WindRAD Scatterometer Quality Control in Rain

Abstract

Rain backscatter corrupts Ku-band scatterometer wind retrieval by mixing with the signatures of the ${\sigma }^{\circ }$ (backscatter measurements) on the sea surface. The measurements are sensitive to rain clouds due to the short wavelength, and the rain-contaminated measurements in a wind vector cell (WVC) deviate from the simulated measurements using the wind geophysical model function (GMF). Therefore, quality control (QC) is essential to guarantee the retrieved winds’ quality and consistency. The normalized maximum likelihood estimator (MLE) residual ($R_n$) is a QC indicator representing the distance between the ${\sigma }^{\circ }$ measurements and the wind GMF; it works locally for one WVC. $J_{OSS}$ is another QC indicator. It is the speed component of the observation cost function, which is sensitive to spatial inconsistencies in the wind field. $R_{n}J$ is a combined indicator, and it takes both local information ($R_n$) and spatial consistency ($J_{OSS}$) into account. This paper focuses on the QC for WindRAD, a dual-frequency (C and Ku band) rotating-fan-beam scatterometer. The $R_n$ and $R_{n}J$ have been established and thoroughly investigated for Ku-band-only and combined C–Ku wind retrieval. An additional 0.4% of WVCs are rejected with $R_{n}J$, as compared to $R_n$ for both Ku-band-only and combined C–Ku wind retrievals. The number of accepted WVCs with high rain rates (>7 mm/h) is reduced by half, and the wind verification with respect to ECMWF winds is generally improved. The C-band measurements are little influenced by rain, so the Ku-based $R_n$ is more effective for the combined C–Ku wind retrieval than the total $R_n$ from both the C and Ku bands. The rejection rate of the combined C–Ku retrievals reduces by about half compared to the Ku-band-only retrieval, with similar wind verification statistics. Therefore, adding the C band into the retrieval suppresses the rain effect, and acceptable QC capabilities can be achieved with fewer rejected winds.

1. Introduction

The satellite Fengyun-3E (FY-3E) is part of the Chinese FY-3 meteorological satellite series and was launched on 5 July 2021. It carries the Wind Radar (WindRAD) rotating-fan-beam scatterometer, the first dual-frequency (C and Ku band) scatterometer. The number of normalized radar cross-section values (the backscattered power from the wind-roughed sea surface, called ${\sigma }^{\circ }\mathrm{s})$ increases significantly as compared to the rotating-pencil-beam (e.g., Haiyang (HY)-2B/C/D [1]) and the fixed-fan-beam (e.g., Advanced Scatterometer (ASCAT)-B/C on Metop [2]) instruments, due to the dual-frequency rotating-fan-beam design. The characteristics of the geometries and the ${\sigma }^{\circ }$ measurements have been discussed in [3], and an improved calibration method designed for WindRAD was introduced in [4]. This paper focuses on the quality control (QC) for rain contamination in Ku-band-involved wind retrievals.

WindRAD level-1 data are organized in wind vector cells (WVCs), a sub-track coordinate system with axes oriented along and across the swath. The scatterometer retrieves wind in each WVC from ${\sigma }^{\circ }\mathrm{s}.$ The ${\sigma }^{\circ }\mathrm{s},$ associated with their respective geometries (azimuth angle, incidence angle, frequency, and polarization), are inverted through a geophysical model function (GMF) with the maximal likelihood estimation (MLE) method to derive the winds [5,6,7,8,9].

Scatterometer winds are operationally used for nowcasting, assimilated into numerical weather prediction (NWP) models, and they are used in many oceanographic and climate studies [10,11,12,13,14]. Therefore, QC is essential to guarantee the quality and consistency of the retrieved winds in these applications. Raindrops are relatively small compared to the radar wavelength, which can cause Rayleigh volume scattering in the atmosphere. The Rayleigh scattering effect is inversely proportional to the fourth power of the wavelength. Larger raindrops and smaller wavelengths lead to more intense Rayleigh scattering. Therefore, Ku-band observations are much more sensitive and are about 40 times more affected by rain than C-band observations; consequently, the number of Ku-band winds flagged by the QC is about ten times as high as for the C band [15,16,17,18]. Another study has shown that, in contrast to the Ku band, the C band is much less affected by direct rain effects, while both are affected by enhanced wind variability [19]. C-band scatterometer products, e.g., from ASCAT, can achieve good wind quality, with a QC rejection rate of less than 0.4% [20,21], and the accepted C-band winds are unaffected by rain [22,23]. Therefore, C-band scatterometers are a qualified reference for the verification of rain contamination for Ku-band scatterometers [17,18]. Under rainy conditions, the Ku-band backscatter signal ${\sigma }^{\circ }$ is generally enhanced, and the rain enhancement effect disturbs Ku-band wind retrievals [24,25,26]. The rain-induced backscatter is generally larger than the wind-induced backscatter, which leads to positively biased retrieved winds up to wind speeds of 15 m/s. More generally, rain cloud backscatter is isotropic, and moderate and heavy rain result in poor wind vector retrieval performance; therefore, WVCs with rain must be identified and flagged.

