End to end simulator for the WIVERN W-band Doppler conically scanning spaceborne radar

The WIVERN (WInd VElocity Radar Nephoscope) mission, soon entering in Phase-0 of the ESA Earth Explorer program, promises to complement Doppler wind lidar by globally observing, for the first time, vertical profiles of winds in cloudy areas. This work describes an end to end simulator of the WIVERN conically scanning 94 GHz Doppler radar, the only payload of the mission. Specific features of the simulator are: the conically scanning geometry; the inclusion of cross-polarization effects and of the simulation of a radiometric mode; the applicability to global cloud model outputs via 5 an orbital model; the incorporation of a mispointing model accounting for thermo-elastic distortions, microvibrations, startrackers uncertainties, etc.; the inclusion of the surface clutter. Some of the simulator capabilities are showcased for a case study involving a full rotational scan of the instrument. The simulator represents a very useful tool for studying the performances of the WIVERN concept and possible trade-offs for the different configurations (e.g. different antenna sizes, pulse lengths, antenna patterns, . . . ). Thanks to its modular structure 10 the simulator can be easily adapted to different orbits, different scanning geometries and different frequencies.


Introduction
Accurate forecasts save lives, support emergency management and the mitigation of impacts, thus preventing losses from severe weather while creating substantial revenue (Bauer et al., 2015). Windstorms are the largest contributor to economic losses caused by weather related hazards, resulting in approximately 500 billion USD (adjusted to 2011) of global damage over the 15 last decade. Together with floods they are the costliest natural hazards in Europe: they account for more than 30% (60%) of total (insured) losses (https://ec.europa.eu/jrc/sites/jrcsh/files/pesetaiv_task_13_windstorms_final_report.pdf). The Aeolus wind lidar have demonstrated a large impact in reducing forecast errors when assimilated by European Weather Forecasting Centers (Rennie et al., 2021). In addition to winds, cloud and precipitation measurements remain key for both Numerical Weather Prediction (NWP) applications and for advancing understanding of cloud processes and their role in climate simulations.
The WIVERN (WInd VElocity Radar Nephoscope) concept has been recently proposed within the ESA Earth Explorer 11 call in order to strengthen the wind, cloud and precipitation observation capability of the Global Observing System. The mission has been selected for Phase 0 studies. It hinges upon a single instrument: a Dual-Polarization Doppler W-band scanning 5 cloud radar with a 3-m circular aperture non-deployable main reflector. The WIVERN antenna conically scans around nadir at an off-nadir angle of 38 • at 12 Revolution Per Minute (RPM). This rotation speed implies the use of one horn for transmission and another one for reception. Flying on a 500-km orbit, the instrument provides a swath of 800 km (see Fig. 1).
The aim of the mission is to complement Doppler lidar winds acquired in clear sky conditions and from the tops of optically thick clouds (Rennie et al., 2021) and other wind observations (at cloud top via geostationary observation derived atmospheric 10 motion vector, close to the ocean surface via scatterometers, via radio soundings) by observations in areas of optically thick clouds, critical for cyclogenesis, that cannot be seen by optical sensors. Observations in these areas have the largest potential to improve forecasts (McNally, 2002). Therefore the WIVERN mission is expected to provide: unprecedented wind observations inside tropical cyclones and mid-latitude windstorms that will routinely reveal the dynamic structure of such destructive systems; 15 observations of convective motions that will validate the representation of convection in models; global profiles of cloud properties and precipitation over an 800 km swath that will better quantify the hydrological cycle and the atmospheric and surface energy budget; first direct observation of tropospheric winds that will underpin the predictions of transport and dispersion of trace gases and pollutants in atmospheric chemistry and air quality models. 20 These advances in the observational capabilities are expected to address three science objectives, with immediate applications and societal benefits.
1. to extend the lead time of useful prediction skills of hazardous weather (e.g., wind-storm, cyclones, floods) by direct assimilation of wide-swath winds from clouds and profiles of radar reflectivity of clouds and precipitation into numerical weather prediction (NWP) models. 25 2. to improve numerical models by providing new metrics and observational verification to assess different NWP parameterisation schemes within such models. NWP and climate models use similar schemes so better NWP models will also augment confidence in climate models.
3. to establish a benchmark for the climate record of cloud profiles, global solid/light precipitation and, for the first time, in-cloud winds, crucial for a better quantification of the Earth's hydrological cycle, and energy budgets, with a significant 30 reduction in sampling errors of current and planned cloud radar missions. WMO requirements for data assimilation into global NWP (Illingworth et al., 2018a) can be found at OSCAR (https://www.wmosat.info/oscar/) and are summarised in Tab. 1. The threshold of 12 h for the observing cycle is quite demanding; three scatterometers with 1200-km swaths can approach this revisit time. Noticeably, the Aeolus non-scanning narrow swath clear sky wind measurements are having a significant effect despite their typical clear-sky uncertainty of 4-5 m/s and their coarse sampling (Rennie et al., 2021); thus, even winds with uncertainty above the WMO threshold and with sampling below threshold 5 have proved extremely valuable for NWP. Horanyi et al. (2014) showed that assimilating winds biased by 1-2 m/s when the random error is around 2 m/s would degrade the forecast so a bias of less than 1 m/s should be added to the specifications of Tab. 1.
In order to achieve these targets WIVERN will adopt: 1. polarization diversity to overcome both the range-Doppler dilemma and the short decorrelation times produced by the 10 Doppler fading associated with the low Earth orbiting satellite velocity (Battaglia et al., 2013); 2. a large antenna (3 m) to achieve a narrow beam, thus a fine vertical resolution and fewer issues related to non uniform beam filling (NUBF) biases (Tanelli et al., 2002).
Previous studies (Illingworth et al., 2018b;Battaglia et al., 2018), based on the CloudSat climatology of cloud reflectivities, have demonstrated that the WIVERN radar should observe between one and two million winds per day that satisfy the WMO 15 "goal" of 2 m/s precision. However it is important to define a rigorous framework where to assess the accuracy and precision of Doppler velocities. For instance errors introduced by satellite mispointing induced by orbital-dependent thermo-elastic distortion of the antenna, by the solar array drive mechanism microvibrations, by the rotating antenna vibration, etc., can seriously affect space-borne Doppler measurements, as previously studied in Doppler scanning radars (Ardhuin et al., 2019) and in Doppler lidars (Weiler et al., 2021).

