Assesment report of existing calculus subsystems used within EARLINET-ASOS
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EARLINETASOS:
European Aerosol Research Lidar Network:
Advanced Sustainable Observation System
Contract RICA 025991
Assesment report of existing calculus
subsystems used within EARLINET-ASOS
compiled by:
I. Mattis, A. Chaikovsky, A. Amodeo, G. D’Amico, and G. Pappalardo
April 1, 2007Contents
1 Introduction 5
2 Theoretical background — lidar equations 7
3 Extinction coefficients from Raman signals 10
3.1 Calculation of the derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 11
3.1.2 Assessment and implication for the automated single-chain software . . . 13
3.2 Estimation of the uncertainty of the derived extinction . . . . . . . . . . . . . . 13
3.2.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 13
3.2.2 Assessment and implication for the automated single-chain software . . . 14
3.3 Determination of zovl and O(z) . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 14
3.3.2 Assessment and implication for the automated single-chain software . . . 15
3.4 Estimation of the Ångström exponent å . . . . . . . . . . . . . . . . . . . . . . 15
3.4.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 15
3.4.2 Assessment and implication for the automated single-chain software . . . 16
4 Backscatter coefficients from the combination of elastic and Raman signals 17
Method A: directly from the signal ratio . . . . . . . . . . . . . . . . . . 17
Method B: via the backscatter ratio . . . . . . . . . . . . . . . . . . . . . 17
General considerations concerning both methods . . . . . . . . . . . . . . 18
4.1 Detection of the reference height and estimation of the reference value βλpar
0
(zref ) 19
4.1.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 19
4.1.2 Assessment and implication for the automated single-chain software . . . 20
5 Lidar ratio 22
6 Optical depth 23
7 Ångström exponents 25
8 Backscatter coefficients from elastic signals only 26
Method A: Iterative method . . . . . . . . . . . . . . . . . . . . . . . . . 26
Method B: Klett-Fernald solution . . . . . . . . . . . . . . . . . . . . . . 27
3Contents
General considerations concerning both methods . . . . . . . . . . . . . . 27
8.1 Assumption of a lidar-ratio profile S par (z) . . . . . . . . . . . . . . . . . . . . . 28
8.1.1 Documentation of the existing algorithms . . . . . . . . . . . . . . . . . . 28
8.1.2 Assessment and implication for the automated single-chain software . . . 29
9 Vertical smoothing and temporal averaging 30
41 Introduction
The objective of Networking Activity 5 ‘Optimisation of data processing’ (NA5) is to provide
all partners with the possibility to use a common processing chain for the evaluation of their
data, from raw signals to final products. Since the lidar systems used in the consortium are of
different type and have different specifications, the measured raw signals need to be prepared
with system-dependent pre-processing routines before they can be used as input for the optical
retrieval algorithms.
The final objective of NA5 is to develop a single-chain software package which contains opti-
mised algorithms to retrieve aerosol optical properties in an automatic way and without the
need for operator interaction. An optimised algorithm will be developed to derive aerosol
microphysical properties from multi-spectral optical properties.
The single-chain software package will consist of the modules
• pre-processing of raw signals,
• retrieval of optical aerosol properties, and
• retrieval of microphysical properties.
The module for the retrieval of optical aerosol properties delivers the following products from
Raman signals:
• extinction coefficient,
• backscatter coefficient,
• lidar ratio,
• optical depth, and
• Ångström exponent.
The following properties are derived from elastic signals only, with additional information from
sun photometer observations when no Raman signals are available:
• backscatter coefficient and
• Ångström exponent.
