1 INTRODUCTION

Sea surface wind speed is a crucial factor in ocean dynamics and air-sea energy exchange, and it plays an important role in weather forecasting and the monitoring of climate change. However, conventional methods of wind speed observation such as ship- and shore-based surveying and buoy measurements cannot meet the dem and s for large-scale all-weather observations. Therefore, satellite radiometer data are increasingly being used to derive global sea surface wind speeds.

At present, in-orbit microwave radiometers such as TMI, WindSat, SSM/I, HY-2 RM, and AMSR2 provide operational data products of sea surface wind speed. The existing information extraction algorithms for passive microwave radiometers can be divided into three categories: statistical algorithms based on field data, semi-statistical algorithms based on simulated brightness temperatures, and nonlinear iterative physical algorithms. However, all the information extraction algorithms have been developed for rain-free conditions, and the direct application of these algorithms for parameter retrieval under rainfall conditions will lead to large errors. Because of the considerable influence of rainfall on atmospheric absorption and scattering, the brightness temperature signal for rain is similar to that of wind speed(Meissner and Wentz, 2009). Thus, it is very difficult to simulate accurately the brightness temperature of rainfall conditions, based on the conventional radiative transfer equation. The retrieval of sea surface parameters under rainfall conditions has always been a problem for passive microwave radiometers. In an attempt to overcome this problem, there has been previous research based on WindSat data(Meissner and Wentz, 2008, 2009, 2012). This study on wind speed retrieval under conditions of rainfall is based on AMSR2 brightness temperature data. The AMSR2 sensor is carried onboard the GCOM-W1 satellite. This is the fi rst of the Global Change Observation Mission(GCOM)water series(W)satellites, developed by the Japan Aerospace Exploration Agency, which was launched on May 18, 2012. This study developed a wind speed retrieval algorithm suitable for hurricane conditions. Referencing the method Wentz used for wind speed retrieval under rainfall conditions using WindSat radiometer data(Meissner and Wentz, 2009), we solved an equation set to obtain atmospheric parameters of upwelling brightness temperature, downwelling brightness temperature, and atmospheric transmittance under rainfall conditions, from which we calculated the AMSR2 brightness temperature. Based on the obtained values of atmospheric transmittance, we established a channel combination of brightness temperatures sensitive to wind speed, but insensitive to rainfall, to improve the accuracy of the retrieval algorithm. Using the derived channel combination, we investigated the applicability of the algorithm to the retrieval of wind speeds under hurricane conditions. This paper is organized as follows. Section 2 describes the multiple data sources and analytical methods used for the brightness temperature simulation, training, and testing of the hurricane wind speed retrieval algorithm. Section 3 presents an analysis of the brightness temperature sensitivity and discussion on the results of the hurricane wind speed retrieval. The final section discusses the principal results and our conclusions.

2 DATA AND METHOD2.1 Data

The data used in this paper comprised NCEP(National Centers for Environmental Prediction)global reanalysis data, AMSR2 L1 microwave radiometer brightness temperature data, and HRD(Hurricane Research Division)H*WIND field data.

The NCEP FNL global reanalysis data are produced every 6 hours on 1°×1° grids. This product is available from the Global Data Assimilation System. The analysis data are available as surface data, including surface pressure, sea level pressure, temperature, sea surface temperature, relative humidity, u -wind and v - wind components, and as 26-layer atmospheric profile data. Some of the physical parameters used in this study are shown in Table 1. Data obtained on 10 days in August 2012 are adopted in this study, and the daily data include four documents for UTC times of 00:00, 06:00, 12:00, and 18:00.

This study used AMSR2 L1 microwave radiometer brightness temperature data to simulate the radiative transfer equation. The AMSR2 sensor has the same band set as the AMSR-E sensor(except 7.3 GHz): 6.925(7.3), 10.65, 18.7, 23.8, 36.5, and 89.0 GHz. The specific parameters are given in Table 2. The data used in the study were the level L1 brightness temperature data, whose scan times, latitudes and longitudes, and channel brightness temperatures are obtained. Data from August to December 2012 were used in the study, which were obtained during 4 456 passes of the satellite.

The H*WIND field analysis data, provided by the National Oceanic Atmospheric Administration’s Hurricane Research Division of the Atlantic Oceanographic and Meteorological Laboratory, were mainly used to build the hurricane wind field retrieval algorithm and to test the algorithm’s efficacy. The H*WIND analysis data combine all available observations of the HRD, including aircraft observations, buoy and ship-derived data and satellite measurements with resolutions of 5–10 km. The hurricane data used in the study were 131 wind fields from six hurricanes that occurred between August and December 2012(Table 3).