Several rain QC methods have been developed for Ku-band scatterometers. A rain GMF was introduced in [18] based on Bayesian retrieval and utilizing the Ku-band sensitivity at HH and VV polarization to the rain (rain GMF). The normalized MLE residual ($R_n$) is the most commonly used QC indicator, which has been implemented for all pencil-beam scatterometers and the CFOSAT rotating fan-beam scatterometer [16,27,28,29]. Rain backscatter is isotropic and causes a deviation between the measured ${\sigma }^{\circ }\mathrm{s}$ and the simulated ${\sigma }^{\circ }\mathrm{s}$ (using the wind GMF). $R_n$ represents the distance between the measured ${\sigma }^{\circ }\mathrm{s}$ and the simulated ${\sigma }^{\circ }\mathrm{s}$. It is calculated per WVC. As such, it locally checks the consistency of all backscatter measurements with the wind GMF. Thus, under rainy conditions, the $R_n$ is much larger than it is under dry weather (wind) conditions. An $R_n$ threshold value is established to distinguish the rainy WVCs. In previous studies, especially for pencil-beam scatterometers, the rejection rate with the $R_n$ indicator tended to be large (with respect to the global rain occurrence), which implies that, even though it reduces the possibility of rainy WVCs in the accepted winds, there are too many good winds rejected. Obviously, we would prefer to lower the false alarm rate with a less tight QC threshold. At the same time, it is important to find a complementary QC indicator to flag the rainy WVCs that are missed by a more tolerant QC threshold. Such an indicator is $J_{OSS}$, which uses the speed component of the observation cost function in the 2D variational ambiguity removal (2DVAR) step to reject additional WVCs [17,30]. $J_{OSS}$ is sensitive to the spatial consistency in the wind field and depending on the neighboring WVCs. As moderate and heavy rain tends to be local and spatially variable, retrieved local speed heterogeneities are an effective indicator of rain. As $J_{OSS}$ is complementary to $R_n$, which works locally in one WVC, it is useful to combine $J_{OSS}$ and Rn to take both local WVC information and spatial consistency into account. Therefore, this article proposes a combined QC method with Rn and $J_{OSS}$, called $R_{n}J$, for Ku-band-only and C–Ku wind retrieval.

Section 2 describes the used datasets and briefly summarizes the $R_n$ and $J_{OSS}$ QC algorithms and their adaptation for WindRAD data. The Ku-band-only and combined C–Ku wind retrieval with $R_n$ and $R_{n}J$ QC methods are analyzed and discussed in Section 3 and Section 4. This is the first time that the QC for combined C–Ku wind retrieval has been investigated. The C band is insensitive to rain and, therefore, by adding the C band in wind retrieval, improved-quality wind vectors emerge. The resulting simulated Ku-band backscatter values improve the rain discrimination in the Ku-band $R_n$. Since the C-band residuals in $R_n$ are affected by wind variability and noise effects, the contribution of the Ku band in $R_n$ is more discriminating for QC than the total $R_n$ of both the C and Ku bands. Thus, the Ku-based $R_n$ is proposed as a quality indicator. It is discussed in Section 4. The conclusions are given in Section 5.

2. Data and QC Algorithms

2.1. WindRAD Data

The operational WindRAD data version was updated in May 2023. The level-1 data status can be requested through the China Meteorological Administration (CMA) data distribution platform (http://data.cma.cn/en (accessed on 10 December 2024)). Level-1 data are organized in WVCs with a size of 20 km × 20 km or 10 km × 10 km. Each WVC contains ${\sigma }^{\circ }\mathrm{s}$ in the C band at 5.40 GHz and in the Ku band at 13.256 GHz with horizontal (HH) and vertical (VV) polarizations. The incidence angles range between 33.0^∘ and 44.0^∘ for the C band and between 36.5^∘ and 44.0^∘ for the Ku band. The characteristics of the WindRAD data have been described in [3].