This report gives a documentation of all calculus subsystems to derive optical aerosol proper-
ties already existing within the consortium. The necessary information was compiled in the
following coordinated and formalized manner: As a first step a list of calculus subsystems
51 Introduction which might be difficult to handle or for which different algorithms to retrieve aerosol opti- cal properties are expected to be used within EARLINET was compiled in the framework of a general discussion during the first EARLINET-ASOS workshop in Munich (March 2006). Then this ‘list of critical calculus subsystems’ was completed by the task leaders of NA5.1 and NA5.3 and finally distributed to all partners. The participants of EARLINET-ASOS as well as Universidad de Granada, Spain and Joint Research Centre Ispra, Italy as new members of the EARLINET consortium provided detailed descriptions of their algorithms according to this list. All reported algorithms were evaluated with respect to their general applicability for the automated algorithms of the single-chain software during an expert meeting in Leipzig in January 2007. This report is organized as follows: In chapter 2 the theoretical background is explained and basic definitions are introduced. Each of the following chapters 3 to 9 corresponds to one of the products of the single-chain software module for the retrieval of optical properties. In the first part of each chapter the general retrieval procedure for the respective product is de- scribed, possible sources of uncertainties are discussed, and the corresponding critical calculus subsystems are listed. This general part is followed by several sections, each of them corre- sponding to one point out of the list of critical calculus subsystems. Each of those sections contains two subsections: In the first one ‘Documentation of the existing algorithms’ all re- ported algorithms are documented, in the second subsection ‘Assessment and implication for the automated single-chain software’ the results of the evaluation process are presented. This report is an essential tool for the software developer of the single-chain module for the retrieval of optical properties. It provides not only the necessary guideline which algorithms have to be implemented into the new software, but also detailed descriptions of basic algorithms and a comprehensive list of publications which was compiled from the contributions of all partners. This report is also a very useful tool for less-experienced participants of EARLINET- ASOS who want to improve or to extend their existing capabilities for the data analysis before the new single-chain software will be operational in autumn 2009. 6
2 Theoretical background — lidar
equations
The basic equation for the analysis of lidar signals is the so-called lidar equation. It describes
the intensity of the measured signals p Pλ depending on range z, several system parameters as
well as on atmospheric parameters:
Z z
p P0 λ τλ c AT p ηλ (z) O(z) p
Pλ (z) = βλ (z) exp −2 αλ (ζ)dζ . (2.1)
2 z2 0
The symbols mean:
Index λ wavelength,
P0λ mean laser power per pulse,
τλ temporal length of a laser pulse,
AT area of the receiver telescope,
p
ηλ (z) transmission of the lidar receiver,
O(z) overlap function,
p
βλ (z) backscatter coefficient, and
αλ (z) extinction coefficient.
The index p indicates the polarization state of the backscattered light with respect to the
polarization of the emitted laser light.
The range-independent parameters can be combined to a constant
P0 λ τλ c AT
Kλ = . (2.2)
2
The overlap function O(z) describes the incomplete overlap between the emitted laser beam and
the receiver field of view near the ground. Above a certain height zovl the overlap is complete
and O(z) is defined to be 1.
The extinction coefficient αλ (z) is a combination of the scattering coefficient αλs and the ab-
sorption coefficient αλa of molecules (mol) and aerosol particles (par):
αλ (z) = αλs,mol (z) + αλs,par (z) + αλa,mol (z) + αλa,par (z). (2.3)
The backscatter coefficient βλ0 (z) for elastic signals (λ = λ0 ) can be summed up from the
backscatter coefficients of molecules and particles:
βλ0 (z) = βλmol
0
(z) + βλpar
0
(z). (2.4)
72 Theoretical background — lidar equations
The backscatter coefficients can be calculated from the number density of the scatterers
mol/par mol/par
N mol/par , their scattering cross-section σλ0 , and the phase function Φλ0 (θ) for the scat-
tering angle θ = π:
mol/par mol/par mol/par
βλ0 = N mol/par σλ0 Φλ0 (π). (2.5)
The backscatter coefficient for the Raman signals (λ = λR )
βλmol
R
= NRmol σλmol
0
Φmol
λ0 (π) (2.6)
is determined by the number concentration of the scattering molecules NRmol .
