Scaling Surface and Aircraft Lidar Results for Space-Based Systems (and vice versa) Mike Hardesty, Barry Rye, Sara Tucker NOAA/ETL and CIRES Boulder, CO 80305

Working Group on Space-based Lidar Winds Why scale ground-based and airborne measurements? Current predictions of spacebased lidar performance are based on models Models must assume values for key parameters such as laser beam quality, laser pulse stability, receiver efficiency, detector noise characteristics, and backscatter Using data from current systems tells us how well we are doing now Scaling question: How would an existing system do if it were looking at the same backscatter from space, but with pulse energy, range, range gate length, receiver aperture, and pulses accumulated scaled to match a space-based system Or, vice versa: If the specifications for a proposed space-based system were scaled to measure from the ground, what performance should it see? Effectively, we are scaling everything but the system efficiency

Working Group on Space-based Lidar Winds Some other points…. A key uncertainty (especially for coherent systems) is the backscatter. For selected cases, we don’t know if the backscatter is representative or anomalous, we only know what the space system would see looking at the same volume of atmosphere If ground-based system scaling to space shows that the current instrument does not perform consistent with the model, we can then peel the onion another layer and look at the assumed model efficiencies and compare with system values Scaling high prf, low energy instruments used on the ground to space (where higher energies and lower prfs are likely to be used) will ideally take into account issues such as transmitted pulse characteristics and background noise effects, which may differ

ParameterCoherent CNR Wavelength (microns)2.05 Energy/pulse (Joules).250 PRF (design) (Hz)10 Optical Eff (total).7 Mixing Eff.4 Detector Eff.8 Collector Diam (meters).2 Backscatter*3e-8 Transmission*0.958 (one way) Cn20 Bandwidth50 Using the parameters in the above table, with a nadir view and constant backscatter, coherent models show that the 830 km would be dB. At 30 deg, the 830 km orbit translates into a ~960 km maximum range and we find 960 km is approximately -28 dB If we had a “ground-based” system with the above listed parameters, but had only 1.1 μJ of pulse energy, and if we focus the beam at the 2km altitude, we should be able to get the same -28 dB return at a 2km altitude/range (zenith looking). If we had a collimated beam, we would need 70 μJ to see –28 dB. We would like to see -12 db (minimum). This would require 40X more energy or 2.8 mJ total. Reducing the aperture diameter to 8 cm, would mean that the system only needs 0.7 mJ to see -12 dB at 2 km. HRDL needs 1.5 mJ to see this type of signal under the model conditions. Let’s try inverting HRDL… Coherent Detection: NPOESS Orbit Note that these calculations were done with constant transmission, constant backscatter, and infinite coherence length.

Coherent system Parameter HRDL Space system Wavelength (microns) Energy/pulse (mJ) PRF (Hz)20010 Pulse Length (ns) System Eff.14 Collector Diam (cm)820 Bandwidth50 Focus (km)2.5Collimated Range (km)2958 Range gate (m,samp)30,10500,166 Pulses averaged Scaling factor dB CNR-11 dB-33 dB # photons/estimate~80~19 Degeneracy Coherent Detection

ParameterValue Wavelength2.05 microns Energy/pulse5 mJ Receiver Aperture Diam.9 cm PRF80 Hz Sampling Rate100 MHz Search bandwidth50 MHz Points per gate64 Gate Width96 meters # pts in FFT256 # bins in signal BW11 = 4.3 MHz # bins in search BW128 = 50 MHz Regarding the processing of this data, the following should be noted The mean was removed from the time-series data for each pulse, at each range gate, before the spectra were calculated and averaged. CNR Calculations are based on averaged spectra (for each range gate) calculated using 100 pulses. This spectral averaging reduces the variance on the signals, but does not affect the CNR amplitude. Gates are independent (i.e. not overlapping) All spectra have been whitened by dividing them by the “noise spectrum”. This noise spectrum was calculated by averaging the spectra over range ( range gates 50 to 59 where there was no return signal) and over time (the 100 pulses) No filtering or demodulation has been applied to the data. S. Tucker NOAA ET Wideband CNR for system with parameters at left Coherent Detection - TODWL β = 3×10 -8

This range gate is after the hard target. For these ranges, the CNR estimate actually reflects a signal bandwidth worth of noise (around the peak noise frequency) ratio, rather than a carrier signal to noise ratio. Coherent Detection - TODWL

The total power in the signal bandwidth is given by summing those values in the frequency bins +/- 5 bins from the peak frequency Wideband and Narrowband CNRs are then calculated as follows: Where P ns is the average noise power (approximated by 1 after whitening), N BW is the number of bins in the signal bandwidth (11) and N wb is the number of bins in the spectrum (N wb = NFFT/2 = 128). The 11/128 ratio is equivalent to the 4.3 MHz to 50 MHz (signal BW to total search BW). Coherent Detection - TODWL

Summary: According to CNR models, the space-based system (with parameters listed above) would see a CNR WB of dB at the 2km altitude (or 960 km range, see plot at left). The TODWL system sees approximately -2 dB of signal at most ranges of interest (see plot on previous page) If we subtract 28.5 dB (found using the scaling factors), the result is dB, close to that of the modeled space-based system CNR. The final question is this: Can we extract a good velocity estimate from a -30 dB signal? Scaling factors (from ground system to Space System) ParameterValue (ground) Value (space) Wavelength (microns)2.05 Energy/pulse (mJ)5250 System Eff (total).12 Collector Diam (cm)923 Backscatter3e-8 Transmission0.92(r.t.) 2km alt.??-29 dB Noise Bandwidth50 Coherent Detection - TODWL

Working Group on Space-based Lidar Winds How many photons are needed? The number of photons needed is a function of the specification for probability of a good estimate and the degeneracy (photons detected per speckle) Optimized system has degeneracy ~1 The NPOESS system assuming β = 3 x (and missing dB are found) has degeneracy ~0.05 This works out to about 0.5 photons for a 0.5 km height gate or ~60 photons per 120 pulses Graph at right indicates that we are in the ballpark, but perhaps a little short, for 50% probability Need to demonstrate ground based signal estimate at low degeneracy! Total photocounts required given degeneracy and specification for fraction of good shots, assuming 1 m/s signal bandwidth and +/- 50 m/s search bandwidth

Parameter Nominal Ground Based System NPOESS (proposed) Direct Detect ADM Wavelength (microns) Energy/pulse (Joules) PRF (design) (Hz)10100 Dwell time (sec)5127 Collector Diameter (meters) Stare angle45 (el)30 (nadir)35 (nadir) Range to 2 km alt. 2.8 km 45º el) º = ~960km º = ~490 km Scaling factor2.5× # 2km alt 25.6× Minimum standard deviation (300/√N) 0.06 m/s 3 m/s1.54 m/s Direct Detection – Space/Ground Inversion Inversion scaling example NPOESS/Ground

Inversion scaling example NPOESS/Ground

Working Group on Space-based Lidar Winds Summary Ground-based data sets can be used as a reality check for spacebased lidar performance specifications Spacebased systems will likely be “photon starved”, thus demonstrating efficiencies is a key to a successful mission HRDL and TODWL data sets are somewhat consistent, and seem to indicate that NPOESS performance (in terms of CNR scaling) within a few dB can be reached (if backscatter coefficients are the same!) More estimates at low signal degeneracies are needed to verify velocity estimation capability Higher energy lasers may have poorer frequency stability than low energy lasers used in comparisons => more photons needed Similarly, direct detection observations with low aperture-energy products are best to simulate space measurements