In this article, we use the 20 km level-2 updated operational version Binary Universal Form of Representation (BUFR) meteorological data products, which consist of internal Ocean and Sea Ice Satellite Application Facility (OSI SAF) data produced at the Royal Netherlands Meteorological Institute (KNMI). The data set runs from August to October 2023 (ascending orbits) for the QC algorithm’s adaption, and we use longer-term data from August 2023 to March 2024 (ascending orbits) for the algorithm’s validation. For descending orbits, the parameters of the QC algorithms investigated in this paper are adjusted, while the methodology is general and applicable along the whole orbit. The QC results show the same effectiveness in ascending and descending orbits; thus, the descending orbits are not shown here. The level-2 products are retrieved with the CMOD7 GMF for the C band and NSCAT-4DS GMF for the Ku band (the sea surface temperature (SST) effect is eliminated). The ${\sigma }^{\circ }\mathrm{s}$ are calibrated with higher-order calibration (HOC) and NWP ocean calibration as a function of the incidence angle and relative antenna angle (NOCant) [4]. NWP ocean calibration (NOC) is a well elaborated and widely used calibration method that assesses the mean difference between the measured ${\sigma }^{\circ }\mathrm{s}$ and the simulated ${\sigma }^{\circ }\mathrm{s}$ from collocated model winds and the corresponding GMF [27]. HOC calibration uses a cumulative distribution function (CDF) matching technique to calculate the ${\sigma }^{\circ }$-dependent calibration. The CDF of the measured ${\sigma }^{\circ }$ is matched to the simulated ${\sigma }^{\circ }$ CDF per incidence angle; this removes non-linearity for each incidence angle. However, it is not constructed to remove the anomalous harmonic azimuth dependencies caused by the antenna rotation. These azimuth dependencies are reduced by NOCant.

2.2. 3IMERG Precipitation Product

The level-3 Integrated Multi-Satellite Retrievals for GPM (3IMERG) precipitation product utilizes information from the Global Precipitation Measurement (GPM) satellite constellation to estimate precipitation over the majority of the Earth’s surface. It is from the National Aeronautics and Space Administration (NASA). The algorithm of 3IMERG products intercalibrates, merges, and interpolates multiple satellite microwave precipitation estimates, as well as microwave-calibrated infrared satellite estimates and precipitation gauge analyses. The system first gives a quick estimate, called the IMERG Early Run, and later provides a better estimate when more data are included (IMERG Late Run). In the end, roughly 3.5 months after the acquisition time, a research-level product including monthly gauge data is provided, called the IMERG Final Run. In this article, the IMERG Final Run V07 product is used [31]. The instantaneous microwave-only precipitation estimate is applied for better consistency with the scatterometer wind products. The chosen precipitation product is called GPM data hereafter.

The GPM product has a spatial resolution of 0.1^∘ and a time resolution of 30 min, covering the latitude range of −60^∘ to 60^∘. Thus, the rain grid is smaller than a WVC (20 km). All the rain grid points overlapping a WVC are taken into account with weighted averaging. The time difference between the GPM data and the scatterometer data is limited to less than 15 min.

2.3. NWP Wind

NWP winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) operational forecast model are used. Hourly forecasts with time steps of +3 h, +4 h, …, and +21 h are available. The model winds have been interpolated in space and time to the WVCs. The equivalent neutral 10 m winds have been converted to stress-equivalent 10 m winds, correcting for the effect of the air mass density [32]. Model winds are available at every scatterometer WVC, and their spatial representativeness and high quality have been investigated in detail in [33], with a careful error assessment of scatterometer winds, in situ winds, and ECMWF model stress-equivalent winds.

2.4. $R_n$ QC Algorithm

The QC indicator $R_n$, or normalized MLE residual, has been widely used for Ku-band scatterometers, as described in Section 1. The MLE is defined for each WVC as [5,6,7,8,9].

$${\displaystyle MLE=\frac{1}{N}\sum _{i=1}^N{(\frac{{\sigma }_{mi}^{\circ }-{\sigma }_{si}^{\circ }}{K_p\left({\sigma }_{mi}^{\circ }\right)})}^2,}$$

(1)

where N is the number of views in a WVC, ${\sigma }_{mi}^{\circ }$ is the backscatter measurement, ${\sigma }_{si}^{\circ }$ is the simulated backscatter through the GMF, and $K_p\left({\sigma }_{mi}^{\circ }\right)$ is the measurement error variance. The geometries (azimuth angle, incidence angle, polarization) of the measured backscatter and the model wind speed and direction are taken as inputs for the GMF, and the output of the GMF is the corresponding simulated backscatter [34]. The MLE is defined as the distance between a set of measured ${\sigma }^{\circ }\mathrm{s}$ and simulated ${\sigma }^{\circ }\mathrm{s}$ that lie on the wind GMF manifold in an N-dimensional space. The normalized MLE residual is defined as $R_n=MLE/\langle MLE\rangle$. $\langle MLE\rangle$ is the expected MLE in a particular WVC across the swath and for a specific wind speed. Thus, $R_n$ is a function of the WVC number and wind speed [16].

