## 2 Materials and Methods
### Module 5: Local Error Check and Dealiasing  
To eliminate any possible existing local errors dealiased by the previous four modules, the ADDA scheme executed a local error check in the final step. The error check scheme compared the dealiased result from module 4 with the average of the valid gates in a designated geometric window. If the difference between the dealiased result from module 4 and the average value was less than the Nyquist interval, then the dealiased result was correct. Otherwise, a new result from the following step replaced the dealiased result from module 4. The average radial velocity of all of the valid gates within a designated geometric window was computed as the consultation geometric wind for the following Equation (3) to calculate an appropriate in Equation (2) at each observation gate:  
\[\mathrm{n}=N\mathit{INT}(\
icefrac{{v_{\mathrm{I}}}}{{2}*v_{\mathrm{max}}}) \tag{3}\]  
where \(\mathit{NINT}\) stands for rounding up to the closest integer. The dimension of the consultation geometric window was determined by the valid gate number m (empirically selected) and changed with the distance between the checked gate and the radar station. For all weather conditions excluding hurricanes and typhoons, m was set to 49 when the range distance was less than 100 km and m was set to 100 when the range distance was larger than 100 km. In the case of a hurricane or typhoon, the dimension of the geometric window was equal to 81 or 225 for distances less or larger than 100 km, respectively, because of the large-scale nature of these storms. The final local error check was not executed until the total number of valid observation gates in this consultation geometric window was larger than 60% of all gate points to prevent uncertainty.  
The above local dealiasing method may possibly fail when the eye location of a tropical cyclone is very close to a radar station, although it worked well for most of the weather cases. Therefore, the ADDA scheme added the following two steps to guarantee the stability of the new scheme. In the first step, ADDA executed new linear least square error dealiasing in each radial direction. The radial velocity value was presumed to meet the linear relation in each radial, as follows: \(v_{\mathrm{T}}=a_{0}*X_{\mathrm{n}}+b_{0}\), where \(v_{\mathrm{T}}\) is the real radial velocity value and \(X_{\mathrm{n}}\) is the range between the radar station and the checked gate. The constant numbers \(a_{0}\) and \(b_{0}\) were obtained by resolving a linear least-square equation with the radial velocity gates along each radial. All the radial velocity gates which did not meet the linear relation \(v_{\mathrm{T}}=a_{0}*X_{\mathrm{n}}+b_{0}\) were dealiased again with Equation (2). In the second step, ADDA performed a new quadratic least square error dealiasing in the azimuthal direction. Because the observed radial velocities were the real wind velocities field casted onto a radar radial beam, in every half-circle observation area, beginning with the first reference radial and ending with the radar radial 180\({}^{\circ}\) away from the reference radial, all of the velocity gates that had the same distance from the radar center in the azimuth direction roughly met a quadratic relation which was similar to a function between 0\({}^{\circ}\) and \(\pm\)180\({}^{\circ}\). Following this, the quadratic least-square fit was applied to determine and dealiase the remaining aliased gates.