αλs,mol
0
(z), βλmol
0
(z), and βλmol
R
(z) can be calculated from air pressure and temperature profiles
taken from radiosonde launchs, from atmospheric models (e.g. US standard atmosphere),
or analysis data sets of numerical weather prediction models. Absorption due to molecules
αλa,mol (z) is neglected for the wavelengths used in EARLINET-ASOS.
The lidar equation for elastic signals at the wavelength λ = λ0 ,
Z z
Kλ0 p ηλ0 (z) O(z) mol par
Pλ0 (z) = βλ0 (z) + βλ0 exp −2 αλ0 (ζ)dζ , (2.7)
z2 0
contains the two unknown parameters particle backscatter coefficient βλpar 0
and particle extinc-
par s,par a,par
tion coefficient αλ0 (z) = αλ0 + αλ0 . From Raman lidar observations the additional Raman
signals Z z
KλR p ηλR (z) O(z) mol
PλR (z) = βλR (z) exp − [αλ0 (ζ) + αλR (ζ)] dζ (2.8)
z2 0
are detected.
The attenuation of the emitted light and of the backscatterd light is described by the extinction
coefficient αλ0 at the emitted wavelength λ0 and by the extinction coefficientαλR at the Raman
shifted wavelength λR , respectively.
Measured lidar signals have to be pre-processed before they can be used to derive optical aerosol
properties. The pre-processing procedure contains the following steps:
1. cloud screening
2. pulse-pileup correction
3. estimation of statistical error
4. background subtraction
5. range correction
6. handling of signals with zenith angle 6= 0
7. correction for depolarization-dependent receiver transmission
8. calculation of the profile of the Rayleigh-scattering coefficient
9. correction for Rayleigh-transmission
810. first temporal averaging to create 15-minute intervals
11. first vertical smoothing up to a height resolution of 30 m
The lidar equations for pre-processed elastic signals and Raman signals can be reformulated
from Equations (2.7) and (2.8) to
Z z
mol
d par
Pλ0 (z) = Kλ0 O(z) βλ0 (z) + βλ0 exp −2 par
αλ0 (ζ)dζ (2.9)
0
and Z z
par
d mol
PλR (z) = KλR O(z)βλR (z) exp − par
αλ0 (ζ) + αλR (ζ) dζ . (2.10)
0
93 Extinction coefficients from Raman
signals
The particle extinction coefficients can be derived directly from vibrational-rotational signals of
nitrogen. According to Eq. (2.10) those signals PλR (z) depend only on the particle extinction
but not on the particle backscatter coefficient. Thus Eq. (2.10) contains only one unknown
quantity α and can be resolved.
First the Raman signal has to be corrected for the incomplete overlap between the emitted
laser beam and the receiver field of view:
d
PλR
g
PλR (z) = . (3.1)
O(z)
Then the logarithm of the Raman signal is calculated, followed by the calculation of the deriva-
tive with respect to height z [Ansmann et al., 1990, 1992a]:
d Pg
λR (z)
αλpar (z) + αλpar (z) = − ln mol . (3.2)
0 R
dz NR (z)
The Ångström exponent å describes the wavelength dependence of the particle extinction co-
efficient with the relation å
αλpar
0
λR
par = . (3.3)
αλR λ0
å is not known and has to be estimated. Typical values are in the range from −0.5 to 2. From
Eq. (3.2) and Eq. (3.3) we finally obtain αλpar
0
(z) to
Pg
λR (z)
d mol (z)
NR
αλpar = − ln å . (3.4)
0
dz λ0
1+ λR
Main sources of uncertainties
Main sources of uncertainties for the extinction retrieval are [Pappalardo et al., 2004]:
• the statistical error that is due to signal detection,
• the systematic error associated with the estimate of temperature and pressure profiles,
103.1 Calculation of the derivative
• the systematic error associated with the estimate of ozone profiles in the UV (can be
neglected for the wavelengths used in the EARLINET consortium),
• the systematic error associated with the wavelength-dependence parameter å,
• the systematic error associated with multiple scattering,
• the error introduced by data-handling procedures such as signal averaging during varying
atmospheric extinction and scattering conditions.
