2016).Here, we demonstrate for the first time how this technique can be modified and adapted to perform error analysis of 2-D to 3-D scanning measurements.
3 Data processing and derivation of WV profiles

DIAL methodology
With the DIAL technique the number density of water vapor (or other trace gases like ozone, methane, etc.) can be measured directly with two backscatter lidar signals.One signal is tuned to a wavelength with strong absorption of WV (P on (r): online signal) and the other signal to a wavelength with weak absorption (P off (r): offline signal).The range r is measured from the lidar system to the scattering volume along the line of sight.The return signals P (r) for each wavelength can be described with the lidar equation of elastic backscattering as (Wulfmeyer et al., 2015) with the transmitted intensity P 0 at the laser frequency ν 0 , the system efficiency η, the speed of light c, the sampling resolution of the system t, the telescope area A tel , the overlap function O(r), the transmission of the atmosphere (r) as the particle and molecular extinction coefficient α par,ν (r) and α mol,ν (r), which are only slightly dependent on frequency ν, the extinction coefficient of water vapor (of the trace gas) α WV (ν, r), the particle and molecular backscatter coefficient β par,ν (r) and β mol,ν (r), the normalized laser spectrum at the ground S L , the spectral broadening due to Dopplerbroadened Rayleigh scattering, DB, the transmission function of the receiver interference filter F R , and P B the background signal.α WV is related to the absorption cross section σ WV and the WV number density N WV by Our laser is designed so that the laser spectrum can be considered a delta distribution.In this case, the derivation of the WV profile becomes independent of any laser parameters, which is called narrow-band DIAL.Furthermore, we assume that the overlap function is either the same for online and offline signals or height independent; we also consider the interference filter transmission function to be constant over the frequency range of interest and not dependent on range.Then, calculating the ratio of Eq. ( 1) for online and offline wavelengths, applying the relation of Eq. ( 3), and solving for the WV number density N WV leads to the narrow-band DIAL equation , where the index "on" and "off" implies that the specific variable is taken at the online or offline wavelength, respectively.Online and offline wavelengths are chosen close to each other because then the particle and molecular extinction and backscatter coefficients for online and offline wavelengths cancel when taking the ratio of the signals in Eq. (4).
All system parameters which are constant with range r cancel because of the derivative.Thus, for DIAL measurements no calibration is needed.Only the values of the absorption cross sections at online and offline wavelength σ on and σ off have to be known very accurately.
The second term in Eq. ( 4) describes the Rayleigh Doppler correction term related to the broadening effect of the laser spectrum by Rayleigh scattering.The particle backscatter coefficient can be calculated from the offline signal (Fernald et al., 1972;Fernald, 1984).Ansmann and Bösenberg (1987) showed that this correction becomes significant when strong particle backscatter gradients are present.However, they only considered that the online laser wavelength is at the peak of the water vapor absorption line.
Within the analyses presented here this effect was not critical, as confirmed not only by comparisons with radiosoundings but also with new sensitivity analyses considering a frequency agile operation of our laser transmitter (Metzendorf et al., 2015).This reduced sensitivity to the Rayleigh Doppler correction was due to two reasons.Firstly, most of the sampled air masses were located within the ABL where no large particle backscatter gradients were present.Secondly, the Rayleigh Doppler effect is strongly reduced if the online frequency is located on the wing of the absorption line.In this case, the integral in Eq. ( 4) becomes approximately wv,on , so the nominator and the denominator of the term cancel -independent of the aerosol gradient.More details can be found in Späth et al. (2015).For the measurements discussed here, we selected an online frequency away from the peak absorption but still strong enough to produce sufficient differential absorption.This selection allowed us to optimize the sensitivity of the DIAL measurements in the range of interest for the moisture values present (Späth et al., 2014).Thus, the so-called Schotland approximation of the DIAL equation (Schotland, 1966(Schotland, , 1974) was used for all cases presented here.With this approximation no backscatter coefficients were needed for the calculation.In the following, the derived moisture values in number density are transformed in absolute humidity ρ in units of g m −3 .The WV cross section σ WV (ν, T , p, N WV ) depends on N WV by self-broadening, temperature T , and air pressure p at a certain frequency ν.These dependencies have been measured very accurately in the laboratory and collected in databases, e.g., the HIgh-resolution TRANsmission molecular absorption database (HITRAN) (Rothman et al., 2013).Selecting specific absorption lines with low ground-state energy, it was shown that the dependence of the cross sections on the atmospheric temperature, pressure, and WV profiles is weak and that it is sufficient to assume mean hydrostatic and adiabatic conditions merely using surface values.This makes DIAL the most accurate WV remote sensing technique to date.

