INTRODUCTION

Data obtained by Earth remote sensing (ERS) satellites have become crucial for climate research, weather forecasting, disaster prevention, and ecological monitoring, and they have various other practical applications. Remote measurements are performed in different frequency ranges (optical, infrared (IR), and microwave) with the use of active and/or passive observation techniques. Microwave radiometry has been proven efficient in global monitoring of the ocean–atmosphere system. This ERS instrument allows one to perform day-and-night measurements; features relatively low radiation absorption in the atmospheric “transparency windows”; and, most importantly, is highly informative.

Among all the microwave frequencies used for remote sensing (RS), three frequencies (~10, 18, and 37 GHz) localized in the “transparency windows” are exactly the ones at which the measured upward-travelling radio radiation is associated closely with the near-water wind field. This provides a unique opportunity to determine the wind parameters remotely. A large number of algorithms for determining the near-surface wind field have already been developed, but the reconstruction efficiency remains an issue. Although this is a matter of present interest, no Russian instruments are involved in experiments on determining the vector of near-surface wind in the ocean.

The full title of the Convergence space experiment (SE) aboard the Russian Orbital Segment (ROS) is “Determination of Detailed Atmospheric Temperature and Humidity Profiles in the Study of the Origin of Atmospheric Cataclysms.” The aim of Convergence is to examine the genesis and evolution mechanisms of large-scale catastrophic atmospheric processes (such as tropical cyclones or midlatitude hurricanes) as the key elements in the process of formation of the global mass and moisture exchange in the ocean–atmosphere system (Sharkov, 2017).

Determining the wind speed and direction through measurements of the own radiothermal emission of the water surface is one objective of the Convergence SE. This SE should help optimize the algorithms of reconstruction of the near-water wind speed and direction and develop the necessary software. The measurement results are planned to be validated by comparing them to independent meteorological data and data from other sensors (Sadovsky and Sazonov, 2017).

The algorithm of reconstructing the near-surface wind direction based on satellite microwave polarimetric measurements has already been developed. It was applied to a model problem and demonstrated to be efficient (Sterlyadkin et al., 2017). It seems logical to test it using real satellite measurement data. As was already noted, the Convergence SE is still at the planning stage. Among all the current satellite radio polarimeters, only the WindSat instrument satisfies the requirements (see below) imposed by the mentioned algorithm for determining the wind direction. Therefore, the aim of the present study is to demonstrate the capabilities of the proposed algorithm using WindSat data as an example.

STATISTICAL ALGORITHM FOR ENHANCING THE RELIABILITY OF MEASUREMENTS AND THE USE OF DIFFERENT FREQUENCY CHANNELS

The possibility of determining the wind direction based on radiometric measurements stems from the azimuthal anisotropy of microwave radiation of a rough water surface. The effect of azimuthal anisotropy consists of the dependence of the measured radio brightness temperature on the angle between the wind direction and the sensing direction. This effect has been discovered by researchers from the Space Research Institute in the 1970s in experiments on radiothermal sensing of the sea surface by radiometric systems with nadir antennas installed aboard a test-bed aircraft (Bespalova et al., 1979, 1982).

It was found that the third Stokes parameter (S3) is affected most by surface radiation anisotropy (Bespalova et al., 1979, 1982; Meissner and Wentz, 2012; Sazonov et al., 2013). This parameter is the difference of brightness temperatures at linear ±45° polarizations: S3(φ, …) = \(T_{{\text{B}}}^{{ + 45}}\)(φ, …) – \(T_{{\text{B}}}^{{ - 45}}\)(φ, …). The anisotropic contribution depends both on the radiation frequency and the magnitude of wind speed U10 (Meissner and Wentz, 2012; Sazonov et al., 2013; Sazonov, 2017). When reconstructing wind direction αw, we assume that the magnitude of wind speed U10 is known from additional sources (e.g., scatterometer measurements) or was determined based on measurement data (Sadovsky and Sazonov, 2017). Therefore, the dependence of S3 on wind direction φ relative to sensing azimuth φs (φ = φw – φs) is also assumed to be known. The typical S3(φ) dependence for frequency f1 = 36.5 GHz is shown in Fig. 1.

Fig. 1.
figure 1

Dependence of the third Stokes parameter (S3) on the relative wind azimuth. Two values (S31 and S32) are determined at two different sensing azimuths for the same surface element, and these two values are then used to find the sets of possible wind directions.

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It can be seen that the value of relative wind azimuth φ is ambiguous at any measured S3. Two angles φ1.1 and φ1.2 correspond to the S31 value in Fig. 1, and four possible angles φ2.1, φ2.2, φ2.3, and φ2.4 correspond to S32. It is impossible to determine in a single measurement which φ value represents the true wind direction. However, if one and the same element of resolution on the surface is measured at different angles, it becomes possible to identify the true direction.

