Lecture 27. Lidar Data Inversion (1)

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1 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Lecture 7. Lidar Data Inversion Introduction of data inversion Basic ideas clues for lidar data inversion Preprocess Profile process Main process next lecture Summary

2 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 From aw Data to Physical Parameters aw Data N S Data Inversion & Error Analysis Data etrieval T V n c β α δ PMC, PSC, Aerosols Clouds Constituent Density Sporadic Layers Meteors Climatology GWs, Tides, PWs Momentum Flux Heat Flux Constituent Flux Instability Data Analysis & Interpretation Science Study

3 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Example Lidar aw Signal Photon Counts aw Data Profiles for 3-Frequency Na Doppler Lidar fa Channel f+ Channel f- Channel Bin Number 3

4 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Introduction: Lidar Data Inversion Lidar data inversion deals with the problems of how to derive meaningful physical parameters from raw data. aw data are usually a column or a row of photon counts, where the positions of photon counts in the column or row mark their time bins, thus the ranges or heights. Data inversion is basically a reverse procedure to the development of lidar equation. It is necessary to understand the detailed physical procedure from light transmitting, to light propagation, to light interaction with objects, and to light detection, in order to conduct data inversion correctly. In this lecture we discuss the data inversion for Na Doppler lidar K and Fe lidar would be similar. 4

5 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Basic Clue : Lidar Equation & Solution From lidar equation and its solution to derive preprocess procedure of lidar data inversion N S, = P LΔt [ A σ hc eff,n c B + 4πσ π,n ]Δ 4π N S, = P L Δt [ σ π,n ]Δ hc N Norm, = N Na, T a T c, ηg + N B + N, T c, = N S, N B N S, N B A T a, ηg + N B = σ eff,n c σ π,n 4π T c, n n 5

6 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Principle of Doppler atio Technique Lidar equation for resonance fluorescence Na, K, or Fe N S, = P L Δt [ σ eff,n c B +σ π,n ]Δ hc efer to Lecture 3 T a Tc, ηg + N B A 4π B = for current Na Doppler lidar since return photons at all wavelengths are received by the broadband receiver, so no fluorescence is filtered off. Pure Na signal and pure ayleigh signal in Na region are N Na, = P LΔt A [ σ eff,n c ]Δ hc 4π T a Tc, ηg N, = P LΔt hc [ σ π,n ]Δ A T a Tc, ηg So we have N S, = N Na, + N, + N B 6

7 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Principle of Doppler atio Technique Lidar equation at pure molecular scattering region 35-55km N S, = P L Δt [ σ π,n ]Δ hc A T a, ηg + N B Pure ayleigh signal in molecular scattering region is N, = P L Δt A [ σ π,n ]Δ T a, ηg hc efer to Lecture 3 So we have N S, = N, + N B The ratio between ayleigh signals at and is given by N, [ N, = σ π,n ]T a,tc,g [ σ π,n ]T a, G = n n T c, Where n is the total atmospheric number density, usually obtained from atmospheric models like MSIS00. 7

8 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Principle of Doppler atio Technique From above equations, the pure Na and ayleigh signals are N Na, = N S, N B N, Normalied Na photon count is defined as N, = N S, N B N Norm, = N Na, N, T c, efer to Lecture 3 From physics point of view, the normalied Na count is N Norm, = N Na, N, T c, = σ eff,n c σ π,n 4π From actual photon counts, the normalied Na count is N Norm, = N Na, N, T c, = N S, N B N, N, T c, = N S, N B N S, N B n T c, n 8

9 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Basic Clue : atio Computation From physics, we calculate the ratios of T and W as T = σ eff f +, +σ eff f, σ eff f a, W = σ eff f +, σ eff f, σ eff f a, From actual photon counts, we calculate the ratios as T = N Norm f +, + N Norm f, N Norm f a, = N S f +, N B N S f +, N B W = N Norm f +, N Norm f, N Norm f a, = N S f +, N B N S f +, N B T c f+, n n + N S f a, N B N S f a, N B T c f+, n n N S f a, N B N S f a, N B N S f, N B N S f, N B T c fa, n n N S f, N B N S f, N B T c f, n n T c f, n n T c fa, n n 9

