EUREC 4 A’s Maria S. Merian ship-based cloud and micro rain radar observations of clouds and precipitation.

. As part of the EUREC 4 A ﬁeld campaign, the research vessel Maria S. Merian probed an oceanic region between 6 ◦ N and 13.8 ◦ N and 51 ◦ W to 60 ◦ W for approximately 32 days. Trade wind cumulus clouds were sampled in the trade-wind alley region east of Barbados as well as in the transition region between the trades and the intertropical convergence zone, where the ship crossed some mesoscale oceanic eddies. We collected continuous observations of cloud and precipitation proﬁles at unprecedented vertical resolution (7-10 m in the ﬁrst 3000 m) and high temporal resolution (1-3 s) using a W-band radar and 5 micro-rain radar (MRR), installed on an active stabilization platform to reduce the impact of ship motions on the observations. The paper describes the ship motion correction algorithm applied to the Doppler observations to extract corrected hydrometeor vertical velocities and the algorithm created to ﬁlter interference patterns in the MRR observations. Radar reﬂectivity, mean Doppler velocity, spectral width and skewness for W-band and reﬂectivity, mean Doppler velocity and rain rate for MRR are shown for a case study to demonstrate the potential of the high resolution adopted. As non-standard analysis, we also retrieved 10 and provided liquid water path (LWP) from the 89 GHz passive channel available on the W-band radar system. All datasets and hourly and daily quicklooks are publically available. Data can be accessed and basic variables can be plotted online via the intake catalog of the online book "How to EUREC 4 A".

This radar suite represents one of the most advanced remote-sensing setup ::::: setups : for measuring trade wind precipitation in and below the cloud. Ground-based cloud radar remote sensing has been used for long time to monitor the vertical structure of clouds and precipitation (Bretherton et al. (2010), Lamer et al. (2015), Leon et al. (2008), Kollias et al. (2007), ), as well as on ships (Zhou et al., 2015). In recent years, the potential of new observables like the Doppler spectra's skewness to 40 detect precipitation forming in the cloud (Kollias et al. (2011b), Kollias et al. (2011a), Luke and Kollias (2013), Acquistapace (2017)) was demonstrated for fixed ground-based sites. However, ship-borne cloud radar Doppler measurements have not been exploited yet. A first analysis of the unique dataset of trade wind cumulus clouds and precipitation collected with the MRR-PRO :::: MRR : and the W-band radar on MS Merian is presented. Considering typical sea wave periods of 9 s, to obtain Doppler observations at sea, integration times have to be chosen shorter than 1 s (Chris Fairall, personal communication). In the

W-band radar
The W-band radar is a frequency modulated continuous-wave (FMCW) 94 GHz dual polarization radar equipped with a ra-90 diometric channel at 89 GHz and is manufactured by Radiometer Physics GmbH (RPG), Germany. The small diameter of its antennas (0.5 m), one to transmit and one to receive, and its compactness (Table 1) make it a well suited instrument to be deployed in complex environments. Küchler et al. (2017) provided an extended description of the radar performance, hardware, calibration and signal processing procedures. :: We ::::::::: calibrated ::: the ::::::: receiver :: of ::: the ::::::: W-band ::::: radar :::: after :::::::: installing :: it :: in ::: the ::::::: position ::::: shown :: in :::::: Figure :: 1. To protect the hydrophobic radome from hydrometeors, the radar is equipped with a blower for both anten-95 nas. The blower is able to produce a thin airflow with up to 20 ms −1 over the antenna radomes (Küchler et al., 2017). Users can set different range resolutions at different altitudes by providing the necessary parameters to the so called "chirp table", i.e. a table storing all the frequency modulation settings. Table 2 shows the chirp table definition adopted for this measurement campaign. We defined the chirp table to have a high vertical resolution below the inversion layer to focus on shallow cumulus clouds ( Table 2). This choice resulted in reaching a maximum detectable range of 10000 m to focus on high vertical resolution 100 of the boundary layer clouds and the inability to measure high cirrus clouds. The range resolution from the sea-level to 1233 m was 7.5 m, while it was 9.2 m between 1233 m and 3000 m. Between 3000 m and 10000 m the range resolution was 34.1 m.
We chose integration times of 0.846 s for heights smaller than 1233 m, 0.786 s between 1233 and 3000 m, and 1.124 s between 3000 m and 10000 m to make the ship motion correction effective. The total sampling time required to measure a full profile resulted in around 3 s.