• Largest extinction uncertainties (up to 50% for heights below zovl ) are caused by the
overlap function O(z) [Wandinger and Ansmann, 2002].
Critical calculus subsystems
Critical calculus subsystems of the extinction retrieval which might be difficult to handle or for
which different algorithms are used within EARLINET are:
• calculation of the derivative,
• estimation of the uncertainty of the derived extinction,
• determination of zovl and of the overlap function O(z) itself,
• assumption of the Ångström exponent å.
3.1 Calculation of the derivative
3.1.1 Documentation of the existing algorithms
There are several methods used in the consortium to calculate the derivative:
• Most of the groups use the linear fit method.
• A digital filter based on a polynomial fit of 2nd order [Ancellet et al., 1989].
• A quadratic function and a median filter of rank 2.
• A method based on Savitzky-Golay filter [Press et al., 1992, pp. 127-128 and 644-647].
• Russo et al. [2006] suggest a new method without an a priori assumption about the
functional behavior of the data to calculate the derivative. This method is not yet used
in the EARLINET consortium.
The linear fit method
The linear fit method is presented in more detail since it is the most popular and a well
established method to calculate the derivative in the extinction retrieval. The extinction coef-
ficient of a certain height bin i(z) is derived with the signal values measured in the height bins
113 Extinction coefficients from Raman signals
[i(z) − (N − 1)/2] to [i(z) + (N − 1)/2]. The number of used height bins N should be an odd
number. N determines the height resolution of the derived αpar -profile. The linear fit method
can be only applied if the Raman signal shows a linear behaviour (y = a + bx) within the height
interval [i(z) − (N − 1)/2] . . . [i(z) + (N − 1)/2]. We can assume that this condition is fulfilled
if the number of N is not too large.
The description of the linear fit method is taken from Press et al. [1989]. First the following
substitutions are defined:
b = − αλpar 0
(z) + α par
λR (z) , (3.5)
xk = z(k), height of bin k,
g
P λR (k)
yk = ln mol , see Eq. (3.2),
NR (k)
!
g
PλR (k)
σk = ∆ ln mol , absolute, statistical uncertainty of yk .
NR (k)
Then the following sums have to be calculated:
i+
(N −1)
i+
(N −1)
i+
(N −1)
i+
(N −1) !2
X2 xk X2 yk X2 1 X2 xk − Sx
Ss
Sx = , Sy = , Ss = , Stt = .
(N −1)
σk2 (N −1)
σk2 (N −1)
σk2 (N −1)
σi
k=i− 2 k=i− 2 k=i− 2 k=i− 2
(3.6)
From those terms we get the parameter b and its variance σb2 :
(N −1)
i+ 2 Sx
1 X y k x k − Ss 1
b = 2
, σb2 = . (3.7)
Stt (N −1)
σk Stt
k=i− 2
The extinction coefficient can be derived from b as follows:
−b
αλpar
0
(z) = å . (3.8)
1 + λλR0
To derive a profile of αλpar
0
(z) the fit window has to be shifted in steps of one bin (i = i + 1)
through the whole troposphere.
There is also the possibility to perform the linear fit with the same weight for all data points.
In this case Equations (3.6) and (3.7) have to be written as
i+
X2
(N −1)
i+
X2
(N −1)
i+
X2
(N −1)
2
Sx
Sx = xk , Sy = yk , Ss = N, Stt = xk − , (3.9)
(N −1) (N −1) (N −1)
Ss
k=i− 2 k=i− 2 k=i− 2
and
i+
X2
(N −1)
1 Sx 1
b = yk xk − , σb2 = . (3.10)
Stt (N −1)
Ss Stt
k=i− 2
123.2 Estimation of the uncertainty of the derived extinction
3.1.2 Assessment and implication for the automated single-chain
software
From the documentation of the methods used in the consortium it cannot be concluded which
of those methods is best applicable for an automated retrieval of extinction profiles. For that
reason different procedures will be implemented into the test version of the single-chain software.