Figure 2 presents the tentative geometry of conical sensing with the satellite moving along a track. The proposed algorithm may be applied to different satellite radiometers if measurements in two swaths are available. WindSat belongs to this group of instruments (Gaiser et al., 2004).

Fig. 2.
figure 2

Geometry of sensing of the same surface elements by a satellite moving along the track.

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It follows from Fig. 2 that, if the initial forward sensing direction makes angle φ31, the same element of resolution will be measured at angle φ32 = φ – φ31 in aft sensing along the track. The difference between the sensing directions is Δφ = φ32 – φ31 = π – 2φ31.

Naturally, the same element of resolution on the surface falls within the aft observation sector after the satellite covers distance L(φ31) = 2Rcos(φ31), where R is the radius of the scan cone on the surface of the Earth along the track. This displacement takes place with time delay Δt = L/V, where V is the satellite flight speed.

Thus, the same element of the underlying surface is measured at angles φ31 and φ32 = π – φ31. Solving the inverse problem, we obtain two values of the third Stokes parameter (S31 and S32) and azimuthal viewing angles φ31 and φ32. In Fig. 1, the initial wind direction is φw = 28°, sensing direction φ31 = –37°, and φ32 = π – φ31 = –147°.

The MicRAWinD algorithm, which was described in (Sterlyadkin et al., 2017), is proposed to be used to reconstruct the wind direction based on the measured values of the third Stokes parameter.

Measurements of the intrinsic radiothermal radiation of the water surface are normally performed at several different frequencies instead of a single one. This is done to increase the reliability of measurements. We propose combining the results in different frequency channels with the measurement errors and the errors of indirect calculations taken into account. It is natural to assume that the signal distribution over the third Stokes parameter is a normal one and the width of this distribution corresponds to the errors of its calculation.

The algorithm of determining the wind direction relies on data on the geophysical parameters of the ocean–atmosphere system and the satellite telemetry. The meteo parameters are integral water-vapor content V, cloud water content L, precipitation rate R, wind speed U10 (at a height of 10 m), water temperature Ts, and salinity S. The Earth incidence angle (EIA), flight direction φf at a given moment, and the sensing direction relative to the flight direction are among the telemetry parameters. These parameters are needed to model the angular dependence (theoretical) of the third Stokes parameter (S3).

A random noise component, which is governed by the sensitivity of radiometers, and errors of determination of the wind speed magnitude, which is determined based on a set of measured brightness temperatures in the process of solving the inverse problem, are always present in actual radiometric systems. In addition, the model may also have errors. In this study, we consider only the radiometer noise, since it was estimated (Sadovsky and Sazonov, 2017) to produce the greatest contribution to the overall error. Owing to errors of measurement of brightness temperatures, the true values of the third Stokes parameter may differ from the measured S31 and S32 values. Therefore, the statistical distribution of probabilities should be taken into account.

With the statistical distribution factored in, the following algorithm is proposed for reconstructing the wind direction based on the results multifrequency measurements of the third Stokes parameter.

(1) The theoretical azimuthal angular dependence of the third Stokes parameter is calculated for the known (determined beforehand) geophysical parameters of the ocean–atmosphere system and the satellite telemetry (Fig. 1):

$$S3(\varphi , \ldots ) = T_{{\text{B}}}^{{ + 45}}(\varphi , \ldots ) - T_{{\text{B}}}^{{ - 45}}(\varphi , \ldots ),$$

where TB(φ, …) is the radio brightness temperatures at linear ±45° polarizations.

(2) The probability distribution functions over S3 (P1(S3, μ1, σ) and P2(S3, μ2, σ)) are formed for the first and second measurements. Probability function P corresponds to a normal distribution with standard deviation σ = δS3= \(\sqrt 2 {{\delta }_{{\text{p}}}}\), where δr is the radiometer sensitivity in a given frequency channel, and mean values equal to the measured values the third Stokes parameter (μ1 = S31 and μ2 = S32).

(3) Probability functions Pi(φ) are calculated. Pi(φ) is the probability that the true wind direction at a measured S3i value has relative azimuthal angle φ: Pi(φ) = Pi(S3i, μi, σ), where i = 1, 2. The probabilities are calculated for discrete angle values φj, where j = 1–360 (Fig. 3).

Fig. 3.
figure 3

Probability functions P1(φ) and P2(φ) define the probability that the true relative wind azimuth is φ under the condition that the measured values of the third Stokes parameter are S31 and S32. The initial wind direction is taken to be φw = 28°, sensing direction φ31 is –37°, and φ32 = –147°. For clarity, σ is set to 0.1 K (the actual sensitivity of WindSat at 37 GHz is 0.25 K).

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(4) Probability functions P1(φ) and P2(φ) are normalized:

$${{P}_{N}}(\varphi ) = \frac{{P(\varphi )}}{{\sum\limits_j {P(\varphi )} }}.$$

Normalized probabilities are used in what follows.

