On the physical mechanism causing strongly enhanced radar backscatter in C-Band SAR images of convective rain over the ocean

ABSTRACT Radar signatures of rain over the ocean have a complex structure since they receive contributions from surface scattering and volume scattering and attenuation by hydrometeors in the atmosphere. These contributions overlap and are often difficult to detangle. While most of the mechanisms contributing to radar signatures of rain over the ocean are well understood, there is one remaining issue that has been discussed controversially in the literature for a long time. It is the question what scattering mechanism causes the areas of strongly enhanced radar backscatter, also called ‘bright blobs’ or ‘bright patches’, which are frequently observed on spaceborne C-band SAR images acquired over tropical and subtropical oceans in the presence of convective rain. Recently, papers have been published in which it is hypothesized that they are caused by radar backscattering at hydrometeors in the melting layer (ML). Although many observational facts seem to support this hypothesis, there exists one strong argument against this hypothesis: It is the observation that the position of the ML radar signatures (bright blob) in the SAR image is not shifted in anti-range from the position, where the rain column hits the sea surface. This absence of a shift is observed when 1) comparing Sentinel-1 SAR images on which rain cells are visible with quasi-concurrently acquired weather radar images and 2) when inter-comparing of SAR images of rain cells acquired concurrently at different frequencies and polarizations. Based on these observations, we discard the hypothesis that the bright blobs are due to volume scattering at hydrometeors in the ML and hypothesize instead that they are due to scattering at splash products at the sea surface. This hypothesis is supported by radar backscattering measurements carried out in the laboratory and from a shore-based platform, which show that, at C-and X-band, strong rain can give rise to strong radar returns also at cross-polarization.


Introduction
On C-band synthetic aperture radar (SAR) images of the ocean, frequently radar signatures of rain are visible.They are quite variable and it is often not straightforward to identify them as radar signatures of rain.They depend, among others, on radar frequency, polarization, incidence angle, rain type, rain rate, rain history and wind speed (Alpers et al. 2016;Contreras and Plant 2006;Jameson et al. 1997;Melsheimer, Alpers, and Gade 1998;Nie and Long 2007).Two types of mechanisms contribute to radar signatures of rain: 1) surface scattering and volume attenuation at the sea surface and 2) volume scattering and volume attenuation in the atmosphere.
Scattering at the sea surface is due to surface scattering associated with variations of the sea surface roughness caused by the impinging raindrops and due to volume scattering caused by scattering at a cloud of secondary water droplets hovering over the sea surface in the case of medium and strong rain.When raindrops impinge onto the sea surface, they generate ring waves and splash products (crowns, stalks, secondary droplets), as well as turbulence in the near-surface water layer.The variation of the smallscale sea surface roughness, and thus of the radar backscatter or normalized radar cross section (NRCS), due to the impact of raindrops onto the sea surface, has been investigated intensively in laboratory experiments (Bliven et al. 1997, Sobieski et al. 2009;Braun and Gade 2006;Liu et al. 2016;Braun, Gade, and Lange 2002).In particular, the scattering at rain-generated ring waves is well understood (see, e.g.Contreras and Plant 2006;Nie and Long 2007;Xu et al. 2015).On the other hand, scattering at splash products is less well understood and has been discussed in the literature controversially for a long, at least since the time, when the Seasat satellite was launched in 1978 (Fu and Holt 1982).The statement which Wetzel (1990) made in his paper on scattering at raindrop splash is still valid today: 'Yet, laboratory investigations of splash scattering have disclosed unexpected features in the scattering behavior that can be explained only by invoking more sophisticated, and as yet speculative, models of the scattering process'.On the other hand, volume scattering at hydrometeors in the atmosphere and attenuation of radar beams by rain have been studied intensively by radio-meteorologists and is also well understood.However, it is less well understood how much radar backscattering at hydrometeors in the ML contributes to the radar signatures of convective rain observed in SAR images of the ocean.
A long-lasting controversial issue is the question, 'what scattering mechanism causes areas of strongly enhanced radar backscatter often observed on spaceborne C-band SAR images acquired over the ocean in the presence of convective rain'?In the following, we shall call them 'bright blobs' or 'bright patches'.This issue got into the focus when it was realized that the bright blobs are not only visible on co-polarization C-band SAR images, but also in the corresponding cross-polarization C-band SAR images, e.g. on C-band SAR images from the Radarsat-2 satellite (Canada), the Sentinel-1a and − 1b satellites (Europe), and the I EOS-04 satellite (India).This observation prompted several authors to hypothesize that they are due to radar backscattering at hydrometeors in the M L (Alpers et al. 2021;Subrahmanyam et al. 2023;Zhao et al. 2021).This hypothesis got a boost from the observation that the linear depolarization ratio (LDR) measured in space-borne C-band SAR images is similar to the LDR measured by radio-meteorologists in radar backscatter experiments from the ML using multi-polarization ground-based radars.The LDR is defined as the ratio of the normalized radar cross section (NRCS) at cross-polarization (in the following termed VH NRCS or HV NRCS) to the one at co-polarization (in the following termed VV NRCS or HH NRCS).Although several observational facts seem to support the ML scattering hypothesis (see Section 5), there exists a strong argument against the hypothesis that ML scattering is the dominant scattering mechanism causing the bright blobs in C-band radar signatures of rain cells: It is the observation that 'foreshortening' of the ML signal is not observed on the SAR images of rain cells.Foreshortening means that, if the scatter element is located aloft in the atmosphere, it must appear on the SAR image displaced in anti-look direction of the SAR antenna by H cot θ, where H is the height of the ML and θ the incidence angle at which the SAR views the ocean surface (see Figure 2 in Section 4).This is because the radar beam reaches the scattering element in the atmosphere earlier than the one on the sea surface (see sketch in Section 4).The following observations have led us to the hypothesis that the dominating scattering mechanism giving rise to the bright areas in C-band SAR images of convective rain over the ocean is surface scattering at splash products: 1) Comparison of radar signatures of rain cells acquired quasi-concurrently by the SAR onboard the Sentinel-1 satellites and the Hong Kong (HK) weather radar, 2) comparison of multi-frequency, multi-polarization SAR images of rain cells acquired concurrently by the SARs flown on a space shuttle in 1994 during the Spaceborne Imaging Radar -C/X-band (SIR-C/X-SAR) mission (Jordon, Huneycutt, and Werner 1995), and 3) polarimetric decomposition analysis.
Although no model has been developed until now dealing with cross-polarization scattering at splash products, there exists experimental data that indicate that radar scattering at splash products can give rise to strong cross-polarization radar backscatter signals.These data come from radar backscatter measurements carried out at crosspolarization at the wind-wave tank of the University of Hamburg and from a tower located at the shore of the North Sea (Braun and Gade 2006;Braun, Gade, and Lange 2002).
The remaining of the paper is organized as follows: In Sections 2 and 3, we briefly describe the ML and splash scatter hypotheses, respectively.In Section 4, we present two Sentinel-1 SAR images, which show radar signatures of rain cells and rain bands containing bright blobs and bright patches.In Section 5, we present methods how to discriminate between ML and splash product scattering.In Section 6, we present data obtained in laboratory and in field experiments, which support of the splash scattering hypothesis.In Section 7, we discuss the results, and in Section 8 we present the conclusions.