The well established linear fit method (with and without weights) will be tested together with
the algorithm suggested in Russo et al. [2006], the Savitzky-Golay filter method, and the other
higher-order fit methods. These methods will be applied in parallel to a large number of
different realistic measurement cases. After the test phase it can be decided which algorithm
is most applicable for an automated analysis of Raman signals measured with very different
lidar systems. Only this method will remain implemented in the operational version of the
single-chain software.
3.2 Estimation of the uncertainty of the derived extinction
3.2.1 Documentation of the existing algorithms
There are several methods used in the consortium to estimate the uncertainty of the derived
extinction:
• an analytical method to derive the extinction uncertainty directly from the measured
signal-to-noise ratio [Rocadenbosch et al., 2004].
• the Estimation of the uncertainty according to the Savitzky-Golay filter method.
• most groups use the uncertainty of the slope parameter of the linear fit.
• the Monte Carlo technique.
The uncertainty of the slope parameter of the linear fit
The uncertainty of the slope parameter of the linear fit can be used to calculate the uncertainty
of the extinction coefficient by means of error propagation. It can be assumed that the uncer-
tainty of the slope parameter ∆b is equivalent to its standard deviation σb (see Equations (3.7)
or (3.10)). Using Equation (3.8) one can derive ∆αλpar0
(z) to
s
2
dαλpar (z) σb (z)
∆αλpar (z) = 0
(∆b)2 = å . (3.11)
0
dz
1 + λλR0
133 Extinction coefficients from Raman signals
The Monte Carlo procedure
The Monte Carlo procedure is based on the random extraction of new lidar signals, each bin of
which is considered a sample element of a given probability distribution with the experimentally
observed mean value and standard deviation. The extracted lidar signals are then processed
with the same algorithm to produce a set of solutions from which the standard deviation is
calculated as a function of height.
3.2.2 Assessment and implication for the automated single-chain
software
According to Section 3.1.2 different methods to calculate the derivative will be implemented
in the test version of the single-chain software. The corresponding methods of uncertainty
estimation of all of those methods will be realized, too. Additionally the Monte Carlo procedure
will be used to provide an independent measure of uncertainty which allows us to compare the
results of the other methods. As in the case of the calculation of the derivative all those
methods to estimate the uncertainty will be extensively tested and only the algorithm which is
most applicable for an automated analysis of Raman signals measured with very different lidar
systems will remain implemented in the operational version of the single-chain software.
3.3 Determination of zovl and O(z)
3.3.1 Documentation of the existing algorithms
• The method of Wandinger and Ansmann [2002] allows one to derive the overlap profile
experimentally.
• The telecover method [Freudenthaler , 2007] allows one to derive the height of complete
overlap zovl experimentally.
• It is possible to derive zovl and to estimate O(z) from measurements at different zenith
angles under homogeneous and stationary atmospheric conditions.
• O(z) and zovl can be theoretically determined by means of raytracing simulations.
• The methods of Kuze et al. [1998], Measures [1992], and Chourdakis et al. [2002] are used
to estimate the overlap function theoretically.
143.4 Estimation of the Ångström exponent å
3.3.2 Assessment and implication for the automated single-chain
software
The determination of O(z) will not be part of the single-chain software, but the correction of
the measured signals as described in Equation (3.1) will be implemented. Since the derived
extinction profile below zovl is highly sensitive to the shape of O(z), only overlap functions
experimentally determined with the method by Wandinger and Ansmann [2002] will be al-
lowed for this correction. The theoretical or raytracing methods cannot provide O(z) with the
required exactness since they need as an input a detailed and exact description of all optical
elements of the lidar transmitter and receiver (including even the smallest misalignments). This
requirement cannot be fulfilled for realistic lidar systems.