Data processing
In case of the UHOH DIAL, the atmospheric backscatter data are recorded for each laser shot.Later, these data are averaged in time over typically 1-10 s and background corrected by subtracting the averaged signal between 25 and 30 km.The absorption cross section profiles for the selected online www.atmos-meas-tech.net/9/1701/2016/Atmos.Meas.Tech., 9, 1701-1720, 2016 and offline wavelengths are determined using profiles of temperature T (z) using a surface value in combination with the temperature gradient from the US Standard Atmosphere, a hydrostatic pressure p(z) also initialized with a surface value and an atmospheric mean temperature in the range of interest.An initial guess for the water vapor number density N WV (z) is taken from the US Standard Atmosphere (NASA, 1976).We take the spectroscopic parameters of water vapor from the latest compilation of HITRAN described by Rothman et al. (2013).
The water vapor profile is then calculated according to Eq. ( 5) (Schotland approximation).The Savitzky-Golay (SaGo) method is applied for the derivative with respect to range r (Savitzky and Golay, 1964).This method calculates the first derivative using a certain number of data points.The resulting range resolution R is approximately half of the SaGo window length, as the weighting function is parabolic (Ehret et al., 2001).Typically our SaGo window range consists of four data points on each side of a specific range, resulting in a range resolution of 9 × 15 m/2 ∼ = 67.5 m.The 15 m step size of the data points used for the derivation of the WV profile is kept.Depending on whether Eqs. ( 4) or ( 5) must be applied, either an iteration is necessary to derive the WV profiles (Eq.4) or a direct derivation is sufficient (Eq.5).However, in both cases the resulting solution is unique and even if an iteration must be applied to find the result it converges very quickly after one to three iterations.The whole chain of data processing is summarized in a flow chart (see Fig. 2).

Analysis of scanning data
Up to this step, the analysis procedure is similar for vertical and for scanning measurements.After calculating the WV of scanning measurement, the data can be plotted and used for further analysis in polar coordinates (r, , φ).Alternatively, the data can be gridded to a regular horizontally and vertically spaced grid (x, y, z) (see also Fig. 2).We prefer gridded data because atmospheric variations are usually horizontally or vertically oriented.3-D data sets can be analyzed by extracting slices of different orientation.
To estimate instrumental noise ρ of vertical measurements, we apply the method of Lenschow et al. (2000) and Wulfmeyer et al. (2016).Here, the autocovariance function (ACF) of the humidity fluctuations for one range bin is determined.The ACF at lag 0 gives the total variance which is the sum of atmospheric variance and noise variance.The atmospheric variance can be separated from the instrumental noise by extrapolating the ACF to lag 0. For conical scanning measurements, this approach can be used without further modification because data points of a certain range are at the same height.
For scanning measurements in RHI mode, the determination of the atmospheric variance is more complicated.When a time series with a large number of fast RHI measurements with small periods between consecutive scans such as tens of seconds (when scanning fast with 6 • s −1 ) or a few minutes (as for the low-elevation scans with one scan per minute) is available, one can just use the time series of data at one range and elevation.However the noise within single RHI data can also be determined.In contrast to conical scans, rings of constant range cover different heights for RHI data and thus clearly different atmospheric variance values; but even more importantly, the instrumental noise within an RHI scan that covers a large part of the ABL differs for fixed range because the humidity and thus the optical depth show large differences (Wulfmeyer and Walther, 2001b).In consequence, one has to group the measured RHI data then in a more sophisticated way.In the following, we suggest such an approach.
We have tested several different concepts for grouping the data.A simple 1-D approach is to take a number of range bins from one slant profile, but as the required number of independent measurement points is about 10, this still leads to very similar problems as discussed above when selecting measurement points of constant range.Thus, we finally decided to group the measured data set with very high resolution two-dimensionally.We calculate the noise estimation with three independent data points of three profiles giving 3 × 3 = 9 data points for each group that is analyzed.The vertical noise profile is then obtained from groups of which the central data points are at a certain horizontal distance to the lidar (Fig. 3).The data set used for the error estimate has the very high resolution over the entire distance range.
When using RHI data sets with very high spatial resolution (in range and elevation), the instrumental noise is much larger than the atmospheric variance.Thus the sequence of the nine data points of each group used for the ACF analysis becomes irrelevant and one can just use lag 0 as the upper limit for the instrumental noise estimation.Finally, the resulting noise values are scaled to the temporal and spatial resolution of the averaged and gridded data according to Ismail and Browell (1989): In doing so, for the temporal resolution of RHI scans, the scaling results in different angle resolutions.
In the following, we present several examples of 2-D and 3-D scans of the WV fields, analyze the results, and apply our new tools for error analyses.

