Lidar Simulation Model: Signal Processing

The LSM has the option to use a narrow band signal to noise model or a consensus curve algorithm for signal processing of the lidar signal.

Poly-pulse Pair Method (Narrow Band SNR)

There are several signal-to-noise (SNR) equations that have been suggested for use with Doppler lidar wind sounders. The narrow band SNR equation (along with default values) that SWA uses in the LSM is:

where

c - speed of light (m/s)

h₁ - heterodyne quantum efficiency

h₂ - optical efficiency

h₃ - beam shape factor

h₄ - truncation factor

J - laser power (Joules)

D - mirror diameter (m)

t - pulse length (sec)

ß - backscatter (m^-1 sr^-1)

e^-2óa(r)dr - 2 way attenuation

hn = photon energy (J)

R - slant range (m)

l - laser wavelength (m)

As with the lidar SNR equation, there are several radial or LOS velocity error estimates, s_r, that have been suggested for use with Doppler lidar wind sounders. While the Cramer-Rao Lower Bound may provide a limit to the extraction of a velocity estimate from a noisy signal, we have the option to chose the more conservative estimate based upon pulse pair autocorrelation processing of the Doppler signal. The following is derived from Eq. (6.22a) in Doviak and Zrnic (1984).

where

l - wavelength (m)

V_max - maximum velocity measured

f- sampling frequency = 2 × V_max/ l

t- pulse duration (sec)

W - normalized frequency spread of return signal (m/s)

V_bw - uncertainty due to pulse bandwidth (m s^-1)

V_atm - uncertainty due to turbulent eddies and windshear within the pulse volume

SNR_w= Ö2p W SNR_N

Consensus Algorithm

Studies by Mike Hardesty and Barry Rye of NOAA have provided a general consensus algorithm used to simulate the processing of space-based Doppler lidar data. The consensus algorithm computes wideband signal-to-noise (SNR_w) for each lidar shot along the slant path as follows:

where

R - range

h - Planck’s constant

V - maximum wind window

h_m - mixing efficiency

h_o - optical transmission

h_qe - quantum efficiency

E_T - energy/pulse

D² - area of primary

t² - two-way transmission

ß - backscatter

l ² - wavelength

The SNR_w is used to look up the probability of detection (POD), false alarm ratio (FAR) and the measurement uncertainty. The model uses the POD and the FAR to compute the probability of consensus as shown below

If the probability of consensus is greater than a random white noise value, the shot passes consensus. Once a shot passes consensus, the consensus algorithm tests if the false alarm ratio is greater than a random white noise value. If true, then the shot is not a false alarm and the line-of-sight uncertainty is set to the user’s defined LOS uncertainty (default - 0.5 m/s).