2.2 Method2.2.1 Data preprocessing2.2.1.1 Data temporal-spatial matching

The atmospheric profile data used in the brightness temperature simulation were the NCEP FNL global reanalysis data, and the measured brightness temperature data were the AMSR2 L1 data. The data matching method used trilinear interpolation for location and time, i.e., the NCEP FNL atmospheric profile data were interpolated trilinearly to the location and time of the AMSR2 measurements(Meissner and Wentz, 2009). The spatial location matching used bilinear interpolation, in which the four nearest NCEP data points around the AMSR2 observation were interpolated bilinearly to the location of the AMSR2 observation point, because the NCEP data resolution is 1°×1°. The temporal matching used linear interpolation, in which the forward and backward time points of the NCEP data around the AMSR2 observation were interpolated linearly to the AMSR2 observation time, because the NCEP data are published every 6 hours. By following this process, we obtained matched data set 1, used for the brightness temperature simulation.

The data used in the training and testing of the algorithm for hurricane wind speed retrieval were the HRD wind field analysis data and AMSR2 brightness temperature data. The spatial location matching method was based on nearest neighbor interpolation. In this process, the four nearest HRD data points around the AMSR2 observation were interpolated to the location of the satellite observation point. The temporal matching used a time window of 0.2 hours. By following this process, we obtained data set 2, used for the training and testing of the algorithm for hurricane wind speed retrieval.

2.2.1.2 Selection of rainfall flag

When matching the AMSR2 brightness temperature with the NCEP data in the simulation, it was necessary to screen the rainfall points from the AMSR2 brightness temperatures. In this study, we adopted the rainfall flag used by Wang and Li(2009)in the parameter retrievals:

where T_V³⁷ and T_H³⁷ denote the V and H-channel brightness temperature at 37 GHz, respectively, and T¹⁸. and T¹⁸. denote the V and H-channel brightness temperature at 18.7 GHz, respectively. The unit in the formula is K.

2.2.2 Brightness temperature simulation under rainfall conditions2.2.2.1 Radiative transfer equation

The basic form of the radiative transfer equation for the microwave band is as follows(Meissner and Wentz, 2009, 2012):

which is: where R_p is the reflectivity of polarization p, T_s is the sea surface temperature, T_C is the cold space temperature, Ω_p is the empirical correction of the downward radiation reflected by the sea surface, T_BU and T_BD are the upwelling and downwelling brightness temperatures, and τ is atmospheric transmittance.

The reflectivity R_p in Eq.3 is obtained from sea surface emissivity(E), which is composed of three parts:

Specular ocean surface emissivity E₀ is the main part, which depends on the frequency(f), incidence angle(θ_i), T_s, and sea surface salinity S . It can be obtained using the Fresnel equations, which are related to the seawater dielectric constant ε, obtained by solving the Debye equation. Wind-induced emissivity ΔE_W and wind-direction-induced emissivity ΔE_φ can be obtained from the emissivity models in Meissner and Wentz(2009, 2012). Windinduced emissivity ΔE_W depends on wind speed W, whereas wind-direction-induced emissivity ΔE_φ depends on wind speed and relative wind direction φ ; both also depend on f and θ_i .

The absorption coefficient for the microwave band s consists of three parts:

where cloud liquid water absorption α_L is related to atmospheric temperature T_a and liquid cloud water density ρ_L ; water vapor absorption α_Vdepends on f, atmospheric temperature(T_a), pressure(P), and humidity(ρ_V), i.e., water vapor density; and oxygen absorption α_O depends on f, T_a, and P . The atmospheric absorption models used in this study refer mainly to the model formula of Liebe(1989) and the ITU-R P.676-7 Recommendation(ITU-R, 2007).

2.2.2.2 Brightness temperature simulation

In no-rain conditions, R_p in Eq.3 can be obtained from sea surface emissivity E, which can be calculated using NCEP wind speed and direction data; therefore, reflectivity R_p is a known quantity. The scatter correction term Ω_p can be accessed using the model provided by Meissner and Wentz(2012). The cold space temperature T_C is set equal to 3 K. The upwelling brightness temperature T_BU, downwelling brightness temperature T_BD, and atmospheric transmittance τ can all be calculated from NCEP atmospheric temperature profile data, relative humidity profile data, and cloud water profile data. These three atmospheric parameters can then be used to simulate the final brightness temperature.