Instrumental setup
To capture the horizontal and vertical WV field and its relation to 2-D ABL turbulence statistics and cloud formation, RHI scanning measurements are preferable.With vertical measurements only observations in the so-called Eulerian specification are possible which means that the atmosphere is observed while advecting through the lidar beam.Here, temporal and spatial changes of the measured data are entangled.
With RHI scans, this is not the case (or at least much less); therefore both temporal and spatial differences of the moisture field in the ABL can be studied.
The UHOH DIAL was operated in RHI mode within the HD(CP) 2 Observation Prototype Experiment (HOPE) near Forschungszentrum Jülich, in western Germany (see http: //www.hdcp2.eu/Campaign-HOPE.2306.0.html).The aim of the experiment was to produce a data set of atmospheric measurements for the investigation of land-atmosphere interaction, cloud formation, aerosol-cloud microphysics as well as weather and climate model evaluation at the 100 m scale.For HOPE, three supersites were set up in a triangular configuration with distances of about 4 km between each other.All these sites were equipped with in situ and remote sensing instruments to measure atmospheric parameters.With the different instruments, the temporal and spatial heterogeneity of the convective boundary layer (CBL) was investigated concerning WV, temperature, and wind fields as well as the distribution of aerosol particles and clouds.The UHOH DIAL was located at the HOPE supersite near Hambach (50 • 53 50.56 N, 6 • 27 50.39E; 110 m a.s.l.).At the same site with the UHOH DIAL, the UHOH rotational Raman lidar (RRL) (Radlach et al., 2008;Hammann et al., 2015) measured temperature and the KITcube (Kalthoff et al., 2013) observed -among others -the wind field with scanning Doppler lidar systems (Träumner, 2010) and the surface energy balance (Kalthoff et al., 2006;Krauss et al., 2010).The UHOH DIAL provided measurements of more than 180 h in 18 intensive observation periods (IOPs) in vertical and different scanning modes.The high-resolution fields of the measured thermodynamic variables are also used to derive higher-order moments of turbulent fluctuations (Muppa et al., 2016;Behrendt et al., 2015a) as well as sensible and latent heat fluxes (Wulfmeyer et al., 2014;Behrendt et al., 2015b).This data set will be used for the verification of current approaches of turbulence parameterizations as well as of the development and tests of new turbulence parameterizations.Further details are found in Wulfmeyer et al. (2016).

