Lidar polarisation GHK-parameter and error calculation: comparison lidar_correction

-:161490e56a2c
+:857c95060313
 permissions and limitations under the Licence.
 Equation reference: http://www.atmos-meas-tech-discuss.net/amt-2015-338/amt-2015-338.pdf
 With equations code from Appendix C
 Python 3.4.2
+Code description:
+From measured lidar signals we cannot directly determine the desired backscatter coefficient (F11) and the linear depolarization ratio (LDR)
+because of the cross talk between the channles and systematic errors of a lidar system.
+http://www.atmos-meas-tech-discuss.net/amt-2015-338/amt-2015-338.pdf provides an analytical model for the description of these errors,
+with which the measured signals can be corrected.
+This code simulates the lidar measurements with "assumed true" model parameters from an input file, and calculates the correction parameters (G,H, and K).
+The "assumed true" system parameters are the ones we think are the right ones, but in reality these parameters probably deviate from the assumed truth due to
+uncertainties. The uncertainties of the "assumed true" parameters can be described in the input file. Then this code calculates the lidar signals and the
+gain ratio eta* with all possible combinations of "errors", which represents the distribution of "possibly real" signals, and "corrects" them with the "assumed true"
+GHK parameters (GT0, GR0, HT0, HR0, and K0) to derive finally the distributions of "possibly real" linear depolarization ratios (LDRcorr),
+which are plotted for five different input linear depolarization ratios (LDRtrue). The red bars in the plots represent the input values of LDRtrue.
+A complication arises from the fact that the correction parameter K = eta*/eta (Eq. 83) can depend on the LDR during the calibration measurement, i.e. LDRcal or aCal
+in the code (see e.g. Eqs. (103), (115), and (141); mind the mistake in Eq. (116)). Therefor values of K for LDRcal = 0.004, 0.2, and 0.45 are calculated for
+"assumed true" system parameters and printed in the output file behind the GH parameters. The full impact of the LDRcal dependent K can be considered in the error
+calculation by specifying a range of possible LDRcal values in the input file. For the real calibration measurements a calibration range with low or no aerosol
+content should be chosen, and the default in the input file is a range of LDRcal between 0.004 and 0.014 (i.e. 0.009 +-0.005).
+Tip: In case you run the code with Spyder, all output text and plots can be displayed together in an IPython console, which can be saved as an html file.
 """
-# !/usr/bin/env python3
 # Comment:  The code works with Python 2.7  with the help of following line, which enables Python2 to correctly interpret the Python 3 print statements.
 from __future__ import print_function
+# !/usr/bin/env python3
 import os
 import sys
 import numpy as np
 ## pp.savefig can be called multiple times to save to multiple pages
 # pp.savefig()
 # pp.close()
 from contextlib import contextmanager
 @contextmanager
 def redirect_stdout(new_target):
 old_target, sys.stdout = sys.stdout, new_target  # replace sys.stdout
 try:
 yield new_target  # run some code with the replaced stdout
 finally:
 sys.stdout.flush()
 sys.stdout = old_target  # restore to the previous value
 '''
 real_raw_input = vars(__builtins__).get('raw_input',input)
 '''
 try:
 import __builtin__
 # PrintToOutputFile = True
 sqr05 = 0.5 ** 0.5
+# ---- Initial definition of variables; the actual values will be read in with exec(open('./optic_input.py').read()) below