If the experimental determination of O(z) cannot be performed, the extinction calculation will
be possible only for heights z ≥ zovl . In this case, zovl has to be derived experimentally with
the telecover method or the scanning method or estimated theoretically.
3.4 Estimation of the Ångström exponent å
3.4.1 Documentation of the existing algorithms
There are several methods used in the consortium to estimate the Ångström exponent å:
• A fixed value of å = 1.5 is used.
• Most groups use the fixed value of å = 1.
• Some groups use variable user-defined values according to actual meteorological condi-
tions.
• Ångström exponents measured with sun photometers can be applied.
• There is an iterative method to derive å from simultaneously measured extinction co-
efficients at 2 wavelengths λ1 = 355 nm and λ2 = 532 nm [formulas provided by F.
Rocadenbosch, UPC]:
ln αλ1 − ln αλ2
å = (3.12)
ln λ2 − ln λ1
1 ∆αλ1 ∆αλ2
ƌ = + .
ln λ2 − ln λ1 αλ1 αλ2
• A three-wavelength method is proposed by Eisele and Trickl [2005].
153 Extinction coefficients from Raman signals
3.4.2 Assessment and implication for the automated single-chain
software
Errors in the estimated value of å result in extinction errors up to 4% [Ansmann et al., 1992b].
This uncertainty is small compared to the statistical error and the uncertainty induced by the
error of the overlap function.
For the single-chain software each group will set one fixed climatological value for å. If there
are correlative sun/star photometer measurements available, the measured values of å can be
uploaded to the single-chain software together with the raw signals of the measurement. In this
case, the actual values of å will be used for the extinction retrieval.
One has to be careful when using the iterative method since the statistical uncertainty of the
measured extinction coefficients αλ1 and αλ2 often is quite large. These large values of ∆α λi
αλi
propagate to a large uncertainty of the wavelength parameter ƌ which easily can be of the
order of the natural variablity of å. Only in case that the Ångström exponent is derived with
a sufficiently low statistical uncertainty the iterative method is useful for a proper estimation
of å.
164 Backscatter coefficients from the
combination of elastic and Raman
signals
There are two methods available to derive backscatter coefficients from the combination of
elastic and Raman signals. Both methods are based on the same idea, have the same advan-
tages and sources of uncertainty. They differ only in the way to perform the mathematical
calculations.
Method A: directly from the signal ratio
In the EARLINET consortium particle backscatter coefficients are derived from the ratio of the
elastic signal [Eq. (2.9)] and the nitrogen Raman signal [Eq. (2.10)] with the method described
by Ansmann et al. [1992b]:
par OλR (z) P d d mol
λR (zref ) Pλ0 (z) βλ0 (z)
βλpar (z) = −β mol
λ0 (z) + βλ0 (zref ) + β mol
λ0 (zref )
0
Oλ0 (z) d d
Pλ0 (zref ) P β mol (zref )
λR (z) λ0
å ! Z z
λ0
× exp (A), A = 1 − αλpar (ζ)dζ. (4.1)
λR zref
0
Method B: via the backscatter ratio
Ferrare et al. [1998] suggested another way to derive βλpar
0
(z). First, they calculate the backscat-
ter ratio
par
β (z) + β mol (z)
Rβ (z) =
β mol (z)
" å ! Z z #
d
β Pλ0 (z) O λR (z) λ0 par
= F exp 1− αλ0 (ζ)dζ (4.2)
d
P λR (z)
Oλ0 (z) λR 0
from the ratio of the elastically backscattered signal d Pλ0 (z) and the nitrogen Raman signal
d β par
PλR (z). F is a calibration factor. In a second step, β (z) is derived from Rβ (z)
β par (z) = βλmol
0
(z) Rβ (z) − 1 . (4.3)
174 Backscatter coefficients from the combination of elastic and Raman signals
The advantage of this method is that it theoretically allows for an absolute calibration of the
lidar system. If the calibation factor F β is derived once under optimal atmospheric conditions
(clean free troposphere), it can be applied to all other measurements under arbitrary conditions
as long as the system configuration does not change.