Under rainfall conditions, because of changes in atmospheric absorption and scattering due to the rainfall and cloud, the upwelling/downwelling brightness temperatures under rainfall conditions cannot be simulated accurately using the usual radiative transfer model. In summary, there are three unknowns on the right-h and side of Eq.3: upwelling brightness temperature T_BU, downwelling brightness temperature T_BD, and atmospheric transmittance τ . Some researchers have found that the difference between the upwelling and downwelling atmospheric temperatures(T_D – _TU)is independent of the quantity of rain and cloud water contained within the atmosphere, i.e., the temperature change due to the rainfall and cloud is almost equal for both T_U and T_D . Therefore, it is justifi ed to substitute the value of(T_D – T_U)with no rain or cloud for the value of(T_D – T_U)under rainfall conditions(Meissner and Wentz, 2009), i.e.:

where T_BDNR is the downwelling brightness temperature, T_BUNR is the upwelling brightness temperature, and τ_NR is the atmospheric transmittance, all under no-rain conditions.

In this way, we can obtain two equations from Eq.3 through V/H polarization of each observation point. Combining these with Eq.6, we can derive Eq.7, which contains three unknowns: T_BU, T_BD, and τ . Solving the equation set provides the values of the three parameters in an atmosphere with rainfall, from which the brightness temperature under rainfall conditions can be simulated.

2.2.3 Sensibility analysis of the brightness temperature

As in the case for rainfall, atmospheric absorption and scattering are enhanced and the brightness temperature signal reduced with decreasing atmospheric transmittance. Therefore, for the development of a wind retrieval algorithm under rainfall conditions, necessary for the retrieval of hurricane wind speeds, this study attempted to find a combination of AMSR2 brightness temperature channels less affected by rain, but sensitive to wind speed.

A channel combination of brightness temperatures is generally considered the combination of V and H polarization of the same band , used to reduce the impact of atmospheric uncertainty on the brightness temperature(Liou, 1980; Hollinger et al., 1990). Equation 3 has the following simplified form according to the assumption of Meissner and Wentz(2009):

where T_BV and T_BH denote the brightness temperature of the V and H channels, respectively, R_V and R_H denote the reflectivity of the V and H channels, respectively, and T_eff is the assumed effective temperature.

According to the simplified form of the radiative transfer equation, if we choose λ = R_H/R_V, the contribution from atmospheric transmittance(τ)can be eliminated. Other researchers have studied the WindSat microwave radiometer and their results have shown that choosing a value for the ratio R_H/R_V of 1.5–1.8 is appropriate for reducing the impact of atmospheric uncertainty on brightness temperature.

However, according to Meissner and Wentz(2009), the combination is not sensitive to wind speed >8 m/s and therefore it is unsuitable for the retrieval of wind speeds in hurricanes under rainfall conditions. A better approach is to consider a combination of different band s, which we demonstrate using the C-band (6H) and X-band (10H). For the C-band and X-band , their reflectivities of H polarization are approximately equal, i.e.:

The combination of the C-band and X-band can be obtained from the simplified radiative transfer equation(Eq.7): If this channel combination is insensitive to rain, then: or:

Atmospheric transmittance under rainfall conditions and the corresponding AMSR2 L2 rain rate can be obtained from data set 1; thus, we can obtain the slope of the atmospheric transmittance τ_6.8 of the C-band with respect to the rain rate(R) and that of the X-band . The values for the two slopes and Eq.10 allow us to determine the coefficient(λ)of the brightness temperature combination, from which we obtain the final brightness temperature channel combination.

2.2.4 Hurricane wind speed retrieval algorithm

In this study, the algorithm for the hurricane wind speed retrieval uses a linear regression algorithm and Back Propagation(BP)neural network algorithm. The basic form of the linear regression algorithm is expressed as(Wentz and Meissner, 2000):

where P_j is a parameter to be retrieved such as sea surface wind speed and ℜ and ℑ are linear functions for which subscript i represents the radiometer channel. The forms of the linear functions are as follows:The BP neural network is a feed forward network of layers trained by an error BP algorithm. The learning rule is to use the steepest descent method through BP to adjust the weights and thresholds of the network continuously, such that the sum of the squared errors of the network is a minimum. The BP neural network topology includes the input layer, hidden layer, and output layer(Fig. 1). In this study, we adopted the three-layer network model(single hidden layer). We used the brightness temperature values for each channel and the combination channel brightness temperatures as the input layer, and the output layer was the parameter to be retrieved, i.e., the sea surface wind speed.