The melting layer scattering hypothesis
The ML is a transition layer in the atmosphere, which is located between the layer containing frozen hydrometeors (above) and the one containing liquid hydrometeors (below).When the frozen ice particles fall through the ML, they change phase from solid to liquid.The hydrometeors in this transition layer consists of ice in the centre and of water in the outer region (Szyrmer and Zawadzki 1999) and have dielectric properties, which are distinctively different from the ones of frozen und liquid hydrometeors.A theory capable of modelling radar backscattering at hydrometeors in the ML has been developed by Holt (1984) andD'Amico et al. (1998).This theory is able to explain data collected in radar backscattering experiments carried out by (experimental) multi-frequency and multi-polarization ground-based radars.In particular, this theory is capable to explain 1) why radar backscattering from hydrometeors in the ML is much stronger at coand cross-polarization than from hydrometeors above and below this layer and 2) why the linear polarization ratio (LDR), which is defined as the ratio of the cross-polarization reflectivity to the co-polarization reflectivity, is strongly enhanced in the ML (up to 10 dB).
The observation that the radar signatures of convective rain in spaceborne C-band SAR images show similar properties as the ones obtained in ground-based radar backscattering measurement from the ML, has led Alpers et al. (2021), Zhao et al. (2021), andSubrahmanyam et al. (2023) to hypothesize that the 'bright blobs' have their origin in scattering at hydrometeors in the ML.In order to support this hypothesis, Alpers et al.As stated in the Introduction, it is a quite demanding task to detangle the contributions of scattering at hydrometeors in the ML and surface scattering to the Cband radar signatures of convective rain over the ocean.In order to tackle this problem, it should be helpful to study radar signatures of convective rain over land surfaces.However, most often, this is not possible, since the landscapes are usually very heterogeneous and it is difficult to separate radar signatures of rain from the background.Exception are tropical rain forests, like the Brazilian rain forest, where the background is quite homogeneous in pristine forest areas.Figure 1a  imaged by the X-band (9.56 GHz) SAR flown on the space shuttle Endeavor during the SIR-C/X-SAR mission in 1994 over the Brazilian rain forest.More X-band SAR images showing radar signatures of rain cells over tropical rain forests are presented in Danklmayer et al. (2009).Figure 1b shows a C-band, VV polarization, SAR mage of a rain cell over the Brazilian rain forest, which was acquired by the Advanced SAR (ASAR) onboard the European Envisat satellite (launched 2002) in the Image Mode (IM).In this mode, the spatial resolution is 30 m and the swath width is 100 km.On both SAR images, radar signatures of rain cells are visible, which consist of a bright patch and an adjacent dark patch stretching into the look direction of the SAR antenna.The bright patches are interpreted as originating from radar back scattering at hydrometeors in the ML and the dark patches as originating from attenuation of the radar beam when propagating through the rain column (see sketch in Section 4).While such features are often detectable on X-band SAR images acquired over tropical rain forests, they are very seldom detectable on C-band SAR images.One reason is that the C-band VV NRCS of the rain forest has values between − 6 and −7 dB (Doblas et al. 2020;Hashimoto, Tsuchiya, and Iijima 1997), which lies above the average VV NRCS of the M signal, which is typically −10 dB.A second reason is that the rain-induced shadow of the radar beam is much weaker for C-band SARs than for X-band SARs, because the attenuation coefficient due to rain is approximately by a factor 4 smaller for C-band than for Xband (see Table 2 in Melsheimer et al. (1998) and Figure 2 in Danklmayer et al. (2009)).However, very rarely (see Figure 1b), probably only when the background NRCS of the rain forest is low and the rain rate is very high, radar signatures of convective rain can also be detected on C-band SAR images of the rain forest (Alpers et al. 2016;Danklmayer et al. 2009).
The height H of the scatter element causing the radar signature (the ML) can be estimated from the length of the shadow.From SAR imaging geometry, which is sketched in (Figure 2a), we obtain the relationship: where D is the width of the rain column in range direction.Applying this formula to the rain cell marked by an arrow in (Figure 1a), and by using the values L = 9 km, θ = 58.3°and D = 0.5 km, we obtain H = 4.54 km, which is a typical ML height in tropical areas (Saha and Maitra 2022).
However, there exist also C-band and L-band SAR images acquired over the Brazilian rain forest showing bright patches at co-polarization with no adjacent dark areas (see Figure 3b in Alpers et al. 2016, and Section 4.2.3 in;CEOS 2018), which are not due to ML scattering.The bright patches in L-band images have been interpreted as being generated by double-bounce reflection from the smooth horizontal water surface in an inundated rain forest area and vertical stems of trees (CEOS 2018).
Thus, we occlude that rain cells over tropical rain forests leave fingerprints on X-and Cband SAR images, which have their origin in scattering at hydrometeors in the ML and in the two-way attenuation of the radar beam by the rain column.On these tropical rain forest images, the principal contributor to the radar signature of convective rain is attenuation of the radar beam by the rain column is and not scattering at the ML.Thus, we expect that the same holds for radar imaging of convective rain over the ocean and that the observed bright patches in C-band SAR images do not originate from scattering at hydrometeors in ML but from scattering at splash products at the sea surface.