The algorithm needs to be adapted for WindRAD data. Firstly, the number of views for a pencil-beam scatterometer is always four for all WVCs across the swath; however, this number varies for the WindRAD rotating-fan-beam scatterometer [3]. Therefore, before calculating $\langle MLE\rangle$, the MLE must be normalized by the number of views in a particular WVC. Secondly, the shape of the threshold is set differently. In [16], the $R_n$ threshold is defined by following the contour line of the $R_n$ as a function of the wind speed. It is defined as a parabolic line for lower wind speeds, combined with a straight line for wind speeds above 15 m/s. However, the WindRAD contour lines of the $R_n$ are different, mainly because the number of views for a WVC is much more than four. Figure 1 is an example of the $R_n$ contour plot (Ku band). The contour lines are more similar to a Gaussian distribution than a parabolic distribution. Thus, a polynomial fit is applied to define the threshold. We still define the threshold as a constant value at wind speeds above 15 m/s, because, otherwise, more and more data are rejected with increasing wind speeds until all high winds are rejected. The threshold at a wind speed lower than 5 m/s is also set to a straight line, since rain generally does not result in low wind speed retrievals. WVCs with $R_n$ higher than the threshold are considered contaminated with rain and flagged. In Section 3.1 and Section 4.1, we give the evaluation of the threshold experiments for the Ku-band and C–Ku bands.

2.5. $J_{OSS}$ QC Algorithm and Its Adaption to $R_{n}J$

Xu and Stoffelen [17] proposed $J_{OSS}$ as a QC indicator in addition to $R_n$ for pencil-beam scatterometers. This method has also shown its capability for the rotating fan-beam scatterometer CFOSAT [30]. In the wind retrieval ambiguity removal (2DVAR) step, a wind field is constructed from the scatterometer wind ambiguities and the NWP winds by minimizing a cost function with constraints on meteorological consistency, which is called the analysis wind field [35]. $J_{OSS}$ is defined as

$$J_{OSS}=f-f_S,$$

(2)

where f is the analysis wind speed derived in 2DVAR, and $f_S$ is the selected retrieved wind speed. In a previous study [17], the $R_n$ QC for the pencil-beam scatterometer appeared to be too conservative, with a high rejection rate (5–6%), and $J_{OSS}$ was used to accept extra WVCs that were rejected by $R_n$. $J_{OSS}$ is an excellent complementary indicator. For WindRAD, a relaxed $R_n$ threshold will be set first. Then, $J_{OSS}$ is used to flag additional rainy WVCs, which are not flagged by $R_n$. In this way, the local information ($R_n$) and spatial consistency ($J_{OSS}$) are both taken into account. The WVCs with $J_{OSS}$ values lower than a certain threshold are considered rain-contaminated. The threshold value was modeled by three straight lines as a function of the wind speed (v) [36], as shown in Equation (3), which also performs well on WindRAD data (see Section 3.2):

$$\begin{array}{c}\hfill J_{OSS}=\left\{\begin{array}{cc}0.3\times v-4.2\hfill & \mathrm{if} v < 9 \mathrm{m}/\mathrm{s}\hfill \\ -1.5\hfill & \mathrm{if} 9 \mathrm{m}/\mathrm{s} \le \mathrm{v} < 18 \mathrm{m}/\mathrm{s}\hfill \\ -0.4\times v+5.7\hfill & \mathrm{if} v > 18 \mathrm{m}/\mathrm{s}\hfill \end{array}\right.\end{array}$$

(3)

3. Ku-Band $R_n$ and $R_{n}J$ QC Results and Discussion

3.1. $R_n$ QC Evaluation

The critical point of the $R_n$ QC method described in Section 2.4 is to set an appropriate threshold. The threshold is a trade-off between the data rejection of all rain-contaminated WVCs and the data rejection of good wind retrievals. WindRAD data from August to October 2023 (more than 37 million WVCs) are used to calculate the $R_n$ distribution. Various experiments are performed to find the optimal trade-off for the threshold. To keep the paper concise, not all of the results of the experiments are shown because the procedure is the same for each of them. Therefore, three thresholds (including the best-fit threshold) are chosen to represent the low, best, and high rejection rates. Figure 2 shows the selected tested thresholds from a low rejection rate to a high rejection rate: V1 (version 1, blue), V2 (version 2, green), and V3 (version 3, red).