3 RESULT AND DISCUSSION3.1 Brightness temperature simulation results

Using matched data set 1, after screening the rainfall points in accordance with the rainfall flags, we used data from 10 days in August 2012, i.e., 291 passes of brightness temperature data, which provided 403 205 pairs of matching data points.

Using matching NCEP data, we calculated the upwelling brightness temperature(T_BU), downwelling brightness temperature(T_BD), and atmospheric transmittance(τ)under rainfall conditions, in accordance with the conventional radiative transfer equation with which, according to Eq.3, we obtained the results of the brightness temperature simulation. Table 4 shows that the RMSE of the simulated results for the 6.8 and 10.7 GHz band s range from 4.6 to 19.1 K. The scatterplots of the simulated results using the measured AMSR2 brightness temperatures are shown in Fig. 2a. Because of the large impact of rainfall on atmospheric absorption and scattering, it is very difficult to simulate the brightness temperature of rainfall conditions; thus, the simulated results based on the conventional radiative transfer equation are poor.

Based on the above idea of solving the three equations simultaneously, we used NCEP data to calculate the values of T_BD, T_BU, τ under rain-free conditions, and then substituted them into Eq.6. Using NCEP data to calculate the parameters in Eq.3, we obtained two equations from Eq.3 through each observation point of V/H polarization. The combination of the three equations provided an equation set with three unknowns: T_BU, T_BD, and τ.Solving this equation set, we determined the values of the three parameters in a rain atmosphere, and then simulated the brightness temperatures under rainfall conditions. Table 5 shows that the RMSE of the simulated results for the 6.8 and 10.7 GHz band s range from 0.5 to 0.8 K. The scatterplots of the simulated results using the measured AMSR2 brightness temperatures are shown in Fig. 2b.

3.2 Brightness temperature sensitivity analysis

Using matched data set 1 to solve the equation set, we obtained the atmospheric transmittance for each channel. We then analyzed their sensitivities to rainfall and wind speed, and determined the channel combination most sensitive to wind speed, but insensitive to rainfall.

Based on the statistics of atmospheric transmittance for the C-band and X-band under different rain rates, the square of the atmospheric transmittance(τ²)as a function of rain rate R was determined, as shown in Fig. 3. In the figure, the dashed lines show the H-channel of 6.8 and 10.7 GHz, and it is obvious that the square of the atmospheric transmittance(τ²)of both channels declines rapidly with the increase of rain rate. The slopes of the lines in the figure are -0.007 2 and -0.018 5 for 6.8 and 10.7 GHz, respectively. Substituting the slopes into Eq.10 provides a value of the combination coefficient λ of -0.39. The square of atmospheric transmittance(τ²)of TB_6.8H –0.39×TB_10.7H, as a function of rain rate R, is shown as the solid line in Fig. 3. It can be seen that the value ofτ²of the combination remains constant with the increase of rain rate(slope is approximately 0), especially for rain rates ＜15 mm/h. Therefore, it can be concluded that the channel combination of TB_6.8– 0.39×TB_10.7 is insensitive to rain.

Based on the statistics of atmospheric transmittance for the C-band and X-band under different wind speeds, the TB as a function of wind speed was determined, as shown in Fig. 4. The dashed lines show the H-channel of 6.8 and 10.7 GHz, and it is obvious that the TB of both channels has a linear relation to wind speed. The solid line shows that the TB of the combination increases with the increase of wind speed, indicating that the channel combination of TB_6.8 –0.39×TB_10.7 is sensitive to wind speed.

In summary, atmospheric transmittanceτ²for the channel combination of TB_6.8H –0.39×TB_10.7H remains constant with the increase of the rain rate(i.e., insensitive to rainfall), while maintaining sensitivity to wind speed. Therefore, the combination is appropriate to retrieve wind speeds under rainfall conditions.