The splash scattering hypothesis
When a rain drops impinge onto the sea surface, they first generate 'crowns' causing a depression of the sea surface from which ring waves and stalks evolve.The stalks carry a ball of water at the top, which, when squeezed off the stalks, can generate several droplets.In the case of medium to strong rain, a dense cloud of droplets is formed hovering over the sea surface where they contribute to the attenuation of the radar beam (Liu et al. 2017).While radar scattering at ring waves has been studied intensively in laboratory experiments and is well understood, this does not apply for scattering at splash products.Most authors hypothesize that the dominant scattering mechanism involving ) and the surface scattering signal ('surface scatt') on the SAR image.When the scattering is caused by scattering at the ML, then the rain signal (red triangle) appears displaced in anti-look direction of the SAR antenna by H cot θ, where H denotes the height of the ML and θ the antenna look direction.When the scattering is caused by surface scattering, then the rain signal (blue rectangle) is positioned at the footprint of the rain column.This signal can be positive or negative relative to the background (here we have depicted only a positive signal); (c) Attenuation of the radar signal by the rain column in range direction, which is large for X-band, but small for C-band; (d) Variation of the X-band co-polarization NRCS in range direction.
scattering from splash products is scattering at stalks (Wetzel 1990;Liu et al. 2017).However, also other scattering mechanisms have been proposed causing the generation of bright patches.Wijesekera and Gregg (1996) hypothesized that they are generated by volume scattering from low-salinity 'puddles', which rain drops generate in the upper water layer when splashing onto the sea surface.Braun (2003) hypothesized that they are generated by surface scattering at the rim of craters, which rain drops form immediately after impacting the water surface.The most recent model dealing with scattering from splash products is the one of Liu et al. (2017).In this model, radar backscatter is modelled as the coherent sum of scattering from a large number of water cylinders representing stalks, which have equal distances from the SAR antenna.The NRCS due to radar backscattering from the stalks is a function of L λ −1 sin θ, where Lis the distance between two neighbouring stalks, λ the wavelength at which the SAR operates, and θ the antenna look direction (incidence angle).In this model, it is assumed that the average distance L between stalks on the water surface is the same as the average distance between raindrops in the atmosphere and is a function of rain rate.Furthermore, also attenuation of the radar beam by rain drops in the atmosphere is included in this model, in particular the attenuation caused by secondary droplets generated by the impact of the primary rain drops onto the water surface.This modal yields the result that, for light to moderate rain, the co-polarization NRCS increases when the rain rate increases, but for heavy rain, it decreases when the rain rate increases.The authors have tested their model by comparing the radar signature of a rain band visible on a SAR image acquired over Northwest Pacific by the C-band SAR onboard the European Envisat satellite with the radar signature visible on a quasi-concurrently acquired weather radar image.They claim that there is good agreement between theory and observation (Liu, Zheng, Liu, Wang, et al. 2016).Although this model seems to be successful in explaining the bright patches often observed on co-polarized C-band SAR images, it cannot explain the observed large radar backscatter at cross-polarization.Such a theory would require a non-Bragg type scattering theory involving double-or multiple-bounce scattering, which is known to generate large cross-polarization backscatter (Ulaby, Moore, and Fung 1981).