Data from August 2023 in the latitude band between −20^∘ and 20^∘, focusing on tropical moist convection processes, are used to evaluate the experiments. Figure 3a–c show the tropical geographical distribution of the rejected winds for V1, V2, and V3, having rejection rates of 1.64%, 2.42%, and 5.44%, respectively. The lower the rejection rate, the worse the rejected wind speed statistics are (Figure 3d–f), since $R_n$ QC starts to reject winds from the WVCs with the highest $R_n$ values (the most likely being rain-contaminated) until it reaches the threshold. The rejected winds with the lowest rejection rate contain the poorest-quality winds. Hence, they have the worst wind statistics (V1). On the other hand, a low rejection rate allows more rain-contaminated WVCs’ winds to be accepted. Figure 4a,b show the V1 $R_n$ accepted winds collocated with the rain rate and the V1 $R_n$ accepted winds collocated only with rain rates above 7 mm/h. Most of the winds with high rain rates are excluded from the accepted winds, but, compared with V2 and V3 (Figure 4c–f), the collocated rain rates of the accepted winds (left panel) for V1 are the highest, and more high-rain-rate (above 7 mm/h) winds are accepted. V3 has the smallest number of WVCs with a rain rate higher than 7 mm/h and the lowest rain rates for the accepted winds. However, the rejected winds’ scatter plot (Figure 3f) shows that the core (the darkest red part of the contour) is closest to the diagonal. In contrast, the cores of V1 and V2 (Figure 3d,e) are further away from the diagonal, with a larger retrieved wind speed bias caused by rain. This indicates that too many good-quality winds (along the diagonal) are rejected with V3 QC. Later on, in Section 3.2, the $J_{OSS}$ method will be combined with $R_n$ to exclude additional rain-contaminated WVCs; thus, V3 $R_n$ is too strict. In conclusion, V1 rejects too few WVCs and keeps more rain-contaminated WVCs as accepted winds. V3 rejects more WVCs that still contain relatively good-quality winds. Hence, V2 $R_n$ is the optimal trade-off between the maximum rejection of low-quality data and the minimum rejection of high-quality data.

A long-term dataset from August 2023 to March 2024 validates the selected $R_n$ QC (Figure 5). The rejection rate of the tropical region is 2.46%, and the wind speed contour plot against the NWP wind shows a similar result as in August 2023 only. The accepted winds with a rain rate above 7 mm/h are 0.014% of the total accepted winds, about half the fraction obtained from the V1 $R_n$ QC (0.026%). C-band wind retrievals are little influenced by rain and can be compared with Ku-band winds. Thus, the Ku-band rejected winds are compared with the collocated accepted C-band winds from WindRAD. The rejected winds have a notable deviation from the C-band winds because rain contamination increases the backscatter, leading to a false large wind retrieval result (Figure 6a). The wind speed probability density function (PDF) of the rejected winds (Figure 6b) is compared to the PDF of the corresponding accepted C-band winds, which is in agreement with Figure 6a. The V2 $R_n$ QC is also applied globally (except for the polar regions to avoid sea ice contamination) with a rejection rate of 3.58% (Figure 7), and the accepted winds with a rain rate above 7 mm/h are about 0.013% of the total number of accepted winds, which is similar to the case in the tropical region. The long-term dataset hence validates the suitability of the chosen V2 $R_n$ QC threshold.

3.2. $R_{n}J$ QC Evaluation

The $R_n$ threshold has been determined in Section 3.1, together with the $J_{OSS}$ threshold (Equation (3)). In the combined method $R_{n}J$, a WVC is rejected when its $R_n$ is higher than the $R_n$ threshold or its $J_{OSS}$ is lower than the $J_{OSS}$ threshold. The flowchart below illustrates the procedure of the $R_{n}J$ method (Figure 8). $R_{n}J$ includes both the rain’s local effect in an individual WVC ($R_n$) and the spatial inconsistency caused by rain ($J_{OSS}$). In this section, data from August 2023 to March 2024 are used.

Figure 9 shows the $J_{OSS}$ collocated with rain as a function of the analysis wind field constructed in the wind retrieval 2DVAR step (see Section 2.5). The WVCs with a $J_{OSS}$ value lower than the threshold (the red line in Figure 9) are flagged, and they are indeed associated with high rain rates. Figure 10 shows the geographical distribution of the rejected winds by $R_n$ and $J_{OSS}$ in the tropics; the rejection rates are 2.46% and 1.18%, respectively. The total rejection rate of $R_{n}J$ is 2.87%. This is lower than the sum of the two rejection rates, since there is some overlap between the two QC methods. An additional 0.41% of all WVCs are rejected by $R_{n}J$ as compared to $R_n$. If the statistics of the rejected winds become worse with more rejected winds, and, at the same time, the statistics of the accepted winds become better or stay very similar, then this confirms that more rejected winds are of low quality and presumably rain-contaminated, which means that $R_{n}J$ is more effective.

