# Reduction of rain-induced errors for wind speed estimation on SAR observations using convolutional neural networks

Aurélien Colin, Pierre Tandeo, Charles Peureux, Romain Husson, Ronan Fablet

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## To cite this version:

Aurélien Colin, Pierre Tandeo, Charles Peureux, Romain Husson, Ronan Fablet. Reduction of rain-induced errors for wind speed estimation on SAR observations using convolutional neural networks. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2023, pp.1 - 13. 10.1109/jstars.2023.3291236. hal-04149533

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Submitted on 3 Jul 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# Reduction of rain-induced errors for wind speed estimation on SAR observations using convolutional neural networks

Aurélien Colin<fnref n="1" />,<fnref n="2" />, Pierre Tandeo<fnref n="1" />,<fnref n="3" />, Charles Peureux<fnref n="2" />, Romain Husson<fnref n="2" />, Ronan Fablet<fnref n="1" />,<fnref n="3" />,

**Abstract**—Synthetic Aperture Radar is known to be able to provide high-resolution estimates of surface wind speed. These estimates usually rely on a Geophysical Model Function (GMF) that has difficulties accounting for non-wind processes such as rain events. Convolutional neural network, on the other hand, have the capacity to use contextual information and have demonstrated their ability to delimit rainfall areas. By carefully building a large dataset of SAR observations from the Copernicus Sentinel-1 mission, collocated with both GMF and atmospheric model wind speeds as well as rainfall estimates, we were able to train a wind speed estimator with reduced errors under rain. Collocations with in-situ wind speed measurements from buoys show a root mean square error that is reduced by 27% (resp. 45%) under rainfall estimated at more than 1 mm/h (resp. 3 mm/h). These results demonstrate the capacity of deep learning models to correct rain-related errors in SAR products.

**Index Terms**—Synthetic Aperture Radar, Deep Learning, Oceanography, Wind.

## I. INTRODUCTION

SYNTHETIC Aperture Radar (SAR) is a powerful tool for studying the ocean surface. C-Band SAR are sensitive to variations in sea surface roughness, and have been used to detect various meteorological and ocean processes, referred to as metocean, such as atmospheric or ocean fronts [1], icebergs [2], oil surfactants from pollution [3] or generated by plankton [4], and some species of seaweed [5]. They are particularly useful for

studying waves [6] and extreme events like cyclones [7], [8]. There has been particular attention given to estimating wind speed using these sensors.

As the number of satellite missions with C-SAR sensors increases and archives of these data accumulate, it is becoming easier to build large SAR datasets. This paper focuses on the Sentinel-1 mission from the Copernicus program, which consists of two satellites, Sentinel-1A (launched in 2014) and Sentinel-1B (launched in 2016, which has been out of operation since December 2021). Sentinel-1C is planned to be launched in 2023. Ground Range Detected Higher Resolution Interferometric Wide-swath (GRDH IW) observations have a range of 250 km, an azimuth of about 200 km, and a resolution of 10 m/px. These observations are mainly routinely acquired over coastal areas. Systematic processes are used to produce geophysical products from these observations, including wind speed estimates. Several Geophysical Model Functions (GMFs) have been developed for this purpose, including CMOD3 [9], CMOD4 [10], CMOD5 [11], CMOD5.N [12], CMOD6 [13], CMOD7 [14] and C_SARMOD2 [15]. These GMFs use the vertical-vertical polarization, which is Sentinel-1's default co-polarization in coastal areas. However, the co-polarization channel saturates at high wind speed [16]. Therefore, the cross-polarization has also been used to estimate the wind speed [7]. In particular, H14E [17] was found to provide accurate wind speed measurements even in extreme events such as category 5 hurricanes [18]. The cross-polarization has the advantage of lower incidence and wind direction dependency [19]. GMFs have also been developed

<footnote n="1">¹ IMT Atlantique, Lab-STICC, UMR CNRS 6285, F-29238, France.</footnote>

<footnote n="2">² Collecte Localisation Satellites, Brest, France.</footnote>

<footnote n="3">³ Odyssey, Inria/IMT, France</footnote>
for horizontal-horizontal polarization [20]. Bayesian nonparametric wind speed estimation has also been proposed, offering the advantage of not relying on wind direction priors that are sensitive to meteorological processes with rapid temporal and spatial evolution [21].

However, these GMFs are sensitive to contami-
nation from non-wind processes. In particular, rain-
fall can either increase or decrease sea surface
roughness [22], making it difficult to correct for its
effects.

Deep learning models, particularly Convolutional
Neural Networks (CNNs), have demonstrated their
ability to detect rain signatures in SAR observations
[23]. These models are known to be able to tackle
denoising [24] and inpainting [25] tasks because
they use contextual information to estimate the
original signal. This paper is dedicated to estimating
wind speed in rainy areas using a model that does
not require an explicit rainfall prior and only uses
the parameters available to GMFs.

