Retrieval of Rain Rates for Tropical Cyclones From Sentinel-1 Synthetic Aperture Radar Images

The purpose of this study was to develop a method for retrieving the rain rate from C-band (∼5.3 GHz) synthetic aperture radar (SAR) images during tropical cyclones (TCs). Seven dual-polarized (vertical–vertical [VV] and vertical–horizontal [VH]) Sentinel-1 (S-1) SAR images were acquired in the interferometric-wide (IW) swath mode during the Satellite Hurricane Observation Campaign. These images were collocated with rain rates measured by the Stepped-Frequency Microwave Radiometers onboard National Oceanic and Atmospheric Administration aircraft. Wind speeds were retrieved from the VH-polarized SAR images using the geophysical model function (GMF) S1IW.NR. We determined the difference between the measured normalized radar cross section (NRCS) based on VV-polarized SAR and the predicted NRCS derived using the GMF CMOD5.N forced with wind speeds retrieved from VH-polarized SAR images. Rain cells were identified as regions in the images where the NRCS difference was greater than 0.5 dB or smaller than −0.5 dB. We found that the difference in the NRCS decreased and the VH-polarized wind speed increased with increasing rain rate. Based on these findings, we developed an empirical function for S-1 SAR rain retrieval in a TC, naming it CRAIN_S1. The validation of the CRAIN_S1 results with Tropical Rainfall Measuring Mission data resulted in a root mean square error of 0.58 mm/h and a correlation of 0.89. This study provides an alternate method for rain monitoring utilizing SAR data with a fine spatial resolution.