General considerations concerning both methods
The value of βλpar
0
(zref ) has to be assumed in a certain reference height zref . It is common
practice to use for this estimate a height range where the unknown scattering due to particles
can be neglected compared to the known scattering from molecules [βλpar 0
(zref ) ≪ βλmol
0
(zref )].
O (z)
For most lidar systems the differential overlap OλλR(z) cancels out since OλR (z) ∼ = Oλ0 (z). In
0
this case, the profile of the particle backscatter coefficient is not affected by the incomplete
overlap between laser beam and receiver field of view and β(z) can be derived for all heights,
even close to the lidar. In case of lidar systems with OλR (z) 6= Oλ0 (z) the differential overlap
function can be determined experimentally by performing a test measurement with the same
interference filters in front of both detectors [Whiteman et al., 1992].
Eqs. (4.1) and (4.2) can be used also to derive backscatter coefficients at λ02 = 1064 nm
in combination with a Raman signal (e.g., λR1 = 607 nm) corresponding to another emitted
wavelength (e.g., λ01 = 532 nm). For such a wavelength pair the exponential term has to be
rewritten to
" å ! Z z # " å å !Z #
z
λ0 λ 01 λ 01
exp 1− αλpar (ζ)dζ → exp 2 − −1 αλpar (ζ)dζ .
λR zref
0
λ 02 λ R1 zref
01
(4.4)
This method works best if both, the 1064-nm signal and the Raman signal are recorded in the
same detection mode (in general photon counting) because in general the dynamic range and
the noise of analog and photon-counting signals are different.
Table 1 shows that the influence of the aerosol extinction [exponential term in Eqs. (4.1) and
(4.2)] is small for moderate optical depths compared to the statistical uncertainty.
Main sources of uncertainties
Main sources of uncertainties for the retrieval of the backscatter coefficient are:
• the statistical error due to signal noise, which is usually derived by means of error prop-
agation,
• the systematic error associated with the estimate of temperature and pressure profiles,
which has values of up to 1.5% [Masonis et al., 2002],
• the systematic error associated with the wavelength-dependence parameter å; in case of
Method A, this error is largest close to the ground, in case of Method B it increases with
184.1 Detection of the reference height and estimation of the reference value βλpar
0
(zref )
Table 1: Influence of the aerosol extinction (Term A in Eq. (4.1)) calculated for different wave-
Rz
length pairs and optical depths 0 αλpar
01
(ζ)dζ for two values of the Ångström exponent,
å = 0.5 and å = 1.5.
Optical depth at 355 nm
wavelength pair 0.2 0.5 1
å = 0.5 å = 1.5 å = 0.5 å = 1.5 å = 0.5 å = 1.5
355/387 ≤ 0.01 ≤ 0.02 ≤ 0.02 ≤ 0.06 ≤ 0.04 ≤ 0.12
532/607 ≤ 0.01 ≤ 0.02 ≤ 0.03 ≤ 0.05 ≤ 0.05 ≤ 0.10
1064/607 ≤ 0.04 ≤ 0.02 ≤ 0.10 ≤ 0.05 ≤ 0.20 ≤ 0.09
height; according to Table 1 this error is about 2%-5% for moost atmospheric conditions.
• the error introduced by data-handling procedures such as signal averaging during varying
atmospheric extinction and scattering conditions,
• the systematic error associated with the differential overlap function (especially if
OλR (z) = Oλ0 (z) is assumed but not experimentally proven),
• uncertainties (up to 10%) caused by the assumption of βλpar
0
(zref ) [Ansmann et al., 1992a].