 # Do you want to calculate the errors? If not, just the GHK-parameters are determined.
 Error_Calc = True
-# ---- Initial definition of variables; the actual values will be read in with exec(open('./optic_input.py').read()) below
 LID = "internal"
 EID = "internal"
 # --- IL Laser IL and +-Uncertainty
 bL = 1.  # degree of linear polarization; default 1
 RotL, dRotL, nRotL = 0.0, 0.0, 1  # alpha; rotation of laser polarization in degrees; default 0
 dY = ['reflected channel', '', 'transmitted channel']
 #  end of initial definition of variables
 # *******************************************************************************************************************************
-# --- Read actual lidar system parameters from ./optic_input.py  (must be in the same directory)
+# --- Read actual lidar system parameters from optic_input.py  (should be in sub-directory 'system_settings')
 InputFile = 'optic_input_example_lidar.py'
-# InputFile = 'optic_input_ver6e_POLIS_355.py'
-# InputFile = 'optic_input_ver6e_POLIS_355_JA.py'
-# InputFile = 'optic_input_ver6c_POLIS_532.py'
-# InputFile = 'optic_input_ver6e_POLIS_532.py'
-# InputFile = 'optic_input_ver8c_POLIS_532.py'
-# InputFile = 'optic_input_ver6e_MUSA.py'
-# InputFile = 'optic_input_ver6e_MUSA_JA.py'
-# InputFile = 'optic_input_ver6e_PollyXTSea.py'
-# InputFile = 'optic_input_ver6e_PollyXTSea_JA.py'
-# InputFile = 'optic_input_ver6e_PollyXT_RALPH.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_2.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_3.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_4.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_5.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_6.py'
-# InputFile = 'optic_input_ver8c_PollyXT_RALPH_7.py'
-# InputFile = 'optic_input_ver8a_MOHP_DPL_355.py'
-# InputFile = 'optic_input_ver9_MOHP_DPL_355.py'
-# InputFile = 'optic_input_ver6e_RALI.py'
-# InputFile = 'optic_input_ver6e_RALI_JA.py'
-# InputFile = 'optic_input_ver6e_RALI_new.py'
-# InputFile = 'optic_input_ver6e_RALI_act.py'
-# InputFile = 'optic_input_ver6e_MULHACEN.py'
-# InputFile = 'optic_input_ver6e_MULHACEN_JA.py'
-# InputFile = 'optic_input_ver6e-IPRAL.py'
-# InputFile = 'optic_input_ver6e-IPRAL_JA.py'
-# InputFile = 'optic_input_ver6e-LB21.py'
-# InputFile = 'optic_input_ver6e-LB21_JA.py'
-# InputFile = 'optic_input_ver6e_Bertha_b_355.py'
-# InputFile = 'optic_input_ver6e_Bertha_b_532.py'
-# InputFile = 'optic_input_ver6e_Bertha_b_1064.py'
 '''
 print("From ", dname)
 print("Running ", fname)
 print("Reading input file ", InputFile, " for")
 '''
 input_path = os.path.join('.', 'system_settings', InputFile)
-# this works with Python 2 - and 3?
+# this works with Python 2 and 3!
 exec (open(input_path).read(), globals())
 #  end of read actual system parameters
 # --- Manual Parameter Change ---
 #  (use for quick parameter changes without changing the input file )
 # DiO = 0.
 # LDRtrue = 0.45
 # F11 assuemd to be = 1  => measured: F11m = IinP / IinE with atrue
 # F11sim = TiO*(IinE + DiO*atrue*A)/IinE
 # -------------------------
 # analyser
-# For POLLY_XTs
 if (RS_RP_depend_on_TS_TP):
 RS = 1 - TS
 RP = 1 - TP
 TiT = 0.5 * (TP + TS)
 DiT = (TP - TS) / (TP + TS)
 ZiT = (1. - DiT ** 2) ** 0.5
 TiR = 0.5 * (RP + RS)
 DiR = (RP - RS) / (RP + RS)
 TTa = TiT * TaT  # *ATP1
 TRa = TiR * TaR  # *ARP1
 F11sim = 1 / (TiO * TiE) * (
-(HR * Etax / K * It / TTa - HT * Ir / TRa) / (HR * GT - HT * GR))  # IL = 1, Etat = Etar = 1