(5) The plots for probabilities P1(φ) and P2(φ) are shifted in angle to the zero sensing azimuth. Dependences P1(φ + φ31) and P2(φ + φ32) are thus obtained (Fig. 4).

Fig. 4.
figure 4

Plots of probabilities P1(φ31 + φ) and P2(φ32 + φ) shifted to the zero sensing azimuth and overall probability PO(φw). The wind direction corresponds to the maximum: φw = max(PO(φ)).

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(6) The overlapping of probabilities is determined for a single channel:

$${{P}_{{\text{O}}}}({{\varphi }_{{\text{w}}}}) = {{P}_{1}}(\varphi + {{\varphi }_{{31}}}){{P}_{2}}(\varphi + {{\varphi }_{{32}}}).$$

The wind direction is then determined as the maximum value: φw = max(PO(φw)) (Fig. 4).

(7) This algorithm is applied to all frequency channels measuring the third Stokes parameter. The wind direction is determined by identifying the maximum of the resulting probability function for all channels:

$${{P}_{{{\text{res}}}}}({{\varphi }_{{\text{w}}}}) = C1{{P}_{{{\text{O}}1}}}({{\varphi }_{{\text{w}}}}) + C2{{P}_{{\text{O}}}}({{\varphi }_{{\text{w}}}}) + C3{{P}_{{\text{O}}}}({{\varphi }_{{\text{w}}}}),$$

where C1, C2, and C3 are weight coefficients representing the reliability of measurements in a given radiometric channel.

Applying the proposed signal processing algorithm, one determines wind direction φw relative to the satellite track direction as the angle at which the PO(φ) probability function is maximized (Fig. 4). The combination of resulting probabilities in different channels makes the solution more stable. However, this data aggregation should be done with the reliability of channel measurements taken into account. One may use, e.g., the anisotropic signal/noise ratio in each radiometric channel as a weight coefficient.

RECONSTRUCTING THE WIND DIRECTION BASED ON SATELLITE MEASUREMENTS

Among all the microwave instruments aboard artificial satellites, only WindSat performs measurements in the complete polarimetric basis (i.e., measures all four Stokes parameters). This instrument is currently (February 2018) in operation aboard the Coriolis satellite, which was launched in 2003. Its scan geometry (Fig. 5) is such that measurements for the ocean–atmosphere system are conducted both in the flight direction and in the opposite direction.

Fig. 5.
figure 5

Scan geometry of the WindSat instrument (Narvekar et al., 2008).

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The averaged (over all channels) widths of the forward and aft swaths are 950 (the viewing angle is 68°) and 350 km (23°) (Gaiser et al., 2004). Thus, the requirement imposed by the algorithm under examination (concerning the availability of two measurements of the same surface element at different angles) is satisfied in a narrow (350 km) swath. The sensitivity of radiometric detectors of WindSat with respect to the third and fourth Stokes parameters at 10.7, 18.7, and 37 GHz is 0.25 K (Gaiser et al., 2004).

As was already noted, the same element of resolution on the surface falls within the forward and aft observation sectors after the satellite covers distance L(φ31) = 2Rcos(φ31), where R is the radius of the scan cone on the surface of the Earth, along the track. R = 850 km for WindSat (Gaiser et al., 2004). If we consider the most distant (in time) surface elements (at φ = 0°/180°), L = 1700 km. This displacement takes place with time delay Δt = L/V, where V is the low-orbit satellite flight speed, which is roughly equal to 7.5 km/s. Thus, Δt = 226, (6) s, which corresponds to less than 4 m. It was demonstrated in (Monaldo, 1988; Freilich and Dunbar, 1999) that the spatial and temporal mismatch between the measurements from buoys and satellite data may be as large as 50 km and 30 min without any significant loss of measurement accuracy. Therefore, a time delay of 4 min between measurements performed by one and the same instrument should not affect the result.

Calibrated and grid-referenced WindSat measurement data and data on the satellite telemetry and the observation angles (environmental data record) were taken from http://www.ifremer.fr/opendap/cerdap1/ oceanflux/satellite/l1/coriolis/windsat in the NetCDF (version 2.0) format. Data on the surface temperature, wind speed, vapor content, precipitation rate, and condensed moisture were taken in the form of maps from http://data.remss.com/windsat/.

CHOOSING A REGION FOR TESTING

The proposed algorithm for determining the wind direction needs to be tested with different combinations of geophysical parameters of the ocean–atmosphere system (i.e., with different water temperatures, values of the atmospheric vapor content, and wind speeds and directions). A small region was selected for testing from the results of measurements performed on April 27, 2007. Figure 6 shows the wind speed and direction map with the testing region highlighted. The geophysical parameters (Fig. 7) of the ocean–atmosphere system vary considerably in this region. Figure 8 shows the measured values of the third Stokes parameter and the azimuthal observation angle for the forward and aft swaths.