3.3 Results of retrieval algorithm

To retrieve wind speeds in a hurricane, based on the channel combination coefficients(λ)obtained in the previous section, the channel combination of TB_6.8H –0.39×TB_10.7H was applied to the linear regression algorithm and the BP neural network algorithm. We used the AMSR2 brightness temperature data and 131 HRD wind fields from six hurricanes that occurred during the second half of 2012 to obtain matched data set 2. This data set comprised 2 372 matching data points, half of which were used for training the algorithm, and the other half for testing its performance.

3.3.1 Results of linear regression algorithm

Half of the matched data set was used to train the algorithm and the final form of the linear regression algorithm was as follows:

The coefficients of Eq.14 are presented in Table 6.

The second half of matched data set 2 was used to test the performance of the algorithm. The st and ard deviation of the retrieval results was 3.1 m/s, and compared with the HRD wind field data, the relative error was 13%, as shown in Fig. 5. Figure 6a shows a histogram of a normal distribution of wind speed retrieval error. It can be seen that the wind retrieval error around ±3 m/s is relatively dense. Figure 6b shows the relationship between wind speed retrieval st and ard deviation and the wind speed, which are shown as values in Table 7. It can be seen that at wind speeds ＜25 m/s, the effect of the algorithm is better, with a smaller retrieval st and ard deviation for 2–4 m/s. For wind speeds ≥ 25 m/s, retrieval errors increase significantly to 4–7 m/s, or even higher. Figure 6c shows the relationship between wind speed retrieval st and ard deviation and the rain rate, which are shown as values in Table 8. It can be seen that the retrieval st and ard deviation shows little change for a variety of rain rates at a wind speed of 2.5 m/s, demonstrating that the algorithm is less affected by rainfall.

3.3.2 Results of BP neural network algorithm

The BP network created for the retrieval of hurricane winds was:

Net=newff(P, T, 7, {’ tansig ’ and ’ purelin ’}, ’trainlm);

The number of hidden layer neurons in the network was seven, the transfer function of the hidden layer was tansig, the output layer transfer function was purelin, and the training function was trainlm.

In the BP neural network algorithm, we used half of data set 2 to train the net, and the other half to test the performance of the algorithm. The st and ard deviation of the retrieval results was 2.1 m/s, and compared with the HRD wind field data, the relative error was 8%, as shown in Fig. 7. Figure 8a shows a histogram of a normal distribution of wind speed retrieval error. It can be seen that the wind retrieval error around ±2 m/s is relatively dense. Figure 8b shows the relationship between wind speed retrieval st and ard deviation and the wind speed, which are shown as values in Table 9. It can be seen that at wind speeds ＜25 m/s, the effect of the algorithm is better, with a smaller retrieval st and ard deviation for 1.5–2.5 m/s. For wind speeds ≥ 25 m/s, retrieval errors increase signifi cantly to 3–4 m/s, or even higher. Figure 8c shows the relationship between wind speed retrieval st and ard deviation and the rain rate, which are shown as values in Table 10. It can be seen that the retrieval st and ard deviation shows little change for a variety of rain rates at a wind speed of 2 m/s, demonstrating that the algorithm is less affected by rainfall.

4 CONCLUSION

In this paper, we developed an algorithm for the retrieval of sea surface wind speed in hurricanes. Based on AMSR2 data, we used the brightness temperature sensitivity to rainfall and wind speed of different channels to determine the appropriate combination for the algorithm, such that it is insensitive to rain, but sensitive to wind speed. The principal results obtained were as follows:

(1)according to the conventional radiative transfer equation, it is difficult to simulate accurately the brightness temperature under rainfall conditions. In this paper, we used the method of solving an equation set to derive the atmospheric parameters of upwelling brightness temperature, downwelling brightness temperature, and the atmospheric transmittance under rainfall conditions, which were used to simulate the AMSR2 brightness temperature under rainfall conditions. The RMSE of the simulation results range from 0.5 to 0.8 K for channels 6.8 and 10.7 GHz.

(2)we used the atmospheric transmittance for each channel obtained from the solution of the equation set, and analyzed their sensitivities to rainfall and wind speed. Based on this, we obtained the channel combination TB 6. 8H –0.39×TB 10.7H, which is insensitive to rainfall, but sensitive to wind speed; thus, it can be used to build a wind speed retrieval algorithm.

(3)in comparison with the HRD wind field data, for the linear regression algorithm, the st and ard deviation of retrieval results was 3.1 m/s, and the relative error was 13%; for the BP neural network algorithm, the st and ard deviation of retrieval results was 2.1 m/s, and the relative error was 8%.