Table 1. Ku-band wind statistics comparison of $R_n$ and $R_{n}J$ against NWP winds, with tropical region latitude [−20^∘, 20^∘], using data from August 2023 to March 2024.

	QC Method	Speed Bias (m/s)	SDD of u (m/s)	SDD of v (m/s)
Rejected winds	$R_n$	2.312	2.34	2.38
	$R_{n}J$	2.491	2.39	2.44
Accepted Winds	$R_n$	0.113	1.15	1.19
	$R_{n}J$	0.096	1.13	1.17

and

Table 2. Ku-band wind statistics comparison of $R_n$ and $R_{n}J$ against WindRAD C-band winds, with tropical region latitude [−20^∘, 20^∘], using data from August 2023 to March 2024.

	QC Method	Speed Bias (m/s)	SDD of u (m/s)	SDD of v (m/s)
Rejected winds	$R_n$	1.469	2.99	2.42
	$R_{n}J$	1.466	3.09	2.53
Accepted Winds	$R_n$	0.367	1.34	1.29
	$R_{n}J$	0.362	1.32	1.28

show the wind statistics of the rejected winds and the accepted winds compared to the NWP winds and the WindRAD C-band winds, respectively. The statistics of the $R_{n}J$ accepted winds vs. the NWP winds are generally slightly better than those of the $R_n$ winds. The rejected winds’ speed bias and the standard deviation of difference (SDD) of the u v components vs. the NWP winds are all worse with $R_{n}J$ than with $R_n$. Similarly, the statistics of the $R_{n}J$ accepted winds against the WindRAD C band are all slightly better than the accepted winds by $R_n$, and the statistics of the rejected winds by $R_{n}J$ are either worse or stay very similar to the rejected winds by $R_n$.

$R_{n}J$ rejects only 0.41% extra winds as compared to $R_n$. However, $R_{n}J$ still has a positive impact on the accepted wind statistics, and the statistics of the rejected winds by $R_{n}J$ are either worse than those of $R_n$ or stay similar. Additionally, $R_{n}J$ accepts only 0.007% of the winds with a rain rate above 7 mm/h; this is half the amount that is accepted by $R_n$ (0.014%). Therefore, $R_{n}J$ has a better capability to filter rain-contaminated WVCs than $R_n$.

4. C–Ku Combined $R_n$ and $R_{n}J$ QC Results and Discussion

4.1. Evaluation of the Ku Contribution to $R_n$ in QC

The MLE of the C–Ku wind retrieval includes both C and Ku frequencies (Equation (1)). However, the C-band measurements are only little influenced by rain; therefore, the contribution of the C-band $R_n$, due to measurement noise, can dilute the effect of rain on the MLE, and it may not be accurate to use the total $R_n$, based on both C- and Ku-band inputs, to set the QC threshold. Figure 11a,b show the total $R_n$ and the Ku-based $R_n$. We first discuss the respective QC results and assess the advantage of using only the Ku-based $R_n$, and we then investigate the optimal threshold for $R_n$.

Data from August to October 2023, with latitudes between −20^∘ and 20^∘, are used. A similar number of rejected winds is required to equally compare the rejected wind statistics between the use of total $R_n$ and the Ku-based $R_n$. As shown in Section 3.1, the $R_n$ QC starts to reject the winds with the highest $R_n$ values; these are most likely rain-contaminated. Thus, a low rejection rate (lower than 1%) is chosen to ensure that the rejected winds contain a minimal number of good-quality winds. Figure 12a,b show the geographical distribution of the rejected winds in the tropical region for the total $R_n$ and the Ku-based $R_n$, with a rejection rate of about 0.7% for both. Against the NWP winds, the rejected wind speed of the Ku-based $R_n$ (Figure 12d) shows a significantly larger deviation from the diagonal compared to the rejected winds using the total $R_n$ (Figure 12c). Therefore, with the same number of rejected winds, the Ku-based $R_n$ can more accurately identify the rain-contaminated WVCs than the total $R_n$. The optimal QC threshold should be obtained from the Ku-based $R_n$.

