Computation of clear-air radar backscatter from numerical simulations of turbulence: 1. Numerical methods and evaluation of biases

Abstract

A numerical simulation of secondary instability and turbulence accompanying Kelvin-Helmholtz shear instability and a numerical algorithm computing radar backscatter from these turbulence volumes are employed to examine the validity of routine assumptions employed in radar studies of atmospheric dynamics that rely on backscatter from refractive index fluctuations. The numerical simulation of KH instability describes turbulence dynamics and character from the onset of instability, through fully developed turbulence, to turbulence decay and restratification at late times. Radar backscatter computations employing the Born approximation and the turbulence fields at multiple times are performed for representative radar frequencies, beam widths, and pulse lengths. Vertical velocities obtained from the Doppler spectra are compared with the true velocities evaluated with the same weighting of the true velocity distributions. Results reveal departures of simulated radar velocity estimates that depend on how many scatterers are included in the scattering volume, how their contributions are weighted in space and time, and the morphology of the turbulence field. Biases include underestimates of vertical velocities where velocities and refractive index fluctuations are correlated, apparent velocities due to advection of tilted scatterers, and an inability to define Doppler velocities with precision where turbulence is strong, but backscatter is weak due to mixing and eradication of refractive index gradients. A companion paper employs these procedures to describe the backscatter power and Doppler velocities for two canonical radars throughout the life cycle of the KH instability. Both studies suggest systematic measurement biases that appear to account for a number of reported measurements. Copyright 2011 by the American Geophysical Union.