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End to end (E2E) simulators are paramount tools for evaluating instrument performances in preparatory mission studies.
Several radar simulators have been developed in the recent years to simulate space-borne radars [e.g. Haynes et al. (2007); Matsui et al. (2013); Dellaripa et al. (2021)]. Novelty of this work is that our radar simulator is tailored to conically scanning

The E2E simulator
Our simulator has been developed within the ESA Earth Explorer program and it exploits recent development of radar simulators. In particular it benefits from the inclusion of polarization diversity pulse pair processing and wide swath scanning (Battaglia et al., 2013;Battaglia and Kollias, 2015), the effect of the "ghosts" introduced by the cross-talk (Wolde et al., 2019) between the H and V channels caused by strongly reflective depolarising targets and surface clutter as derived from air-10 borne measurements (Battaglia et al., 2017) and the simulation of passive mode to provide brightness temperatures at W-band  (Battaglia and Panegrossi, 2020). A simplified 2D-version of the simulator has recently been applied to CloudSat observations and co-located ECMWF 3D winds to provide an intial assessment of errors introduced by different sources related to NUBF, aliasing, averaging and to the noise in the Doppler spectra estimators (Battaglia et al., 2018).
The WIVERN simulator can cope with data produced by state-of-the-art high-resolution cloud-resolving models as the basis for creating scenes that are used as input to various radiative transfer programs and instrument simulation modules.