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The embedded passive channel operates at 89 GHz with a bandwidth of 2 GHz and measures the calibrated brightness temperature (TB). In the W-band, atmospheric gases are relatively transparent. The absorption coefficient of atmospheric gases in the lower troposphere is of the order of 1 dB/km (Ulaby et al., 1981). In contrast, cloud liquid water produces a strong attenuation (≈ 1 dB km −1 g −1 m 3 , (Ulaby et al., 1981)) in this frequency band. Since the passive measurements are sensitive to the presence of liquid water, the TB measured at 89 GHz can be used in a retrieval of liquid water path (LWP) (Küchler et al., The W-band radar data collected during the EUREC 4 A campaign have been post-processed using a software package, that includes processing and de-aliasing of compressed and polarized spectra. The code is an update and a subsequent restructuring of the first program version provided by Küchler et al. (2017) and it is available at https://github.com/igmk/w-radar/tree/new_ 125 output_structure. No ::::: liquid : attenuation correction has been applied to the data yet. The post-processing routine produces as output a technical data file including all radar specific variables, and a physical data file, available in two versions. One version (compact) : , :::::::: structured :: as ::::: daily :::: files, : includes: radar moments (equivalent reflectivity factor ::::: (from :::: now :: on :::::: called ::::::::: reflectivity), mean Doppler velocity negative towards the ground, Doppler spectral width, Doppler spectrum skewness, Doppler spectrum kurtosis)

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The other version (complete radar data), ::::::::: organized :: in :::::: hourly ::::: files, includes all the previous variables plus additional radar variables like the Doppler spectrum, the bin mean noise power and the sensitivity limit. In addition to the standard processing, we derived and added the mean Doppler velocity field corrected for ship motions to the variables listed above in both versions of the files. The compact version has been enhanced with Climate and Forecast (CF) conventions (https://cfconventions.org/) to allow online plotting using the EUREC 4 A book (https://howto.eurec4a.eu/intro.html). Section 3.1 and 3.2 describe the post-140 processing applied to the data and section 5 explains the available data products.

Data Processing
This section describes the corrections applied to the data to obtain the final reference dataset. Subsection (3.1) describes the drift problem in time between the radar and the ship clock that both radar datasets undergo. Synchronization of the two is 205 thus necessary and preliminary before applying any ship motion correction. Subsection (3.2) shows how to calculate the ship motion correction term for both radar datasets and subsection (3.3) assesses the correction algorithm. Finally, subsection (3.4) shows how to filter interference for MRR-PRO data.

Tackling time drift between ship and radar time stamps
At the beginning of the campaign, we synchronized the ship and radar clock. However, the ship and radar clock cumulated a 210 time lag ∆T that varies with time between 1 and 4 s. To calculate the time-varying ∆T , we use the heave rate time series and the time series of the mean Doppler velocity averaged over the cloudy range gates < V d > :::::: < v d > of each radar profile (see section 3.3 for more details on why using the heave rate time serie). For stationary radars, i.e. radars not moving in time, the mean Doppler velocity (V d :: v d ) measures the mean velocity of the hydrometeors in the radar volume with respect to the radar that results as superposition of the air motion and the sedimentation speed of the drops. The average of V d :: v d over the cloud of cloud droplets is negligible and updrafts and downdrafts present in the cloudy column are averaged out. In precipitation regions instead (for example in Figure 5 ) after 6:17:07), it becomes more and more negative, because of a larger and persistent downdraft. When the radar is moving (like on the ship), < V d > :::::: < v d > additionally tracks the radar motion ( Figure 5)).
We then applied the resulting time lag ∆T to the ship data and interpolated this shifted series to the exact radar time, obtaining the best correction term for each time stamp. We iterated the procedure for every radar chirp sequence since they all have different time stamps. Only after matching the time series of data from the ship and data from the radar, we could apply the ship motion correction.