I. INTRODUCTION
I T IS well known that rain is an essential factor in oceanography. It plays an important role in the energy exchange at the air-sea interface [1] and is especially important for predicting the tracks of tropical cyclones (TCs) [2], [3]. Rain observations in coastal waters are generally collected using a ship-based approach. However, this method is rarely applied for rain monitoring under high sea states, i.e., typhoons and hurricanes. Remote sensing is an advanced technology capable of observing rainfall over the global seas [4]. The meteorological Tropical Rainfall Measuring Mission (TRMM) was launched in 1997 by the National Aeronautics and Space Administration and the Japan Aerospace Exploration Agency. Although the TRMM is specially designed for quantitative measurement of tropical and subtropical rainfall with a spatial resolution of 0.25°(∼25 km) [5], TRMM data are too coarse for studying sea surface dynamics at the small (submesoscale) scale. Synthetic aperture radar (SAR) is an active sensor that operates at microwave frequencies. It has the ability to conduct sea surface observations at all times and under all weather conditions [6]. Compared with real aperture radar, the spatial resolution of SAR at the azimuthal/flight direction is significantly better, e.g., 1 m pixel size for the German TerraSAR-X (TS-X) in the X-band [7] and for the Chinese Gaofen-3 (GF-3) in the C-band [8]. This improvement in resolution is due to the motion of water particles parallel to the satellite platform, i.e., the Doppler shift. However, the Doppler shift also renders sea surface waves with lengths larger than a specific value undetectable. This unique characteristic of SAR is referred to as velocity bunching [9]. Traditionally, low-to-moderate wind speeds can be operationally retrieved from co-polarization (vertical-vertical [VV] and horizontalhorizontal [HH]) SAR images using a well-developed geophysical model function (GMF). This function describes the empirical relationship between the SAR backscattering signal and the wind vector [10], e.g., the C-band model (CMOD) family for the C-band [11], the X-band model (XMOD) for the X-band [12], and the L-band model (LMOD) for the L-band [13]. The co-polarized SAR backscattering signal encounters a saturation problem at high wind speeds (>25 m/s) [14], [15]. Therefore, hurricane/typhoon winds are usually inverted from crosspolarization [vertical-horizontal (VH) and horizontal-vertical (HV)] SAR images [16], [17]. The effect of heavy rain on wind speed estimation has been discussed in several research reports [18], [19], [20], [21] that have concluded that heavy rain has a significant influence on co-polarized microwave backscattering. To address this issue, a few studies have developed approaches for TC wind retrieval from co-polarized scatterometers [22] and SAR [23] data. SAR wave retrieval methodology can be divided into two main categories: theoretical schemes based on the SAR mapping mechanism [24], [25], [26] and empirical models [27], [28]. Although these methods are suitable for SAR wave retrieval under regular sea states, wave retrieval during TCs is a challenge This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ because the SAR backscattering is distorted by the effects of velocity bunching.
A few clusters on the SEASAT SAR have been identified as rainfall footprints [29], [30]. During storms, rain cells are clearly observed by spaceborne SAR [31], [32] at high incidence angles, but the pattern of the rain cells is generally less apparent at low incidence angles. Rain cells affect the SAR backscattering signal through three mechanisms [33]: turbulence or damping of small-scale waves produced by winds [34]; various splash products generated by raindrops such as ring waves, stalks, and crowns [35], [36]; and enhancement of the roughness caused by downdrafts of large-scale wind flow associated with raindrops [37]. Although these phenomena contribute to the SAR roughness, ring waves are assumed to be the dominant feature in the co-polarization channel [38]. In our recent study [39], ring waves with a wavelength of less than 125 m were clearly observed in the SAR-derived wave spectra. Because rain-induced backscattering dominates the sea surface backscattering in moderate to heavy rains, a scatterometer-derived rain GMF [34], [35] for three different incidence angle ranges was developed using HHpolarized RADARSAT-1 (R-1) scanning SAR (ScanSAR) images collocated with NEXRAD data. Although this approach has been implemented for coarse-resolution SAR (i.e., a 500 m pixel size for R-1 ScanSAR), a more complicated rain retrieval GMF will be needed for fine-resolution SAR at wide incidence angles.
Mastenbroek and de Valk [25] determined that the TRMM rain rate is linearly correlated with the difference between the SAR-measured normalized radar cross section (NRCS) and an NRCS simulated using a theoretical SAR backscattering model based on GF-3 SAR images acquired during TCs. Therefore, we developed a rain retrieval algorithm based on several dualpolarized Sentinel-1 (S-1) SAR images acquired during TCs with wind speeds of up to 70 m/s. These images were acquired in the interferometric-wide (IW) swath mode. The sea state during TCs is complicated, with high winds, extreme waves, strong currents, and breaking waves. In the literature, the SAR-measured NRCS consists mainly of resonant Bragg-wave backscattering modulated by the wind, waves, and current [40], and a non-Bragg (NB) scattering component caused by breaking waves [41], [42]. In this study, the sea state during a TC was simulated using a numeric wave model WAVEWATCH-III (WW3) [43], in which winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA-5) and the sea surface current from the hybrid coordinate ocean model (HYCOM) are treated as the forcing field [44]. Using the model-simulated sea state and the HYCOM current, an improved composite surface radar backscattering model based on the Bragg scattering theory was used to calculate the resonant NRCS component at moderate incidence angles [45], [46]. The NB contribution was estimated using an empirical function [47] and by taking the SAR-derived winds obtained from a VH-polarized S-1 SAR image using a GMF (i.e., the S-1 IW mode wind speed retrieval model after noise removal, S1IW.NR) [48]. We observed a difference between the observed NRCS and the simulated NRCS in the rain cells forming the basis for the rain rate retrieval algorithm we developed.
The remainder of this article is organized as follows. The datasets, i.e., the dual-polarized S-1 SAR images, ERA-5 wind elds, HYCOM sea surface currents, rain rate measurements from the Stepped-Frequency Microwave Radiometers (SFMRs) onboard National Oceanic and Atmospheric Administration (NOAA) aircraft, the TRMM rain data, and the settings of the WW3 model, are introduced in Section II. Section III describes the methodology of the SAR roughness simulation, NB estimation, and rain cell identification. Section IV presents the results of the rain cell identification and rain rate retrieval. This section also presents the validation of the rain rate against the SFMR observations. Section V concludes this article.

A. SAR Images
Seven dual-polarized (VV and VH) S-1 SAR images produced as a Level-1 product were obtained from the Satellite Hurricane Observation Campaign (SHOC). These images were acquired in the IW swath mode in both the azimuthal and range directions with a pixel size of 40 m (80 m spatial resolution) and incidence angles of 30°-50°. Information about the images is listed in Table I. The collected images in VV polarization are shown in Fig. 1.