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This provides the ability to simulate satellite overpasses and subsequent measurement processes. In this control environment, forward and retrieval models can be evaluated and compared against the "truth" of the input model scene. Similarly each error source can be evaluated separately based on the assumption that, as a first approximation, the different error sources can be assumed independent, so that the total quadratic error (bias) can be computed as a quadratic sum (an absolute sum) of the different errors (Battaglia and Kollias, 2015). For instance, the satellite motion NUBF-induced errors can be estimated 10 by computing the velocities running the simulator with or without satellite motion and then taking the differences of the two (Battaglia et al., 2018).
A schematic for the overall structure of the simulator is depicted in Fig. 2 with a list of current and potential additional capabilities tabulated in Tab    winds] for a WIVERN "cross section" that will be examined later  are presented in the bottom coloured panels. (Kendon et al., 2017). The first intercomparison of GSRMs was conducted in the context of the DYAMOND (the DYnamics of the Atmospheric general circulation On Non-hydrostatic Domains) project (Stevens et al., 2019).
Here, output from the GSRM that participated in the DYAMOND project, the System for Atmospheric Modeling (SAM, Khairoutdinov and Randall (2003) which employs an anelastic form of the non-hydrostatic equations was used as input to the WIVERN radar simulator. The SAM has a horizontal resolution of 4.3 km and 74 vertical layers. Details of the SAM model 5 configuration can be found in Stevens et al. (2019). The model output is available at the DYAMOND project web site via https://www.esiwace.eu/services/dyamond latitudes.An example of the simulation of five orbits is shown in Fig. 3. By running several orbits it is possible to compute for 5 each location the mean and maximum (i.e. the worst case scenario) revisit time of the WIVERN radar footprint; the latter is plotted as a function of latitude and longitude in the left panel of Fig. 4. The maximum revisit time has a strong latitudinal behaviour with a minimum in the equatorial band (peaking at more than 5 days) and a secondary peak at ∼ ±46 • (exceeding 3 days at some longitudes). The maximum (blue line) and mean (red line) revisit time averaged over all longitudes as a function of latitude are shown in the right panel of Fig. 4. While the maximum revisit time presents different local maxima, the mean 10 revisit time is monotonically decreasing from the Equator to the Poles with a mean value of 1.5 days in the Tropical band and of less than 1 day above 50 • latitude, which leads to an average global revisit time of once a day between ±82deg latitude.
The radar is sounding the atmosphere down to the ground with a range resolution of 500 m. Fig. 5 and Fig. 6 illustrate the observing slant geometry; the actual vertical resolution will be the result of the slant range resolution, the antenna beamwidth and the satellite altitude (Meneghini and Kozu, 1990). Note that, for a uniform cloud, 90% (99%) of the backscattering power is coming from a region whose vertical extent is 640 m (980 m). The horizontal sampling pattern is a function of the rotation speed. The values used here (Tab. 3) are the result of a preliminary optimization for wind product performance (sensitivity and spatial resolution).

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Scattering properties (extinction and backscattering coefficients, single scattering albedo and asymmetry parameters) at each model grid point are computed by adding up the contributions from the different hydrometeors (cloud water, cloud ice, rain, snow). The total scattering, backscattering and extinction coefficients are derived by adding up the single-particle scattering, backscattering and extinction cross sections for the different hydrometeor species according to their particle size distributions.
The single scattering albedo is just the ratio between the scattering and the extinction coefficients; the asymmetry parameter   is derived as a weighted average of the different species asymmetry parameters with the scattering coefficients as weights.
Mie theory (Bohren and Huffman, 1983) is used to compute the single-particle scattering properties. The class "Snow" (which represents all large ice particles) is assumed to have a constant density of 0.1 g/cm 3 . The simulator can accommodate ice species with different densities and axial ratio (e.g. a set of other Look-Up- Table from Rayleigh-Gans approximation is also available from previous studies (Mróz et al., 2021)); it only requires to switch the reference scattering Look-Up- Table. 5 In order to simulate the cross-polar reflectivities linear depolarization ratios (LDR) values are assigned to the different hydrometeor species based on LDR climatology collected at the Chilbolton observatory (see Battaglia et al. (2018)). The