Derivation of the ship motion's correction formula
In the following we will derive the equations to remove ship movements from the observed radar Doppler velocities with and without a working stabilization platform. The algorithm applies to both radars. The only difference is that while for the W-band radar the correction was applied to the mean Doppler velocity, for the MRR-PRO the whole Doppler spectra is shifted by the correction. We will adopt bold notation for vectors i.e. v = (v x , v y , v z ) where v i are the components of the vector v along the The ships coordinate system is defined by a right handed system with unit vectorsê x , in direction of the bow,ê y towards star board andê z perpendicular to the decks downwards ( Figure 4). With the ship moving in the waves this coordinate system is rotated by roll and pitch angles. This rotation is described by a rotational matrix R (see appendix C4 ::::::: equation ::: C4 :: in :::::::: appendix : C). By applying the R on unit vectors of the ship system we get a coordinate system withê z pointing vertically downward 250 in the direction of earth gravitational acceleration g, and vectorsê x andê y horizontally pointing in the direction of the ship's bow and starboard respectively. We call this system the horizontal coordinate system (Figure 4).ê z = [0, 0, 1] is the pointing direction of theẑ axis of the horizontal coordinate system and points downward.
The radar observes Doppler velocities relative to its own movement along its radar beam and they are positive for movements away from the radar, i.e. upward for a vertical pointing instrument. The Doppler velocity measured by the radar is 255 the projection of the particle's velocity vector on the radar line of sight. Therefore, the component of the velocity vector of the hydrometeors w signal measured by the radar is positive when hydrometeors move upwards. The pointing direction of the radar in the horizontal system is denoted asê p . During times the stable table is working it isê p = −ê z (ê p pointing upwards, e z pointing downwards). The velocity observed by the radar is the relative velocity between hydrometeors (v hydr ) and the movement of the radar (v radar ) projected onto the pointing direction of the radar (ê p ) that is: where all vectors are given in the horizontal ship coordinate system and the dot represents the scalar product. The movement of the hydrometeors can be decomposed in the horizontal system into a component along the vertical axis and one in the where the term v hydr,s is the hydrometeor fall speed in the horizontal reference system (z component), and v wind,s the horizontal wind vector in the horizontal reference system ::: (for ::: the ::::::::: derivation, ::: see :::::::: appendix :: B) : . Hence, we get: Now solving Eq. 4 for v hydr,s that is the hydrometeors fall speed in the horizontal reference system, we get: In the case of a working stabilization platform the radar pointing vector is exactly upwards and accordingly the scalar product e z ·ê p is equal to -1 asê z is pointing downwards. In the limit of a non moving ship we get v hydr,s = −w signal where the opposite sign is given by the fact that the ship reference system has an opposite z direction to the one in the radar convention. Finally in the common definition with falling hydrometeors having negative velocities we get: The pointing direction of the radarê p in Eq. 5 changes depending on whether the stabilization platform is working or not: if the stabilization platform is working perfectly, we assume thatê p = [0, 0, −1].

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-If the stabilization platform is not working the pointing vector of the radar is moving with the ship coordinates system.
Accordinglyê p0 has to be rotated with the ships rotation matrix R in the horizontal system and we getê p = R * ·ê T p0 . The table typically got stuck at an arbitrary position and thus the radar is pointing in an arbitrary direction. We reconstruct this direction by taking roll and pitch at time t 0 just before the table got stuck and assuming that the radar was pointing at this moment vertically. Orientation of the radar in the ship system is thusê p0 = R −1 (t 0 ) * (−ê z ) ::::::::::::::::::: pendix C and D for more details).
The velocity vector v radar in Eq. 2 is composed of various contributions to the motion: where the velocities that add up to the radar movement are:

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(we neglect the surge and sway contribution), and it is given by v trasltrans :::: = [0, 0, w heave ]. ::: (see :::::::: appendix :: E ::: for ::: the ::::::::: derivation). : -The course velocity vector v course is due to the travel of the ship along its course, and it is given by where ψ is the yaw and v s is the intensity :::::::: magnitude : of the ship velocity vector . ::: (see :::::::: appendix :: E ::: for ::: the ::::::::: derivation). : -The rotation velocity vector v rot describes the movement due to the rotation of the ship (roll, pitch, yaw) and the fact that the instruments are not deployed in the center of rotation but at distances r MRR-PRO and r W-band from it. Its (Appendix (C) for the derivation of the full expression).