+(HR * Etax / K * It / TTa - HT * Ir / TRa) / (HR * GT - HT * GR))  # IL = 1, Etat = Etar = 1  ;  AMT Eq.64; what is Etax/K? => see about 20 lines above: = Eta
 return (GT, HT, GR, HR, K, Eta, LDRsimx, LDRCorr, DTa, DRa, TTa, TRa, F11sim)
 # *******************************************************************************************************************************
-# --- CALC truth
+# --- CALC truth with assumed true parameters from the input file
 GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(RotL0, RotE0, RetE0, DiE0, RotO0,
 RetO0, DiO0, RotC0, RetC0, DiC0,
 TP0, TS0, RP0, RS0, ERaT0,
 RotaT0, RetT0, ERaR0, RotaR0,
 RetR0, LDRCal0)
 print("{0:12}{1:7.4f}±{2:7.4f}/{3:2d}, {4:7.4f}±{5:7.4f}/{6:2d}".format("RP,RS           :", RP0, dRP, nRP, RS0,
 dRS, nRS))
 print("{0:12}{1:7.4f},{2:7.4f}, {3:7.4f},{4:7.4f}, {5:1.0f}".format("DT,TT,DR,TR,Y   :", DiT, TiT, DiR, TiR, Y))
 print("{0:12}".format(" --- Combined PBS + Pol.-filter ---"))
 print("{0:12}{1:7.4f},{2:7.4f}, {3:7.4f},{4:7.4f}".format("DT,TT,DR,TR     :", DTa0, TTa0, DRa0, TRa0))
+print("{0:26}: {1:6.3f}± {2:5.3f}/{3:2d}".format("LDRCal during calibration in calibration range", LDRCal0,
+dLDRCal, nLDRCal))
 print()
 print("Rotation Error Epsilon For Normal Measurements = ", RotationErrorEpsilonForNormalMeasurements)
 print(Type[TypeC], Loc[LocC])
 print("Parallel signal detected in", dY[int(Y + 1)])
 print("RS_RP_depend_on_TS_TP = ", RS_RP_depend_on_TS_TP)
 # print("{0:8.5f} |{1:8.5f}->{2:8.5f},{3:9.5f}->{4:9.5f} |{5:8.5f}->{6:8.5f}".format(LDRCal, LDRtrue, LDRsim, LDRtrue2, LDRsim2, LDRmeas, LDRCorr))
 # print("{0:8}       |{1:8}->{2:8}->{3:8}".format(" LDRCal"," LDRtrue", " LDRsimx", " LDRcorr"))
 # print("{0:6.3f}±{1:5.3f}/{2:2d}|{3:8.5f}->{4:8.5f}->{5:8.5f}".format(LDRCal0, dLDRCal, nLDRCal, LDRtrue, LDRsimx, LDRCorr))
 # print("{0:8}       |{1:8}->{2:8}->{3:8}".format(" LDRCal"," LDRtrue", " LDRsimx", " LDRcorr"))
 # print(" --- LDRCal during calibration")
-print("{0:26}: {1:6.3f}±{2:5.3f}/{3:2d}".format("LDRCal during calibration in calibration range", LDRCal0,
-dLDRCal, nLDRCal))
 # print("{0:8}={1:8.5f};{2:8}={3:8.5f}".format(" IinP",IinP," F11sim",F11sim))
 print()
 K0List = np.zeros(3)
 LDRsimxList = np.zeros(3)
 LDRCalList = 0.004, 0.2, 0.45
+# The loop over LDRCalList is ony for checking whether and how much the LDR depends on the LDRCal during calibration and whether the corrections work.
+# Still with assumed true parameters in input file
 for i, LDRCal in enumerate(LDRCalList):
 GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(RotL0, RotE0, RetE0,
 DiE0, RotO0, RetO0,
 DiO0, RotC0, RetC0,
 DiC0, TP0, TS0, RP0,
 print("{0:8},{1:8},{2:8},{3:8},{4:9},{5:8},{6:9}".format(" GR", " GT", " HR", " HT", "  K(0.004)", " K(0.2)",
 "  K(0.45)"))
 print("{0:8.5f},{1:8.5f},{2:8.5f},{3:8.5f},{4:9.5f},{5:9.5f},{6:9.5f}".format(GR0, GT0, HR0, HT0, K0List[0],
 K0List[1], K0List[2]))
 print('========================================================================')
 print("{0:9},{1:9},{2:9}".format("  LDRtrue", "  LDRsimx", "  LDRCorr"))
-LDRtrueList = 0.004, 0.02, 0.2, 0.45
-for i, LDRtrue in enumerate(LDRtrueList):
+#LDRtrueList = 0.004, 0.02, 0.2, 0.45
+aF11sim0 = np.zeros(5)
+LDRrange = np.zeros(5)
+LDRrange = 0.004, 0.02, 0.1, 0.3, 0.45
+# The loop over LDRtrueList is ony for checking how much the uncorrected LDRsimx deviates from LDRtrue ... and whether the corrections work.