Surface model
Surface σ 0 are assumed to be normally distributed around -25 dB and -8 dB for sea and land respectively with 3 dB standard deviation whereas the surface LDR is assumed to be -14 dB and -6 dB for sea and land with 1 dB standard deviation (Battaglia et al., 2017). In case of coastal regions a weighted mean accounting for the surface type fraction is taken.

Point target response 5
The point target response (PTR) could be assumed to be a simple top hat with a pulse length, τ p , of 3.3µs. More sophisticated PTR function could be used in order to optimise the equivalent noise bandwidth and PTR width. The PTR is used as convolution function along range for all the radar observables.

Antenna pattern
Since the WIVERN antenna is circular a simple Gaussian antenna pattern is assumed with a one-way gain equal to: where G 0 is the antenna gain in the boresight direction, θ a is the antenna polar angle with respect to the boresight and θ 3dB is the antenna 3-dB beamwidth. Any antenna pattern inclusive of side lobes can be added by simply sampling it on the angles 5 used later on for the solid angle integration.

Simulations of radar observables
Both the volume scattering from the atmosphere and the surface scattering from the ground-return must be accounted for when computing the radar observables.
The power received by the radar from the atmosphere, P atm r (t) is given by an integral over the backscattering volume (Bringi 10 and Chandrasekar, 2001): where η is the radar reflectivity, P tr is the transmitted power, λ is the wavelength of radar, k ext is the extinction coefficient.
Practically in order to compute the reflectivity factor corresponding to the atmosphere the three dimensional integral in Eq. (2) is first broken into an integral over the solid angle (defined with respect to the boresight direction); this allows computing Z 15 for ranges r i sampled at distance δr (=100 m in our case but adjustable to the specific need): where Ω 2A is the two-way antenna main-lobe solid angle (equal to πθ 2 3dB /(8 ln 2) for a Gaussian antenna); the solid angle integral is performed by sampling 7 polar and 21 azimuthal angles with respect to the antenna boresight. Then Z atm δr (r) is convoluted with the point target response: where w P T R is the normalised point target response.
The power received by the radar from the surface at a range r, P surf r (r) is computed by an integration performed over the surface, Σ, which is obtained from the intersection between the surface and the spherical shell with radius between r − ∆r/2 and r + ∆r/2 with ∆r = cτ p /2 (Meneghini and Kozu, 1990): where σ 0 is the normalised radar cross section (NRCS). The surface contribution can be written as an equivalent reflectivity term as: The integral I surf defined in Eq. (5)  The total reflectivity signal is obtained by adding up the atmospheric and the surface contributions, e.g. for the V-channel: both are saved in order to compute the impact of the clutter on the radar observables at low altitudes.

