# Antarctic Surface Ice Velocity Retrieval from MODIS-Based Mosaic of Antarctica (MOA)
## 3 Methods
### Post-Processing  
The primitive displacement fields cannot be analyzed directly since they are often contaminated by severe noise from spurious matching. Hence it is indispensable to correct the initial output before inferring valuable knowledge. In the following part, an accuracy improvement strategy consisting of three steps is developed.  
Usually, the data below the certain SNR threshold, which denotes poor tracking quality, are sweeped out. Considering the spatial heterogeneity in an immense ice sheet, it is obviously unsuitable to use single criteria. To make the threshold adaptive, each drainage has its own threshold based on the residual velocity's decreasing pattern within an outcrop mask (see Figure 5). Here in this first post-processing step, the SNR threshold, which approaches the asymptote, was tuned and determined manually by visual inspection. The automated method could be developed in the future, allowing for efficiently filtering as many outliers as possible while retaining a majority of valid measurements. However, we found that the first procedure is still not always helpful in getting rid of all mis-correlation.  
In order to improve the initial output further, the performances of various classical filter configurations were tested before the low-pass Butterworth filter was chosen. Assuming that the shear strain of ice is relatively low and that there is little velocity variation in the adjacent pixels, a low-pass filter acts as a second step of post-processing, like a smoother. To make full use of computational resources and speed up the numerical fast Fourier transform (FFT), the real and imaginary parts were assigned with the \(X\) and \(Y\) dimensions in the flow field, respectively. Afterwards, the filtered complex array was separated into real and imaginary parts again, as the smoothed \(X\) and \(Y\) dimensions in the flow field in subsequence of the inverse FFT transformation.  
Considering the coarse resolution and long time span of the MOA dataset, a mask was applied in which both the \(X\) and \(Y\) dimension velocity magnitudes are less than 30 m\(\cdot\)a\({}^{-1}\) (about 1/5 pixel of MOA image) or larger than 1500 m\(\cdot\)a\({}^{-1}\) in the MEaSUREs dataset. On top of that, the statistics of the difference between MOA-based velocity and MEaSUREs velocity in each drainage are shown in Figure 6. To obtain a reliable final result, they were used to exclude any measurements whose difference with respect to the MEaSUREs dataset is beyond triple standard deviation recursively, as the third post-processing step.  
The above three post-processing steps, including SNR thresholding, the Butterworth filter, and the triple standard deviation truncation, excluded most outliers in the raw tracking field. In the end, the results in seven drainages were resampled to 750 m and mosaicked into a complete Antarctic velocity dataset. In some cases, spatial interpolation is the optional choice to fill the data void when necessary (see Figure 8). All these processing and the following analysis steps are summarized as a flowchart in Figure 1.