Discrimination between ML and splash scattering
One way of discriminating between ML and splash scattering in SAR images of the ocean is by comparing the location of the bright patch on the SAR image with the location where the rain hits the sea surface.When the scattering is due to surface scattering, then the radar signature of the rain must be located at the position where the rain hits the sea surface.On the other hand, when the scattering is due scattering at a scatter element located aloft in the atmosphere, then the radar signature must appear on the SAR image displaced from this position.This effect is called 'foreshortening' by radar scientists and is a purely geometric effect due to the SAR imaging geometry as shown schematically in Figure 2. Foreshortening causes a shift the scatter element in anti-range direction (antilook direction of the SAR antenna) by d = H cot θ, where H is the height of the scatter element and θ the incidence angle of the radar beam.This is because the radar beam reaches scattering elements in the atmosphere earlier than the ones on the sea surface.
Usually, it is assumed that at C-band (but not at X-band) the attenuation of the radar beam by the rain column is very small and can be neglected.However, if this assumption were incorrect, then the bright patches in C-band SAR images should always be accompanied by dark areas (shadows) in antenna look direction.Although dark areas are sometimes visible adjacent to bright areas on C-band SAR images of convective rain over the ocean, they are not located persistently on the down-look side of the bright areas.When they are observed adjacent to bright patches, they are due to attenuation of the short gravity waves, which, according to Bragg scattering theory, are responsible for the radar backscattering (Valenzuela 1978).Turbulence generated in the upper water layer by the impacting rain drops damps the short gravity waves and thus reduces the N RCS.Applied to the ML imaged by the SAR onboard the Sentinel-1 satellites, which in the Interferometric Wide Swath (IM)) mode, operates at incidence angles between 9 • and 46°, we obtain, when assuming that the height of the ML is 4500 m, for the shift d in anti-range direction (foreshortening) the values 4.3 km ≤ d ≤8.1 km.When no foreshortening is observed in SAR images, then the backscattered signal cannot have its origin in a scatter element located above the sea surface but must have its origin in a scatter element located on the sea surface.We apply in the following three methods to determine whether the radar signature results from ML or surface scattering: 1) Comparison of the position of radar signature of a rain cell in a SAR image with the one in the quasi-concurrently acquired weather radar images; 2) Inter-comparison of radar signatures of rain cells visible on SAR images acquired concurrently at different frequencies and polarizations; 3) Polarimetric decomposition analysis.Concerning the first method, one has to be aware of the fact that there is usually a smalltime delay between the acquisition of both images, such that the rain cell could have moved during the two data acquisitions causing an error in the determination of position difference.However, the analysis of Zhao et al. (2021) has shown that in the comparison of Sentinel-1 SAR with quasi-concurrently acquired NEXRAD weather radar images, no systematic difference between the position of rain cells on SAR images and weather radar images is detectable, which contradicts the ML scattering hypothesis.
The second method relies on L-, C-and X-band SAR data acquired concurrently by a multi-frequency and multi-polarization SAR flown onboard a space shuttle during the SIR-C/X-SAR mission in 1994.Figure 3 shows an example of a rain cell imaged concurrently by SIR-C/X-SAR over the Gulf of Mexico.Note that at all polarizations, the L-band SAR images show dark patches at positions where all other SAR images show partly bright patches.The dark patches in the L-band images must have their origin in surface scattering, since it is well known that microwaves of wavelengths of the order of 20 cm, which is the wavelength at which L-band SARs operate, are very little scattered and attenuated by rain (Oguchi 1983;Ulaby, Moore, and Fung 1981).This has also been observed in many SIR-C/X-SAR images acquired over tropical rain forests, on which no rain L-band radar signatures are detectable (Danklmayer et al. 2009;Jameson et al. 1997).Over the ocean, on the other hand, the observed L-band radar signatures of rain cells can readily be explained by surface scattering.When rain drops splash onto the sea surface, they generate turbulence in the upper water layer, which dampens the short-scale sea surface waves, and thus, according to Bragg scattering theory (Valenzuela 1978), reduce the NRCS.Thus, rain-struck sea areas appear on L-band SAR images always as dark patches.(For a more detailed discussion on this issue, see Melsheimer et al. (1998) and Jameson et al. (1997).Because of the undisputable fact that the dark patches in the L-band SAR images have their origin in surface scattering, we use the L-band SAR images of rain cells as reference for determining the position of the radar signatures of rain cells in the corresponding C-and X-band SAR images.(Note that the X-band SAR of SIR-C/X-SAR operates only at VV polarization).
At the same position, where the L-and images show a dark patch, the C-band images show bright patches at all polarizations.They are particularly pronounced at crosspolarization.Note that there is a special feature visible in the X-band VV polarization image.It is an extended dark area behind the bright area in look direction of the SAR antenna.We interpret the dark area as caused by attenuation (shadowing) by the rain column, since attenuation is, at X-band, by a factor of 4 larger than at C-band (Oguchi 1983), see discussion in Section2.
Figure 4a shows a cluster of rain cells imaged concurrently by SIR-C/X-SAR at different frequencies and polarizations (LHH, LVH, CVV and CVH), and (Figure 4b) shows the variation of the NRCS along the transects inserted as black lines in (Figure 4a).They show that, at the position where the L-band HH NRCS and HV NRCS values are decreased, they are increased at C-band.Finally, we present in Figure 5 an L-band and a C-band SIR-C X-SAR SAR image acquired concurrently at VV polarization over the Gulf of Mexico at an incidence angle of 33.3°.With this incidence angle, the Bragg wavelength is 21.4 cm for Lband and 4.5 cm for C-band They show in detail that in the sea area where he L-band backscatter is reduced, it is increased at C-band.
An often-used method to determine the scattering mechanism causing an observed radar signature is polarimetric decomposition analysis (Cloude and Pottier 1996;Lee and Pottier 2009;Pottier 2014).Alpers et al. (2016) have applied this method to a Cband Radarsat-2 SAR image showing the radar signature of a rain cell off the coast of Florida, which includes bright patches in the co-and cross-polarization SAR images.They concluded from their polarimetric decomposition analysis that surface scattering, and not volume scattering, is the dominating scattering mechanism.In this case, surface scattering must include, next to Bragg scattering, also higher order scattering.Although they stated in their paper that 'the scattering mechanism causing the bright patches in C-band, co-polarized SAR images of rain cells could not be determined', we would, from the present perspective, interpret the result of this polarimetric decomposition analysis as support of the hypothesis that the bright patches are due to scattering at splash products.