Fig. 6.
figure 6

Map of the wind speed and direction taken from http://data.remss.com/windsat/.

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Fig. 7.
figure 7

Geophysical parameters for the test region. http://www.remss.com/missions/windsat/.

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Fig. 8.
figure 8

Radio brightness temperature at three frequencies and azimuthal viewing angles of the WindSat instrument. http://www.ifremer.fr/opendap/cerdap1/oceanflux/satellite/ l1/coriolis/windsat.

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Since one and the same surface needs to be measured at different angles to determine the wind direction, the resulting swath used to reconstruct the wind parameters is narrower than both the forward and the aft WindSat swaths. In addition, only the areas with available data on the geophysical parameters of the ocean–atmosphere system are used to solve the problem, since these data are needed to calculate the model dependence of the third Stokes parameter on the relative wind direction. Errors associated with the determination of geophysical parameters and the modeling are neglected (only the instrument sensitivity is taken into account).

All the parameters in Figs. 7 and 8 are referenced to a uniform 0.25° grid (for convenience), but data with accurate coordinate values are used in calculations.

The direct problem (modeling of the azimuthal dependence of the third Stokes parameter (Fig. 1)) is solved by calculating radio brightness temperatures, which may be measured by a satellite at the given geophysical parameters of the ocean–atmosphere system and scanning parameters. The radio brightness temperatures at linear ±45° polarizations are calculated in accordance with the model of radiothermal radiation of the ocean and the atmosphere, which was developed based on the results of a long-term analysis of satellite data and is described in (Wentz and Meissner, 2000; Meissner and Wentz, 2004, 2012).

Data from the chosen region were analyzed four times (Fig. 9) with the proposed algorithm. The first three calculations were performed for individual frequencies. In the fourth calculation, the wind direction was determined based on the maximum of the resulting probability function for all channels.

DISCUSSION

The results are presented in Fig. 9 in the form of vector maps of the wind direction, where different colors represent different directions. It can be seen that, in some areas, the determined wind direction agrees with the data (product) presented at http://www.remss.com/ missions/windsat/. In other areas, the mismatch is considerable. It should be noted that, since in situ measurements for the entire region are not available, the comparison between the reconstructed wind direction and the product was qualitative.

Fig. 9.
figure 9

Results of a reconstruction of the wind direction based on the WindSat measurements of the third Stokes parameter.

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For example, the wind direction in the area with a latitude of –50° to –45° and a longitude of –112° to –106°, reconstructed based on the measurements at individual frequencies and on their combination, is the same as that in the first map in Fig. 9. The directions also agree (although somewhat less accurately) in the area with a latitude of –45° to –40° and a longitude of ‒111° to –116°. The wind speed in this area is 3–5 m/s. Since the third Stokes parameter is proportional to the wind speed, the accuracy of determination of the wind direction decreases as the wind falls. The wind speed in the area with a latitude of –39° and a longitude of –113° is below 3 m/s, and it becomes impossible to unambiguously determine the wind direction (vectors are directed differently in the figure).

The wind direction in the area with a latitude of ‒32° to –45° and a longitude of –106° to –111° is reconstructed erroneously at all three individual frequencies (and even if they are combined). Such errors are related to the fact that, as is evident from Figs. 7 and 8, the wind in this area is aligned with the observation direction in the forward and aft swaths. It can be seen in Fig. 1, which presents the dependence of the third Stokes parameter on the relative wind direction, that the S3(φ, …) value is close to zero when the wind direction is collinear with the 0° and 180° viewing directions. The wind direction reconstruction is ambiguous in this case.

In order to resolve these uncertainties, one may introduce the comparison with neighboring points (free from such ambiguities) into the procedure of direction determination (i.e., refine the results after solving the inverse problem). Such approaches are widely used in the analysis of satellite measurements.

CONCLUSIONS

The results of tests of the MicRAWinD algorithm for determining the wind direction based on the WindSat radiopolarimeter measurements demonstrate clearly that this algorithm operates efficiently. The wind field was reconstructed rather accurately with the use of both single-frequency radiometric observations and multifreqeuency measurements. It was demonstrated that a wind field pattern agreeing in general with the products offered by RSS (http://www.remss.com) may be obtained even without the application of special correction methods.

In addition, the time required to reconstruct the wind direction on a common PC is comparable to the satellite measurement time. This implies the possibility of online data processing (if the geophysical parameters of the ocean–atmosphere system are known (were reconstructed with the use of other fast algorithms)).

Several weeks (months) of measurements need to be processed to obtain quantitative estimates. Although the processing time is comparable to the satellite measurement time, the algorithm still operates rather slowly if applied to a large volume of data. Naturally, this study is already underway; its results will be published separately.