In the first section, we present the SAR data used
to train the model and the ancillary information
available. The second section describes the method-
ology used to build the dataset, with special atten-
tion given to ensuring a balanced representation of
rainfall observations. The final section presents the
results on the training set and confirms them with
in-situ measurements from buoys, demonstrating
the model's ability to correct for rain overestimates.

II. DATASET

The SAR measurements used in this chapter
come from 19,978 IW observations acquired glob-
ally between March 03rd, 2018 and the February
23rd, 2022, inclusive. Each of these observations
covers approximately 44 000 km² and has a reso-
lution of 100 m/px, downscaled from the GRDH
products available at 10 m/px. The radiometric
information used as input is the Sea Surface Rough-
ness (SSR) defined in [26] as the normalized radar
cross section σ₀ divided by the σ₀ of a wind of 10
m/s and a direction of 45° relative to the antenna
look angle. The σ₀ of this neutral wind is given by
the GMF CMOD5.N.

Obtaining global information on rain that can be
used in conjunction with SAR observations can be
difficult. A previous study conducted using a global
Sentinel-1 dataset found only 2,304 partial colloca-
tions with the satellite-based radar GPM/DPR [27]
out of 182,153 IW. "Partial collocations" refers to
instances where at least 20x20 km of a swath is
observed by the spaceborne weather radar 20 min-
utes before or after the SAR observation. Coastal
ground-based radars like NEXRAD [28] could pro-
vide rainfall estimates, but they are affected by
topography and may not capture all wind regimes.
Therefore, SAR-based rain estimation is preferred
to maximize the number of available observations
and simplify the collocation process. We used a
recent SAR rainfall estimator [23] that emulates
NEXRAD's reflectivity and proposes three rainfall
thresholds that roughly correspond to 1 mm/h, 3
mm/h, and 10 mm/h.

Ancillary information, such as incidence angle
and satellite heading, is retrieved from Sentinel-1
Level-2 products. It also includes collocations with
atmospheric models from the European Centre for
Medium-Range Weather Forecasts, which provide
modelled wind speed and direction, as well as the
surface wind speed computed by the GMF. The
atmospheric models have a spatial resolution of
0.25x0.25 degrees and a temporal resolution of 3
hours [29], while the GMF is computed at a spatial
resolution of 1 km/px and corresponds to the ob-
servation itself. The GMF used in Level-2 product
is IFR2 [30] until July 2019 and CMOD5.N [12]
afterwards. The ancillary information contained in
the Level-2 products is available at a spatial resolu-
tion of 1 km/px. However, it is interpolated to 100
m/px to match the grid of the radiometric channels.

III. METHODOLOGY

This section presents the methodology for build-
ing the rain-invariant wind speed estimator. We first
describe the deep learning architecture of the model,
then we discuss the creation of the dataset, which is
biased to have a large number of rain examples. The
final section describes the evaluation procedure.
A. Deep Learning Model

The architecture used in this chapter is the UNet
architecture [31] depicted in Fig. 1. UNet is an
autoencoder architecture with the advantage of be-
ing fully convolutional, meaning it has translation
equivariance properties (translations of the input
result in translations of the output). In addition,
skip connections between the encoder and the de-
coder facilitate training, especially by reducing the
vanishing gradient issue [32]). Introduced in 2015,
UNet has been used in various domains and has
demonstrated its importance for segmentation of
SAR observations [33], [23], [34].

The output of the model always contains a single
convolution kernel, activated by the ReLU function
to ensure that the prediction is in the interval [0,
+∞]. All convolution kernels in the hidden layers
are also activated by ReLU functions. The model is
set to take input of 256x256 pixels during training,
but since the weights only describe convolution ker-
nels, it is possible to use the model for inference on
images of any shape as long as the input resolution
remains at 100 m/px. Variants of the model are
trained with different numbers of input channels.
The architecture is modified by changing the size
of the first convolution kernel, which is defined as
a kernel of size (3, 3, c, 32), where c is the number
of input channels.