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To simulate a Doppler radar with polarization diversity profiles cross-polar returns are also needed. These are obtained performing the same integrals but using the cross-polar reflectivities via LDR and the cross polar surface NRCS, σ HV 0 . The cross-polar reflectivities will be important to compute the appearance of the "ghosts" (Battaglia et al., 2013;Illingworth et al., 2018b;Wolde et al., 2019). WIVERN will transmit pairs of 3.3 µs long pulses at a pulse repetition frequency of 4 kHz, as illustrated in Fig. 7. The pulses will be sent in pairs alternatively horizontally and vertically polarised with a separation of 15 20 µs. This will achieve a maximum unambiguous velocity of ±40 m/s, sufficiently high for unfolding the highest winds.
The reflectivity signal received in the V-channel, Z V , is the combination of the co-polar V-signal, Z V V (continuous red line) combined with the anticipated cross talk of the H-signal, Z HV (dashed red line): The hatched regions highlight the ranges where the cross-signal exceed the copolar signal and therefore will significantly 20 modify the reflectivity signal.
Similarly the signal received in the H-channel, Z H , is the combination of the co-polar H-signal, Z HH , (continuous blue line) combined with the delayed cross talk of the V-signal, Z V H , (not shown): The order of the polarization state of each pulse pairs is switched from pulse to pulse (see bottom panel in Fig. 7) in order to 25 cancel out differential phase shift during propagation between the radar and the targets and for any difference in the lengths of the two polarization transmission lines (Pazmany et al., 1999). Therefore, if we assume no differential reflectivity (Z HH = Z V V = Z co ), reciprocity (Z HV = Z V H = Z cx ) and the same gain in the two linearly polarized channels, for M -pairs of pulses what is practically measured is :  pairs correspond to 2 ms, equivalent to a 1 km distance along the scanning track. Note that the order of the polarization state of each pulse pairs is switched from pulse to pulse in order to cancel out differential phase shift effects between the two channels. Top panel: example of the return echoes from a scene including an ice cloud, a cloud free region and warm rain above a strongly reflecting surface. The returns in the H channel are plotted in blue, those in the V channel (lagging by 20 µs) in red. The dashed red line corresponds to the interference caused by the blue H pulse encountering a depolarising target. A very high depolarisation ratio of -10 dB has been used to exacerbate this effect that leads to "ghosts" in the red H channel. The hatched areas represent ranges where the "ghosts" exceed the co-polar signal; in this case the one from the ground and the warm rain is much more serious (and appears shifted upward by circa 3 km in correspondence to the cloud free region) than the one caused by the large Z gradients at the top of the cloud. A similar reasoning applies to the H-channel (not shown for clarity of purpose).
in the co-polar channel for the first M pulses of the pair and: where V is the backscattering volume (coloured region in Fig. 6), v atm LOS is projection of the the satellite velocity minus the hydrometeor velocity (the result of the wind speed and the hydrometeor fall-speed) along the line of sight (LOS) and Z co is 5 the measured co-polar reflectivity factor; note that the ghosts echoes will have random phase, so will not produce any bias in the wind but only a loss of precision (Pazmany et al., 1999;Battaglia et al., 2018;Wolde et al., 2019). NUBF effects (Battaglia and Kollias, 2015;Battaglia et al., 2018) Eq. (12) can be assessed by setting the satellite velocity equal to zero and looking at the deviation of Doppler velocities.
Similarly to Eq. (5) the Doppler associated with the surface will be equal to: where v surf LOS is projection of the the satellite velocity onto the line of sight; here we assume that the surface is still but any movement could be added if, for instance, ocean currents were available.

Polarization diversity pulse pair processing
A complete description of the simulation of I and Q time series for a system adopting polarization diversity is described 15 in Battaglia and Kollias (2015). Here we adopt a simpler approach and use theoretical results to derive the noisiness of the reflectivity and velocity fields.
For reflectivities, since the Doppler spectral widths, σ v , are expected to exceed 3 m/s for all scanning directions, we can consider reflectivity measurements, separated by a pulse repetition interval (P RI), as independent (for instance the correlation function for 3 m/s and a time lag equal to 250 µs is 0.0072). Therefore the number of independent samples practically is 20 identical to the number of samples. For each single pulse we simulate the total power P as a combination of noise, N (equal to -18 dBZ) and signal, S [equal to the expressions given in (10-11)] by using the fact the probability distribution of power is a simple exponential with a standard deviation equal to the mean (Doviak and Zrnić, 2006), i.e.: with r is a random number uniformly distributed between 0 and 1. Note that, since we oversample in range every 100 m, the 25 application of Eq. (14) must be performed before the deconvolution in range (Eq. 4) because oversampled reflectivities and Doppler velocities are not independent. Power is averaged along track by simply averaging single pulses powers. Since the WIVERN footprint moves at about 500 km/s, 8 pulses must be averaged per km for each of the two channels (Fig. 7).
Doppler velocities estimated via pulse-pair processing also have intrinsic noise associated with the phase and thermal noise and to the cross-polarization interference. Uncertainties depend on the signal to noise ratio (SN R), the radar Doppler spectral width and the number of averaged samples (Battaglia et al., 2013;Illingworth et al., 2018a). Following Pazmany et al. (1999), the estimate of the variance of the mean Doppler velocity for M independent pulse pair samples can be written as: A Gaussian random noise with standard deviation corresponding to Eq. (15) is added to the velocities, which are then folded 5 back into the Nyquist interval, v N y = λ 4T hv .