B. Rain Data
During the hurricane season, synchronous wind and rain measurements are collected by SFMR following the flight of the NOAA aircraft [see the red line in Fig. 1(c)]. The TRMM data are a valuable remote-sensed source for studying the climatology of tropical precipitation variability [49]. The spatial resolution of the rainfall rate data measured by the TRMM satellite is 0.25°grids, with an interval of 3 h. It should be noted that SFMR observations (largely the wind speed and rain rate) were available for four of the images (Hurricanes Maria, Lionrock, Hermine, and Isaias), whereas the other images were collocated with TRMM rain data (Hurricanes Irma, Dorian, and Delta). In this study, the SFMR measurements were used to develop an SAR rain retrieval algorithm, and the SAR-derived rain rate was validated against the TRMM data. Due to insufficient TRMM data collocated with SFMR observations, a comparison between the TRMM and SFMR is not made in this work. However, the SFMR observations are well-calibrated and have been used in research on SAR wind retrieval [48]. Fig. 2 shows the TRMM rain map of Hurricane Maria [corresponding to Fig. 1(a)] in which the rain band around the cyclone's center is apparent and has a rain rate of up to 10 mm/h.

C. Hindcast Waves From WW3 Model
Information about the sea state is required to simulate the SAR sea surface roughness. However, extreme wave retrieval during a TC is a challenge because the SAR roughness is modulated by currents, breaking waves, and rainfall [50]. Therefore, the sea states during TCs were simulated using a third-generation numeric wave model, i.e., WW3. The ERA-5 data, with 0.25°F ig. 2. TRMM rain maps during Hurricane Maria corresponding to the image in Fig. 1(a).  grids and an interval of 3 h, were used as the forcing field. The water depth data from the bathymetric topography of the General Bathymetry Chart of the Oceans (GEBCO) has a 1 km horizontal resolution. The ERA-5 wind map for September 23, 2017 at 10:00 UTC during Hurricane Maria is shown in Fig. 3. As was determined in earlier research [51], wave simulations of typhoons are influenced by high wind-induced currents and sea level rise. Sea surface current and sea-level data from HYCOM with a 1/12°(∼8 km) grid spatial resolution and a 1-h interval were collected simultaneously and used as the forcing field in the WW3 model. The HYCOM current and sea-level maps for September 23, 2017 at 09:00 UTC during Hurricane Maria 1) The simulated regions included the entire track and occurrence for each TC using rectangular grids.
2) The 2-D wave spectrum was resolved into 24 regular azimuthal directions with a 15°step, and the computation step was set as 300 s time steps in both the longitudinal and latitudinal directions.
3) The frequency bins were logarithmic and ranged from 0.04118 to 0.7186 at an interval of Δf/f = 0.01. 4) The spatial resolution of the simulated wave spectrum was set at 0.05°grid with an interval of 30 min. 5) The parameterizations of switches ST2 and STAB2 for the input/dissipation terms [22] and the four wave components (quadruplets) of the wave-wave interactions followed the generalized multiple discrete interaction approximation [17]. The HY-2B altimeter was specifically designed for global wave monitoring, even during TCs. Currently, some satellites, e.g., Jason-2 [52] and the Chinese Haiyang-2B (HY-2B), provide a wave product following the footprint of their flight with a ∼0.3 m root mean square error (RMSE) for significant wave height (SWH) under low-to-moderate sea states (SWH < 7 m) [53]. Therefore, available measurements from the HY-2B altimeter were used to validate the WW3 simulated during the duration of Hurricanes Dorian, Isaias, and Delta. However, HY-2B wave data were not available for the duration of the other TCs. Fig. 5 shows the case map of the WW3-simulated SWH of Hurricane Delta on October 8, 2020 at 00:07 UTC. The statistical analysis yielded an RMSE of 0.23 and a correlation coefficient (COR) of 0.91 (see Fig. 6) with an SWH of up to 3 m, indicating that the use of WW3-simulated waves in this study was reliable.

III. METHODOLOGY
In this section, the sea surface backscattering model for simulating the SAR roughness [54] is described, including the wind, wave, and current terms. In particular, the empirical model for the NB estimation caused by wave breaking is introduced. Then, the method of rain cell identification in the images is presented using VV-and VH-polarized SAR winds. Finally, the empirical algorithm of rain retrieval is proposed.
The process for retrieving the rain rate from dual-polarized S-1 IW SAR is illustrated in Fig. 7.

