# Ocean Wind Retrieval Models for RADARSAT Constellation Mission Compact Polarimetry SAR
## 1 Introduction  
The Canadian RADARSAT Constellation Mission (RCM) is scheduled for launch in early 2019 and will provide Compact-Polarimetry (CP) synthetic aperture radar (SAR) data. RCM is the evolution of the RADARSAT Program and the successor of RADARSAT-2, which is a satellite constellation carrying three identical C-band SAR satellites. The RCM CP mode consists of a right hand circular transmit and linear/circular receive radar signal, namely right circular-vertical (RV) polarization, right circular-horizontal (RH) polarization, right circular-right circular (RR) polarization and right circular-left circular (RL) polarization. The CP configuration is designed for Earth observation; compared with conventional linear dual-polarization SAR, compact polarimetry SAR can obtain abundant high-resolution information with wider swath [1]. Researchers have shown that CP SAR is an efficient imaging mode for ocean surface observation and, therefore, elucidation of algorithms and models for retrieval of ocean surface features and marine variables like wind is critically important [2]. Compact polarization SAR is a dual-polarization radar system which transmits circular (or 45\({}^{\circ}\)) components and receives two orthogonal polarization components (V or H) with relative phase [3; 4]. Accurate information of ocean surface can be obtained from C-band radar data. The main process of physical mechanism is the interactions between the microwaves and related surface water waves. The major interaction is denoted as Bragg scattering when the wavelengths of ocean surface waves are of the same order of radar wavelength. For practical application, wind retrievals from SAR images can be accomplished by C-band geophysical model functions (GMFs), because radar measurements are sensitive to the ocean-surface roughness which is determined by the surface wind field [5]. The GMF is a set of functions between wind vectors and radar backscatter signals denoted as the normalized radar cross section (NRCSs) including dependence on the radar incidence angles. The C-band GMF model series (CMOD4, CMOD5 and CMOD5.N [5; 6]) are used for vertical-vertical (VV) polarization data. For horizontal-horizontal (HH) polarization, there are generally two ways to achieve ocean wind retrieval: (1) conversion of the HH backscatter to VV by a polarization ratio (PR) which is a ratio of VV-polarized NRCS to HH-polarized NRCS [7], or (2) construction of a new relationship between wind vectors and radar backscatters [8]. In terms of C-band linear cross-polarization (VH and HV) ocean backscatter data, C-2 PO and C-3 PO models are available for wind retrieval [9; 10]. For wind retrieval from CP SAR mode, recent studies have attempted to retrieve wind speed by converting right circular-vertical (RV) polarization data into linear dual-polarization data, taking advantage of CMOD5 and CMOD5.N models [11; 12]. However, the configurations for RV and VV polarizations are different and the CMOD model series were originally developed for C-Band VV-polarized scatterers rather than SARs. In view of this situation, we propose two new models in this paper to retrieve wind from C-band RV-pol and RH-pol measurements. CMOD is a well-behaved parameterization to retrieve wind speed, allowing the NRCS to be dependent on the principal parameters, such as radar incidence angle, relative wind direction and wind speed [5]. However, as there are 28 CMOD coefficients, the process of optimizing the CMOD model to CP data sets to generate a new GMF (for CP SAR) is not feasible using normal computing clusters, because of the requirement to adjust such large number of CMOD coefficients to represent the CP parameters. In order to avoid excessive computation, a sensitivity analysis of the coefficients can play a significant role in optimizing the generation of a new GMF for RV-polarization. The sensitivity analysis is a method to adjust the models by changing the coefficients within a specific range of variations in order to optimize the parameterization and simplify the computation [13; 14].