Application of the correction and additional smoothing
When the table is working and the radar is pointing vertically all horizontal vector components vanish and the expression of 290 the corrected hydrometeor velocity reduces to: where v traslz :::::: v transz and v rotz are the z components of the vectors v trasl ::::: v trans and v rot . In this case, for calculating the velocity terms we need roll, pitch, heave rate. All these data are provided by the ship navigation system. Angles roll and pitch are necessary because the rotation of the ship moves the radar vertically. Course (heading ::: yaw : and speed) are not necessary as 295 the they are horizontal components not seen by the vertical looking radar.
When the table is not working, the pointing vector of the radar is most of the time not vertical and may have a horizontal component (scalar products ofê p with horizontal vector components do not vanish). Accordingly course of the ship and horizontal wind may contribute to the signal. We therefore need additional parameters heading ::: yaw : and speed of the ship and the horizontal wind above. The first two are provided by the ships navigation system. For the wind we used the output  Figure 3). When comparing the original (Figure 6 a)) to the corrected mean Doppler velocity field (Figure 6 b)), one can quickly notice that many of the intense and frequent vertical bars disappear, providing a more homogeneous and continuous field. However, the correction cannot entirely remove the disturbances, as shown in Figure 6 b) by some visible 310 vertical bars remaining despite the correction. Some possible reasons for the mismatch observed are the distance between the MRU sensor and the radar equipment, especially considering that we measured by hand the radar equipment's position. We are also assuming that the stabilization platform keeps the radar perfectly in zenit, but it is hard to quantify the accuracy of such hypothesis :::: since : a little error in the zenith alignment can produce disturbances. Moreover, the time lag quantification ∆T can be unprecise due to the reinitialization of the chirp generator of the W-band radar. Such time is random and adds an unknown 315 uncertainty to the time stamps assigned to the measurements. Finally, the coarse temporal resolution of the MRU data makes an interpolation to the radar data necessary. Fig ::::: Figure : 5 nicely shows the rapidly changing w ship which misses due to its coarse temporal resolution the real minima and maxima making an interpolation challenging. We applied a running mean over three time stamps (i.e., over a 9 s time interval) to account for these limitations (Figure 6 c)). The final signal obtained shows an almost continuous field in mean Doppler velocity. folded back into this interval. Such frequencies do play a role that is not resolved by MRU nor by the radar itself. The final smoothing over the 9 s time window removes the high frequency components and it is thus crucial to obtain a better signal to 335 noise ::: ratio. However, the 9 s smoothing degrades the average horizontal resolution : given V ship, mean the mean ship speed, the degradation would change from V ship, mean * 1 s to V ship, mean * 9 s. : of ::: the ::::::::: V hyd, mean :: by : a :::::: factor :: of :: 9. For an average ship speed of 3 ms −1 , the resolution would change from 3 m to 27 m, resulting in a slightly higher resolution than the vertical 30 m one.
However, daily maximum speeds for the ship can reach also 9 ms −1 , producing thus a coarser resolution.

Removal of Interference patterns and correction for ship motions for MRR-PRO dataset 340
The MRR-PRO electronics interfered with the ship instrumentation and with the stabilization platform electronics during the whole campaign. To be able to use the data collected, we removed the interference patterns using a noise removal mask. The interference draws periodical disturbances with peak intensity decreasing with height. Since the interference peaks are larger than the mean noise level calculated using the Hildebrand-Sekkon method by the manufacturer's processing (Hildebrand and Sekhon, 1974), multiple small peaks appear in the MRR-PRO spectra. The mean Doppler velocity and the spectral width of 345 such noise spectra are random, depending on which noise peak is the highest ( Figure A1).
The MRR-PRO dataset produced by the software of the manufacturer is initially processed with the MRR-PRO postprocessing tool developed by Albert Garcia-Benadi (publication in preparation) (Pre-processing and anti-aliasing steps in ship motion correction can be applied to those data because their integration time is larger or similar to the typical wave period (see Figure 7 a)) and Doppler variations due to heave motions are smoothed out. We resampled the data collected from the 19 to the 25 January 2020 with 5 s to a 10 s integration time, to reduce the impact of ship motions completely.
The post-processing of the data collected with 1 s integration time, i.e. from the 25 January to the 19 February 2020, is more complex(see Figure ??). For the 1 s resolution data, the tool from Garcia-Benadi ::::::::::::::::::::::: Garcia-Benadí et al. (2021) cannot remove 355 the interference patterns as it did for the 10 s integration time dataset. Hence, to obtain Doppler spectra without interference we applied a noise removal mask (Interference filter in Figure 8) based on specific conditions: 1. We calculated for each spectrum the prominence of all its spectrum peaks, i.e. each peak's ability to stand out from the surrounding baseline of the signal. Then, we derived the difference between the maximum and minimum prominence and calculated their difference (∆P ). The difference is tiny for spectra containing only interference patterns and no signal 360 from hydrometeors, while it is significantly larger for a Doppler spectrum detecting hydrometeor backscattering (see for reference on Figure A1). Spectra affected by interference patterns were removed by selecting spectra with ∆P > 1 mm 6 mm −3 , where the threshold value of one was determined empirically; 2. In addition, we posed a condition on the spatial continuity of mean Doppler velocity (mdv) in the lowest 600 m. The mdv obtained from spectra affected by interference shows very large random absolute values. Doppler spectra detecting 365 hydrometeors produce continuous mdv field in space. We discarded all profiles where the difference of consecutive mdv values along the profile shows more than 8 abrupt peaks (threshold decided empirically).
3. We apply a spatial filtering to remove spurious noisy pixels: the filters excludes all pixels where ∆P > 1 that have less than 3 adiacent neighbours fullfilling the same condition.

