It has been more than 40 years since satellites began to observe some major parameters of the oceans. However, sea-surface salinity, which is recognized widely as an important oceanic variable, has been measured from space only since the launch of the first spaceborne L-b and radiometer in November 2009, as part of the Soil Moisture and Ocean Salinity(SMOS)mission(Mecklenburg et al., 2012). Aquarius is the second satellite mission for the remote monitoring of salinity, which was launched by NASA in June 2011(LeVine et al., 2010). The principal payload of Aquarius is an L-b and microwave radiometer/scatterometer that has been found to be sensitive to salinity variation through a series of earlier spaceborne and airborne experiments(Droppleman and Mennelin, 1970; Lerner and Hollinger, 1977; Blume et al., 1978). The radiometer of Aquarius has three feed horns that measure the brightness temperature(TB)of the sea surface at different incidence angles. Benefiting from the swath of 390 km, Aquarius covers the global oceans within 1 week. However, the sea-surface wind can induce extra roughness of the sea surface and the foam effect, which could cause a fake salinity signal in the TB. As the sensitivity of the L-b and TB to salinity is less than 1 K(Kelvin)under all conditions, this wind-induced fake signal could result in severe errors in salinity retrieval(Boutin et al., 2012; Yin et al., 2012). Consequently, measurement of the sea-surface salinity from space remains a challenge. To estimate the wind-induced roughness effect, the Aquarius system also includes a microwave scatterometer to measure and correct the roughness effect caused by the wind(LeVine et al., 2007).

SMOS and Aquarius have both been in operational phase for a number of years, and have routinely provided salinity data products. Many researchers have assessed the quality of the retrieved salinity data and found large discrepancies under conditions of high wind speed(Boutin et al., 2012; Guimbard et al., 2012; Reul et al., 2012a; Yin et al., 2012). One possible reason for this is that the performance of the forward model degrades under conditions of high wind speed, combined with the non-negligible measurement uncertainty of the scatterometer, especially in intensively convective systems such as hurricanes, where wind-speed measurement is probably contaminated by rain(Meissner et al., 2011).

Based on sensitivity analyses of TB to rain, some researchers(Meissner and Wentz, 2009; Yueh et al., 2010; Amarin et al., 2012)have tried to find channel combinations that are non-sensitive to rain, but sufficiently sensitive to wind speed. An all-weather wind-speed algorithm that also uses the C-b and , in addition to higher-frequency channels, has been developed and applied to the latest versions of WindSat products(Meissner and Wentz, 2009). Actually, based on numerical simulation, it has been shown that the L-b and TB exhibits high atmospheric transparency(>0.98) and moderate sensitivity to wind(0.2–0.3 K/(m/s)). Consequently, the Aquarius microwave radiometer itself offers a new means for the measurement of sea-surface wind speed. Reul et al.(2012b)found that the L-b and emissivity of the ocean is less sensitive to roughness and foam than the higher C-b and microwave frequencies and thus they developed a statistical wind-speed algorithm for SMOS. The results of this algorithm agree well with the H*Wind analysis products provided by the Hurricane Research Division(HRD)of the Atlantic Oceanographic and Meteorological Laboratory, and prove the applicability of an L-b and passive remote sensor for the measurement of sea-surface wind speed.

In this article, we concentrate on estimations of sea-surface wind speed based on the TB of the L-b and radiometer onboard Aquarius. The data sets and method are described in Section 2. The results and discussion are presented in Sections 3 and 4, and the conclusions are summarized in Section 5.

The Aquarius data of V2.0 were provided by NASA(data access: http://oce and ata.sci.gsfc.nasa.gov/ Aquarius). The time coverage of the Aquarius data is 2012 and there were 10 644 passes involved in this research. The data format of Aquarius is the L2 SCiproduct that includes all the main data from the radiometer and scatterometer, and some auxiliary meteorological data from NCEP(Wentz et al., 2012). In this research, numerous data fields including the TB, wind speed from the scatterometer and daily NCEP Global Data Assimilation System(final analysis)product, and locations and times of the observations, were decoded and extracted from original Aquarius data. To avoid contamination from sea ice and l and , all Aquarius data for which the corresponding SST was less than 0°C, l and fraction was >0.1%, and sea ice fraction was >0.1% were filtered.

