Lecture 29. Lidar Data Inversion (2)

Transcription

1 Lecture 9. Lidar Data Inversion ) q Pre-process and Profile-process q Main Process Procedure to Derive T and V R Using Ratio Doppler Technique q Derivations of n c from narrowband resonance Doppler lidar q Derivation of β q Derivation of n c from broadband resonance lidar q Error analysis for photon noise q Summary 1

2 Read Data File PMT/Discriminator Saturation Correction Chopper/Filter Correction Subtract Background Remove Range Dependence x R ) Add Base Altitude Estimate Rayleigh z R km Normalize Profile By Rayleigh z R km Preprocess Procedure and Profile-Process Procedure for Na/Fe/K Doppler Lidar q Read data: for each set, and calculate T, W, and n for each set q PMT/Discriminator saturation correction q Chopper/Filter correction Integration q Background estimate and subtraction q Range-dependence removal xr, not z ) q Base altitude adjustment q Take Rayleigh z R Rayleigh fit or Rayleigh mean) q Rayleigh normalization N N λ,z) = N Sλ,z) N B N S λ,z R ) N B z z R Main Process q Subtract Rayleigh signals from Na/Fe/K region after counting in the factor of T C

3 Basic Clue 1): Lidar Equation & Solution q From lidar equation and its solution to derive preprocess procedure of lidar data inversion $ N S λ,z) = P L λ)δt ' $ & )[ A ' σ % hc λ eff λ,z)n c z)r B λ) + 4πσ R π,λ)n R z)]δz& % 4πz ) $ N S λ,z R ) = P L λ)δt ' $ & )[ σ R π,λ)n R z R )]Δz % hc λ & % N Norm λ,z) = N Na λ,z) T a λ)t c λ,z)) ηλ)gz) ) + N B + ò N R λ,z R )T c λ,z) = N Sλ,z) N B z N S λ,z R ) N B z R A z R ' ) T a λ,z R ) ηλ)gz R ))+ N B z z = σ eff λ,z)n c z) 1 R σ R π,λ)n R z R ) 4π 1 T c λ,z) n Rz) n R z R ) 3

4 Main Ideas to Derive Na T and W q In the ratio technique, Na number density is cancelled out. So we have two ratios R T and R W that are independent of Na density but both dependent on T and W. q The idea is to derive temperature and radial wind from these two ratios first, and then derive Na number density using computed temperature and wind at each altitude bin. q To derive T and W from R T and R W, the basic idea is to use look-up table or iteration methods to derive them: 1) compute R T and R W from physics point-of-view to generate the table or calibration curves, ) compute R T and R W from actual photon counts, 3) check the table or calibration curves to find the corresponding T and W. 4) If R T and R W are out of range, then set to nominal T and W. q However, because the Na extinction coefficient is involved, the upper bins are related to lower bins, and extinction coefficient is related to Na density and effective cross-section. The solution is to start from the bottom of the Na layer. 4

5 Main Process Procedure q Compute Doppler calibration curves from physics R W = σ eff f +,z) σ eff f,z) σ eff f a,z) R T = σ eff f +,z) +σ eff f,z) σ eff f a,z) 5

6 Main Process Procedure q Compute actual ratios R T and R W from photon counts q Look up these two ratios on the calibration curves to infer the corresponding Temperature and Wind from isoline/isogram. +60 m/s 170 K 6

7 Constituent Density q Normalized Photon Count to the density estimation n c z) = % ' & N Sλ,z) N B N R λ,z R ) N B z z R 1 T c λ,z) n Rz) n R z R ) * 4πσ Rπ,λ)n R z R ) ) σ eff λ,z)r B λ) Normalized Photon Count From the preprocess q The effective cross-section Temperature and wind dependent we need to estimate the temperature and wind first in order to estimate the density 7

8 Load Atmosphere n R, T, P Profiles from MSIS00 Start from Na layer bottom T C z=z b ) = 1 Calculate Nnorm z=z b ) from photon counts and MSIS number density for each freq N Norm λ,z) = N S λ,z) N B z N S λ,z R ) N B z R 1 T c λ,z) n R z) n R z R ) Calculate R T and R W from N Norm Main Process Create look-up table or calibration curves From physics R T = σ eff f +,z) +σ eff f,z) σ eff f a,z) R W = σ eff f +,z) σ eff f,z) σ eff f a,z) Look-up Table Calibration Are ratios reasonable? No Yes Find T and W from the Table Set to nominal values or MSIS T = 00 K, W = 0 m/s Calculate Na density n c z) 8