Performance and analyses of RHI scans
Our measurements were performed during IOP 4 on 20 April 2013.On this day, the HOPE domain was under the influence of a high pressure system located with its center over the Baltic Sea.The main wind direction was northeast to east as confirmed by the radiosoundings.Figure 4 shows temperature, humidity, and wind velocity profiles of the radiosonde launched at 07:00 UTC at the lidar site.The horizontal wind speed within the ABL was between 8 and 10 m s −1 with a minimum of 5.5 m s −1 at a height of 1250 m above ground level of the lidar site (a.g.l.).Temperature and absolute humidity were quite low on this day with ground values of only 5 • C and 4.5 g m −3 , respectively.Between 06:00 and 07:00 UTC (local time was UTC+2), only thin cirrus clouds were present at heights between 7 and 8 km as found by the offline backscatter signal.The surface temperature profile shows that a very shallow unstable surface layer started to develop by surface heating but it was not deeper than 200 m.The complex vertical layering is particularly visible in the absolute humidity profile, which shows a series of moisture layers with a thickness of 100 to 200 m, up to 1.4 km a.g.l.However, the virtual potential temperature profile shows that the top of the residual layer was at around 800 m a.g.l., while the top of the developing mixed layer was at 200 m a.g.l.There was another temperature inversion at around 1.6 km a.g.l. that may be related to more synoptic meteorological conditions such as large-scale subsidence.
RHI scanning measurements of the humidity field in the HOPE region were performed on 20 April 2013 between 06:03 and 07:24 UTC.The time resolution for this analysis is 10 s.With a scan speed of 0.15 • s −1 , this results in an angle resolution of 1.5 • .With a covered elevation angle range of 85 • each of these RHI scans took around 10 min.Due to the longer path of the laser beam through the aerosol-loaded air in lower elevation and the corresponding higher extinction as well as due to the higher moisture in the boundary layer and the corresponding stronger attenuation of the online signal, we averaged the data according to the following procedure.We calculated the absolute humidity with different range resolutions R to keep the angle resolution.Afterwards, the radial data were gridded to a horizontal-vertical grid with a resolution of 50 m.Finally, the data with different resolutions were merged according to the horizontal distance: up to a distance of 1.3 km R = 142.5 m, up to 2.5 km R = 307.5 m, up to 3.0 km R = 457.5 m, and up to 4.2 km R = 997.5 m.
A noise error analysis was carried out as described in Sect. 3 and profiles for the horizontal distances of 1.3, 2, 3, and 4 km are shown in Fig. 5.For all distances, the error profiles show a significant increase above the top of the ABL because there are much fewer aerosol particles present which act as scatterers.The top of the ABL height increases from the near range (1.3 km) to the far range (4 km).At a horizontal distance of 1.3 km the top of the ABL is at 0.9 km a.g.l.while it is 200 m higher (1.1 km a.g.l) at a distance of 4.0 km.Below the top of the ABL, the noise values are below or around 0.2 g m −3 , and above the top of the ABL the noise reaches values between 0.5 and 0.8 g m −3 .This results in an upper limit of a relative noise error of < 6 % within the ABL.The noise profile for 1.3 km distance does not show the smallest values but this is maybe due to the assumption of neglecting atmospheric fluctuations which become relatively larger when the instrumental noise decreases.
Figure 6 shows scanning humidity measurements in the HOPE region on 20 April 2013 between 06:03 and 07:24 UTC.The measurements were performed towards the two other experimental sites of the HOPE campaign: towards the Leipzig Aerosol and Cloud Research Observations System (LACROS) southwards and towards the Jülich Obser-vatorY for Cloud Evaluation (JOYCE) southwestwards.The plots are geolocated to the Earth surface and cover a horizontal range of 0.7 to 4.2 km up to an altitude of 2 km a.g.l.
In the near range of the RHI scans we omitted the data up to 950 m because of no full overlap of the field of view of the transmitting and receiving telescopes.
The WV field in the two scanning directions showed several similarities but also significant differences, revealing the heterogeneities of the ABL in the region.In both directions, three moist layers with drier layers in between can be identified.The altitudes of the layers differ significantly.Towards LACROS, the moist layers were at 500, 1100, and 1500 m a.g.l.while towards JOYCE they were at 300, 1000, and 1400 m a.g.l. for the measurements for the first two scans between 06:03 and 06:27 UTC (Fig. 6a).One hour later (Fig. 6b), the measurements show the same number of layers but the height of the lowest one increased to 600 and 500 m a.g.l. for LACROS and JOYCE directions, respectively.In general, we see that the ABL was more moist in the direction of LACROS than in the direction of JOYCE.In order to illustrate this, we have averaged the scanning data horizontally.The averaged vertical humidity profiles of the four RHI measurements of Fig. 6 are shown in Fig. 7.In the profiles, the layer structure discussed above can be identified.The humidity profile of the radiosonde at 07:00 UTC does not fit with an averaged DIAL profile and shows also different structures but the profile stays within the variability of the DIAL measurement towards LACROS.However, different to the DIAL measurements, a radiosonde measures only along its flight path and, thus, can only sample a snapshot of the atmospheric constitution.In this case, northeasterly wind caused a horizontal wind-driven displacement of the radiosonde of about 3 km when it reached an altitude of 2 km a.g.l.The horizontal variability within a certain range can also only be determined with scanning DIAL measurements.For these reasons, horizontally averaged profiles of scanning DIAL measurements are better suited for comparisons with model simulation outputs which also give profiles representative of a whole model grid box (Milovac et al., 2016).
Interestingly, in one of the scans (Fig. 6b towards JOYCE) clouds appear, while all others are cloud-free.Four clouds can be identified in the offline backscatter signals at distances and altitudes of 300 and 700 m a.g.l., of 600 and 600 m a.g.l., of 1.5 km and 500 m a.g.l., and of 3 km and 500 m a.g.l., respectively.The large extinction of the clouds prohibits measurements inside the clouds and beyond, resulting in radial structured gaps in the data (plotted transparently in Fig. 6b).At 560 m a.g.l. the profiles of the radiosonde (Fig. 4) show a zero-crossing in the temperature and a relative humidity of only about 80 %.The DIAL measurements show values of about 4.5 and 5 g m −3 below the clouds at 1.5 and 3 km distance, respectively.As at least 100 % relative humidity is needed for cloud formation, this corresponds to a required absolute humidity of 4.8 g m −3 at a temperature of 0 • C. Clearly, the observed clouds are related to locally higher moisture values as revealed by the DIAL scans, which are also seen in Fig. 7d by an upper limit of the 1σ standard deviation above 5 g m −3 in heights between 300 and 700 m a.g.l.
The measurement 1 h before already showed these humidity values at around 250 m a.g.l.altitude, which was not sufficient to reach saturation but indicate that the humidity came from the ground and reached the condensation level during the last scan.For the first time with the UHOH DIAL, the latter configuration was applied during the Surface Atmosphere Boundary Layer Exchange (SABLE) field campaign in August 2014.The SABLE campaign took place near Pforzheim (48 • 55 45.85 N, 8 • 42 19.57E; 320 m a.s.l.) in the Black Forest (southwest Germany) as part of the Research Unit 1695 "Regional Climate Change" of the German Research Foundation (DFG; see https://klimawandel.uni-hohenheim.de/startseite?&L=1).The UHOH DIAL was collocated with the UHOH RRL for temperature measurements and with three Doppler lidar systems for measuring the wind velocities as well as with a synergy of surface in situ sensors distributed in the fields, e.g., eddy covariance stations (Wizemann et al., 2015).The results of these campaigns shall contribute to an improved understanding of the relations between surface properties and boundary layer characteristics, shallow cumulus convection, as well as convection initiation.
During the special observations period (SOP) 2 on 22 August 2014, the 3-D WV field was observed with a volume scan.On this day, a low pressure system over Scandinavia and a high pressure system over eastern Europe provoked westerly flow in the SABLE domain.Stratus clouds occurred over the measurement site with a bottom height of about 2.5 km a.g.l.These clouds reduced the surface heating, so no convective boundary layer formed.Consequently, we can assume that the structures of the moisture field were largely advected and modified locally mainly by orography.There was a small hill with a top height of 375 m a.s.l. at 0.6 km distance to the south while the terrain in the near range of the lidar was mainly flat.The radiosonde from 09:30 UTC showed at the ground a temperature of 16 • C and a relative humidity of 60 %.The wind was calm (< 1.5 m s −1 ) at the ground up to 300 m a.g.l. and increased then to 6 m s −1 at 600 m a.g.l. in an east-northeast direction.