Characteristics of trade wind cumulus clouds and precipitation
To give an overview of the meteorological conditions encountered on each of the 32 days of campaign, Table 3 lists the daily 380 mean atmospheric temperature (T2m), rain rate (RR), liquid water path (LWP), relative humidity (RH) and pressure (P) for each day of the campaign. They are collected at the radar base, which is approximately 20 m above sea level. We compared the obtained IWV values with the IWV retrieved from GNSS by Bosser et al. (2021). The mean of the IWV 390 retrieved from W-band radar single-channel retrieval is 31.7 kgm −2 , the median is 32.3 kgm −2 and the standard deviation of the distribution is 5.15 kgm −2 . The bias between the mean value of the IWV distribution from W-band and the IWV distribution from GNSS is 3.4 kgm −2 , which is consistent with the bias estimated with ground-based GNSS stations reported in Figure 9 of Bosser et al. (2021). The spread between the GNSS and the radar derived values of IWV can be due to the strongly varying bias component that affects the GNSS IWV estimations from MS Merian (Bosser et al., 2021), as well as to limitations in the 395 IWV single channel retrieval.
To show the full potential of the collected radar dataset, we display one case study of an extended precipitating cloud field occurring on 12 February 2020 from 15:30 :: 00 : to 17:00 UTC in the trade wind alley at about • 13.5 N and • 57 W. On that date, the ship encountered a cloud system identifiable as a flower type ::::::::::::::: (Bony et al., 2020) using the corrected reflectances from Moderate Resolution Imaging Spectroradiometer (MODIS) TERRA (Platnick et al., 2003), with a diameter between 200 and 400 250 km that generated precipitation during the afternoon (Figure 10 c)). When comparing the signals observed by the W-band radar (Figure 10 a)) and the MRR-PRO (Figure 10 b)), the different sensitivities of the two instruments become evident; while the W-band is capable of detecting cloud and precipitating hydrometeors, the MRR-PRO is sensitive to larger raindrops only.
The interference patterns reduced the ability of the MRR-PRO to detect precipitation in a way that it is difficult to quantify.   (Figure 11 f)). The 420 case study highlights a large variability of fall speeds in the lowest 300 m, possibly connected with sub-cloud layer dynamics.
The fall speed field can also trace such dynamics, as the vortex structure in Figure 8 d). In contrast with the reflectivity and fall speed fields, :::: Also : the rainfall rate does not show a substantial variation ::::: shows : a ::::::::: substantial :::::::: decrease :: as ::: rain :::::::::: approaches ::: the :::::: ground during the selected case study (Figure 11 g)). During the case study the stabilization platform worked continuously and above 1000 gm −2 should not be considered as reliable because of contamination due to rain.

Data availability
The data presented in this paper can be accessed at AERIS repository and on the ARM database in NetCDF format, under (https://doi.org/10.25326/235) (Acquistapace et al., 2021c). This DOI was assigned to the new version of the dataset, produced after fixing a bug in the standard post-processing script and correcting the LWP neural network dataset. In the dataset:

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technical radar variables were removed and stored in hourly technical files that can be accessed upon email request to the manuscript's corresponding author.
-A Doppler velocity variable has been added to facilitate the usage of the Doppler spectrum variable.
-A compact data version suitable (including only radar moments :::: radar :::::::: moments ::: and :::::::::: geolocation) for the EUREC 4 A intake catalog has been produced following CF conventions. In the EUREC 4 A book now available at https://howto.eurec4a.eu, 435 some example codes on how to read the data and plot basic quantities are available for users. More support will be added here in the future.
together with the outdated version of the radar data. The MRR-PRO data can be accessed at AERIS repository and on ARM databases (https://doi.org/10.25326/233) (Ac-440 quistapace et al., 2021a). Data are organized in daily NetCDF files. Also this dataset is following CF conventions and is included in the EUREC 4 A intake catalog with example codes for basic operations with the data.
Finally, the code used for post-processing the W-band radar data is published on github (https://github.com/ClauClouds/ w-radar). The post-processing software for MRR-PRO data will be published in a devoted publication (Garcia-Benadi, 2021, in preparation) : is :::::::: published :: in :::::::::::::::::::::: Garcia-Benadí et al. (2021). The code for ship motion correction and interference filtering and for 445 deriving the plots of the paper can be accessed at zenodo https://doi.org/10.5281/zenodo.5014088. All the data are visualized in hourly and daily plots on the quicklook browser https://bit.ly/3xLkb9b. For improving the data visualization (Zeller and Rogers, 2020), we created color palettes using the Colorgorical tool (Gramazio et al., 2017), and we used them for all plots of the quicklook browser as well as for many of the graphics of this publication.
As underlined in the introduction, we experienced various challenges deploying active remote sensing instruments on the MS Merian research vessel. For encouraging and facilitating future deployments on ships, we collected some issues we encountered that future technological developments could solve.
The ship motion correction algorithm described here has also been tested on the radar data collected on the Meteor research vessel, where the ship navigation system data used 0.1 s (10 Hz) time resolution. We noticed that increasing the time resolution 455 of the ship position data from 1 Hz to 10 Hz is beneficial for the ship motion correction. Spectral analysis of the data from MS Merian indicates that there are components of the ship movement at frequencies above 0.5 Hz which had to be filtered out by a simple gliding average smoothing operator. We therefore recommend using 10 Hz for future campaigns.
A significant limitation to the exactness of the correction came from the need to synchronize the radar clocks with the GPS time from the ship. This is necessary to assign the right correction to be used for the measurements. The synchronization 460 problem is a well-known issue for aircraft measurements, and more research is needed to tackle this point. At least for ship purposes, a possible solution could come from including a high-resolution sensor in the radar that can tell the radar inclination and heave for each radar partial chirp sequence time stamp with high precision. Currently W-band radar position data (inclination, and elevation) are provided with the time resolution of the total sampling time, which is approximately 3 s and is too poor for an effective correction of ship motions.