9 Reach Layer Top No Calculate T C z+δz) Using n c z) and σ eff z) Calculate N Norm z+δz) from photon counts and MSIS number density for each freq Calculate R T z+δz) & R W z+δz) from N Norm Yes Save T, W, n c with altitude Main Process Continued) Look-up Table Calibration Are ratios reasonable? Yes Find T and W from the Table No Set to nominal values or MSIS T = 00 K, W = 0 m/s Calculate Na density n c z) 9

10 Derivation of T C Transmission Caused by Constituent Extinction) q T C caused by constituent absorption) can be derived from & z ) & z ) T c λ,z) = exp σ eff λ,z)n c z)d z+ = exp σ ' z bottom * eff λ,z)n c z)δz+ + ' * n c z) = % ' & N S λ,z) N B N R λ,z R ) N B z z R + 1 T c λ,z) n R z) n R z R ) z bottom * 4πσ R π,λ)n R z R ) ) σ eff λ,z)r B λ) σ = σ + σ e D L / T c λ,z) = exp1 1 0 z z bottom % N S λ,z) N ' B & N R λ,z R ) N B z z R 1 T c λ,z) n Rz) n R z R ) * 4πσ R π,λ)n R z R ) ) R B λ) Δz

11 A Step in the Main Process: Estimating Transmission T C ) Na Layer Bin 3 Bin Bin 1 T c_ 3 = T c_ exp σ eff _ n c_ Δz) T c_ = T c_1 exp σ eff _1 n c_1 Δz) T c_1 =1 11

12 Main Process Step 1: Starting Point 1. Set transmission T C ) at the bottom of Na layer to be 1. Calculate the normalized photon count for each frequency N Norm λ,z) = N S λ,z) N B z N S λ,z R ) N B z R 1 T c λ,z) n R z) n R z R ) 3. Take ratios R T and R W from normalized photon counts R T = N Norm f+, z) + N Norm N f, z) Norm a f, z) R W = N Norm f+, z) N Norm N f, z) Norm a f, z) 4. Estimate the temperature and wind using the calibration curves computed from physics 1

13 Main Process Step : Bin-by-Bin Procedure 5. Calculate the effective cross section using temperature and wind derived 6. Using the effective cross-section and T C = 1 at the bottom), calculate the Na density. n c z) = % ' & N S λ,z) N B N R λ,z R ) N B z z R 1 T c λ,z) n R z) n R z R ) * 4πσ R π,λ)n R z R ) ) σ eff λ)r B λ) 7. From effective cross-section and Na density, calculate the transmission T C for the next bin. z + T c λ,z) = exp z z σ eff λ,z)n c z)d z) = exp σ bottom * eff λ,z)n c z)δz - ), z bottom 13

14 Na Density Derivation q The Na density can be inferred from the peak freq signal n Na z) = N norm f a,z) σ a 4πn R z R )σ R = N norm f a,z) σ a 4π Pz R ) Tz R ) 1 q The Na density can also be inferred from a weighted average of all three frequency signals. q The weighted effective cross-section is σ eff _ wgt = σ a +ασ + + βσ where α and β are chosen so that σ eff _ wgt T = 0; σ eff _ wgt v R = 0 q The Na density is then calculated by λ n Na z) = 4πn R z R )σ R N norm f a,z) +αn norm f +,z) + βn norm f,z) σ a +ασ + + βσ 14

15 Read Data File PMT Saturation Correction Chopper Correction Subtract Background Remove Range Dependence x R ) Add Base Altitude Take Rayleigh z R km Process Procedure for Deriving β Integrate and/or smooth profiles to improve SNR Load Atmosphere n R, T, P Profiles from MSIS00 Calculate Rz) and βz) Smooth Rz) and βz) By Hamming Window FWHM = 50 m Normalize Profile By Rayleigh z R km Calculate z c, σ rms, β total 15