WindSat is the first spaceborne polarimetric microwave radiometer with the primary objective of the remote sensing of the sea-surface wind vector. WindSat has operated successfully in orbit since its launch in January 2003. The WindSat data(data access: ftp://ftp.remss.com/windsat)used in this work were the latest version(V7.0.1)geophysical product from the Remote Sensing System. The WindSat product includes all st and ard parameters such as SST, water vapor, cloud liquid water, and wind vector. It is worth noting that the all-weather wind-speed data in this product significantly improve wind speeds in rainy conditions. The resolution of the all-weather wind-speed data is 39 km×71 km in rain.

The buoy data(data access: http://www.ndbc.noaa. gov)were provided by the National Data Buoy Center(NDBC)of NOAA. Data obtained in 2012 from 110 buoys were included in this research. Typically, the temporal resolution of the buoys varied from 10 min to 2 h. The locations, observation times, and observed wind speeds were extracted from the original buoy data file.

The tropical cyclone wind vector analysis product H*Wind(data access: http://www.aoml.noaa.gov/ hrd)was supplied by NOAA’s HRD, and used to verify the capability of Aquarius for measuring wind speed in conditions of tropical cyclones. The H*Wind wind vector analysis product is based on multi-source wind-speed data(e.g., ships, buoys, aircraft, and satellites), and was provided in gridded form with a spatial resolution of 5–10 km(Powell et al., 2010). The locations, observation times, and wind speeds were extracted from 115 wind vector field data obtained for 11 tropical cyclones in 2012.

Microwave radiometers are directly sensitive to the wind-induced roughness of the sea surface and not the wind speed(Meissner and Wentz, 2009). As indicated in a previous study, the minimum time for wind to produce roughness on the sea surface is 10 min. Consequently, the scale factor of 0.88, used in previous research(Meissner and Wentz, 2009), was adopted here to convert the original 1-min sustained wind speeds of H*Wind to 10-min sustained wind speeds.

The area studied in this research encompasses the oceans of the low and middle latitudes(60°S–60°N). Because of the various spatial and temporal resolutions of the multi-source data used in this work, different intervals were used to match the Aquarius data with the WindSat, NDBC, and H*Wind data.

The orbits of both Aquarius and WindSat are sun synchronous and these two satellites share the same descending equatorial crossing time of 06:00 AM(local solar time). The inclination angle of Aquarius is 98°, which is close to that of WindSat’s inclination angle of 98.7°. The similar orbital parameters ensure a good match between Aquarius and WindSat. The temporal interval between Aquarius and WindSat is set at 1 h. The Aquarius data in each WindSat data grid were averaged to mitigate the effects of r and om error. Consequently, 778 507 data elements were available for the Aquarius-WindSat matchup data set. As shown is Fig. 1a, because of the similarity of their orbits, the global data set is distributed evenly across the study area.

Fig. 1 Spatial distribution of matchup data a. Aquarius and WindSat; b. NDBC buoy. Blue dots represent all NDBC buoys, red spots represent the seven buoys that match Aquarius.

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The situation is quite different for the matchup between Aquarius and NDBC buoy. The spatial locations of the NDBC buoys are stable, and the temporal resolution of buoy measurements varies from 10 min to 2 h. At the same time, compared with the swath size of >1 000 km, typical of a scanning microwave radiometer, Aquarius has a relatively narrow swath of 390 km. Because of the different incidence angles for the three beams of Aquarius, the present work focused on the first beam of Aquarius, which means the swath of Aquarius data was reduced to about 100 km. Consequently, the spatial and temporal intervals are set to 50 km and 10 min, respectively, which provided just 201 measurements from seven buoys for matching with Aquarius data. The spatial locations of these buoys are shown in Fig. 1b.