Performance and analyses of the volume scan
The area around the DIAL site was observed by performing a series of 360 • conical scans around the vertical with elevation angles of 50, 60, 70, 80, and 90 • .Figure 8 shows a 3-D view of the 50 • cone of the volume scan between 08:40 and 09:40 UTC.For this measurement, the scan speed was 0.4 • s −1 , resulting in a total duration of 15 min per cone.Consequently, the full volume with five cones was scanned within 75 min.The start and the end directions were southward-oriented and the scanner moved for the 50, 70, and 90 • cone clockwise and counter-clockwise for the other scans of 60 and 80 • .The WV calculation was performed with 10 s averaged profiles and a 67.5 m range resolution.For plotting, the WV data were transferred from the polar coordinates to Cartesian coordinates and each profile was expanded over an azimuth range of 4 • .
The instrumental noise was determined with the method of Lenschow et al. (2000) for each elevation angle separately.Profiles of the absolute and relative noise are shown in Fig. 9. Above 400 m a.g.l., the noise level increases with height.The noise at the same height a.g.l. is higher for lower elevation angles than for higher elevation angles because the range for the same height a.g.l. is larger.The profile of the low- est elevation angle shows a maximum noise of < 0.35 g m −3 or < 7 % at 750 m altitude a.g.l.Below 400 m a.g.l., the noise also increases, but here due to overlap effects.However, this does not occur in the absolute humidity data as the noise is < 0.8 g m −3 .
The measurement in Fig. 8 shows two moist layers.The lower layer reached altitudes up to between 300 and 400 m a.g.l. with humidity values of 7-8 g m −3 .This layer was topped by a drier layer with 5.6 g m −3 and a second moist layer at 600 m a.g.l. with a humidity of about 6.5 g m −3 .
To get an insight into the whole volume, Fig. 10a shows cross sections and illustrates the whole data set of the volume scan three-dimensionally.In addition and for orientation, the cutting planes are depicted of which the water vapor distribution is then shown in Fig. 10b-i The heights of the layers in Fig. 10 are almost similar for all directions.Because of the full cloud cover on this day, convection was very weak and no large eddies were initiated.Thus, the moist layer from the ground grew slowly and varied according to underlying orography.Here, in south direction at a distance of 0.6 km from the DIAL a small hill was located with an increase of the surface elevation of about 55 m.The measurements of the lowest elevation angle in Fig. 10b-d show indeed a higher altitude of the boundary layer of about 50 m at a distance of 0.5 km southwards.Also to the east a small trend to higher altitudes of the top of the boundary layer can be observed.This is also indicated by the horizontal plane image in Fig. 10i for the southeasterly direction and a distance of 0.6 km.This area corresponds in our case to the lee side of the small hill; therefore the higher moisture might be explained by a modification of the moisture field by shifted overflow lifting.
Averaging the volume data horizontally provides the mean humidity profile.The profile was plotted in Fig. 11 up to an altitude of 0.8 km a.g.l.The thin lines mark the horizontal WV variability similar to Fig. 7.The radiosonde profile at 09:30 UTC is given in the diagram as well.Again, there were differences between DIAL and radiosonde measurements but the radiosonde captured similar moisture layers and stayed almost within 1 standard deviation of the DIAL profile.During the SABLE campaign (see Sect. 5), these lowlevel scanning measurements were performed to investigate the properties of the atmospheric surface layer.The lowelevation scans covered elevation angles between 0 and 12 • .In order to reach a high vertical resolution, the scan speed was 0.2 • s −1 , which resulted in a time duration of 1 min per scan.

