# Evaluation of Spaceborne GNSS-R Retrieved Ocean Surface Wind Speed with Multiple Datasets
## Theory and Methods
### Delay-Doppler Map Observables  
So far, two types of operational wind speed retrieval algorithm have been used in airborne or spaceborne GNSS-R: (1) through the optimal fitting between the simulated DDM by the Z-V theoretical model and actual observed DDM; and (2) using the DDM derived observables to matchup the collocated wind from another observing system to model an empirical GMF, then using GMF to map the new observable to predict wind speed. The method of using the DDM deconvolution to restore the scattering coefficient, then computing the probability density function (PDF) of the surface slope to relate the wind state, is still undergoing further theoretical research [27]. Usually, multiple DDM observables can be used to establish the separated GMF and predict corresponding wind speed, therefore, an optimal weighting estimator is needed to estimate the weighting coefficients to calculate the final weighted wind speed. Due to the influence of parameter uncertainty such as DDM observation noise, receiver antenna gain, and the effective isotropic radiated power (EIRP) of different GNSS satellites, it is difficult to generate very accurate reference DDM from the DDM simulator [6]. At the same time, the whole DDM from a spaceborne platform corresponds to a larger sea surface area, so the glistening area can be more than 400 km in diameter [28; 29]. To meet the specific spatial resolution of inversed wind speed, the latter approach is commonly used in the current GNSS-R field. Before modeling the empirical GMF, the original DDM needs to be calibrated and wrapped according to the bistatic radar forward equations to remove non-geophysical effects, which are usually calibrated as bistatic radar cross-sections [15; 21]. Based on the requirement of retrieved spatial resolution, the wind speed inversion model has been established to extract observables in a specific delay Doppler window from DDM [24], which is less affected by observed noise, and sensitive to wind speed around the specular point. Furthermore, the processing of time average is carried out to improve the SNR of observables [24].  
[PERSON] et al. proposed five DDM observables for the UK-DMC project to exploit the characteristics of DDM that sensitively respond to variations in wind speed, including the Delay-Doppler Map Average (DDMA), Leading Edge Slope (LES), Trailing Edge Slope, Delay-Doppler Map Variance (DDMV), and Allan Delay-Doppler Map Variance (ADDMV) [22]. However, the current UK TDS-1 and CYGNSS mission can only extract DDMA and LES, as both projects directly provide DDM after non-coherent processing in DDMI without raw intermediate frequency (IF) signals published. Since the limitation of spatial resolution, TES observables also cannot be adopted [24]. DDMA represents the average value of the BRCS near the specular point. The LES is the leading edge slope of the integral delay waveform (IDW), and the IDW is obtained from scattering power DDM by summing the columns along the Doppler axis in the specific Delay/Doppler window. Readers can refer to the method in [24] to calculate the inversion observations.