# Evaluation of Spaceborne GNSS-R Retrieved Ocean Surface Wind Speed with Multiple Datasets
## Theory and Methods
### Wind Speed Retrieval Algorithm  
The fundamental process of the spaceborne GNSS-R wind speed retrieval algorithm is shown in Figure 1 as follows. (a) calibrate the DDM and compute DDM observables, we directly used the DDM of BRCS in the CYGNSS Level 1 dataset, where the calibration can be found in [15; 21]; (b) improving the SNR by time-averaging while satisfying the requirement of spatial resolution; (c) DDM observables matchup the ground surface truth wind speed from other observing techniques to establish training samples; (d) considering the geometry configuration of the bistatic radar system to form the mapping relation between DDM observables and referenced wind speed; (e) using the algebraic parametric model to smooth the 2D GMF to remove the influence of insufficient training dataset and observation noise; (f) estimating the weighting coefficients of different observables by the minimize variance (MV) estimator; and (g) using the model for wind speed predictions. In this paper, a refined wind speed algorithm is presented based on [19], the NWP and CCMP wind products are used as ocean surface truth wind speed. Matching the observables with reference wind to form the inversion model, counterparts were obtained by bilinear interpolation in space and linear interpolation in time. In fact, the modeled GMF is a series of mapping relations between the DDM observables and referenced wind speed at different incidence angles but presented as a discrete point. The dynamic range of derived wind speed is limited below 35 m/s, and the incidence angle ranges from 0\({}^{\circ}\) to 70\({}^{\circ}\). This study does not distinguish the effects of different sea surface states on GNSS-R wind speed retrieval. In the incident angle dimension, GMF is modeled under different incident angles starting from 0.5\({}^{\circ}\) in a step length of 1\({}^{\circ}\). At a certain incidence angle, wind speeds starting from 0.05 m/s increments to 35 m/s in the step length of 0.1 m/s, and the weighted average observables at different wind speed bins are calculated to form discrete empirical mapping relationships. In order to expand the training samples, the training data can be overlapped in both dimensions. At a certain incident angle, all the matched data pairs falling within the left and right two step length intervals (steps by 1\({}^{\circ}\)) are taken as the model training samples. At a certain wind speed range, the weighted DDM observables are calculated by taking the data in the left and right two step length intervals as well, but it should be noted that the step length of the wind speed interval needs to be re-determined according to the wind speed probability density. The strategy in [19] was directly used in this paper. In both dimensions, the training data within different intervals use different weights, and samples within the first step length interval from certain incidence angle/wind speed take twice the weight. The weighting strategy can be explained in Figure 2. There are four different cases for the sample points to construct a specific discrete point for GMF to map between the observable and wind speed at a certain incidence angle: (1) the sample located in the first step length interval around the incident angle and the first step length around specific wind speed, as shown in the blue region in Figure 2, with a scale factor is 4; (2) the sample located within the first step length range of the incident angle and the second step length size around the wind speed, as shown in the purple area in Figure 2 with a scale factor is 2; (3) the sample point is located in the second step length interval around the current incident angle and in the interval of the first step length around the wind speed, as shown in the green area in Figure 2 with a scale factor is 2; and (4) the sample point is located in the second step length interval around the current incident angle and in the second step length interval around the wind speed, as shown in the gray area in Figure 2 with a scale factor is 1.