Biao Zhang1, William Perrie1, Paul A. Hwang2, Yijun He3, 4. 1Fisheries and Oceans ... However, Vachon and Dobson [6] recommended the same formulation ...
A NEW POLARIZATION RATIO MODEL FROM C-BAND RADARSAT-2 FINE QUAD-POL IMAGERY Biao Zhang1, William Perrie1, Paul A. Hwang2, Yijun He3, 4 1
Fisheries and Oceans Canada, Bedford Institute of Oceanography, NS, Canada Remote Sensing Division, Naval Research Laboratory, Washington DC, USA 3 Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China 4 Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences, Qingdao, China 2
ABSTRACT We propose two new analytical polarization ratio (PR) models based on the RADARSAT-2 Quad-Polarization (HH+VV+HV+VH) observations over the ocean. One is a function of incidence angle only and the other has additional dependence on wind speed. Comparisons are presented with theoretical and empirical PR models from the literature. The new PR model with wind speed and incidence angle dependence is shown to compare best with observed RADARSAT-2 data. An assessment of the PR model with only incidence angle dependence is given using CMOD algorithms and HH-polarized images. Results suggest that this PR model can accurately convert normalized radar cross sections (NRCS) in HH polarization to VV polarization and retrieve wind speeds from RADARSAT-1 or RADARSAT-2 HH polarization images. Index Terms— Polarization Ratio, Wind Speed, RADARSAT-2, Quad-Polarization 1. INTRODUCTION In recent years, different available empirical geophysical model functions (GMF), such as CMOD4, CMOD_IFR2, CMOD5 and CMOD5.N [1-4], are employed, which relate the normalized radar cross section (NRCS) of the ocean surface to the local near-surface wind speed, wind direction relative to antenna look direction, and radar incidence angle. Although many CMOD algorithms have been established for vertically polarized images, however no similar well-developed and validated wind retrieval model exists for wind speed retrievals from RADARSAT-1 (only operated at horizontal polarization) or RADARSAT-2 images acquired at HH polarization. To meet this deficiency, a hybrid model function was developed that consists of a CMOD type function and a polarization ratio (PR). The nature of the PR is an active area of investigation, and several empirical and theoretical PR models have been
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proposed [5-9]. These models have been applied in numerous studies for wind speed retrieval from RADARSAT-1 images [10-12]. However, these PR models tend to not be completely suitable for C-band HH polarization wind retrievals, because they are somewhat limited by their formulations. For example, the Thompson et al [5] PR model neglects wind speed and wind direction dependence and is given by (1 D tan 2 T ) 2 (1) PR (1 2 tan 2 T ) 2 where D is a empirical parameter equal to 0.6. The D parameter was suggested to have a constant value of 0.6 to yield consistency with multi-frequency dual-polarization radar observations from a limited set of RADARSAT-1 imagery acquired at HH polarization. Wind speed would be overestimated if D was set as 0.6, especially for high wind speeds. However, Vachon and Dobson [6] recommended the same formulation with D 1 for RADARSAT-1 SAR ocean wind retrievals. Mouche et al. [7] also proposed a PR model dependent on both incidence angle and wind direction, based on C-band airborne real aperture radar, with both vertical and horizontal polarizations. Furthermore, Johnsen and Guitton [8] suggested a physically-based model, called the extended generalized curvature model (GCM) by incorporating scattering from wave breaking. The GCM model can describe analytically electromagnetic scattering from an elevated conducting curved surface, and the extended GCM model can be used to simulate NRCS in VV and HH polarizations and thus estimate the PR. The performance of this model is dependent on using a unified directional spectrum for long and short wind-driven wave and wave breaking statistics. The special imaging capability of C-band RADARSAT-2 in quad-polarization mode (HH+VV+HV+VH) provides an encouraging opportunity to investigate PR dependence on the sea surface. Here, the study presented is aimed at the construction new PR models and assessment of their performance in wind speed retrievals from RADARSAT-2 images acquired at HH
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polarization, in conjunction with a new CMOD algorithm. We show that our PR models perform very favourably compared to SAR data. 2. DATASETS RADARSAT-2 images from fine quad-polarization acquisition mode provide fully polarimetric observations. In this study we use the images with each of the four combinations of H and V for both transmit and receive polarization (HH, HV, VH, and VV). The range of incidence angles for quad-polarization data is between 20q and 49q. It should be noted that the fine quad-polarization data have an extremely low noise floor, and that cross-talk between different channels is corrected. We collected RADARSAT-2 quad-polarization images from selected geographic locations that are collocated with 52 in situ National Data Buoy Center (NDBC) buoy measurements of ocean wind vectors and waves, from December 2008 to April 2010. The buoy measurements and the RADARSAT-2 observations are required to occur within a spatial interval