Mispointing modelling
For accurate winds the pointing of the radar beam formed by the antenna must be known very accurately; for instance a 140 µrad uncertainty produces to a 1.0 m/s LOS wind uncertainty. The antenna boresight direction can be identified by two angles: the elevation and the azimuthal angle (see Fig. 5); the former can be monitored by controlling the sea surface return  frequencies, going from zero to the Nyquist critical frequency f c . The one-sided PSD is then mirrored into a two-sided power spectrum. Since the total power must be preserved, the values in the two-sided PSD are half the values of the one-sided PSD, except for the ones associated with the frequencies 0 and ±f c .
The amplitude of the two-sided spectrum of the signal is calculated from the two-sided PSD by taking the square root and adding to each sample a random phase in the [0, 2π] interval. The spectrum is forced to be conjugate symmetric, so that 5 the IFFT returns a real-valued time series for the mispointing angle. An example of such a time series for a single antenna revolution is shown in Fig. 10 (left panel) with the corresponding LOS velocity error (right panel). The amplitude of the velocity error is a strong function of the azimuthal position. If φ is the azimuthal angle measured clockwise from the forward direction then the error can be approximated as: 10 which clearly shows that the error is minimised close to the forward and backward directions and amplified at side views.
When inputting a realistic PSD as derived from initial industrial studies (internal communications, confidential) the error due to azimuthal mispointing remains always smaller than 0.17 m/s, thus it will provide a very small contribution to the Doppler velocity error budget.

Radiometric mode
WIVERN is also envisaged to have a radiometric mode. During the 250 µs time between transmitted pulse pairs, there will be a dedicated time (of the order of 10%) with a dedicated broad bandwidth receiver for each receiver. The brightness temperatures in the two polarization modes are simulated by an Eddington radiative transfer model (Kummerow, 1993) by using the slant one-dimensional approximation (Battaglia et al., 2005). Land emissivities are polarization independent and assumed to be 5 equal 0.9 whereas ocean emissivities are computed via the TESSEM model (Prigent et al., 2017) with the 10 m wind and the SST from the model product.
3 Applications of the E2E simulator