+# LDRsimx = LDRsim = Ir / It    or      1/LDRsim
+# Still with assumed true parameters in input file
+for i, LDRtrue in enumerate(LDRrange):
+#for LDRtrue in LDRrange:
 GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(RotL0, RotE0, RetE0,
 DiE0, RotO0, RetO0,
 DiO0, RotC0, RetC0,
 DiC0, TP0, TS0, RP0,
 RS0, ERaT0, RotaT0,
 RetT0, ERaR0, RotaR0,
 RetR0, LDRCal0)
 print("{0:9.5f},{1:9.5f},{2:9.5f}".format(LDRtrue, LDRsimx, LDRCorr))
+aF11sim0[i] = F11sim0
+# the assumed true aF11sim0 results will be used below to calc the deviation from the real signals
 file = open('output_files\output_' + LID + '.dat', 'r')
 print(file.read())
 file.close()
 sys.stdout.flush()
 f.close
 sys.stdout = old_target
 '''
 if (Error_Calc):
-# --- CALC again truth with LDRCal0 to reset all 0-values
+# --- CALC again assumed truth with LDRCal0 and with assumed true parameters in input file to reset all 0-values
 GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(RotL0, RotE0, RetE0, DiE0,
 RotO0, RetO0, DiO0, RotC0,
 RetC0, DiC0, TP0, TS0, RP0,
 RS0, ERaT0, RotaT0, RetT0,
 ERaR0, RotaR0, RetR0,
 LDRCal0)
 # --- Start Errors calculation with variable parameters ------------------------------------------------------------------
 iN = -1
 N = ((nRotL * 2 + 1) *
 (nRotE * 2 + 1) * (nRetE * 2 + 1) * (nDiE * 2 + 1) *
 LDRmin = np.zeros(5)
 LDRmax = np.zeros(5)
 F11min = np.zeros(5)
 F11max = np.zeros(5)
-LDRrange = np.zeros(5)
+#LDRrange = np.zeros(5)
-LDRrange = 0.004, 0.02, 0.1, 0.3, 0.45
+#LDRrange = 0.004, 0.02, 0.1, 0.3, 0.45
 # aLDRsimx = np.zeros(N)
 # aLDRsimx2 = np.zeros(N)
 # aLDRcorr = np.zeros(N)
 # aLDRcorr2 = np.zeros(N)
 aERaT = np.zeros(N)
 atime = clock()
 dtime = clock()
 # --- Calc Error signals
-# GT, HT, GR, HR, K, Eta, LDRsim = Calc(RotL, RotE, RetE, DiE, RotO, RetO, DiO, RotC, RetC, DiC, TP, TS)
 # ---- Do the calculations of bra-ket vectors
 h = -1. if TypeC == 2 else 1
+'''
 # from input file: measured LDRm and true LDRtrue, LDRtrue2  =>
 ameas = (1. - LDRmeas) / (1 + LDRmeas)
 atrue = (1. - LDRtrue) / (1 + LDRtrue)
 atrue2 = (1. - LDRtrue2) / (1 + LDRtrue2)
+'''
 for iLDRCal in range(-nLDRCal, nLDRCal + 1):
 # from input file:  assumed LDRCal for calibration measurements
 LDRCal = LDRCal0
 if nLDRCal > 0: LDRCal = LDRCal0 + iLDRCal * dLDRCal / nLDRCal
-GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(RotL0, RotE0, RetE0,
+GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim = Calc(RotL0, RotE0, RetE0,
 DiE0, RotO0, RetO0, DiO0,
 RotC0, RetC0, DiC0, TP0,
 TS0, RP0, RS0, ERaT0,
 RotaT0, RetT0, ERaR0,
 RotaR0, RetR0, LDRCal)
 else:
 LDRsimx = 1./LDRsim
 LDRsimx2 = 1./LDRsim2
 '''
 # ----- Backward correction
-# Corrected LDRCorr from forward simulated LDRsim (atrue) with assumed true G0,H0,K0
+# Corrected LDRCorr  with assumed true G0,H0,K0 from forward simulated (real) LDRsim (atrue)
 LDRCorr = (LDRsim * K0 / Etax * (GT0 + HT0) - (GR0 + HR0)) / (
 (GR0 - HR0) - LDRsim * K0 / Etax * (GT0 - HT0))
+'''
 # -- F11corr from It and Ir and calibration EtaX
 Text1 = "!!! EXPERIMENTAL !!!  F11corr from It and Ir with calibration EtaX: x-axis: F11corr(LDRtrue) / F11corr(LDRtrue = 0.004) - 1"
 F11corr = 1 / (TiO * TiE) * (
-(HR0 * Etax / K0 * It / TTa - HT0 * Ir / TRa) / (HR0 * GT0 - HT0 * GR0))  # IL = 1  Eq.(64)
+(HR0 * Etax / K0 * It / TTa - HT0 * Ir / TRa) / (HR0 * GT0 - HT0 * GR0))  # IL = 1  Eq.(64); Etax/K0 = Eta0.
