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

Abstract

[1] 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.

Mesospheric gravity wave momentum flux estimation using hybrid Doppler interferometry

“…A good contemporary review of the well-known biases inherent in volume-scatter-derived wind measurements in the presence of correlations between refractive index fluctuations and the underlying dynamics is provided by Fritts et al (2012c). This study used a numerical algorithm to compute off-zenith backscatter from simulated Kelvin-Helmholtz instabilities in the mesospheric region (Franke et al, 2011), and revealed the biases in the obtained Doppler spectra as a function of the stage of turbulence development. Simulation-based approaches like this clearly underpin future investigations of the validity of the partial reflection Doppler techniques employed in the present paper.…”

Computation of clear-air radar backscatter from numerical simulations of turbulence: 2. Backscatter moments throughout the lifecycle of a Kelvin-Helmholtz instability

“…Following F11, we assume radar backscatter from the life cycle of a KH instability described by an LES description of KH instability evolution for Ri = 0.05, Re = 10 4 , and a Prandtl number Pr = ν / κ = 1. We assume KH and radar parameters appropriate to higher levels of the atmosphere, where effects of humidity can be neglected.…”

“…A large Re also allows for rapid breakdown of the KH billows (or cat's eyes) via secondary instabilities arising initially in the billow exteriors that lead to turbulence generation, penetration throughout the billow, shearing of the billows to a horizontally uniform turbulence layer, and eventual restratification as turbulence subsides. Additional details are provided by F11 and references therein. For our simulation, the initial horizontal mean wind is given by U ( z ) = U o tanh ( z / h ), with U o = 5 m s −1 and h = 150 m, such that U z = U / h = 0.0333 s −1 , the KH instability has a most unstable horizontal wavelength L = 12.566 h , and the billow and turbulence layer will approach a typical depth of D ∼6 h ∼900 m and allow radar sampling representative of such measurements in the MLT.…”

“…The companion paper by Franke et al [2011] (hereafter F11) employs the Born approximation computed in the time domain for radar backscatter developed for isotropic turbulence by Tatarskii [1961, 1971] and extended to more general anisotropic turbulence and Fresnel backscatter by Doviak and Zrnik [1984], Muschinski et al [1999], and Muschinski [2004]. Backscatter power and mean Doppler shift are computed for representative turbulence volumes defined by a large‐eddy simulation (LES) of KH instability at Re = 10,000 (evaluated for realistic descriptions of turbulence against our DNS simulations at Re = 2500) and compared with vertical velocities obtained directly from the LES data described by F11. These comparisons reveal a potential for radar measurement biases that depend on measurement parameters and the character of the turbulence field.…”

“…Our purposes in this paper are to employ the LES description of turbulence due to KH instability and the method for computation of radar backscatter described by F11 to exhibit expected radar responses throughout the life cycle of a KH instability. Specifically, we assess radar backscatter power and the first moment of the Doppler spectrum for an assumed vertical beam and compare the vertical velocities computed directly (without radar biases) from the same LES volumes.…”