B. Dataset balancing procedure

In this section, we describe the process for
building a balanced dataset. Our goals are to (I)
ensure that the wind distribution of each dataset
is close to the real-world distribution, (II) prevent
information leak between the training, validation,
and test subsets, (III) ensure that the groundtruth
wind speed, obtained from an atmospheric model,
accurately represents the real-world wind speed,
and (IV) include enough rain samples to allow the
model to learn from them.

a) *Rain and rainless patches selection:* As discussed earlier, rainfall estimation is provided by a deep learning model at a resolution of 100 m/px, on the same grid as the SAR observation. Therefore, it is possible to separate the observations into two

<figure><img src="image_3.png" /><figcaption>**Fig. 1:** Architecture of the UNet model used for estimating the wind speed.</figcaption></figure>

areas, $\mathcal{A}^+$ and $\mathcal{A}^-$, based on the 3 mm/h threshold
from the rainfall estimation.

$$
\mathcal{A}^+ = \{x : \text{Rainfall}(x) \ge 3\,\text{mm/h}\} \quad (\text{Eq. 1})
$$

$$
\mathcal{A}^{-} = \{x : \text{Rainfall}(x) < 3\,\text{mm/h}\} \quad (\text{Eq. 2})
$$

However, most SAR observations do not con-
tain rain signatures. Collocations with GPM’s dual
polarization radar, a satellite-based weather radar,
indicated that the probability of rain rates higher
than 3 mm/h was 0.5%. Thus, by dividing the SAR
observations into tiles of 256 by 256 pixels, we
call ”rain patches” the tiles with more than 5% of
their surface predicted to have rain rates higher than
3 mm/h, and ”rainless patches” those without rain
signatures. We denote $n_+$ as the number of rain
patches and $n_-$ as the number of rainless patches.
To ensure that the model will learn regardless of
the rain-situation, we set $n_+ = n_-.$

Fig. 2 indicates collocations between the reanaly-
sis from ERA5 and the satellite-based weather radar
GPM/DPR. It shows the wind speed distribution
for rainfall higher than 3 mm/h (a), 30 mm/h (b),
and the overall distribution (orange curve). Stronger
rainfall is associated with a lower probability of
strong wind speeds. However, the impact is mostly
marginal at moderate rain rates.

<figure><img src="image_4.png" /><figcaption>**Fig. 2:** Distribution of ERA5 wind speed collocated with surface rain rate from GPM/DPR for rainfall higher than 3 mm/h (a) and 30 mm/h (b). They amount for 0.55% and 0.02% of the collocations, respectively. The orange curve in the figure shows the wind distribution regardless of the rainfall.</figcaption></figure>

b) Restriction to a priori Accurate Model Wind Speeds: Atmospheric models have been known to have coarse resolution (0.25x0.25 degrees spatially, 3 hours temporally) and to be unable to accurately depict fine-scale wind fields. However, they are computed globally and independently of the SAR observations. On the other hand, SAR-based wind fields from the GMFs are known to be accurate on rainless patches, but are diversely affected by rainfall. At low and moderate wind speeds, impinging droplets lead to an overestimation of the wind speed. Under high wind speed conditions, dominant attenuation results in an underestimation of the wind speed. Because of the difficulty of collocating a sufficient quantity of high wind speed and rainfall events, this study mainly aims to correct the wind speed overestimation. We

calculate Δ<sub>A−</sub> as the discrepancy between the GMF
and the atmospheric model on rain-free pixels.

$$
\Delta_{A-} = \mathrm{MSE}_{|A-}(\mathrm{Atm}, \mathrm{GMF}) \quad (\mathrm{Eq. } 3)
$$

In our experiments, the threshold was set at
Δ<sub>A−</sub> < 1 m/s. All patches containing a higher
discrepancy between the two wind speed sources
were discarded. By ensuring agreement between the
atmospheric model and the SAR-based GMF on
rainless patches, we assume that the atmospheric
model is close to the real wind speed and use it as
a target for optimizing the deep learning model.

c) Balancing to the real-world wind distribu-
tion: It should be noted that this condition ensures accurate modeled wind speeds and rain distribution, especially because the rainfall estimator is known to overestimate rainfall at high wind speeds.

We denote:

• P⁺ as the wind speed distribution on n⁺.

• P⁻ as the wind speed distribution on n⁻.

• P as the wind speed distribution on n⁻ ∪ n⁺.

Balancing the dataset to the real-world wind
distribution translates to the following condition:

$$
\forall x, P(x) = \frac{n_{+}P^{+}(x) + n_{-}P^{-}(x)}{n_{+} + n_{-}} \quad (\text{Eq. 4})
$$

As we choose to keep all rain patches and to set
$n_+ = n_-$, Eq. 4 leads to:

$$
\forall x, P^{-}(x) = \frac{1}{2}(P^{+}(x) - P(x)) \quad (\text{Eq. 5})
$$

For some wind speeds x, P⁺(x) is higher than
twice P(x). In these cases, we relax the condition
from Eq. 5 in order to avoid removing rain patches.
Fig. 3 depicts the wind speed distribution for rain
and rainless patches. The mean squared error be-
tween P and 1/2(P⁺ + P⁻) reach 8.8%.