Examples of SAR images showing bright blobs and bright patches
In this section, we present two Sentinel-1 SAR images together with auxiliary data, which show radar signatures of rain cells and a rain band in areas of the South China Sea, which are in reach of the HK weather radar.In both cases, the radar signatures contain areas of enhanced radar backscatter at VV and at VH polarization.They both allow interpretation in terms of the ML volume scattering hypothesis as well as in terms of splash scattering hypothesis.The Sentinel-1a SAR images were acquired in the Interferometric Wide Swath (IW) mode.In this acquisition mode, the spatial resolution is 5 m × 20 m, the swath width is 250 km and the incidence angle range is 29° -≤ θ-≤ 46°.In the IW mode, several combinations of polarizations are available.Here, we use only SAR images acquired concurrently at VV and VH polarizations.The weather radar images are from the two Sband weather radars (operating at 2.82 and 2.92 GHz) of the HKO located 600 m above sea level, which operate in tandem for real-time and uninterrupted monitoring of weather.

The 6 August 2020 event
Figure 6a shows a Sentinel-1a SAR image acquired at 10:25 UTC on 6 August 2020 over the South China Sea and (Figure 6b) shows the corresponding reflectivity image of the HK weather radar.In order to get an insight into the structure of the rain cells, we have plotted in Figure 6(c,d) the variation of the height profile of the reflectivity along the transects '1' and '2', respectively.The height profiles are derived from the HK weather radar data.The inserted solid red lines denote the height of the Freezing Level (FL) as measured by a radiosonde launched in HK at 12:00 UTC, and the dashed red lines denote the estimated height of the ML.
In tropical regions, the height of the ML is typically 600 to 800 m lower than the height of the FL (Saha and Maitra 2022).(On 17 August 2019, the height of the ML measured at HKwas700 m lower than the height of the FL, see Section 5.2).The observation that, in the first case, the radar signature of a rain cell is associated with bright blobs, and in the second case, it is not associated with bright blobs, can be explained by the ML volume scattering hypothesis as well as by the splash scattering hypothesis.The explanation by the splash scattering hypothesis as follows: In the first case, where bright blobs are present, the updraft wind was strong enough to lift moist air from the sea surface up to the FL.When the frozen hydrometeors fall through the ML, they give rise to strong radar backscatter.In the second case, where no bright bobs are present, the updraft is too weak to lift moist air up to the FL and thus, there are no hydrometeors that can fall through the ML and give rise to strong radar backscatter.The explanation by the splash scattering hypothesis is as follows: In the first case, where bright bobs are present, the rain rate at the sea surface is sufficiently large (45 dBZ, which scales to a rain rate of about 25 mm/h) such that a large number of splash products are generated, which give rise to strong radar backscatter and thus to the generation of bright blobs.In the second case, where no bright bobs are present, the rain rate at the sea surface is too low (20 dB which scales to a rain rate of about 1 mm/h) to cause strong splashing.In this case, radar backscattering is not dominated by scattering at splash products, but by Bragg scattering at rain generated ring waves.