Performance and analyses of the low-level RHI scans
Low-elevation scanning measurements were performed during the SABLE campaign on IOP 4 on 12 August 2014 between 11:00 and 12:00 UTC.The results are presented in Fig. 12.For the WV calculation, 1 s averaged profiles and a SaGo window length of 135 m were used.All scans of the 1 h period (52 scans) were averaged with 1 • angle resolution, resulting in a final time resolution of 260 s.Then, the data were gridded to an x-y grid with a resolution of 50 m × 10 m.
With the high spatial resolution, small variations in the absolute humidity values (notice color scale 9.4-10.4g m −3 in Fig. 12) at different heights and distances can be identified.The instrumental noise for the low-elevation scan was estimated with the ACF method.The data were used in the initial radial polar coordinates and data points of all scans at a certain range bin covering a 1 • angle range were selected for the ACF calculation.The resulting errors were then scaled with Eq. ( 6) from the 1 s time resolution.In Fig. 13, the noise errors were plotted as error bars with the absolute humidity profiles at the distances of 400, 800, and 1200 m, respectively.All three profiles show a constant noise level for the whole profile which can be expected for the small covered height range because all data points of one profile belong to a similar range bin and as the profile stays within in the boundary layer the optical thickness is constant over the whole height range.Of course, the noise level increases with distance but the noise value stays lower than 0.3 g m −3 for 400 m, lower than 0.4 g m −3 for 800 m, and lower than 0.9 g m −3 for 1200 m.These values translate to relative values of less than 0.3 %, less than 0.4 %, and less than 1 %, respectively.
The humidity values close to the ground are higher than above and at 1200 m distance the humidity was higher than at 800 m distance.Because these measurements are close to the ground, it is possible to relate these changes in horizontal direction to the vegetation at the ground.For the measurement in Fig. 12, the vegetation can be separated into three categories.In the near range up to 450 m there was a maize field, up to 1050 m the ground was covered with grassland, and further away we scanned over forest.The terrain around the DIAL site was mainly flat except for a small hill in a southern direction at a distance of 0.6 km reaching an altitude of 375 m a.s.l.Along the scan direction towards a southwesterly direction; the terrain profile was flat for the maize field and slightly uphill for the grassland, while the forest was located on the small hill at a distance of 1300 m.The measurement in Fig. 12 shows that there was more water vapor in the atmosphere above the maize field and above the forest, which was likely due to higher evapotranspiration than above the grassland.
This 1 h mean profile close to the ground is similar to what was measured by Eichinger et al. (2000) with a scanning Raman lidar.However, with the WVDIAL technique a larger range can be investigated.In the future, such data can be used to estimate the spatial distribution of the latent heat flux over different kinds of land cover (Wulfmeyer et al., 2014).For this purpose, the Monin-Obukhov similarity theory (MOST) (Monin and Obukhov, 1954;Brutsaert, 1982) can be applied using the slope of such a vertical humidity profile and simultaneously obtained friction velocity u * .