of 10 km and a time interval of 30 min. This approach resulted in 784 pairs of RADARSAT-2 images with collocated buoy data, in different sea states. The meteorological conditions for our dataset include wind speeds from 1 to 26 m/s, and significant wave heights in the range 0.5-8.7 m. 3. METHOD As mentioned in the introduction of this paper, there is no well-developed and validated wind retrieval model for wind speed retrievals from RADARSAT-1 (only operated at horizontal polarization) or RADARSAT-2 images acquired at HH polarization. To use C-band HH data, we propose two simple analytical PR models based on the analysis of our data. Using quad-polarization images and collocated NDBC buoy data, we investigate the relation between polarization ratio, PR, and radar incidence angle as well as wind speed. The variation in PR with incidence angle T as observed from RADARSAT-2 quad-polarization images is shown in Figure 1 in comparison with other PR representations described in the literature [5-9]. We use a nonlinear least square method to fit the collocated datasets (784 RADARSAT-2 observed PR and incidence angles), thereby deriving a new PR formulation which we hereafter refer to as model I, given as (2) PR A exp(BT ) C [Linear units] where A, B, and C are constant coefficients, given in Table 1. Figure 1 shows that the PR with our model I, and from the RADARSAT-2 data increase rapidly with increasing incidence angles (above 20q), reaching 3 dB at incidence angle 40q. Figure 1 also shows that the two PR formulations suggested by Mouche et al. [5] overestimate RADARSAT-2
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observations over the whole range of incidence angles, and at 35q, by more than 1.4 dB. We found that their model 1 [7] under crosswind conditions is closer to RADARSAT-2 measurements than under downwind conditions, or than their model 2 [7]. It is notable that the models mentioned in the literature do not consider PR dependence on the wind speed. In this study, the range of buoy-measured wind speeds is between 1 and 26 m/s. This range of data allows us to investigate the effect of wind speed on PR. Therefore, we built another PR model, hereafter referred to as model II, which is a function of wind speed and incidence angle (3) PR P (T )U 10Q T [Linear units] where (4) P(T ) P1 * T 2 P 2 * T P3 (5) Q(T ) Q1 * T Q 2 where polynomial coefficients P1, P2, P3, Q1 and Q2 are given in Table 2. 4. RESULTS AND ANALYSIS For the assessment of performance for our two proposed PR models, we make comparisons with the various empirical and theoretical PR models previous mentioned in the literature [5-9], and with RADARSAT-2 observations. The comparisons are shown in the Figure 2. Among the models plotted in Figure 2, our model II (considering both wind speed and incidence angle dependence) gives among the best comparisons to RADARSAT-2 observations, resulting in a bias of 0.02 m/s, standard deviation of 0.40 m/s, and scatter index of 0.22. Although our model I (considering only incidence angle dependence) is not better than our model II, it can be easily used in operational applications to construct a hybrid model with a CMOD algorithm and thus retrieve wind speeds from RADARSAT-1 or RADARSAT2 images acquired at HH polarization. In this paper, 109 HH-polarized RADARSAT-2 images are collocated with NDBC buoys and measured wind speeds and wind directions at 0.25q resolution from QuikSCAT Level 3 wind vector products, to assess the performance of our model I. In making this assessment, model I is first employed to convert the NRCS values in HH polarization to VV polarization. Comparisons between estimated NRCS values in VV polarization are shown in Figure 3 to be in good agreement with observed NRCS values, with bias of -0.11 dB and a standard deviation of 1.03 dB. Secondly, the inverted NRCS in VV polarization and several selected CMOD algorithms are used to retrieve wind speeds. The comparisons between retrieved wind speeds and buoy measurements are shown in Figure 4. It is found that CMOD5.N is able to achieve the smallest bias of 0.18 m/s and a root mean square error of 1.49 m/s. Figure 5 shows a wind map from our model I in conjunction with CMOD5.N as well as a RADARSAT-2
image acquired at HH polarization on December 25, 2009 at 03:19 UTC. In this case, we firstly resample the SAR data from the original 50 m pixel spacing to 1 km, and then, at each image pixel, we linearly interpolate the weather model wind directions from the 1q u 1q longitude-latitude grid of the Navy Operation Global Atmospheric Prediction System (NOGAPS) model to the geographic position of the pixel. The reason for selecting model wind directions was that QuikSCAT mission ended on November 23, 2009. Using these NOGAPS wind directions and the SAR-measured NRCS at each pixel, as well as CMOD5.N, we compute the associated wind speeds as shown in Figure 5. There are two NDBC buoys (46076, 46061) and one C-MAN station (PILA2) in the Figure 5. The retrieved wind speeds for 46076, 46061 and PILA2 are 17.2 m/s, 13.3 m/s and 13.9 m/s, in good agreement with measured wind speeds for 46076, 46061 and PILA2, which are 15.9 m/s, 14.1 m/s and 12.4 m/s, respectively.
from [7] (downwind). (d) Model 1 from [7] (crosswind). (e) Model from [8]. (f) Model from [5]. (g) Model from [9]. (h) Model II from this study. (i) Model from [6].