Case study: system over Labrador
The simulator rationale is demonstrated for a case study simulating an overpass over Labrador. The satellite is moving north-10 ward and is scanning counterclockwise; the satellite ground track over North America is shown in Fig. 8 with a detail of the scanning pattern shown only for the region off the Labrador coast (Panel A). A full scan circle (5 s) is simulated in detail (Panel B): the slant view of the radar beam for the full revolution is used to compute the antenna weighted hydrometeor water content, W C, (Fig. 11A) and LOS winds (Fig. 11B): A variety of cloud and precipitation types is present in the scene with multiple layers of ice and liquid clouds at different heights and with disparate thicknesses. The LOS winds show a characteristic alternating sign behaviour associated with the 5 conically scanning geometry and present some strong vertical wind shears. Note that the clutter signal tends to decrease to very low levels (<-30 dBZ) at a height of 1 km. This confirms previous findings (Illingworth et al., 2020); however, attention should be paid in future work to antenna sidelobes that can effectively enhance clutter contamination on Doppler signal especially over land (see Fig. 8 in Illingworth et al. (2020)). 15 The surface Doppler (sampled at very fine range resolution) shows its characteristic behaviour with zero velocity at the surface range and a pattern of positive and negative velocities at other ranges with a strong dependence on the scanning azimuthal angle, which is used as an alternative x-axis coordinate in the bottom right panel. The azimuthal angle is measured clockwise from the forward looking direction (where it is in the same direction as the satellite motion). When the radar is side-looking the surface appears perfectly still at all altitudes whereas when the radar is looking in the forward or backward directions there is a strong variability with altitudes; as a result, the bias in Doppler velocities induced by clutter contamination will depend on the signal to clutter ratio, the altitude and the azimuthal scanning direction. Overall, when averaging over heights and azimuthal angles, the clutter contamination will produce a bias towards zero Doppler velocities, i.e. the ground 5 clutter will tend to mute the boundary layer winds.
20 https://doi.org/10.5194/amt-2021-342 Preprint. Discussion started: 24 November 2021 c Author(s) 2021. CC BY 4.0 License. Figure 13. Linear depolarization ratio (LDR, left) and signal to ghost ratio (SGR, right) in correspondence to the revolution shown in Fig. 8B as a function of height. The LDR clearly shows the significant depolarizations by the melting layer that is straddling the heights around 4 km and by the surfaces with clear transitions from strong depolarizing land to weaker depolarizing sea surfaces. When no clouds are present the cross talk signal the SGR becomes −∞; thus the SGR is capped at -10 dB. This is the case for several instances at an height of ±2.3 (which corresponds to a slant range of 3 km) in coincidence with surface-cross talk.
The LDR values shown in the left panel of Fig. 13 clearly have highest values in the melting layer and the land surfaces.
These two regions are the major sources of ghosts as can be deduced by looking at the SGR (right panel of Fig. 13), with strongly negative values associated with the ghosts generated by the surface at heights straddling ±2.3 km and with larger SGRs at about 6 km associated with the ghosts caused by the melting layer. Ghosts tend also to appear at cloud top, a phenomenon which, if not accounted for, will tend to artificially thicken high clouds.

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The two panels of Fig. 14  Another WIVERN product is the H and V-polarized brightness temperatures (Fig. 15). Due to the difference in emissivities there is a clear separation of the vertical and horizontal T B s over the ocean. With increasing optical thicknesses the two T B s tend to get closer and closer. This T B enhancement due to emission over cold backgrounds is expected to be useful for rain 5 retrievals. In fact, because of the reduced and more variable ocean NRCS, surface reference technique-based PIA estimates will be more challenging and more sparse in WIVERN configuration than for nadir-looking radars; in addition T B s are known to have a better sensitivity than PIAs (Battaglia et al., 2020), i.e. they will produce a detectable signal at smaller optical thicknesses (compare blue and red line variability). The coincident sampling of reflectivity profiles and T B s will be unique and provide insights into supercooled liquid clouds in snow over the ice-free ocean (Battaglia and Panegrossi, 2020) and the evolution of 10 large ice particles in deep convection.

WIVERN performance assessment
The E2E simulator represents a perfect tool to study the performances of the WIVERN mission. Apart from the errors related to the Doppler estimators in the pulse-pair processing [formula (15)] and the mispointing (Tanelli et al., 2005) there are other sources of uncertainties in polarization diversity Doppler radar measurements such as errors linked to wind shears  either associated with the platform motion (Tanelli et al., 2002;Kollias et al., 2014) or to the atmospheric winds (Battaglia et al., 2018), to clutter contamination (Illingworth et al., 2020), to aliasing (Battaglia et al., 2013;Sy et al., 2014), to multiple scattering (Battaglia and Tanelli, 2011). The contribution of each of these errors can be quantified unambiguously by running two simulations where the effect is turned on and off.

