Lecture 30. Further Consideration on Lidar Data Inversion

Transcription

1 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 derivation

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 Read 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 Range-dependence removal (xr, not z ) Base altitude adjustment Take Rayleigh z R (Rayleigh fit or Rayleigh mean) Rayleigh normalization N N (λ,z) = N S (λ,z) N B N S (λ,z R ) N B z z R Main Process Subtract Rayleigh signals from Na/Fe/K region after counting in the factor of T C

3 Main Process Step : Starting Point. Set transmission (T C ) at the bottom of Na layer to be. 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 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( f N ( f, z) Norm a, z) R W = N Norm ( f+, z) N Norm( f N ( f, z) Norm a, z) 4. Estimate the temperature and wind using the calibration curves computed from physics 3

4 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 = (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 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. T c (λ,z) = exp( z σ eff (λ,z)n c (z)dz) z = exp z σ bottom eff (λ,z)n c (z)δz z bottom 4

5 Load Atmosphere n R, T, P Profiles from MSIS00 Start from Na layer bottom E (z=z b ) = 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 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) 5

6 Reach Layer Top No Calculate E(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) 6

7 Derivation of T C (Transmission Caused by Constituent Extinction) T C (caused by constituent absorption) can be derived from z z T c (λ,z) = exp σ eff (λ,z)n c (z)dz = 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 + 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) = exp z z bottom N S (λ,z) N B N R (λ,z R ) N B z z R T c (λ,z) n R (z) n R (z R ) 4πσ R (π,λ)n R (z R ) R B (λ) Δz 7

8 A Step in the Main Process: Estimating Transmission (T C ) Na Layer Bin 3 Bin Bin T c_ 3 = T c_ exp( σ eff _ n c_ Δz) T c_ = T c_ exp( σ eff _ n c_ Δz) T c_ = 8

9 Reach Layer Top No Calculate E(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 Yes Main Process Smooth n c, T, and W for T C Recalculate T C (z) using the smoothed n c, T, and W Re-compute T, W and n C using above procedure with updated T C Save T, W, n c with altitude Calculate R T (z+δz) & R W (z+δz) from N Norm Look-up Table Calibration Are ratios reasonable? No Set to nominal values or MSIS T = 00 K, W = 0 m/s Yes Find T and W from the Table Calculate Na density n c (z) 9

10 Na Density Derivation 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 P(z R ) T(z R ) λ 4.07 The Na density can also be inferred from a weighted average of all three frequency signals. 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 The Na density is then calculated by 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 0

11 Na Density Derivation 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 P(z R ) T(z R ) λ 4.07 The Na density can also be inferred from a weighted average of all three frequency signals as explained above. The Na density can also be inferred from each individual frequency, and in principle, all three frequencies should give identical results of Na density. n Na (z) = N norm ( f ±,z) σ ± 4πn R (z R )σ R = N norm ( f ±,z) σ ± 4π P(z R ) T(z R ) λ 4.07