A. SAR Backscattering Model
SAR backscattering returns depend on sea surface roughness due to gravity-capillary Bragg resonant waves and wave-induced NB backscattering. Over the last few decades, the use of advanced radar backscattering to calculate and simulate the NRCS of the ocean surface at moderate incidence angles has become well developed. These methods incorporate wave-current interactions and the upwind/downwind differences in the NRCS [55]. Traditionally, the normalized Bragg wave resonant contribution σ 0 is defined as the average of the radar backscattering cross section (RCS) σ in the horizontal x and vertical y directions The relationship between the RCS σ and the dimensional wave spectrum E is as follows: where In (2)-(5), k b is the wave number of the resonant Bragg waves related to the radar wave number k 0 (e.g., 5.3 cm for GF-3 and 3.1 cm for TS-X), ϕ b is the direction of the Bragg waves, and w is the weighting function of the Bragg scattering. This accounts for the geometric modulation caused by the elevation or tilt toward the radar antenna, and it has a larger effective area for the radar than a horizontal facet of the same x and y dimensions within the reference plane. σ P 0 is the Bragg scattering in the co-polarization channels (i.e., P denotes HH or VV polarization), θ is the incidence angle, ϕ is the radar look direction vertical to the flight platform, and S p and S t are the slopes of the tilted Bragg scattering facets parallel and vertical to the radar look direction, respectively. It should be noted that RCS σ is assumed to be an invalid value, and d is the filter threshold (value of 0.25) when 4sin 2 (θ-S p ) < d 2 .
The Bragg scattering σ P 0 is calculated as follows: In (6)-(8), ε is the permittivity of seawater. PP and QQ denote the co-polarization option (VV or HH): if PP is set as VV, b PP is the scattering coefficient for VV polarization b VV , and QQ is the scattering coefficient for HH-polarization b HH . θ i is the effective incidence angle; that is, the radar incidence angle θ modulated by the slopes S p and S t . where The slopes S p and S t are a function of the sea surface elevation ζ in the radar look direction ϕ, and they are modulated by the waves and currents. Collectively, according to the above theoretical rationale, the NRCS is conveniently predicted using four parameters: 1) the wave energy spectrum; 2) the current speed; 3) the radar incidence angle; and 4) the radar azimuth angle. In this study, the wave energy spectrum during the TC was derived by hindcasting using the WW3 model. The HYCOM current was applied directly.

B. NB Estimation
According to its theoretical principle, the NB contribution can be calculated using a dual-polarized (VV and HH) SAR image [56]. However, S-1 SAR images are available only for the VV and VH polarization channels. In a recent study [47], more than 1000 quad-polarized RADARSAT-2 (R-2) SAR images were collocated with measurements from National Data Buoy Center buoys monitored by NOAA. It was found that the NB contribution is exponentially related to the wind speed. Wave breaking is determined by fetch, which is correlated with the sea surface wind speed U 10 . In practice, the NB contribution σ wb in the co-polarized SAR NRCS is as follows: In (12)- (18), θ is the radar incidence angle and ϕ is the azimuth angle following the flight platform. Although σ wb can be easily calculated when the sea surface wind speed U 10 is known, the empirical approach does not require the HH and VV polarized SAR images. As was previously mentioned, the wind speed U 10 is necessary for the NB estimation; therefore, the cyclonic winds were inverted from the VH-polarized S-1 SAR images, which were used in the above model.

C. Rain Cell Identification
The entire SAR image was divided into 128 × 128 pixel (azimuth × range) subscenes with a spatial coverage of 5 × 5 km to match the image with the WW3-simulated waves and HYCOM currents. The winds were retrieved from the VH-polarized S-1 image using GMF S1IW.NR [48]. Next, the VV-polarized NRCS was simulated using CMOD5.N [11] and the VH-polarized SAR winds. We determined that the wind directions were prior information in the CMOD5.N. Although the wind directions can be estimated from the homogenous pattern on the SAR image corresponding to the wind-induced low-frequency features of the SAR intensity spectrum [57], these features are distorted by high sea states and breaking waves. Regardless, the spectrum-based method is usually implemented for about 30% of acquisitions of S-1 IW swath mode under a moderate sea state [58]. In this sense, cyclonic winds with a spiral direction and an inflow angle of 20°in the polar coordinate system were used [59].
Due to the significant attenuation effect of rainfall on VVpolarized SAR images, we assumed that the difference between the simulated NRCS and the SAR-measured NRCS in the VVpolarized channel was produced by rain cells. The method for rain cell identification involved calculating the threshold value, which was proposed by Shen et al. [60]. The threshold value was set as follows: where σ VV 0 is the observed NRCS (dB) and σ CMOD5N 0 is the NRCS simulated using CMOD5.N. In this study, the threshold value was assumed to be ±0.5 dB, that is, the values greater than 0.5 dB or smaller than −0.5 dB are identified as rain cells.