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Finally, we strongly recommend a preliminary test phase to the campaign, as we did in this work. The time spent before the campaign in testing the instruments allowed us to take care and solve small details that could have strongly affected the measurement quality, like the vibration of the pole or the best setup for the computer connections onboard the RV. We experienced interference problems on the ship. Interference is always hard to detect and to solve, but we recommend making some test measurements with all instruments and checking the raw data obtained. In our case, the MRR-PRO interference was 470 not visible on the quicklooks of the control system, but it significantly impacted the observations. In a test phase, interference could be tackled and possibly solved.
We developed an algorithm to correct the Doppler observations from ship motions and successfully applied it to the W-band dataset. The algorithm initially calculated the time shift between the radar time stamps and the ship navigation system time to 485 identify the radar position with respect to the motion reference unit as best as possible. It then applies the correction term to the mean Doppler velocity. For the MRR-PRO data, in addition to the ship motion correction algorithm, we also developed advanced post-processing techniques to filter out interference problems between the MRR-PRO and the stabilization platform.
We first removed the interference pattern, and we then applied the correction directly to the Doppler spectra. Then, we used the standard post-processing to derive the moments and the other rain-related variables from the corrected Doppler spectra.

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The corrected fields remove most of the typical striped pattern due to heave motion in the mean Doppler velocity (W-band) and fall speed (MRR-PRO ) that ship motions cause to Doppler measurements. The correction for ship motion was applied to the entire dataset. However, for 35% of the data, the stabilization platform did not work. We corrected this data subset using the horizontal wind profile extracted from NWP ICON-LEM model runs and horizontal ship velocity.
A unique feature of the dataset is the high temporal and vertical resolution; the time resolution is 3 s (W-band) and 1 s 495 (MRR-PRO ). Below 3000 m, i.e., where most of the cumulus liquid clouds develop, the range resolution of the W-band is 9 m or 7 m, while the one of the MRR-PRO is 10 m. The profiles of the W-band radar moments detected with unprecedented detail showed characteristics patterns that will be explored in future works, especially for what concerns the spectral width and skewness. MRR-PRO variables like the fall speed contain important detailed information on the dynamical evolution of the rain in the sub-cloud layer and its interaction with the dynamics. We exploited the passive 89 GHz channel available on the 500 W-band radar to retrieve LWP in cloudy conditions and IWV in clear-sky situations. The LWP retrieval is a neural network retrieval provided by the radar manufacturer, while the IWV is derived from a single-channel quadratic regression between the 89 GHz brightness temperatures obtained in clear-sky and the IWV measured by the radiosoundings launched at the exact times. We assessed the IWV retrieval by comparing it to the IWV estimations obtained by GNSS (Bosser et al., 2021). We found a bias of 3.4 kgm −2 , in agreement with what :::: was reported in Bosser et al. (2021).

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The high resolution of the collected datasets and the possibility of synergies with the other instrumentation on board, i.e., Raman lidar, wind lidar, cloud kite, make the described observations a benchmark dataset for future analysis as model studies and evaluations, comparing satellite retrievals and process studies. We made the data public and accessible on the AERIS and the ARM database platforms to achieve these purposes. Moreover, we also made the data accessible online via the EUREC 4 A intake catalog, and hourly and daily quicklooks are available online for browsing into the data.