The 17 August 2019 event
Figure 7a shows a section of the Sentinel-1a SAR image acquired at 10:33 UTC on 17 August 2019 and (Figure 7b) shows the quasi-concurrently acquired radar reflectivity image of the HK weather radar.They show in the lower section a broad cluster of rain cells (to the right) and a rain band.Both features are associated with strongly enhanced NRCS values relative to the surrounding areas.(Figure 7c) shows the variation of the VV NRCS and the VH NRCS along a transect through the bright area.The VV NRCS and VH NRCS curves show the typical characteristics of radar signatures of bright patches, where the shape of the VH NRCs curve matches well the one of the VV NRCS curve.Figure 7d shows the height profile of the radar reflectivity measured by the HK weather radar along the transect inserted in (Figure 7b).The inserted solid and dashed red lines denote the FL height (5201 m) and the ML height (4500 m), respectively.The FL height was measured by a radiosonde launched in HK at 12:00 UTC, and the ML height was retrieved from vertical VV and HH reflectivity data of the by the HK weather radar (for more details, see Alpers et al. 2016).The height profile of the radar reflectivity shows high reflectivity of about 50 dBZ at the height o the ML as well as on the sea surface.Thus, this height profile of the reflectivity is compatible with the ML scattering hypothesis as well as with the plash scattering hypothesis since 1) the density of hydrometeors (a proxy for reflectivity, which is about 50 dBZ) at the height of the ML is large enough to give rise to strong radar backscattering at co-as well as at cross-polarization and 2) the rain rate at the sea surface (48 mm/h corresponding to 50 dBZ) is large enough such that scattering at splash products dominates the scattering mechanism causing the generation of bright patches in co-and cross-polarization C-band SAR images of the ocean.

Laboratory and field measurements at cross-polarization
In the early 2000 years, multi-polarization radar backscattering measurements were carried out at X-band in the laboratory (at a wind wave tank) and at S-, C-and X-band from an elevated platform located at the shore of the North Sea by the University of Hamburg in the framework of a Ph.D. thesis (Braun, Gade, and Lange 2002).These measurements have shown that rain wof high rain rate splashing onto the water surface generates high co-and cross-polarized radar returns at C-and X-band.Figure 8 shows Doppler spectra of C-band cross-polarization radar returns, obtained from radar backscattering data.collected by a multi-frequency scatterometer mounted on a shore-based platform (Braun and Gade 2006).Figure 8a shows the Doppler spectrum in the case of no rain, and (Figure 8b) shows he Doppler spectrum in the case of heavy rain (35 mm/h).When integrating over the frequency, one obtains the result that the heavy rain has increased the NRCS by 8 dB (Braun 2003).This enhancement of the C-band HV NRCS lies in the range of the enhancement of the VH NRCS in bright patches observed in Sentinel-1 C-band SAR images.
The laboratory measurements were carried only at X-band.They show, for medium to high rain rates, similar results as C-band measurements in the field with respect to the increase of the NRCS at co-and cross polarization.As an example, we show in Figure 9 the X-band VV NRCS as function of wind speed for different rain rates.The plot shows, among others, that the HV NRCS increases by 7 to10 dB when, at windspeeds between 0 and 4 m/ s, rain with a rain rate of 50 mm/h splashes onto the water surface.Thus, these measurements provide evidence that rain with high rain rate s can generate high radar returns also at cross-polarization.