The dataset can be further balanced to ensure
that, for each wind speed, the number of rain and
rainless patches is equal. However, this leads to
remove of 84% of the data. Appendix 1 compares
the performance of this second dataset. As did not
provide improvements, this dataset is left out of the
main document.
<figure><img src="image_5.png" /><figcaption>**Fig. 3:** Wind speed distributions for rain (blue) and rainless (red) patches. Orange curve correspond to the real world wind distribution.</figcaption></figure>

1) Training, Validation and Test Set Division:

After extracting the patches following the distri-
butions P+ and P-, they are split into training,
validation, and test sets. Each subset preserves the
same distributions. Furthermore, to avoid informa-
tion leakage, if a patch from one IW is in a subset,
every patch from the same IW belongs to the
same subset. The stochastic brute forcing method
described in Algorithm 1 draws random IWs and
computes the distribution of the validation and test
subsets, compares them to the overall distributions,
and returns the solution that minimizes the differ-
ence. In this algorithm, P̄e indicates the wind speed
distribution multiplied by the number of patches
in e and divided by the total number of patches.
It ensures that the validation and test subsets each
contain approximately 10% of all the patches.

The initial 19,978 IW observations account
for 105,164 rain patches and 2,094,370 rainless
patches. At the end of the process, the distribution
in the subsets is as follow:

* 168,349 patches from 14,169 IWs in the training set;

• 20,944 patches from 1,763 IWs in the test set;

* 21,010 patches from 1,763 IWs in the validation set.

Before training the model, we compute the mean
and standard deviation of each channel on the
training set and use them to normalize the in-
puts during training, validation, and inference. The

<figure><img src="image_6.png" /><figcaption>**Algorithm 1:** Stochastic brute forcing</figcaption></figure>

output, however, is not normalized. We train the
model for 100,000 weight updates (i.e. steps of the
stochastic gradient descent) to minimize the Mean
Square Error (MSE) between the prediction and the
wind speed from the atmospheric model, with a
batch size of 16 and a learning rate of 10⁻⁵ using
the Adam optimizer.

C. Evaluation procedure

To evaluate the impact of each input channel, we
train various variants of the model:

• I uses only the VV channel.

* II uses the VV channel, the incidence angle and the *a priori* wind direction.

* III uses both the VV and the VH channel, the incidence angle and the *a priori* wind direction.

* IV uses both the VV and the VH channel, the incidence angle, the *a priori* wind direction and the wind speed prior.

• V uses only the wind speed prior.
All channels are interpolated to 100 m/px and
concatenated on the same grid.

Incidence angles and wind directions from ECMWF atmospheric model are obtained from the Level-2 products and notably used for the computation of the GMF. Therefore, architecture II contains the same inputs as the GMF though interpolated at a finer resolution.

Each architecture is trained five times to reduce
the impact of random initialization on the evalua-
tion results. The results is presented as the mean
and standard deviation over these five independent
trainings.

We compare the results using the Root Mean
Square Error (RMSE) and the Pearson correlation
coefficient (PCC). The PCC is formulated in Eq. 6.

$$
PCC_{Y,\hat{Y}} = \frac{E[(Y - \mu_Y)(\hat{Y} - \mu_{\hat{Y}})]}{\sigma_Y \sigma_{\hat{Y}}} \quad (\text{Eq. 6})
$$

The results are computed against both the
groundtruths from the atmospheric model, which
provides a large test set, and against collocations
with buoys, which have good temporal resolution
and are in-situ measurements.

IV. RESULTS

A. Benchmarking experiments

The performance of the models compared to ECMWF are calculated on the test subset for each input variant and the baseline GMF. The results of this analysis can be found in Table I. It appears that the most important input is the GMF itself, as both IV and V have better results than the other variants. I, II and III are unable to achieve better results than the GMF, except under strong rainfall, even though II and III have access to all the channels used by the GMF.

Examples of rain-induced wind speed overesti-
mation are presented in Fig. 4. Fig. 4.a shows the
SSR on a logarithmic scale, with bright patterns
appearing in the observation and segmented as
rainfall in Fig. 4.c. These patterns correlate with
high wind speeds estimated by the GMF in Fig. 4.b.
The deep learning method in Fig. 4.d ignores this
spike in the SSR, but it also seems to underestimate

the wind speed in the bottom-left quarter of the
observation. Both of these behaviours are especially
visible in the transect shown in Fig. 4.f.