+'''
+# Corrected F11corr  with assumed true G0,H0,K0 from forward simulated (real) It and Ir (atrue)
+Text1 = "!!! EXPERIMENTAL !!!  F11corr from real It and Ir with real calibration EtaX: x-axis: F11corr(LDRtrue) / aF11sim0(LDRtrue) - 1"
+F11corr = 1 / (TiO * TiE) * (
+(HR0 * Etax / K0 * It / TTa - HT0 * Ir / TRa) / (HR0 * GT0 - HT0 * GR0))  # IL = 1  Eq.(64); Etax/K0 = Eta0.
 # Text1 = "F11corr from It and Ir without corrections but with calibration EtaX: x-axis: F11corr(LDRtrue) devided by F11corr(LDRtrue = 0.004)"
 # F11corr = 0.5/(TiO*TiE)*(Etax*It/TTa+Ir/TRa)    # IL = 1  Eq.(64)
 # -- It from It only with atrue without corrections - for BERTHA (and PollyXTs)
 if (nRotaR > 0): PlotSubHist("RotaR", aRotaR, RotaR0, dRotaR, iRotaR, nRotaR)
 if (nLDRCal > 0): PlotSubHist("LDRCal", aLDRCal, LDRCal0, dLDRCal, iLDRCal, nLDRCal)
 plt.show()
 plt.close
 '''
+# --- Plot F11 histograms
 print()
-#print("IT(LDRtrue) devided by IT(LDRtrue = 0.004)")
 print(" ############################################################################## ")
 print(Text1)
 print()
 iLDR = 5
 for LDRTrue in LDRrange:
 iLDR = iLDR - 1
-aF11corr[iLDR,:] = aF11corr[iLDR,:] / aF11corr[0,:] - 1.0
+#aF11corr[iLDR,:] = aF11corr[iLDR,:] / aF11corr[0,:] - 1.0
+aF11corr[iLDR,:] = aF11corr[iLDR,:] / aF11sim0[iLDR] - 1.0
 # Plot F11
 def PlotSubHistF11(aVar, aX, X0, daX, iaX, naX):
 fig, ax = plt.subplots(nrows=1, ncols=5, sharex=True, sharey=True, figsize=(25, 2))
 iLDR = -1
 for LDRTrue in LDRrange:
 if (nRotaR > 0): PlotSubHistF11("RotaR", aRotaR, RotaR0, dRotaR, iRotaR, nRotaR)
 if (nLDRCal > 0): PlotSubHistF11("LDRCal", aLDRCal, LDRCal0, dLDRCal, iLDRCal, nLDRCal)
 plt.show()
 plt.close
 '''
 '''
 # only histogram
 #print("******************* " + aVar + " *******************")
 fig, ax = plt.subplots(nrows=5, ncols=2, sharex=True, sharey=True, figsize=(10, 10))
 iLDR = -1
 bins=200, log=False, alpha=0.2, normed=False, color = '0.5', histtype='stepfilled')
 plt.tick_params(axis='both', labelsize=9)
 plt.plot([LDRTrue, LDRTrue], [0, np.max(n)], 'r-', lw=2)
 plt.show()
 plt.close
+# --- End of Plot F11 histograms
 '''
 # --- Plot LDRmin, LDRmax
 fig2 = plt.figure()
 plt.plot(LDRrange, LDRmax - LDRrange, linewidth=2.0, color='b')

comparison: lidar_correction_ghk.py

lidar_correction_ghk.py

Mercurial > public > atmospheric_lidar_ghk / file comparison

comparison: lidar_correction_ghk.py

lidar_correction_ghk.py