10 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Principle of Doppler atio Technique From physics, the ratios of T and W are then given by T = N Norm f +, + N Norm f, N Norm f a, σ eff f +,n c σ = π, f + n + σ eff f,n c σ π, f n σ eff f a,n c σ π, f a n = σ eff f +, +σ eff f, σ eff f a, W = N Norm f +, N Norm f, N Norm f a, σ eff f +,n c σ = π, f + n σ eff f,n c σ π, f n σ eff f a,n c σ π, f a n = σ eff f +, σ eff f, σ eff f a, Here, ayleigh backscatter cross-section is regarded as the same for three frequencies, since the frequency difference is so small. Na number density is also the same for three frequency channels, and so is the atmosphere number density at ayleigh normaliation altitude. efer to Lecture 3 0

11 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Principle of Doppler atio Technique From actual photon counts, the ratios T and W are T = N Norm f +, + N Norm f, N Norm f a, N S f +, N B N S f +, N B = W = N Norm f +, N Norm f, N Norm f a, N S f +, N B N S f +, N B = T c f+, n n + N S f a, N B N S f a, N B T c f+, n n N S f a, N B N S f a, N B N S f, N B N S f, N B T c fa, n n N S f, N B N S f, N B T c fa, n n T c f, n n efer to Lecture 3 T c f, n n

12 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Basic Clue 3: T, V, n C, or β Derivation Compute actual ratios T and W from photon counts, and then look up these two ratios on the calibration curves to infer the corresponding Temperature and Wind from isoline/isogram. If there is only T ratio, then infer the temperature from the calibration curve, like the Fe Boltmann lidar case. Constituent e.g., Na density can be inferred from the peak freq signal n Na = N norm f a, σ a β PMC = 4πn σ = N norm f a, σ a 4π P T Volume backscatter coefficient can be derived as where [ N S N B ] n [ N S N N B ] N n N β N β N,π = β 4π Pπ = P N T N

13 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 How Does atio Technique Work? Compute Doppler calibration curves from physics Look up these two ratios on the calibration curves to infer the corresponding Temperature and Wind from isoline/isogram. -40 m/s Isoline / Isogram 80 K efer to Lecture 3 3

14 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Considerations in Data Inversion How to obtain related information like date, time, location, base altitude, operation conditions? -- from data header and other info sources How to obtain range or altitude information? -- from bin number, data header and other source = n bin t bin c / = cosθ + base is range, n bin is bin number, t bin is bin width in time, c is light speed, is absolute altitude, θ is off-enith angle, and base is the base altitude relative to sea-level. 4

15 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Na Doppler Lidar Schematic Preprocess Procedure Discriminator 5

16 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 ead Data File PMT/Discriminator Saturation Correction Chopper/Filter Correction Subtract Background emove ange Dependence x Add Base Altitude Estimate ayleigh km Normalie Profile By ayleigh km Preprocess Procedure and Profile-Process Procedure for Na/Fe/K Doppler Lidar ead data: for each set, and calculate T, W, and n for each set PMT/Discriminator saturation correction Chopper/Filter correction Integration Background estimate and subtraction ange-dependence removal x, not Base altitude adjustment Take ayleigh ayleigh fit or ayleigh mean ayleigh normaliation N N, = N S, N B N S, N B Main Process Subtract ayleigh signals from Na/Fe/K region after counting in the factor of T C 6

17 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Profile-Process Procedure Indicated from the lidar equation and its solution, the profile process for Na Doppler lidar data is Background estimation and subtraction - N B ange-dependence removal x Base altitude adjustment + Base ayleigh normaliation [/N S -N B ] More considerations on lidar hardware and detection - preprocess procedure PMT and discriminator saturation correction Chopper or electronic gain correction Integration in time and/or range bins to obtain sufficient signal-to-noise ratio SN 7

18 Total Bin # LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step. ead aw Data Headers + One Column Photon Counts ASCII or Binary Low Bin # # of Freq Set No. Profile No. # of Shots Photon Counts Month Aimuth Angle Day Year-000 Bin esolution Off- Zenith Angle Time UT Base Lat Longi Altitude km 8 Frequency Number