<figure><img src="image_7.png" /><figcaption>**Fig. 4:** Observation from the November 11th 2018 at 04:56:47. Sea Surface Roughness (SSR) of the VV channel in dB (a), geophysical model function estimated wind speed in m/s (b), deep learning estimated wind speed in m/s (d), prediction of the rainfall estimator (c) and transects of the green (e) and red (f) lines, with rainfall predicted higher than 10 mm/h indicated as grey areas.</figcaption></figure>
<table><caption>**Table I:** Comparison of the five variants of the model and the two datasets. RMSE and PCC are computed on the respective test set and for five training with random initialization. Results are given as mean and standard deviation in brackets. The best result for each metric is indicated by ★. Results better than the GMF are in bold.</caption><thead><tr><th rowspan="2">MODEL AND<br>CHANNELS</th><th rowspan="2">RAIN RATE</th><th colspan="2">RMSE</th><th colspan="2">PCC</th></tr><tr><th>Balanced<br>Dataset</th><th>Neutral<br>Dataset</th><th>Balanced<br>Dataset</th><th>Neutral<br>Dataset</th></tr></thead><tbody><tr><td rowspan="4">I<br>[VV]</td><td>[0, 1[mm/h</td><td>1.38 [0.016]</td><td><b>2.40 [0.019]</b></td><td>89.9% [0.19%]</td><td>74.2% [0.42%]</td></tr><tr><td>[1, 3[mm/h</td><td>1.64 [0.046]</td><td><b>2.78 [0.038]</b></td><td>92.7% [0.39%]</td><td>79.5% [0.58%]</td></tr><tr><td>[3, 10[mm/h</td><td>1.59 [0.038]</td><td><b>3.18 [0.070]</b></td><td><b>92.7% [0.38%]</b></td><td>78.9% [0.62%]</td></tr><tr><td>≥ 10mm/h</td><td><b>2.12 [0.052]</b></td><td><b>★3.27 [0.135]</b></td><td><b>81.7% [1.03%]</b></td><td>74.3% [0.90%]</td></tr><tr><td rowspan="4">II<br>[VV, INC, WDIR]</td><td>[0, 1[mm/h</td><td>0.87 [0.009]</td><td><b>2.26 [0.019]</b></td><td>96.2% [0.06%]</td><td>77.7% [0.24%]</td></tr><tr><td>[1, 3[mm/h</td><td>1.04 [0.086]</td><td><b>2.87 [0.061]</b></td><td>97.2% [0.47%]</td><td>77.6% [0.24%]</td></tr><tr><td>[3, 10[mm/h</td><td><b>1.19 [0.053]</b></td><td><b>3.39 [0.193]</b></td><td>96.2% [0.37%]</td><td>75.0% [3.04%]</td></tr><tr><td>≥ 10mm/h</td><td><b>2.27 [0.151]</b></td><td>3.86 [0.700]</td><td><b>81.7% [1.89%]</b></td><td>63.2% [9.19%]</td></tr><tr><td rowspan="4">III<br>[VV, VH,<br>INC, WDIR]</td><td>[0, 1[mm/h</td><td>0.83 [0.002]</td><td>2.18 [0.006]</td><td>96.5% [0.02%]</td><td>79.3% [0.07%]</td></tr><tr><td>[1, 3[mm/h</td><td>0.93 [0.020]</td><td><b>2.73 [0.022]</b></td><td>97.7% [0.07%]</td><td><b>80.1% [0.29%]</b></td></tr><tr><td>[3, 10[mm/h</td><td><b>1.09 [0.022]</b></td><td><b>3.25 [0.052]</b></td><td><b>96.7% [0.07%]</b></td><td>78.0% [0.44%]</td></tr><tr><td>≥ 10mm/h</td><td><b>2.13 [0.050]</b></td><td><b>3.68 [0.310]</b></td><td><b>83.9% [0.66%]</b></td><td>70.8% [2.95%]</td></tr><tr><td rowspan="4">IV<br>[VV, VH,<br>INC, WDIR, GMF]</td><td>[0, 1[mm/h</td><td><b>★0.64 [0.007]</b></td><td><b>★1.90 [0.028]</b></td><td><b>★97.9% [0.04%]</b></td><td><b>★85.0% [0.33%]</b></td></tr><tr><td>[1, 3[mm/h</td><td><b>★0.63 [0.015]</b></td><td><b>★2.29 [0.075]</b></td><td><b>★98.9% [0.03%]</b></td><td><b>★87.1% [0.56%]</b></td></tr><tr><td>[3, 10[mm/h</td><td><b>★0.78 [0.040]</b></td><td><b>★2.55 [0.132]</b></td><td><b>★98.4% [0.08%]</b></td><td><b>★87.1% [1.12%]</b></td></tr><tr><td>≥ 10mm/h</td><td><b>★1.63 [0.162]</b></td><td><b>3.37 [0.113]</b></td><td><b>★90.9% [1.17%]</b></td><td>73.4% [2.31%]</td></tr><tr><td rowspan="4">V<br>[GMF]</td><td>[0, 1[mm/h</td><td><b>0.67 [0.003]</b></td><td>3.16 [2.650]</td><td><b>97.7% [0.02%]</b></td><td>80.7% [17.55%]</td></tr><tr><td>[1, 3[mm/h</td><td><b>0.68 [0.005]</b></td><td>4.17 [3.582]</td><td><b>98.8% [0.01%]</b></td><td><b>82.5% [12.67%]</b></td></tr><tr><td>[3, 10[mm/h</td><td><b>0.88 [0.021]</b></td><td>4.53 [3.739]</td><td><b>98.0% [0.03%]</b></td><td><b>83.4% [8.19%]</b></td></tr><tr><td>≥ 10mm/h</td><td><b>1.94 [0.087]</b></td><td>4.79 [2.917]</td><td><b>87.9% [0.66%]</b></td><td>74.0% [8.19%]</td></tr><tr><td rowspan="4">GMF</td><td>[0, 1[mm/h</td><td>0.77</td><td>2.41</td><td>97.0%</td><td>81.2%</td></tr><tr><td>[1, 3[mm/h</td><td>0.84</td><td>3.16</td><td>98.1%</td><td>80.0%</td></tr><tr><td>[3, 10[mm/h</td><td>1.25</td><td>3.42</td><td>96.5%</td><td>81.9%</td></tr><tr><td>≥ 10mm/h</td><td>4.65</td><td>3.70</td><td>52.5%</td><td><b>★ 75.4%</b></td></tr></tbody></table>