Discussion of results
The detection of rain on SAR images of the ocean from space-borne platforms is a challenging task, since the radar signatures of rain receive contributions from scattering at the sea surface and from volume scattering at hydrometeors in the atmosphere and from attenuation of the radar beam by the rain column, which are overlapping processes.In this paper, we have put the focus on radar imaging of convective rain by C-band SARs, like the ones flying on the Sentinel-1 (Europe), Radarsat-2 (Canada) and EOS-04 (India) satellites.While most of the scattering mechanisms contributing to the radar signatures of rain over the ocean are well understood, there has been one question unanswered since the time of the launch of the Seasat satellite in 1978: What is the scattering mechanism generating the often-observed areas of high reflectivity (bright blobs or bright patches) in SAR images of the ocean in the presence of convective rain?Recently, several authors (Alpers et al. 2021;Subrahmanyam et al. 2023;Zhao et al. 2021) have hypothesized that it is scattering at hydrometeors in the melting Radar doppler spectra at C-band, HV polarization, measured from a shore-based platform at an incidence angle of 35° when there was no rain (a) and when there was rain with a rain rate of 35 mm/h and a wind speed of 6.5 m/s).(b).The time difference between the data acquisition (without rain/with rain) was 34 min.When integrating over the frequency, one obtains the result that rain with high rain rate (35 mm/h) increases the HV NRCS by 8 dB (Braun 2003).Reproduced from Braun and Gade (2006).layer (ML).They were led to this hypothesis by the observation that the bright bobs and bright patches are not only visible in co-polarization C-band SAR images, but also in cross-polarization C-band SAR images of the ocean.Evidence was provided by comparing SAR data with weather radar data and with data from the Global Precipitation Measurement (GPM) mission.The radar signatures of these bright patches have similar properties as radar signatures of the ML measured by radio-meteorologists in ground-based radar backscatter experiments.In particular, the values of the linear depolarization ratio (LDR) are similar.However, there is one observational fact that does not comply with the ML hypothesis: It is the observation that the position of the ML radar signatures (bright blobs) as seen on the SAR image is not displaced from the position, where the rain column touches the sea surface.The displacement results from a purely geometric effect due to the radar imaging geometry, see Figure 2.However, this displacement is not detected in SAR images when comparing them with weather radar images or when inter-comparing SAR images acquired concurrently at different frequencies and polarizations.Although occasionally, displacements of the radar signatures are observed when comparing SAR and weather radar images, they are of random nature and are due to the fact that the data were not acquired exactly concurrently and that rain events are dynamical phenomena.However, no systematic displacements in anti-range direction of rain features visible on SAR images and on weather radar images has been detected (Zhao et al. 2021).Thus, these observations do not comply with the M scattering hypothesis, but they do comply with the surface scattering hypothesis.
The most convincing argument against the ML scattering hypothesis comes from the comparison of SAR images of rain cells acquired concurrently at multi frequency and multipolarization.Such images are available from the space shuttle SIR-C/X-SAR mission in 1994.In our analysis, we have taken the L-band radar signature as reference for the position where the rain hits the sea surface.The L-band radar signature of rain splashing onto she sea surface is characterized by a reduction of the NRCS relative to the surrounding rain-free area.This has been observed in a large number of SIR-C/X-SAR images (Jameson et al. 1997) and is also in X band 0 (dB) Wind speed (m/s) Figure 9. at X-band, HV polarization, measured in the laboratory at an incidence angle of 29° as function of wind speed and rain rate.It shows, among others, that the HV NRCS increases with rain rate, but is independent of wind speed at rain rates between 50 and 300 mm/h.Reproduced from Braun (2003).
accordance with scattering theory (Melsheimer, Alpers, and Gade 1998).In addition, it is well known that L-band electromagnetic waves (which, in the case of SIR-C/X-SAR, have a wavelength of 23.5 cm) are scattered and attenuated very little by rain in the atmosphere (Oguchi 1983).As noted by Olsen et al. (1978), even for rain rates as high as100 mm/h, the attenuation is less than 1 dB.Thus, from the theoretical point of view, it is impossible that the interaction of L-band radar waves with hydrometeors in the ML would generate patches of strongly reduced radar backscatter in L-band SAR images.The crucial observation is that, in the same area where the L-band SAR images show dark patches, the C-band images show bright patches at VV and VH polarizations, which we attribute to scattering at splash products.As shown in many analyses (see, e.g.Jameson et al. 1997;Melsheimer, Alpers, and Gade 1998), the L-band radar signatures of rain on the sea surface are always negative (reduced NRCS values).However, at C-band, the radar signatures can be positive or a negative depending, among other parameters, on rain rate and wind speed (Braun and Gade 2006).While surface scattering theories have been developed capable of explaining the frequently observed large C-band radar returns (bright patches) at co-polarization (Liu, Zheng, Liu, Sletten, et al. 2017), no theory exists until now to explain the associated strong radar backscattering observed at cross-polarization.However, radar backscattering measurements carried outrom a shorebased platform have shown that heavy rain (in this case 35 mm/h) can give rise to strong radar backscattering at cross-polarization.This shows that not only volume scattering at hydrometeors in the ML can generate large cross-polarization radar returns, but also scattering at splash products.Thus, surface scattering at splash products is a viable mechanism capable to explain the frequently observed bright patches in co-and cross-polarization Cband SAR images of the ocean in the presence of convective rain.
Another method to determine whether the observed radar signatures caused by volume or surface scattering is polarimetric decomposition analysis.Such analysis was carried out on a multi-polarization C-band Radarsat-2 SAR image showing the radar signature of a strain cell which includes bright patches in the co-and cross-polarization SAR images (Alpers et al. 2016), This analysis has led to the result that surface scattering is the dominating scattering mechanism, which includes Bragg scattering and higher order surface scattering.

Conclusions
In this paper, we have revisited radar signatures of convective rain over the ocean with the aim of determining which scattering mechanism causes the often-observed bright blobs or bright patches often observed on co-and cross-polarization C-band SAR images of the ocean when there are strong rain cells and rain bands present.We conclude that not volume scattering at hydrometeors in the ML generates these features, but surface scattering at splash products.In order to verify this hypothesis, we have analysed 1) Sentinel-1 SAR images acquired over the ocean together with quasi-concurrently acquired weather radar images and 2) multi-frequency/multi-polarization SAR images of rain cells acquired concurrently during the SIR-C/X-SAR mission.We argue, that, if the radar signature had its origin in scattering at a scatter element aloft in the atmosphere, then, according to SAR imaging geometry, it should be displaced on the SAR image from the position where the rain column hits the sea surface.This displacement can be determined 1) by comparing the position of the radar signature of a rain cell on the SAR image with the one on the weather radar image and 2) by comparing radar signatures of rain cells visible in SAR images acquired concurrently at different frequencies and polarizations as provided by the SIR-C/X-SAR mission in 1994.In the second case, the position of the L-band radar signatures of the rain cell serves as a reference because the observed L-band radar signature is unique (' dark') and can only be attributed to surface scattering.There is much experimental as well as theoretical evidence that the observed L-band radar signatures cannot be due to volume scattering or attenuation by hydrometeors in the ML.Since no displacements has been observed in the analysed C-band SAR images, we conclude the often-observed bright blobs or bright patches visible on C-band SAR images of convective rain over the ocean result from surface scattering at splash products.An additional support of the surface scattering hypothesis comes from a polarimetric decomposition analysis.However, at present, there exists no scattering model capable of explaining the observed high radar backscatter at co-polarization as well as at cross-polarization.One way of achieving large cross-polarization radar backscatter would be to include in the scattering model double-bouncing (first scattering at the sea surface and then at stalks or droplets).
(2021) compared radar signatures of convective rain visible on Sentinel-1 SAR images with weather radar data acquired quasi-concurrently by the Hong Kong Observatory (HKO), Zhao et al. (2021) compared them with weather radar data of the US NEXRAD network, and Subrahmanyam et al. (2023) compared radar signatures of a rain band visible on a SAR images of the Indian EOS-04 satellite with data of the Global Precipitation Mission (GPM) (Igarshi and Endo 2014).