Summary and outlook
The measurements of the spatial distribution of water vapor by the UHOH DIAL in three different scanning modes were presented.The UHOH DIAL uses a frequency-stabilized Ti:sapphire resonator as laser transmitter and emits laser pulses at 818 nm.The output power for scanning measurements is currently limited to 1.6 W due to the maximum power which can be transmitted by the optical fiber used.The 20 cm transmitting and 80 cm receiving telescopes form the scanner unit which allows scanning measurements of the whole hemisphere (180 • elevation, 360 • azimuth) with scan speeds between 0.1 and 6 • s −1 .For data analyses typical range and temporal resolutions of 50-300 m and 1-10 s, respectively, are used.A new method to determine the noise level of scanning measurements was developed and shows uncertainties of < 7 % within the ABL.With the DIAL technique it is now possible to determine 3-D WV fields with high temporal and spatial resolution including a specific analysis of noise error fields.Therefore, the significance of WV structures in these 2-D and 3-D fields can be studied and specified in great detail.
Scanning measurements in RHI mode were performed in two directions during HOPE with elevation angles from 5 to 90 • up to a horizontal distance of 4 km.With these scans the humidity field was investigated regarding turbulent and mesoscale variability as well as cloud formation.Similar layers for both directions but also differences in altitudes of the layers or in the WV content were observed in the WV field.Four scans depict the evolution of the layers within 90 min.In the last measurement of the series, clouds appear at the top of the lowest moist layer where the conditions of 100 % relative humidity for cloud formation were locally fulfilled.Horizontally averaged vertical profiles show also a higher humidity variability for that measurement.The noise at the top of the ABL increases strongly but the noise error remains < 6 % within the ABL.
For the first time, a conical volume scan performed during the SABLE campaign presents the 3-D spatial WV distribution within a distance range of 0.8 km around the DIAL.The data show two moist layers with some variations in height for different directions.These variations can be related to variations in the surface elevation, e.g., in a southeast direction a small hill with a slightly higher elevation was located.The instrumental noise for this case was calculated to be < 0.5 g m −3 or < 7 %.
Low-elevation scanning measurements revealed the humidity structures close to the ground.The presented data were averaged over 1 h of scanning measurements and cover a height range from 20 to 140 m a.g.l. of the instrument.The horizontal variation of the WV field can be related to the heterogeneity of the vegetation at the ground.The errors for these kinds of measurements were estimated to be < 0.3 g m −3 or < 0.3 % at 400 m and < 0.9 g m −3 or < 1 % at 1200 m horizontal distance throughout the measured height range.
In conclusion, all scanning modes are applicable to observe the spatial distribution of water vapor in the lower atmosphere.Depending on the focus of the research, the scan pattern can be adapted regarding the covered elevation and azimuth angle ranges.
In future work, these kinds of measurements can be extended to estimate evapotranspiration above different land cover and soil types using the Monin-Obukhov similarity theory.More measurements over different terrains and a larger set of vegetation types as well as under different meteorological conditions will be made.Furthermore, a combination with other instruments (temperature rotational Raman lidar, Doppler lidar, eddy covariance stations, towers, aircraft) will be highly beneficial.In this context, it will be very interesting to perform simultaneous observations of the surface layer and the top of the ABL for heat and WV budget studies.Comparison with LES will allow for validations and improvements of parameterization schemes regarding LA feedback which is essential for further advancements of numerical weather prediction models and climate projections.

Figure 1 .
Figure 1.(a) Photograph of the DIAL system in the field during the SABLE experiment.(b) Setup of the UHOH DIAL system with transmitter unit, the scanner unit with transmitting and receiving telescope, and the detection path with data acquisition.TM -transmitting telescope mirror, PM -primary mirror, SM -secondary mirror, HR -high-reflection mirror, BR -beam reducer, APD -avalanche photo diode, PD -photo diode, FC -fiber coupler.

F.
Späth et al.: 3-D water vapor field in the atmospheric boundary layer

Figure 2 .
Figure 2. Flow chart of data processing.The backscatter coefficients β par (r) and β mol (r) are only used if the Rayleigh Doppler correction (Eq.4) is required.For the cases presented here, we used the Schotland approximation (Eq.5).