## B. Application to SAR observation with groundtruthed in-situ data

However, ECMWF wind speeds are model data and not in-situ, which can be obtained using anemometers on buoys. Using the dataset created in [35], 4732 collocation points between Sentinel-1 and NDBC buoys are identified. The rain prediction model estimates that 4643 of these points are rainless, 75 record rainfall of more than 1 mm/h, and 14 record rainfall of more than 3 mm/h. On a side note, the height at which in-situ measurements were taken varies, with most being between 3.8 m and 4.1 m above sea level. As mentioned in [35], the SAR inversion and deep learning prediction are both normalized to the altitude of the corresponding in-situ measurement. Denoting $w$ the wind speed at 10 m estimated from the SAR, the wind speed at elevation $h$ is given by the exponential law [36]:

$$w_h = w \cdot \left( \frac{h}{10} \right)^{0.11} \quad (\text{Eq. 7})$$

Table II indicates that the performances of the deep learning are higher than the GMF for both the Root Mean Square Error and the Pearson Correlation Coefficient for all rain ranges. The RMSE decreases by 0.04, 0.37 and 1.33 m/s for rainless, light rain, and moderate rain-situations, respectively. The bias decreases by 0.26 and 1.01 m/s under light and moderate rain, but increases by 0.02 m/s for rainless situations. Table II also demonstrates the importance of the dataset building scheme as a dataset composed of collocations without the aforementioned sample selection, referred to as the "neutral dataset," consistently has lower performances than the balanced dataset.

Fig. 5 presents a comparison of the performances against NDBC buoys for various wind speeds. Unfortunately, collocations are scarce at very low and high wind speeds, which are the intervals where both the GMF and deep learning models have higher errors.
<table><caption>**Table II:** Bias, Root Mean Square Error, and Pearson Correlation Coefficient of model IV, the GMF, for each rainfall level. The best result for each metric and rainfall level is indicated by ★. Results better than the baseline are in bold. Results are given as mean and standard deviation in brackets.</caption><thead><tr><th></th><th></th><th>Balanced Dataset</th><th>Neutral Dataset</th><th>GMF</th></tr></thead><tbody><tr><td rowspan="3">Bias</td><td>&lt; 1mm/h</td><td>0.73 [0.04]</td><td>1.32 [0.04]</td><td>★ 0.71</td></tr><tr><td>[1, 3]mm/h</td><td>★1.38 [0.04]</td><td>1.47 [0.04]</td><td>1.64</td></tr><tr><td>&gt; 3mm/h</td><td>★0.92 [0.07]</td><td>1.96 [0.29]</td><td>2.38</td></tr><tr><td rowspan="3">RMSE</td><td>&lt; 1mm/h</td><td>★1.44 [0.03]</td><td>1.76 [0.12]</td><td>1.48</td></tr><tr><td>[1, 3]mm/h</td><td>★1.81 [0.04]</td><td>1.95 [0.18]</td><td>2.18</td></tr><tr><td>&gt; 3mm/h</td><td>★1.60 [0.10]</td><td>2.42 [0.21]</td><td>2.93</td></tr><tr><td rowspan="3">PCC</td><td>&lt; 1mm/h</td><td>★93.6% [0.16%]</td><td>92.9% [0.20%]</td><td>93.4%</td></tr><tr><td>[1, 3]mm/h</td><td>★96.3% [0.22%]</td><td>93.4% [0.19%]</td><td>95.3%</td></tr><tr><td>&gt; 3mm/h</td><td>★95.9% [0.35%]</td><td>93.4% [2.04%]</td><td>91.3%</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 5:** Evaluation of the Root Mean Square Error across the wind speed (a) and number of collocation with NDBC buoys in rainless areas (b).</figcaption></figure>

In the following, we observe two cases where rainfall was detected on the buoy position at the time of observation.

