# pyart.core.antenna_to_cartesian#

pyart.core.antenna_to_cartesian(ranges, azimuths, elevations)[source]#

Return Cartesian coordinates from antenna coordinates.

Parameters
• ranges (array) – Distances to the center of the radar gates (bins) in kilometers.

• azimuths (array) – Azimuth angle of the radar in degrees.

• elevations (array) – Elevation angle of the radar in degrees.

Returns

x, y, z (array) – Cartesian coordinates in meters from the radar.

Notes

The calculation for Cartesian coordinate is adapted from equations 2.28(b) and 2.28(c) of Doviak and Zrnic 1 assuming a standard atmosphere (4/3 Earth’s radius model).

\begin{align}\begin{aligned}z = \sqrt{r^2+R^2+2*r*R*sin(\theta_e)} - R\\s = R * arcsin(\frac{r*cos(\theta_e)}{R+z})\\x = s * sin(\theta_a)\\y = s * cos(\theta_a)\end{aligned}\end{align}

Where r is the distance from the radar to the center of the gate, $$\theta_a$$ is the azimuth angle, $$\theta_e$$ is the elevation angle, s is the arc length, and R is the effective radius of the earth, taken to be 4/3 the mean radius of earth (6371 km).

References

1

Doviak and Zrnic, Doppler Radar and Weather Observations, Second Edition, 1993, p. 21.