Figure 1 .
Figure 1.(a) VV polarization X-band SAR image acquired over the Brazilian rain forest at VV polarization during the SIR-C/X-SAR mission at an incidence angle of 58° at 18:14 UTC on 12 April 1994, showing Para River to the right (large dark area) and several radar signatures of rain cells, one of which is marked by a black arrow.It consists of a small bright patch followed by a long dark area in SAR antenna look direction caused by shadowing (reproduced from Melsheimer et al. 2001); (b) VV polarization C-band SAR image acquired by the SAR flown onboard the Envisat satellite over the Brazilian rain forest on 24 April 2010 at 13:51 UTC.The inserted white arrows denote the antenna look direction (reproduced from Alpers et al. 2016).

Figure 2 .
Figure 2. (a) Sketch of the SAR imaging geometry of a rain cell.The long vertical rectangle denotes the rain column and the red rectangle the ML; (b) Positions of the ML signal ('M scatt ') and the surface scattering signal ('surface scatt') on the SAR image.When the scattering is caused by scattering at the ML, then the rain signal (red triangle) appears displaced in anti-look direction of the SAR antenna by H cot θ, where H denotes the height of the ML and θ the antenna look direction.When the scattering is caused by surface scattering, then the rain signal (blue rectangle) is positioned at the footprint of the rain column.This signal can be positive or negative relative to the background (here we have depicted only a positive signal); (c) Attenuation of the radar signal by the rain column in range direction, which is large for X-band, but small for C-band; (d) Variation of the X-band co-polarization NRCS in range direction.

Figure 3 .
Figure 3. L-, C-, and X-band SAR images of the same area over the gulf of mexico acquired concurrently at multi-frequency and multi-polarization during the SIR-C/X-SAR mission at 08:11 UTC.On 18 April 1994.They show a strong dependence of the radar signature of a rain cell on radar frequency and polarization.Reproduced from Melsheimer et al. (1998).

Figure 4 .Figure 5 .
Figure 4. (a) L-and C-band of the same area over the Gulf of Mexico acquired concurrently at multifrequency and multi-polarization during the SIR-C/X-SAR mission at 17:53 UTC on17 April 1994 showing a cluster of rain cells; (b) Variation of the L-and C-band HH NRCS and HV NRCS (termed here 'effective NRCS') along the transects inserted in the images in (a) as black lines.The solid line refers to L-band and the dotted line to C-band.Reproduced from Melsheimer et al. (1998).

Figure 6 .
Figure 6.(a) VV polarization SAR image acquired by Sentinel-1a at 10:25 UTC on 6 August 2020 over the South China Sea east of HK; (b) Radar reflectivity image acquired quasi-concurrently with the Sentinel-1a image by the HK weather radar at 110:06 UTC17 on 6 August 2020.The inserts '1' and '2' denote rain cells associated with bright blobs and not associated with bright blobs, respectively; (c) Height profile of the radar reflectivity along the transects through the rain cell '1'; (d) Same as (c), but along the transect through rain cell '2'.The inserted dashed black line in (c) and (d) denotes the height of the F L (5325 m), and the solid red line denotes the height of the ML (4600 m).

Figure 7 .
Figure 7. (a) Section of a VV polarization SAR image acquired by Sentinel-1a at 10:33 UTC on 17 August 2019 over the south china sea south of HK; (b) Corresponding section of radar reflectivity image from the HK weather radar acquired quasi-concurrently with theSentinel-1a image at 10:19 UTC; (c) Variation of the NRCS at VV and at VH polarization along the transects inserted in (a); (d) Height profile of the radar reflectivity along the transect inserted in (b) as inferred from data of the HK weather radar.The inserted dashed black line in (d) denotes the height of the F L (5201 m), and the solid red line denotes the height of the ML (4500 m).

Figure 8 .
Figure8.Radar doppler spectra at C-band, HV polarization, measured from a shore-based platform at an incidence angle of 35° when there was no rain (a) and when there was rain with a rain rate of 35 mm/h and a wind speed of 6.5 m/s).(b).The time difference between the data acquisition (without rain/with rain) was 34 min.When integrating over the frequency, one obtains the result that rain with high rain rate (35 mm/h) increases the HV NRCS by 8 dB(Braun 2003).Reproduced fromBraun and Gade (2006).