The spatial coverage of the H*Wind product is relatively limited and the temporal interval between H*Wind products is several hours. Therefore, the temporal window between Aquarius and H*Wind was set to 2 h, and the H*Wind data were interpolated linearly to the observation locations of Aquarius. Finally, 525 measurements from seven wind fields of H*Wind matched the data of Aquarius.

Based on the radiative transfer model, the top of atmosphere(TOA)TB is as follows:

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Fig. 2 H*Wind fi eld of Hurricane Sandy a. October 27, 2012; b. October 28, 2012. Black solid line represents track of Aquarius.

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Because of the long wavelength, the atmosphere is more transparent to L-b and radiation and the typical value of transmission is >0.98. Consequently, the TB signal received by Aquarius is primarily from the fl at and wind-induced rough sea surface. The radiation of calm sea comprises the largest part, which is related to the complex dielectric constant of seawater described by the Fresnel equations:

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The TB from the wind-induced rough sea surface is portrayed by several analytical and statistical models(Gabarro et al., 2004; Johnson, 2006; Hwang, 2012).

During wind-speed retrieval, the TB from the fl at sea surface, which is independent of wind speed, becomes a kind of noise. As the TB of the fl at sea surface is primarily affected by SST and sea-surface salinity, the dependence of specular sea surface TB on SST and salinity is studied. Based on the dielectric constant model of seawater developed by Klein and Swift(1977), the TB of a calm sea surface can be simulated under different conditions of SST and salinity.

As shown in Fig. 3a, the salinity signal in the TB is about 4 K, which is comparable with the windinduced TB. Therefore, the wind-speed algorithm could treat the wind signal in the same manner as the salinity signal, which could cause additional error in the remote sensing of wind speed were the salinity signal not corrected. Regarding the SST, the situation is complex because the response of the TB to SST is clearly nonlinear(Fig. 3b). As both polarizations of TB reach their peak values at 15°C, two retrieval algorithms have to be developed, respectively, for conditions lower and higher than 15°C.

Fig. 3 Simulated TB under different conditions of (a) salinity and (b) SST

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Tab. 1 Matchup data of Aquarius and HRD wind fi eld

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Tab. 2 Statistics of Aquarius retrieval results compared with WindSat radiometer

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The matched Aquarius-WindSat data set was divided into two sub-sets based on SSTs higher and lower than 15°C, respectively. For each set, one third of the data were selected r and omly for the training data set and the remainder used as the validation data set. The neural network(NN)used in the present work was a two-layer feed forward method consisting of a single hidden-layer NN and an output layer. The hidden layer had 10 neurons and the output layer just one, i.e., wind speed. The transfer functions for the hidden and output layers were the tan-sigmoid function and pure linear function, respectively. The training function was the Levenberg-Marquardt method. The input parameters of the NNs were the TB(H/V Polarization), SST, and salinity of Aquarius measurements. Finally, two separate NNs(L_NN, H_NN)were trained for conditions of low and high SST.

Tab. 3 Statistics of wind speed compared with the NDBC buoy measurements

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Tab. 4 Statistics of wind speed compared with the H*Wind product

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Based on the validation data set, the wind-speed results of the NNs were compared with the WindSat all-weather wind-speed product, and the scatter plot and histogram are shown in Fig. 4. The results of the NNs compare with the WindSat measurements very well. The RMSE is about 1 m/s and correlation coefficient(R)is >0.9. The H_NN has a negative bias of ~0.23 m/s, whereas there is no obvious bias in L_ NN.

Fig. 4 Scatter plots and histograms of Aquarius wind-speed retrieval results a, b. L_NN; c, d. H_NN.

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The wind-speed data of the NNs were also validated against NDBC in situ measurements. Simultaneously, the wind-speed data measured by the Aquarius scatterometer(Yueh et al., 2012) and the auxiliary wind-speed data included in Aquarius data products(provided by NCEP)were also compared with the NDBC buoy measurements. The results reveal that L_NN and H_NN have mean biases of 1.2 and 0.4 m/s, respectively, and that the biases of the scatterometer and NCEP data are better than 0.6 and 0.4 m/s, respectively. The statistical results shown in Table 3 have had the mean biases removed. The RMSEs of the NNs are about 1 m/s and the correlation coefficients >0.9. Consequently, compared with the scatterometer and NCEP data, the results of the present work display better r and om errors and larger systemic errors.