16 Process Procedure for β of PMC Load Atmosphere n R, T, P Profiles from MSIS00 R = [ N S z) N B ] z [ N S z RN ) N B ] z RN n z ) R RN n R z) Calculate Rz) and βz) β PMC z) = % ' &' [ N S z) N B ] z [ N S z RN ) N B ] z RN n Rz) * n R z RN ))* β Rz RN ) Smooth Rz) and βz) By Hamming Window FWHM = 50 m Calculate z c, σ rms, β total σ rms = i β R z RN,π) = β 4π Pπ) = Pz RN ) Tz RN ) 1 λ ) β PMC z i ) z i z c i β PMC z i ) z c = i β PMC z i ) z i i β PMC z i ) β total = β PMC z)dz 16

17 Example Result: South Pole PMC 17

18 Load Atmosphere n R, T, P Profiles from MSIS00 Start from layer bottom T C z = z b ) = 1 Calculate σ eff z = z b ) Process Procedure for n c using broadband lidar Calculate n c z) Calculate T C z+δz) using σ eff z) Calculate σ eff z+δz) Calculate n c z+δz) Using T C z+δz) and σ eff z+δz) Smooth n c z) By Hamming Window Save n c z) with altitude Calculate Abundance, etc Reach Layer Top No Yes 18

19 Process Procedure for n c q Computation of effective cross-section concerning laser shape, assuming nominal T and W) q Spatial resolution - binning or smoothing q temporal resolution integration or smoothing -- in order to improve SNR q Transmission T C extinction coefficient) q Calculate density q Calculate abundance, peak altitude, etc. 19

20 To Improve SNR q In order to improve signal-to-noise ratio SNR), we have to sacrifice spatial and/or temporal resolutions. q Spatial resolution - integration binning) - smoothing q temporal resolution - integration - smoothing 0

21 Analysis of Error Caused by Photon Noise q Use the temperature error derivation for 3-freq Na lidar as an example to explain the error analysis procedure using a differentiation method. For 3-frequency technique, we have the temperature ratio R T = σ eff f + ) + σ eff f ) σ eff f a ) = N f +) + N f ) N f a ) q Temperature error caused by photon noise is given by 1 st order apprx.) ΔT = T R ΔR T = T ΔR T R T R T / T R T S T = R T / T q Define the temperature sensitivity as R T We have ΔT = T R T ΔR T = R T R T / T ΔR T R T = 1 S T ΔR T R T Error coefficient R T relative error 1

22 Error Coefficient and ΔR T /R T q The temperature error coefficient can be derived numerically R T R T / T = R T [R T T + δt) R T T)]/δT q We can derive the error of 3-freq R T caused by photon noise " 1+ 1 % $ ' ΔR T # R = T & R T 1/ * * 1+ B N fa ) 1/ * N fa * )* " 1+ % + $ '- # R T &- " $ 1+ 1 %- '- # R T &,- 1/ Hint: An example for -freq ratio technique, R T = N fc / N fa ΔR T R T = ΔN f c N fc ΔN f a N fa ΔN fc ) = N fc + B, ΔN fa ) = N fa + B # % $ ΔR T R T & ' rms = # % $ ΔN fc N fc ΔN f a N fa & ' = # % $ ΔN fc N fc & ' # + ΔN f a % $ N fa & '

23 Other Possible Errors or Biases Transmitter SHG 53 nm 1064 nm Frequency- Doubled Nd:YAG Pulsed, Q- Switched Laser Shutter Driver Oscilloscope Doppler Free Spectroscopy AOM Driver Photodiode Hot Na Vapor Cell ND Filter SM Fiber Wave- meter λ/ λ/4 Shutter 0 cm AOM 10 cm AOM 0 cm Acousto-Optic Modulation Periscope Pulsed Dye Amplifier λ/ To Sky CMOS Optical isolator Master Oscillator CW 53 nm Pump Laser Collimator Single- Mode Ring Dye Laser Iris Ring Dye Laser Control Box f - f a f + Actuated Steering Mirror 1) Laser freq locking error, ) pulsed laser freq chirp, 3) laser line shape and linewidth, 4) Hanle effect, 5) metal layer saturation, etc. 3

24 Summary q The pre-process and profile-process are to convert the raw photon counts to corrected and normalized photon counts in consideration of hardware properties and limitations. q The main process of T and V R is to convert the normalized photon counts to T and V R through iteration or looking-up table methods. q The main process of n c or β is to convert the normalized photon counts to number density or volume backscatter coefficient, in combination with prior acquired knowledge or model knowledge of certain atmosphere information or atomic/molecular spectroscopy. q Data inversion procedure consists of the following processes: 1) pre- and profile-process, ) process of T and V R, 3) process of n c and β, etc. 4