1) 2017-01-08 01:58:19 at NDBC 46054: The observation from 2017-01-08 01:58:19 covers the north of the Californian Channel Islands (Fig. 6.a). Several meteorological buoys are dispersed over the channel, including NDBC 46054 and NDBC 46053, which are indicated as red dots. The wind speed over the area is mostly around 6 m/s, but a squall line appears at the position of NDBC 46054 and spans over a dozen kilometers. A surge in the air column reflectivity is recorded by weather radar from the NEXRAD network. The ground station is located at 119 km. The GMF indicates very

<figure><img src="image_9.png" /><figcaption>**Fig. 6:** Sea surface roughness from the January 08th 2017 at 01:58:19 in VV channel (a), zoom on an area of 35x35 km centred on the buoy NDBC 45054 (b), NEXRAD base reflectivity acquired at 01:57:58 (c), wind speed given by the GMF (d) and by the deep learning model (e).</figcaption></figure>

high wind speeds, higher than 20 m/s (Fig. 6.d). The deep learning model attenuates these values to between 6 m/s and 8 m/s (Fig. 6.e).

For NDBC 46054, only one measurement of wind speed and direction per hour is available. It recorded a wind speed of 6.3 m/s eight minutes before the SAR observation. The GMF and the deep learning
model estimated wind speeds of 15.1 m/s and 5.9 m/s, respectively. While the temporal resolution of NDBC 46054 is one measurement per hour, NDBC 46053 records data every ten minutes. Furthermore, the gust front appears to be moving toward the right part of the observation. This can be seen in the time series in Fig. 6 as a large variation in wind direction between 02:40:00 and 03:00:00. The variation in wind speed seems to precede the variation in direction, first increasing then decreasing to a lower wind regime. On NDBC 46053, the GMF and the deep learning model agree on a wind speed of 4.5 m/s, which is slightly lower than the in-situ data of 5.4 m/s. Since the distance between NDBC 46054 and NDBC 46053 is approximately 60 km, the progression of the gust front can be estimated to be around 90 km/h. With a width of around 5 or 6 km, the whole system would pass the buoys in three minutes. This means that even NDBC 46053 may not have been able to accurately estimate the wind speed due to its low temporal resolution. However, it is worth noting that even the gust speed at NDBC 46054, defined as the maximum wind speed over a given number of seconds, does not record a speed higher than 9 m/s.

2) SAR-20191006T232853 NDBC-41009:

The observation from 2019-10-06 23:28:53 was recorded on the east coast of Florida. While most of the swath covers the marshes around Orlando and Cap Canaveral rather than the ocean, convective precipitation can be observed in the right part of the image (Fig. 8.a). The cells are moving downward (north-north-east), as indicated by the stronger gradient of the convective front. Since the wind from the convection is opposing the underlying wind regime, an area of lower wind speed appears as an area of lower backscatter. Rainfall was detected by a weather radar from the NEXRAD network located at 64 km (Fig. 8.c). The GMF is impacted by these rain signatures and estimates a very high local wind speed (Fig. 8.d). The deep learning model is less affected by the rain signatures, but also appears to blur the low wind speed area (Fig. 8.e).

The time serie from NDBC 41009 in Fig. 9
indicates that the lower backscattering was indeed

<figure><img src="image_10.png" /><figcaption>**Fig. 7:** Time series of the NDBC buoy wind mea-
surements around January 08th 2017 01:58:19 for
NDBC 46054 (a) and NDBC 46053 (b), and the
estimation from the GMF, the deep learning model
and the atmospheric model.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 8:** Sea surface roughness from October 06th 2019 at 23:28:53 in VV channel in dB (a), zoom on an area of 35x35 km around the buoy NDBC 41009 (b), NEXRAD observation acquired at 23:27:33 (c), wind speed given by the GMF (d) and by the deep learning model (e).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9:** Time series of the NDBC buoy wind measurements around October 06th 2019 at 23:28:53 for NDBC 41009, and the estimation from the GMF, the deep learning model and the atmospherical model.</figcaption></figure>

caused by a drop in wind speed rather than a change
in direction, as the latter does not significantly
change during the passage of the convective cell
(possibly because the underlying wind regime is
strong). It does record a sudden drop in wind speed
to 7.5 m/s one minute after the SAR observa-
tion, while the GMF and the deep learning model
estimated wind speeds of 13.7 m/s and 8.9 m/s,
respectively.