D. Rain Retrieval
The dataset included more than 1000 matchups with rain rates measured by the SFMR. We analyzed the relationships between the difference in the NRCS and the VH-polarized wind speed and the SFMR rain rate at incidence angles of 30°-50°. It should be noted that data for rain rates of <2 mm/h were excluded due to the occurrence of a few disturbances of the sea roughness induced by the small amount of rain. Fig. 8(a) and (b) shows the analysis results within a distance of 100 km from the cyclones' eyes. For incidence angles of 30°-50°with a 5°interval, the Fig. 8. Relationships between the SFMR rain rate and two variables: (a) Difference in the NRCS within a distance of 100 km from the cyclones' eyes. (b) VH-polarized SAR wind speed within a distance of 100 km from the cyclones' eyes. The relationship between the SFMR rain rate and two variables: (c) difference in the NRCS beyond a distance of 100 km from the cyclones' eyes and (d) VH-polarized SAR wind speed beyond a distance of 100 km from the cyclones' eyes. difference in the NRCS decreases with increasing rain rate, while the VH-polarized wind speed increases significantly with increasing rain rate. However, this type of behavior is relatively weak due to the smaller amount of precipitation beyond 100 km from the cyclones' eyes [see Fig. 8(c) and (d)].
As mentioned in [35], the rain-induced component in NRCS is expressed as a polynomial function of rain rate without considering the sea state. Based on the above findings, the rain rate is related to several factors of SAR. Therefore, a function referring to the empirical model CWAVE for SAR wave retrieval was constructed for rain rate retrieval from SAR images, denoted as CRAIN_S1 [28] where R is the rain rate (mm/h); the imaging parameters s i include the difference in the NRCS σ d (dB), the incidence angle θ (30°to 50°with an interval of 5°), and the VH-polarized wind speed U 10 ; and a i,j is a coefficient vector determined by matchups by using the least square regression. It should be noted that CRAIN_S1 is specifically adopted within and beyond 100 km from the cyclones' eyes. Table II lists the coefficients of CRAIN_S1, in which the subscripts 1, 2, and 3 represent the variables σ d , θ, and U 10 , respectively, e.g., a 12 is the coefficient for the term σ d ×θ. Fig. 9 compares the simulated values of CRAIN_S1 with the SFMR rain rate data, yielding a 1.41 mm/h RMSE and a 0.82 COR.

IV. RESULTS
As was mentioned by Shi et al. [61], the rain rate is correlated with the difference in the SAR roughness during TCs after removing the influence of the Bragg resonant component. The Bragg resonant component in the NRCS was calculated using the profiles, including the VH-polarized SAR-derived wind, HYCOM current, and WW3-simulated waves. An empirical model was implemented to calculate the NB component using the VH-polarized SAR-derived wind and the radar incidence angle and azimuth angle corresponding to the disturbance of the rain cells. Fig. 10 shows maps of the VH-polarized SAR winds corresponding to the images in Fig. 1, i. Fig. 11(a) and (b) shows the difference between the sum of simulated NRCS and SAR-measured NRCS. Fig. 12 shows the map of the rain cell identification. This figure shows additional detail of the rain cells compared with the TRMM map in Fig. 2, especially at the rain wall around the cyclone eye. We  determined that the pattern of the rain cells was consistent with the TRMM data.
In the validation dataset, about 100 matchups with TRMM data were available for the three cyclones. The SAR-derived rain rate for the S-1 SAR image acquired at 10:44 UTC on September 23, 2017, during Hurricane Maria, is shown in Fig. 13. In addition, we applied CRAIN_S1 to three S-1 SAR images acquired during TCs and compared the retrieval results with the rain rate product of the TRMM. In Fig. 14, the RMSE of the rain rate is 0.58 mm/h and the COR is 0.89 (with rain rates of up to 8 mm/h). This indicates that the CRAIN_S1 algorithm can be applied for rain rate retrieval from dual-polarized S-1 SAR images acquired during TCs. However, it is necessary to verify that there are no available TRMM data for extreme rain rates of >20 mm/h in the validation procedure, indicating that the effectiveness of the proposed method needs to be further studied. Thus, the accuracy of the retrieval results obtained using CRAIN_S1 is expected to be  further improved through abundant datasets with a wide range of incidence angles and heavy rainfall to enhance the applicability of the empirical model for NB estimation during TCs.