Various experiments like those described in Section 3.1 have been performed to select the optimal threshold (not shown). The chosen threshold is shown in Figure 11b. It is a good trade-off between maintaining the good-quality winds and rejecting the rainy WVCs as much as possible. The rejection rate calculated with data from August 2023 to March 2024 is 1.11% in the tropical region, about half of the rejection rate for the Ku-band-only case (2.46%). At the same time, and with this reduced rejection rate, the rejected and accepted wind statistics against the NWP winds and the C-band WindRAD winds (

Table 3. Rejected and accepted wind statistics (C–Ku) against NWP winds and against C-band WindRAD winds using the Ku-based $R_n$, using data from August 2023 to March 2024.

	Compared Against	Speed Bias (m/s)	SDD of u (m/s)	SDD of v (m/s)
Rejected winds	NWP winds	2.301	2.24	2.35
	C-band (WindRAD)	1.375	2.28	2.40
Accepted Winds	NWP winds	0.120	1.14	1.22
	C-band (WindRAD)	0.359	1.27	1.22

) do not show a large difference compared to those of the Ku-band-only case (Table 1 and Table 2). In addition, the percentage of accepted winds with a rain rate above 7 mm/h is 0.041%, which is three times as high as when the Ku-band $R_n$ is used (0.014%). This indicates that, by adding C-band measurements to the wind retrieval, the rain effect is suppressed, and some of the WVCs rejected by the Ku-band $R_n$ are now accepted by C–Ku. Thus, the C–Ku wind retrieval can achieve similar QC results in terms of rejected and accepted wind statistics and still reject fewer WVCs. Hence, the C band has clear added value in rainy conditions, allowing us to obtain improved vector winds.

4.2. $R_{n}J$ QC Evaluation

The combined QC method $R_{n}J$ is also applied in the C–Ku wind retrieval with the same procedure as in Section 3.2. The data from August 2023 to March 2024 are evaluated in the tropical region with latitudes within [−20^∘, 20^∘].

The rejection rate when using $J_{OSS}$ QC is 0.73%, the rejection rate when using $R_n$ QC is 1.11%, and the rejection rate when using $R_{n}J$ QC is 1.53%. Hence, 0.42% of extra data are rejected using $R_{n}J$ as compared to $R_n$, which is almost the same number as for the Ku-band retrievals (0.41%). Figure 13 shows the speed contour plot of the rejected winds against the NWP winds using $R_n$ (a) and $R_{n}J$ (b). The rejected winds from $R_{n}J$ QC deviate more from the diagonal than the rejected winds from $R_n$ QC. The statistics of the rejected winds for $R_{n}J$ against the NWP winds and the WindRAD C-band winds (

Table 4. Wind statistics (C–Ku) for $R_n$ QC and $R_{n}J$ QC against NWP winds, for tropical latitude region [−20^∘, 20^∘], using data from August 2023 to March 2024.

	QC Method	Speed Bias (m/s)	SDD of u (m/s)	SDD of v (m/s)
Rejected winds	$R_n$	2.301	2.24	2.35
	$R_{n}J$	2.690	2.42	2.50
Accepted Winds	$R_n$	0.120	1.14	1.22
	$R_{n}J$	0.103	1.12	1.20

and

Table 5. Wind statistics (C–Ku) for $R_n$ QC and $R_{n}J$ QC against WindRAD C-band winds, for tropical latitude region [−20^∘, 20^∘], using data from August 2023 to March 2024.

	QC Method	Speed Bias (m/s)	SDD of u (m/s)	SDD of v (m/s)
Rejected winds	$R_n$	1.375	2.82	2.40
	$R_{n}J$	1.293	2.97	2.60
Accepted Winds	$R_n$	0.359	1.27	1.22
	$R_{n}J$	0.355	1.25	1.21

) are all worse than for $R_n$, although the wind speed bias against the WindRAD C-band winds is slightly better (very similar), which might be because the C–Ku winds contain the same C-band source. The accepted wind statistics for $R_{n}J$ QC are all slightly better than the accepted wind statistics for $R_n$ QC (Table 4 and Table 5). As described in Section 3.2, only when the extra rejected winds are rain-contaminated (low quality) will the statistics of the rejected winds become worse with more rejected winds, whereas the statistics of the accepted winds will become better or stay similar. Therefore, as discussed above, the extra rejected winds by $R_{n}J$ are rain-contaminated, which is not detected by $R_n$. Furthermore, the accepted winds with rain rates above 7 mm/h are about 0.027% of the total wind count, a reduction of more than one-third as compared to $R_n$ QC (0.041%). In conclusion, the $R_{n}J$ can further identify the rain-contaminated WVCs and works consistently for C–Ku wind retrieval.