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Future work will focus on improving the quality of the correction: when the wind lidar corrected dataset from MS Merian will be published, it will provide horizontal wind profiles for the entire campaign and thus allow to obtain a better correction for the 35% of the dataset collected when the stabilization platform did not work.
Video supplement. The corresponding author realized a short video from the campaign that was approved by the ship board and is available online at the following link: https://www.youtube.com/watch?v=EdWNS77qMNA 515 Appendix A: LWP retrieval using neural network This appendix describes the neural network retrieval developed to retrieve LWP from the single passive channel at 89 GHz of the W-band radar, exploiting radiosoundings launched in the region of the campaign. The dataset consisted of the 3 radiosonde stations collocated in Grantley Adams International Airport (Barbados), International airport of "Le raizet" (Guadaloupe) and Piarco international Airport (Trinidad) and the one location from the ERA-Interim reanalysis (see Table A1). All available 520 profiles from Jan 1994 to Dec 2016 were used. In total, there were 41588 profiles. We used 29111 (70%) randomly chosen profiles for the ANN training and 10% of the dataset for the validation. We used the remaining 20% for the retrieval evaluation (test dataset). For each profile, we calculated the LWP following Löhnert and Crewell (2003). A radiative transfer model was used to simulate TB values at 89 GHz. The absorption of oxygen and water vapor was calculated according to Rosenkranz (Rosenkranz, 1998(Rosenkranz, , 1999. The absorption by liquid water was calculated using the Rayleigh scattering approximation and the 525 model from Liebe et al. (1991) and Liebe et al. (1993).
We used as input variables for the ANN training the simulated brightness temperatures (TB), day of the year, near surface temperature, relative humidity, and pressure. The values of temperature, relative humidity, and pressure closest to the surface were taken from profiles. The calculated LWP was used as the target variable. The input and the target variables were normalized using the min-max function. The ANN consists of two layers: a hidden layer with 5 neurons and an output layer with one 530 neuron. The hyperbolic tangent is used as an activation function for all neurons. The standard error backpropagation algorithm was used for the training. After the training, we evaluated the retrieval using the test dataset. The retrieval root mean square error (RMSE) is 33 gm −2 . During the radar operation, the ANN uses TBs measured by the passive channel and measurements of the surface temperature, relative humidity, and pressure from the weather station.
Appendix B: Calculation of the wind speed in the ship ::::::::: horizontal reference system v wind,s

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In the Earth reference system, the horizontal wind vector in absolute coordinates is given with the zonal component towards East, and the meridional component towards North ::: and : it ::::::::: represents ::: the :::::::: direction ::::: where ::: the ::::: wind :: is :::::: coming ::::: from. If it has a speed v wind,E and a direction indicated by α with respect to the :::::::: clockwise ::::: from North, it can be written in Cartesian coordinates as: After applying the rotational matrix of ship motions, the ship :::::::: horizontal : coordinate system (see Fig. 4) has: x axis to the heading ::: yaw : of ship, horizontal, perpendicular to the gravity acceleration g, y axis to the starboard of ship, right side, horizontal, perpendicular to g, If ::: yaw : ψ is indeed given relative to heading, the equations describing the wind in the ship :::::::: horizontal : reference system are: because the ship :::::::: horizontal coordinate system is rotated clockwise by ψ − 90, and the y-axis of the ship has opposite direction with respect to the Earth reference system.
We can hence re-write Equation 6 as: Appendix C: Calculation of the rotation vector v rot Let's define η the rotation angle resulting from ship motions. The rotation matrix R * associated with a generic rotation η, is the product of the rotation matrices associated with the roll, pitch and yaw, in the way the angles provided by the MRU sensor on the ship are defined. The prescribed order for the MS Merian is roll (θ), pitch (φ), heading (yaw ) ::: yaw : (ψ), heave. The general expression for the rotation matrix is hence given by: where A is the rotation matrix for the roll, B is the rotation matrix for the pitch, and C is the rotation matrix for the yaw. The expressions for A, B, C are: The expression for R * is: cos ψ cos φ sin φ sin θ cos ψ − sin ψ cos θ sin φ cos θ cos ψ + sin ψ sin θ sin ψ cos φ cos ψ cos θ + sin ψ sin φ sin θ − sin θ cos ψ + sin ψ sin φ cos θ − sin θ cos φ sin θ cos φ cos θ The heading term ψ is necessary only when the stabilization platform gets stuck and we ignore it when stabilization platform works. We call R the rotational matrix obtained when neglecting ψ, that applies for 65% of the data. Rotational movement 560 of the ship leads to translational movement of the instrument because it is not located in the center of mass of the ship. The location of the radar with respect to the center of mass at any moment of the rotation is r rot = R * r radar . Its velocity is the derivative with respect to time : v rot = d/dt(R * r radar ) = dR/dt * r radar , with x, y and z the coordinates of the radar location vector on the ship.

