# On-Board Wind Scatterometry
## 3 Wind Scatterometry Processing Chain and On-Board Processing Modifications
### The On-Board Pre-Processing  
A scatterometer pre-processing procedure is implemented by the L1 processor. It generates L1 NRCS from L0 data. In traditional L0 processing steps, when noise that is simultaneously obtained with observations has been subtracted, the signal-to-noise ratio (SNR) can be calculated [34]. Following this comes a key step for pre-processing, i.e., eliminating observing geometry and antenna pattern effects. Generally, frequency modulation for each pulse is adopted for the enhancement of resolution, and different frequencies of return signals measured from the scatterometer are mapped to different ground distances. In a pulse, fast Fourier transform (FFT) bins can be divided into different slices. The number of slices is determined by beam width [40; 41]. Doppler effects in frequency (Doppler frequency) are due to Earth's rotation and sensor speed relative to Earth's surface. When the Doppler frequency, center frequency shift, and frequency modulation slope of the signals are compensated for, the frequencies of a slice can be mapped to different slant range distances. Combinations of FFT bins of a return pulse into slices are achieved before forming L0 data in order to make sure each slice has the same ground coverage. In this procedure, the bin grouping is achieved with a look-up table (LUT) that provides an estimated Doppler frequency. This LUT is calculated according to predicted positions of scatterometer in its orbit. When an observation is conducted, differences of the true Doppler frequency with this LUT are estimated and compensated for in the L1 processor by considering the observing position. Together with antenna orientation, a slice location on the ocean's surface and a corresponding antenna gain factor can be obtained. The factor that embodies the antenna gain effect with a specific geometry in observation is referred to as the calibration factor, namely the X-factor. When the value of signal power of a slice is divided by the X-factor, NRCS can be calculated. Then, their standard deviations (K\({}_{\text{p}}\)) can be calculated when the NRCS of all slices are determined [34]. The whole procedure is shown in Figure 3a. The core algorithm is bordered by the dashed rectangle. It is used to calculate the discretized integrating for the X-factor in Equation (1) [40]:  
\[ \begin{split} X&=\frac{c_{p}^{2}}{T_{p}}\sum_{k=k_{ s}}^{k_{c}}\sum_{i\in T}\left(\frac{\delta A_{i}S_{i}(t_{lm})_{S_{i}}(t_{lm})}{r_{i}^ {2}}\right)\\ &\cdot\left|\sum_{n=m_{s,i}}^{n_{s,i}+N_{p,i}}\exp\left\{2\pi j \left(f_{b,i}T-\frac{k}{N}\right)n\right\}\right|^{2}\end{split}  \tag{1}\]  
In Equation (1), the X-factor is written as X. \(C\) represents constants related to routine insert loss. The insert loss related temperature is \(T_{p}\). \(k_{s}\) and \(k_{e}\) are the start and end FFT bin numbers in a slice, respectively. \(F\) represents the observing region, which is composed by \(i\) small patches on the Earth's surface, to realized the discretized summary in Equation (1). There are \(N\) samples of small patches in a pulse. This number is determined by observing the window time \(T\). \(f_{b,i}\) is the center frequency of the \(i\)th patch. During \(T\), a small patch gives a return signal that may affect different bins. \(A\) and \(g\) are the area and gain of the \(i\)th patch. \(N_{p,i}\) represents the number of small patches captured in the observation time of a slice. \(n_{s,i}\) is the start patch. [40]. In Figure 3a,b, the determination of X involves a  
Figure 3: Traditional pre-processing routine (**a**) and on-board procedures with newly included look-up tables (LUTs) (**b**). geolocation procedure. First, position coordinates are expressed in satellite coordinate system (referred to as relative position in Figure 3), and then they transformed into the ground coordinate system, which is used more often in applications [40]. Figure 3b shows the pre-processing for the on-board routine. Modifications made from traditional processing can be spotted by taking reference from Figure 3a.