Figure 3 .
Figure 3. Spatial distribution of the grouping of the measured data used for the noise estimation for a single RHI scan.For each group of nine data points, either black pluses or red dots, the ACF is calculated.Different symbols are used for better understanding when the data points are close to each other.Dashed lines indicate each second profile.

Figure 4 .
Figure 4. Profiles of temperature, virtual potential temperature, absolute and relative humidity, horizontal wind speed, and wind direction measured with the radiosonde on IOP 5 on 20 April 2013 at 07:00 UTC.

Figure 6 .
Figure 6.3-D illustration of the WV field in the HOPE domain.The scanning measurements were performed towards LACROS and JOYCE on IOP 4 on 20 April 2013 between (a) 06:03 and 06:27 UTC and (b) 06:59 and 07:24 UTC.The UHOH DIAL system was located at the Hambach site and scanned towards the other supersites LACROS and JOYCE.The distances to the other sites were around 4 km.In (b) the gaps in the data occur from clouds at the top of the CBL.Background image from Google Earth.

Figure 7 .
Figure 7. Spatially averaged humidity profiles of the scanning measurements of Fig. 6.The profiles in (a) are of the scans towards LACROS and in (b) towards JOYCE.The thick solid lines show the mean profiles of each scan and the thin lines indicate the horizontal variability of humidity (1σ standard deviation) within the scan range.The radiosonde profile at 07:00 UTC was plotted with a dashed line with the two closest scans (b and c).
With volume scans, the relation of the moisture field to surface properties can be investigated more in detail.The observation of 3-D humidity is either possible by a series of fast RHI scans using different azimuth angles or by a series of continuous 360 • scans with different elevation angles.

Figure 8 .
Figure 8. Conical scan of SOP 2 on 22 August 2014 between 08:40 and 08:55 UTC.The cone has an elevation angle of 50 • .The data were plotted for a height range from 0.2 up to 0.8 km a.g.l.The white circles indicate the height in 0.2 km steps and the grey dashedpointed circles show their projection down to the ground.The black solid line marks the start and end direction of the conical scan; the scanner unit moved clockwise.The scales are given in km.

Figure 9 .
Figure 9. Absolute noise ρ and relative noise ρ/ρ profiles of selected parts of the volume scan with the corresponding temporal and spatial resolution of 10 s and 67.5 m, respectively.
. The figure contains three vertical cross sections in a north-south direction (panel b-d) and three in a west-east direction (panel e-g) as well as horizontal cross section planes at two height levels (panel h-i).The vertical cross section images depict the vertical structure at different distances to the DIAL similar to what was shown above with RHI scans.In Fig.10b-g the vertical planes are positioned at ±0.2 and 0.0 km distance with respect to the vertical line above the DIAL location.The horizontal cross section plane can also of course be placed at any height of interest.These plots show the WV distribution with respect to the azimuth angle but in contrast to conical scan plots, the data are not shown along the line of sight but rather at one height the data of all conical scans of different elevation angles of the volume scan are shown.The cross section images depict also the moist layers in the two lower elevation angle scans.

Figure 10 .
Figure 10.Cutting planes through the 3-D data set provides cross section images.(a) Schematic illustration of the 3-D data set with the cutting planes.(b-i) Horizontal and vertical cross section images of the different cutting plans of (a).The black lines in (b-g) indicate the top of the boundary layer.The dotted lines in (a) illustrate the location of the horizontal planes (h-i).

Figure 11 .
Figure 11.Spatially averaged absolute humidity profiles of the volume scan of Fig. 10 (08:40-09:55 UTC).The thick solid line shows the mean profile of the scanned volume and the thin lines indicate the horizontal WV variability (1σ standard deviation) within the scan range.The radiosonde profile launched at 09:30 UTC was plotted with a dashed line.

Figure 12 .
Figure 12.One-hour mean WV field between 11:00 and 12:00 UTC on IOP 4 on 12 August 2014.The covered angle range was 0 to 12 • ; the scan speed was 0.2 • s −1 ; a single scan took 1 min.For the water vapor calculation, 1 s averaged data were used.The land cover along the line of sight is also shown.The dotted lines indicate the location of the vertical profiles shown in Fig. 13.

Figure 13 .
Figure 13.Absolute humidity profiles for the RHI scan of Fig. 12 for the horizontal distances of 0.4, 0.8, and 1.2 km.The noise errors are also shown.The location of the WV and noise profiles are indicated by the dotted white lines in Fig. 12.

Table 1 .
Instrument specifications of the UHOH DIAL for scanning WV measurements.