570
Adopting the point as a symbol for the temporal derivative, the rotational velocity results in: Appendix D: Calculation ofê p0 andê p When the stable table stops working it leaves the table and thus the instrument in an arbitrary orientation denoted by a fix vector e p0 ::: e p0 : in the (rolling and pitching) ship system. This vector can be transformed to the horizontal system by multiplication 575 with rotation matrix R * (see Appendix C) asê p(t) = R * * e p0 : ::::::::::::::: e p (t) = R * * e p0 : e pêp (t) :::: = R * * [ê p0x ,ê p0y ,ê p0z ] (D1) e p0 :::: where :::::::::::::::::::: e p0 = [ê p0x ,ê p0y ,ê p0z ] can be calculated from the position in which the table was when it got stuck. The stabilization platform angles at the time t 0 when the table got stuck can be obtained as follows. For the roll where the inverse rotational matrix R * −1 is calculated as: where A −1 , B −1 and C −1 are the rotational matrices associated to the roll, pitch and yaw angles of the table at the time t 0 : θ table S |t 0 , φ table S |t 0 and ψ table S |t 0 . The expressions of the matrices A −1 , B −1 and C −1 can be obtained from the expressions 590 of A, B, C, by using negative angles.
Appendix E: Calculation of v course and v trasl :::::: v trans

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The course vector v course is determined by the ship velocity v s and its heading :::: yaw ψ. We decided to calculate the ship velocity by deriving the UTM coordinates given by the MRU-GPS system of the ship with respect to time. We hence get: v course = [v s sin ψ, v s cos ψ, 0] The translation vector v trasl :::::: v trans that the ship undergoes has three components: heave: it is the variation of the z position due to the waves and it is provided by the MRU system. Its projection along 600 the radial beam might be of the order of the hydrometeor fall speed. Figure A1. Interference in the MRR-PRO data: a) mean Doppler velocity for one selected hour. The black vertical lines correspond to the selected times for plotting the spectra shown in panels C : c) : to F : f). b) Same, for reflectivity. c) Height spectrogram of MRR-PRO Doppler spectra collected at 8 : 1:25 : 33:40 :: 00 : UTC during rain, where the horizontal white dashed lines indicate the heights selected for plotting the spectra shown in e) and f). d) same for Doppler spectra collected at 8 : 1:32 :: 50:40 :: 00, in the noise. Ee) Doppler spectra collected along the vertical selected profile for rain : at :::::: various :::::: heights. F : f) Doppler spectra collected along the vertical selected profile for noise : , :: at :::::: various ::::: heights.
surge and sway are the short term variations of the position in the x/y direction compared to the ship velocity slowly varying term. They are not provided by the MRU system but can be derived from the ship velocity data by applying a short time averaging. We will neglect their contribution, since it should be small as long as the point vectorê p0 does not deviate more than 10 • from the vertical direction. 605 We can then write: v trasltrans :::: = w heave ·ê z = [0, 0, w heave ] whereê z is the unit vectorê z = [0, 0, 1] and the heave velocity results in being positive downwards.
Author contributions. Claudia Acquistapace took care of the data curation, the funding acquisition and the project administration for the 610 deployment of the instruments on the ship. She also developed the software used for the post-processing and prepared the manuscript original draft. Jan H. Schween was involved for methodology and conceptualization of the post-processing algorithms; Nils Risse and Giacomo Labbri were involved in the data visualization. Alexander Myagkov helped to specify observational settings for the W-band radar, applied and described the LWP retrieval developed by RPG, and assisted in checking W-band radar data. Albert Garcia Benadí was involved in the programming and the execution of the MRR-PRO post-processing while Rosa Gierens took care of the programming and the execution Rötthenbacher for deploying the MRR-PRO on the MS Merian and for the the fruitful discussion on in the development phase of the correction algorithm. We want to thank Annika Daehne for the administrative support she provided across the different phases of the campaign.
We also would like to acknowledge the ship crew for the brilliant support offered in the installation of the equipment onboard MS Merian and for facing all the technical issues encountered during the campaign. We thank Daniel Klocke, for running ICON simulations that were used for correcting the radar data from ship motions. Finally, we thank Markus Ritschel for the fruitful discussions onboard MS Merian on 635 how to implement the correction for ship motions, and the scientific crew onboard MS Merian for the collaborations developed onboard, with a special thanks to Prof. Eberhard Bodenschatz for finally fixing the stabilization platform. We thank Juan Antonio Bravo Aranda and Lukas Pfitzenmaier for the work done for developing the post-processing radar Matlab software tool that was used in this work. Table 3. Daily mean values of the main surface variables observed on the MS Merian during the EUREC 4 A campaign: T2m is the air temperature 2m above the radar base, which is approximately 20 m above sea level, RR is the rain rate. The liquid water path (LWP) is derived from the collocated 89 GHz channel microwave radiometer and RH and P are the relative humidity and air pressure from a weather station positioned next to the radar equipment.