# RadxDealias James and Houze 2001

### Overview

RadxDealias implements a four-dimensional scheme to correct folded velocity data. Based on James and Houze 2001, RadxDealias uses a combination of corrected velocity data from a previous radar volume close in time and environmental soundings to help unfold velocity data.

### Background

Doppler radars observe atmospheric motions by analyzing frequency shifts of pulses that backscatter off of hydrometeors moving toward or away from the radar. In order to reconstruct a wave, one needs to observe both the peaks and troughs of a wave (i.e., the sampling frequency needs to be double the frequency of the wave). Dealiasing (or folding) of Doppler velocity data occurs when the moving hydrometeors produce a frequency shift that is too high for a radar's pulse repetition frequency (PRF) to resolve. The phase shift measured by the radar may differ from the true phase shift by $\displaystyle{ \pm2n\pi }$, where n is an integer. The maximum unambiguous velocity a radar can measure, the Nyquist velocity ($\displaystyle{ V_n }$), is defined as $\displaystyle{ V_n=\pm\frac{PRF\lambda}{4} }$. Although there is no way of knowing whether velocity at a single gate is folded, users can use nearby observations and large radial discontinuities in velocity to diagnose regions where aliasing has occurred. RadxDealias is one algorithm that automates the unfolding process for large radar datasets.

### Dealiasing

Fundamentally, RadxDealias attempts to unfold velocity data by adjusting the velocity value at each gate by Nyquist intervals such that the velocity value at a gate is similar to values at gates that are nearby, both spatially and temporally. Working from higher to lower elevation angles, RadxDealias steps through several processes: quality control, deliasing using velocity data from a prior radar volume (or an environmental sounding, if no prior volume exists) as a reference, dealising using velocity data in the 8 neighboring gates from the same tilt as a reference, dealiasing using velocity data from nearby windows of 11x11 or 21x21 gates as a reference, and finally, comparing any remaining folded gates to the environmental sounding.

##### Quality Control

First, radar volumes are cleaned by discarding gates with reflectivity values outside a user-defined range (e.g., 0 to 80 dBZ, generally). Next, a Bergen and Albers filter can be applied to remove isolated gates.

##### Initial Dealiasing

Gates are first compared to the corresponding gates in the previous radar volume in time and in the previous (i.e., higher) elevation angle. All gates that can be dealiased to within $\displaystyle{ 0.25V_n }$ of those prior gates are modified and marked as "good" data. If a prior radar volume does not exist, the environmental sounding data is used instead. Note: environmental soundings tend to produce more errors than a previous radar volume.

##### Spatial Dealiasing

Remaining "bad" gates are next compared with the 8 neighboring gates within the same tilt. For this step, the adjusted velocity must agree with all neighboring "good" gates within a horizontal wind shear tolerance of $\displaystyle{ 0.4V_n }$. This spatial dealiasing occurs twice, first scanning the tilt angle in the clockwise direction and then in the counterclockwise direction. On the third and final pass, the tolerance is increased to $\displaystyle{ V_n }$ and the adjusted velocity must agree with a majority of the neighboring "good" gates. All gates that are successfully changed in this step are marked as "good" data.

##### Window Dealiasing

Remaining "bad" gates are next compared with gates in neighboring azimuth-range windows. If the default 11x11 window has less than 5 gates of "good" data, a larger window of 21x21 is used. If that larger window still has too few "good" data values, the gate is saved for the final dealiasing step. All values that fall within $\displaystyle{ 0.4V_n }$ of the population mean are adjusted and marked as "good" gates, as long as the standard deviation is within a user-defined threshold.

##### Auxiliary Dealiasing

Finally, any remaining gates are attempted to be corrected with the environmental sounding data, but only if such data exists. The adjusted value is accepted only if it falls within $\displaystyle{ 0.5V_n }$ of the environmental wind value. A maximum of 10 passes that alternate scanning in the clockwise and counterclockwise directions are performed and any remaining gates that cannot be unfolded are deleted.

### Sounding Quality

In the course of dealiasing radar data, it may become necessary to visualize to what degree the environmental sounding is influencing the final output. RadxDealias allows for the output sounding or Velocity Azimuth Display (VAD) velocities to be saved to the output files instead of the dealiased velocities by setting output_soundVol = TRUE. This option may be helpful in debugging.

### References

James, C. N., & Houze , R. A., Jr. (2001). A Real-Time Four-Dimensional Doppler Dealiasing Scheme, Journal of Atmospheric and Oceanic Technology, 18(10), 1674-1683. Link