Wind shear errors
For instance the wind shear errors which tend to occur when reflectivity and velocity gradients are present at the same time within the backscattering volume, as can happen at the boundaries of clouds, can be computed from the difference between v AW in Eq. (18) and the expression of v atm D in Eq. (12) with v sat set to 0. Results are shown in the left panel of Fig. 16 in correspondence to the revolution shown in Fig. 8B. Strong wind shears appear in this case at near-surface altitudes (see 5 Fig. 11b), which results in significant wind shear errors exceeding ±1m/s affecting the measurements at the low altitudes, but  The statistics is computed for 20 orbits over the scene depicted in Figs. 11-14. The dotted lines represent the 10th and 90th percentile (typically with absolute value lower than 2.0 m/s) whereas the continuous line corresponds to the median value (always very close to zero because many NUBF errors are equal and opposite so will tend to cancel out).

Non uniform beam filling: satellite motion-induced biases
Similarly, estimates of the NUBF errors can be obtained by comparing the expression of v atm D in Eq. (12) with and without v sat set to 0. targets. In addition, surface modelling accounts for the clutter returns from land and sea surfaces. The simulator also outputs estimates of Doppler measurement errors, such as those due to intrinsic noise, to cross-talk noise between the two diversely polarized channels and introduced in presence of reflectivity gradients (wind shear and non-uniform beam filling errors). Ad-30 ditional disturbances originate from the antenna azimuthal mispointing errors, represented in terms of an absolute knowledge error power spectrum.
Preliminary findings show that mispointing errors associated with the antenna azimuthal mispointing are expected to be lower than 0.3 m/s (and strongly dependent on the antenna azimuthal scanning angle), wind shear and non-uniform beam filling errors have generally negligible biases when full antenna revolutions are considered, NUBF causes random errors strongly dependent on the antenna azimuthal scanning angle but typically lower than 1 m/s and cross-talk effects are well predictable so that areas affected by strong cross-talk noise can be flagged. The noise random errors are dependent on the SNR and the possible 5 presence of ghosts and can be reduced by averaging over a higher number of pulses (i.e. by using a longer integration time).
In summary our results show that the quality of the Doppler appears to strongly depend on several factors: the strength of the cloud reflectivity, the antenna pointing direction relative to the satellite motion, the presence of strong reflectivity and/or wind gradients, the strength of the surface clutter. Overall, the total wind errors seem to meet the mission requirements in a good portion of the clouds detected by the WIVERN radar, which is a very encouraging finding at the beginning of Phase 0 studies.

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The characterization of the errors and the isolation of each single error source makes the E2E simulator a perfect tool to verify mission performances and compliance with requirements, which will be part of the Phase 0 studies beginning in December 2021. Different problematic areas will be investigated (with, possibly, the introduction of new features, see Tab. 2).
1. By changing the antenna gain [Eq. 1)] it will be possible to study the impact of antenna side-lobes in affecting the minimum height close to the surface at which winds can be observed by the WIVERN radar without suffering significant 15 biases from the clutter return.
2. By modifying the point target response it will be possible to define the optimal trade-off between sensitivity and effective vertical resolution; this could also include studies related to pulse compression and effects associated with the range sidelobes.
3. Different modes could be employed for WIVERN operations including an interlaced LDR mode and different T hv 20 interleaved modes. Such modes, very beneficial for identifying the ghost returns and for optimizing noise measurement and aliasing errors, could be optimized via E2E simulations.
4. More sophisticated surface modelling could be introduced by including the dependence on the surface winds over ocean and different surface types/orography over land.
5. Cloud scenes at finer horizontal resolution ( 1 km) that resolve convection could be used in the simulator at regional 25 (if not global) scale; this will enable to evaluate WIVERN performances in presence of convective motions. 6. A multiple scattering module based on the two-stream approximation (Hogan and Battaglia, 2008) could be applied to the 1D WIVERN slant column and used to flag multiple scattering contaminated profiles.
7. Additional polarimetric variables like specific differential phase (K DP ) and the co-polar cross-correlation coefficient (ρ HV ) could be simulated.