V. CONCLUSION
In the field of remote sensing, algorithms for wind and wave retrieval from co-polarized SAR images are readily available for use under low-to-moderate sea states (U 10 < 20 m/s). Utilizing SAR backscattering in the cross-polarization channel, strong winds during TCs have also been inverted using cross-polarized GMFs, a process that can be practically implemented using data from various C-band SAR sensors. Although the effect of rain on the SAR roughness has been investigated and the characteristics of its effect on C-and X-band SAR have been studied, a quantitative approach for SAR rain retrieval from SAR images has been lacking. In this study, an analytical approach for SAR rain rate retrieval was developed.
We obtained seven S-1 SAR IW images from the dualpolarization channel (VV and VH) of the SHOC. Of these images, four images in Hurricanes Maria, Lionrock, Hermine, and Isaias were collocated with rain observations from the SFMR and were used to develop a rain rate retrieval algorithm. The remaining three images of Hurricanes Irma, Dorian, and Delta were used to validate the SAR-derived rain rate against TRMM data. The wind field was inverted from the VH-polarized image using the GMF S1IW.NR, which was then input into the GMF CMOD5.N to simulate the VV-polarized NRCS. The difference between the CMOD5.N-simulated and SAR-measured NRCS was calculated, and rain cells were identified as cells with values greater than 0.5 dB or smaller than −0.5 dB. The rain cell identification results are more detailed than the calibrated TRMM products.
The Bragg resonant component related to strong wind, waves, and current during a TC was obtained using a polarimetric microwave radar backscatter model. The NB contribution induced by wave breaking was estimated using an empirical model. We found that the SFMR rain rate had a linear correlation with the difference in the NRCS (values measured with SAR minus the composite values of the Bragg resonant and NB component) and the VH-polarized wind speed. Therefore, an empirical function was derived for SAR rain rate retrieval and specifically tuned for distances within and beyond 100 km from the eye of the TC. The fitting results were compared with SFMR measurements, yielding a COR of 0.82 for the rain rate. The validation against the TRMM data yielded an RMSE of 0.58 mm/h for the rain rate, with rain rates of up to 8 mm/h. In conclusion, the proposed approach is a promising technique for SAR rain monitoring during TCs, although this method relies on the model-simulated wave spectrum and has limitations outside of the TC eye due to the weak relationship between the difference in NRCS and rain rate.
In the near future, more images with wide range incidence angles and high rain rates will be obtained and the empirical model for NB estimation will be adapted for high sea states to improve the accuracy of SAR rain retrieval.

ACKNOWLEDGMENT
The authors greatly appreciate the provision of the Sentinel (S-1) synthetic aperture radar (SAR) images by the European Space Agency via https://scihub.copernicus.eu and the provision of the source code for the WAVEWATCH-III model free of charge by the National Centers for Environmental Prediction of the National Oceanic and Atmospheric Administration (NOAA). The ERA-5 data were obtained from http://www. ecmwf.int. The sea surface current and sea-level data from HYCOM were openly accessed from https://www.hycom.org. The General Bathymetric Chart of the Oceans bathymetry data were downloaded from ftp.edcftp.cr.usgs.gov. The rainfall observations and the information about hurricane's best tracks were collected by the Stepped-Frequency Microwave Radiometers on board NOAA aircraft. The Haiyang-2B (HY-2B) data were provided by the National Satellite Ocean Application Service through an authorized account via https://osdds.nsoas.org.cn. The rain data from the Tropical Rainfall Measuring Mission were obtained via ftp.trmmopen.gsfc.nasa.gov and the typhoon parameters were provided by the Japan Meteorological Agency via http://www.jma.go.jp.