Furthermore, the current study focuses on the challenging tropical regions featuring high rain rates and low to moderate winds. This is also the region where rain brings the most extensive spatial variability in both rain and wind. However, the principle of the $R_{n}J$ should also be applicable outside the tropics, following earlier investigations. Moreover, cases with high rain rates and extreme winds (e.g., hurricanes) are interesting to examine further. Special attention may be needed for higher latitudes with the influence of sea ice and different precipitation types.

5. Conclusions

Wind products with improved QC are vital for users such as operational meteorologists, as this provides more high-quality winds in areas with dynamic weather, such as near deep moist convection, which are otherwise difficult to track. Improved wind quality and low rejection rates are also beneficial for wind research applications.

WindRAD is a dual-frequency rotating-fan-beam scatterometer with C-band and Ku-band antennas. C-band measurements are only little influenced by rain, whereas Ku-band measurements are very sensitive to heavy rain because of their shorter wavelength. In this work, the QC in association with rain contamination for Ku-band and C–Ku wind retrievals is thoroughly investigated, focusing on the tropical region. The normalized MLE residual $R_n$ and the combined method $R_{n}J$ ($R_n$ and $J_{OSS}$) are adapted to the WindRAD measurements. The $R_n$ threshold permits a trade-off between a high rejection rate for low-quality winds and a low rejection rate for good-quality winds. $J_{OSS}$ considers spatial consistency, and it is an excellent complementary indicator in detecting rainy WVCs [17]. The $R_{n}J$ is a combination of $R_n$ and $J_{OSS}$ that makes use of both the local information (MLE) and the spatial consistency ($J_{OSS}$).

For Ku-band wind retrieval, first, an optimal $R_n$ threshold is set and then the $R_n$ QC is combined with $J_{OSS}$ QC. An additional 0.41% of WVCs are rejected when $R_{n}J$ QC is used. With more rejected winds, the statistics of rejected winds are worse than the results with $R_n$ QC, indicating that more rejected winds are most likely rain-contaminated. The statistics of accepted winds are all slightly better than with $R_n$ QC. Moreover, the number of accepted WVCs with a high rain rate (>7 mm/h) is reduced by half for $R_{n}J$ QC, as compared to $R_n$ QC. In conclusion, the combined $R_{n}J$ QC method can distinguish rain-contaminated WVCs better than the $R_n$ QC method.

An important opportunity for C–Ku wind retrieval is to use the Ku-based $R_n$ instead of the total (C and Ku) $R_n$. The Ku-based $R_n$ results and the total $R_n$ results are compared for the same rejection rate of 0.7%. The rejected wind speed contour plot against NWP winds has a larger deviation from the diagonal for the Ku-based $R_n$ than for the total $R_n$. The reason for this is that rain does not influence the C-band observations to any substantial extent, and, hence, the C-band measurement noise contribution to $R_n$ may lead to false alarms in rain detection. Thus, the Ku-based $R_n$ QC is more effective than the total $R_n$ QC to identify rainy WVCs.

In total, 1.11% of the C–Ku wind retrievals are rejected by the Ku-based $R_n$ QC, which is reduced by about half compared to the Ku-band-only retrievals. At the same time, and with the reduced rejection rate, the statistics of the accepted and rejected winds do not differ much from those using Ku-band-only retrievals. When using the Ku-based $R_n$ and looking at the WVCs with a high rain rate of over 7 mm/h, three times more accepted winds are retrieved using C–Ku than using the Ku band only. This indicates that combining the C band with the Ku band suppresses the rain effect in wind retrieval and hence achieves good-quality winds with fewer rejected WVCs. The Ku-based $R_n$ and $R_{n}J$ for C–Ku retrievals are also compared. An additional 0.42% of WVCs are rejected by the Ku-based $R_{n}J$. As for the Ku-band-only retrieval, the statistics of the rejected winds are worse than the results with $R_n$ QC, and, at the same time, the statistics of the accepted winds are slightly improved compared to the result with $R_n$ QC. Therefore, the Ku-based $R_{n}J$ can accurately exclude more rainy WVCs, and its performance characteristics are consistent with the Ku-band-only wind retrieval results. Above all, the $R_{n}J$ is an optimal QC method to detect rain contamination for wind retrievals where Ku-band observations are used. The Ku-based $R_n$ is the key to improving QC for C–Ku wind retrieval. Adding the C-band observations to wind retrieval suppresses the rain effect, and the same QC capabilities (in terms of accepted wind statistics) can be achieved with fewer rejected WVCs.

The very different rain effects for the C band and Ku band may furthermore be exploited in the future for rain correction and, as such, further improve the quality of the WindRAD ocean surface vector winds in rainy areas. In addition, WindRAD may have a good ability to measure rain rates, which may be exploited in such future work.