Based on the matchup data set of Aquarius and the H*Wind data described in Section 2.5, the preliminary results of the algorithm for hurricanes are presented in this section. The matchup data were divided r and omly into two sub-sets and averaged for algorithm development and validation. The parameters of the NN were the same as for the global algorithm.

As shown in Fig. 5, benefiting from the high transparency of the L-b and TB, the performance of the algorithm for hurricanes is good. There is no obvious bias in the NN algorithm, and the biases of the scatterometer and NCEP data are 3.4 and 2.0 m/s, respectively. The RMSE and correlation coefficient of the NN are also superior to the Aquarius scatterometer and NCEP data with values of 1.5 m/s and 0.9, respectively. It should be mentioned that because of the narrow swath of Aquarius, the amount of matchup data between Aquarius and H*wind is quite small; therefore, the results shown here are treated as preliminary and it is acknowledged that the performance of this algorithm needs further study.

Fig. 5 Scatter plots of retrieval results a. NN; b. scatterometer; c. NCEP.

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In the present work, the mean bias and st and ard deviation were obtained within the wind-speed range of 0–20 m/s with an increment of 0.5 m/s. As shown in Fig. 6, the mean bias and st and ard deviation for both L_NN and H_NN increase as the wind speed becomes higher. The degradation is clearer for H_NN than for L_NN, and the mean bias and st and ard deviation are >2 m/s under conditions of high wind speed. A possible reason for this is that with warmer seawater, the L-b and TB is more sensitive to the salinity signal, which causes additional errors in the wind-speed retrieval(Qiand Wei, 2012).

Fig. 6 Dependence of retrieval error on wind speed a. L_NN; b. H_NN. Solid line represents the mean bias, vertical bar is ±1 standard deviation.

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Raindrops change the absorption and scattering characteristics of the atmosphere and cause splashing on the sea surface, which can have an impact on windspeed measurements(Boutin et al., 2013; Tang et al., 2013). Therefore, the remote sensing of wind speed in rainy conditions remains a challenge. However, the situation of Aquarius is quite different because Aquarius works at a lower frequency(1.4 GHz), for which the atmosphere is more transparent. The retrieval results of the two NNs under different rainy conditions(0–10 mm/h)are shown in Fig. 7. The L_ NN has a positive bias that increases from 0 to 1.8 m/s as the rain rate increases, and the st and ard deviation is more stable and better than 2 m/s under all conditions. Conversely, the bias of the H_NN is negative and oscillates between -1 and 0 m/s, and the st and ard deviation is 1.4–2.4 m/s. This preliminary result reveals the feasibility of using an L-b and radiometer for wind-speed measurements under rainy conditions.

Fig. 7 Dependence of retrieval error on rain rate a. L_NN; b. H_NN. Solid line represents the mean bias, vertical bar is ±1 standard deviation.

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In this research, the development of wind-speed retrieval algorithms for the Aquarius L-b and radiometer, based on a neural network method, is described. The algorithms are validated and compared against in situ data and remote sensing data. The RMSE of the global algorithm is about 1 m/s and the RMSE of the algorithm for hurricanes is about 1.5 m/s. The r and om errors of both algorithms are superior to the Aquarius scatterometer and the daily NCEP Global Data Assimilation System product. The results reveal the feasibility of using Aquarius as a new tool for the remote sensing of wind speed, even in rainy conditions.

The authors would like to thank both anonymous reviewers for their useful comments and the National Aeronautics and Space Administration(NASA), RSS(Remote Sensing System), NDBC(National Data Buoy Center), and HRD of AMOL(Hurricane Research Division of Atlantic Oceanographic and Meteorological Laboratory)for providing the Aquarius, WindSat, NDBC buoy, and H*Wind data, respectively.