V. CONCLUSION

Previous studies have shown that high-resolution
rain signatures can be automatically extracted from
SAR observations. Using this SAR rainfall seg-
menter, we built a wind estimation dataset where
50% of the patches contain rainfall examples. Sam-
ples were chosen so that a SAR-based and a SAR-
independent wind speed model agree on non-rain
pixels, ensuring that their estimates are close to the
true wind speed. A UNet architecture was trained on this dataset to estimate wind speeds based on the SAR-independent atmospheric model. We tested several input combinations and found that the most important parameter was the wind speed prior from the geophysical model function, which the deep learning model had difficulty emulating.

Collocations with buoy in-situ measurements show that the model outperforms the current Geophysical Model Function (GMF) on rain areas, reducing the RootMean Square Error (RMSE) by 27% (resp. 45%) for rain rates higher than 1 mm/h (resp. 3 mm/h). On rainless areas, performances are similar with a small reduction of the RMSE by 2.7%. However, since the buoys have a time resolution of ten minutes, some quick sub-mesoscale processes, such as gust fronts, are difficult to register. The limited spatial range of the buoys also makes it challenging to observe rare phenomena. Future work should address these concerns.

APPENDIX

A secondary dataset was created differing with
the main dataset by Eq. 4. Here, the balancing
policy is defined as:

$$
\forall x, P(x) = P^{+}(x) = P^{-}(x) \quad (\text{Eq. 8})
$$

The distributions $P^+$ and $P^-$ are presented in Fig. 10. The balancing is performed for every wind speed, which lead to remove 84% of the rain patches -especially at 5 and 10 m/s- since the number of rain patches at 8 m/s is limited.

Models were optimized under the same training
process as in subsection III-B1, in particular with
the same number of weight updates. Comparison
with the first balancing scheme display lower per-
formances despite the more accurate balancing, as
indicated Table III.

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    </tr>
  </tbody>
</table>

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**Aurélien COLIN** After graduating from the IMT Atlantique as an engineer, he began a Ph.D and is currently studying the segmentation of various meteorological and ocean phenomena on Synthetic Aperture Radar using deep learning models.

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

**Pierre TANDEO** was born in France in 1983. He received the M.S. degree in applied statistics from Agrocampus Ouest, Rennes, France, and the Ph.D. degree from the Oceanography from Space Laboratory at IFREMER, Brest, France, in 2010. Then, he spent two years as a Postdoctoral Researcher with the Atmospheric Science Research Group, University of Corrientes, Argentina, and three years at Télécom Bretagne, Brest, France. Since 2015, he is an associate professor at IMT Atlantique, Brest, France, and a researcher at Lab-STICC, CNRS, France. Since 2019, he is an associate researcher at the Data Assimilation Research Team, RIKEN Center for Computational Science, Kobe, Japan. His main research interests are focused on IA, data assimilation, and inverse problems for geophysics.

<figure><img src="image_16.png" /></figure>

**Charles PEUREUX** is a research engineer at CLS since 2020 where he is mainly involved with SAR oceanography. He previously worked at IFREMER where he defended his thesis on the observation and modelling of the directional properties o short gravity waves. Thereafter, he worked on the SKIM satellite mission, especially for the production of high resolution sea state numeral simulations.

<figure><img src="image_17.png" /></figure>

**Romain HUSSON** is a scientist and project engineer at CLS, in the Environmental Monitoring and Climate Business Unit. After working as intern at NASA JPL and as YGT at ESRIN on SAR wind-wave-current activities, he completed in 2012 his PhD in Physical Oceanography at CLS Brest developing methods to estimate synthetic swell field from SAR wave mode observations. Since then, he has been involved

in several applicative and R&D projects such as wind/wave products for marine renewable energy and contributed to several ESA and European projects such as Cal/Val activities for ENVISAT and S-1 mission performance center as Level-2 expert.

<figure><img src="image_18.png" /></figure>

**Ronan FABLET** is a Professor at IMT Atlantique and a research scientist at Lab-STICC in the field of Data Science and Computational Imaging. He is quite involved in interdisciplinary research at the interface between data science and ocean science, especially space oceanography and marine ecology. His current research interests include deep learning for dynamical systems and applications to the under-

standing, analysis, simulation and reconstruction of ocean dynamics, especially using satellite ocean remote sensing data.