Fig. 3. Observed NRCS in VV polarization from RADARSAT-2 measurements versus equivalent values calculated from observed HH-polarized data of the same scene combined with our model I in this study.
Fig. 1. Polarization ratio (PR) as a function of incidence angle, from RADARSAT-2 quad-polarization measurements in the dataset. Various other PR models are also plotted (see legend on the plot and the text). Fig. 4. Comparisons of retrieved wind speeds from RADARSAT-2 images acquired at HH polarization and our model I with buoy wind observations, using (a) CMOD_IFR2, (b) CMOD4, (c) CMOD5, and (d) CMOD5.N. 5. CONCLUSIONS
Fig. 2. PR models derived from the various empirical and theoretical models compared to RADARSAT-2 data: (a) Model 2 from [7]. (b) Model I from this study. (c) Model 1
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In this paper, we built two simple analytical models of the polarization ratio, PR; one is a function of only incidence angle (model I), the other is a function of both incidence angle and also wind speed (model II). We compared the PR values estimated by our models I and II with those computed from selected theoretical and empirical models proposed in the literature, and we showed that our model II compares best to the RADARSAT-2 observations with the
smallest bias, 0.02 dB, and standard deviation, 0.40 dB. Thus, the effect of wind speed on PR can not be neglected. Furthermore, CMOD algorithms and 109 RADARSAT2 images acquired at HH polarization are used to assess model I. Results suggest that NRCS in HH polarization is able to be accurately converted to VV polarization with our model I in conjunction with CMOD5.N. This approach is able to achieve the smallest wind speed retrieval bias, 0.18 m/s, and root mean square error, 1.49 m/s, surpassing those of CMOD_IFR2, CMOD4 and CMOD5. For these reasons, we recommend that our model I and CMOD5.N should be used to construct a hybrid model for retrieving wind speeds.
6. REFERENCES [1] A. Stoffelen, D. Anderson, “Scatterometer data interpretation: estimation and validation of the transfer function CMOD4” J. Geophys. Res, vol. 102, pp. 5767-5780, 1997. [2] Y. Quilfen, B. Chapron, T. Elfouhaily, K. Katsaros, and J. Tournadre, “Observation of tropical cyclones by high-resolution scatterometry” J. Geophys. Res, vol. 102, 7767-7786, 1998. [3] H. Hersbach, A. Stoffelen, S. de Haan, “An improved C-band scatterometer ocean geophysical model function: CMOD5” J. Geophys. Res, vol. 112, C03006, doi: 10.1029/2006JC003743, 2007. [4] H. Hersbach, “Comparison of C-band scatterometer CMOD5. N equivalent neural winds with ECMWF” J. Atmos. Oceanic Technol, vol. 27, pp. 721-736, 2010. [5] D. Thompson, T. Elfouhaily, B. Chapron, “Polarization ratio for microwave backscattering from the ocean surface at low to moderate incidence angle” in Proc. IGARSS, July 1999, pp. 16711673. [6] P. W. Vachon and F. W. Dobson, “Wind retrieval from RADARSAT SAR images selection of a suitable C-band HH polarization wind retrieval model” Can. J. Remote Sens, vol. 26, no. 4, pp. 306-313, 2000.
Fig. 5. SAR wind map derived using the CMOD5.N inversion with our model I and a RADARSAT-2 image at HH polarization at 03:19 UTC on December 25, 2009. Table I Coefficients of model I in this study Coefficient A B C
[8] H. Johnsen and G. Guitton, “Sea-surface polarization from ENVISAT ASAR AP data” IEEE. Trans. Geosci. Remote. Sens, vol. 46, pp. 3637-3646, 2008.
Fitted values 0.5474 0.0333 -0.0802
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Table II Coefficients of model II in this study Polynomial coefficient P1 P2 P3 Q1 Q2
[7] A. Mouche, D. Hauser, J. F. Daloze, and C. Guerin, “Dual polarization measurements at C-band over the ocean: Results from airborne radar observations and comparisons with ENVISAT ASAR data” IEEE. Trans. Geosci. Remote. Sens, vol. 43, pp. 753769, 2005.
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Fitted values 0.0012 -0.0162 0.9559 -0.0006 -0.0505
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Acknowledgments. We thank CSA for funding “Full polarization retrievals of ocean waves and winds”, and China Academy of Sciences Knowledge Innovation Program (Grant No. KZCX2-YW-201).
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[12] R. P. Signell, J. Chiggiato, J. Horstmann, J. Pullen, and F. Askari, “High-resolution mapping of Bora winds in the northern Adriatic sea using synthetic aperture radar” J. Geophys. Res, vol. 115, C04020, doi: 1029/2009JC005524, 2010.