19 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Another Example of Lidar aw Data Total Bin # Low Bin # # of Freq Set No. Profile No. # of Shots Photon Counts Month Aimuth Angle Day Year-000 Bin esolution Off- Zenith Angle Time UT Base Altitude km Lat Frequency number Longi 9

20 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step. Nonlinearity of PMT + Discriminator For small input photon flux, PMT output photon counts are proportional to the input photon counts: op = S = i η QE When the input photon flux is considerably large, the output photon counts are no longer linear with input photons. Nonlinearity of PMT occurs: op = S e Sτ p A discriminator is used to judge real photon signals and also has a saturation effect, i.e., its output photon counts are smaller than input photon counts when input count rate is large: o = id + id τ d 0

21 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Nonlinearity of PMT + Discriminator Since PMT output is the input of discriminator id = op we obtain o = where S = i η QE S e Sτ p + S τ d e Sτ p = S e Sτ p + S τ d e Sτ p η QE is the quantum efficiency of cathode Maximum output count rate is reached when S =/τ p o max = τ p e +τ d τ p = omax τ d e

22 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 PMT+Discriminator Saturation Correction o = S e Sτ p + S τ d e Sτ p Output Count ate [MH] o = i e i τ p Na lidar PMT + discriminator + i τ d e i τ p τ P = 3. ns τ d = 0 ns S = i η QE Input Count ate [MH] S

23 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Nonlinearity of PMT + Discriminator 6 PMT + Discriminator Saturation Correction for Fe Lidar 4 Output Count ate [MH] o = i e i τ p + i τ d e i τ p τ p = 0ns τ d =0ns Input Count ate [MH] 3

24 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step 3. Chopper Correction Chopper function is measured and then used to do chopper correction for lower atmosphere signals aw Photon Counts Time us 4

25 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Chopper Correction Chopper Curve from aw Data Smoothed Chopper Function 5

26 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 6 [ ],,, a L B S G T A n hc t P N N η π σ Δ Δ = [ ] B a L S N G T A n hc t P N + Δ Δ =,,, η π σ Step 4. Subtract Background NB N S, = P L Δt hc σ eff,n c B +σ π,n [ ]Δ A 4π T a Tc, ηg + N B

27 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Background Estimate Background is estimated from high altitude signal 600 aw Data Profiles for 3-Frequency Na Doppler Lidar Photon Counts fa Channel f+ Channel f- Channel Background Estimate Bin Number There could be titled background due to PMT saturation 7

28 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step 5. emove ange Dependence [ N S, N B ] = P LΔt [ σ hc π,n ]Δ AT a, ηg θ h h = cosθ 8

29 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step 6. Add Base Altitude "Altitude relative to mean sea level " = Observed Height + Base Altitude = h + Base = cosθ + Base Altitude Observed Height Sea Level Base Altitude 9

30 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Step 7. ayleigh Normaliation Estimate of ayleigh Normaliation Signal - ayleigh Fit or Sum 30

31 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 3 ayleigh Normaliation,,, B S B S Normaliation N N N N N = Photon Counts at ayleigh Normaliation Altitude km Normaliation Altitude 40 km

32 LIDA EMOTE SENSING POF. XINZHAO CHU CU-BOULDE, FALL 0 Summary Lidar data inversion is to convert raw photon counts to meaningful physical parameters like temperature, wind, number density, and volume backscatter coefficient. It is a key step in the process of using lidar to study science. The basic procedure of data inversion originates from solutions of lidar equations, in combination with detailed considerations of hardware properties and limitations as well as detailed considerations of light propagation and interaction processes. Output of the preprocess and profile process is Normalied Photon Count, which is a preparation for the main process to derive temperature, wind, density, or backscatter coefficient, etc. 3

Lecture 30. Further Consideration on Lidar Data Inversion

Lecture 30. Further Consideration on Lidar Data Inversion Aerosol and Cloud Lidar -- Finish Remaining of Lecture 9 Resonance Doppler lidar data processing -- Further consideration on T c -- Na density