Critical calculus subsystems
Critical calculus subsystems of the retrieval of the backscatter coefficientwhich might be difficult
to handle or for which different algorithms are used within EARLINET are:
• detection of the reference height or reference height interval zref where the assumption
βλpar
0
(zref ) ≪ βλmol
0
(zref ) is valid,
• estimation of the reference value βλpar
0
(zref ).
4.1 Detection of the reference height and estimation of the
reference value βλpar
0
(zref )
4.1.1 Documentation of the existing algorithms
There are several methods used in the consortium to estimate reference height and reference
value:
• A fixed height range in the stratosphere can be defined.
• Most groups scan the free troposphere for a height interval with clear conditions. This
is done either by eye or automatically by comparing the measured elastic signal with the
194 Backscatter coefficients from the combination of elastic and Raman signals
pure molecular Raman signal (Rayleigh-fit method). If these two signals fit together in
a certain height range (i.e. the signal ratio is constant with height), this is an indication
for the absence of aerosols.
• It has to be considered, that the statistical uncertainty of the elastic signal or of the signal
ratio within the scanned height range is sufficiently low (e.g. signal-to-noise ratio ≥ 10).
• If the variability of a signal or of a signal ratio within a certain height interval is larger
than its statistical uncertainty then this behaviour is a further indication for the presence
of aerosols.
• If there are simultaneous measurements with a near-range and a far-range telescope or
with analog detection mode (near-range) and photon-counting detection mode (far-range)
available, then the reference height range and reference value are determined for the
far-range profile. The reference value of the near-range signal is determined such that
the derived backscatter coefficients in both ranges fit together within a range where the
statistical uncertainty of both signals is approximately equal [Mattis and Jaenisch, 2006].
• The reference value is generally assumed to be βλpar
0
(zref ) = 0 in the consortium.
• One group uses fixed values of stratospheric backscatter ratios of Rβ (355 nm) = 1.02; Rβ
(532 nm) = 1.07; Rβ (1064 nm) = 1.54 which are in agreement with the current values for
stratospheric aerosol background load [Deshler et al., 2006] and an Ångström exponent
of å β = 1.
4.1.2 Assessment and implication for the automated single-chain
software
All methods mentioned above to estimate the reference range and reference value work well if
there are aerosol-free height ranges in the free troposphere and if the statistical uncertainty of
the signal ratio is not increased by the presence of low clouds.
Calibration in the stratosphere is not possible for small systems or in cloudy cases when the
signal-to-noise ratio in the stratosphere is too low. Furthermore, the well-defined, homogeneous
and clear stratospheric conditions can be disturbed by a major volcanic eruption at any time.
The calibration in the free troposphere is problematic because there are often thin aerosol
layers up to the tropopause [Mattis et al., 2006]. For small systems or in cloudy cases the
signal-to-noise ratio in the free troposphere is low and such thin layers are difficult to detect.
This problem is even worse at 355-nm wavelength at which β par is very small compared to β mol .
⇒ In case of multi-wavelength observations, the elastic signal measured at the longest wave-
length has to be used to detect an appropriate reference height interval.
⇒ It has to be checked for each lidar system in the consortium whether its stability and repro-
ducibility are sufficiently good to allow an absolute calibration (Method B). If this condition is
204.1 Detection of the reference height and estimation of the reference value βλpar
0
(zref )
fulfilled, the calibration factor F β can be derived from each measurement with a clean free tro-
posphere. This set of calibration factors can be used to estimate F β for all other measurements
under suboptimal conditions.
215 Lidar ratio
The particle lidar ratio is defined as the ratio of the particle extinction coefficient and the
particle backscatter coefficient:
αλpar (z)
Sλpar (z) = 0
par . (5.1)
0
βλ0 (z)
The lidar ratio can be derived only from indepently determined profiles of αλpar 0
(z) and βλpar
0
(z).
This condition is fulfilled if the Raman method is used. Furthermore both profiles must have
the same effective height resolution (see Section 9). The lidar-ratio profiles cannot be derived
in height ranges where the particle concentration is very low, i.e. αλpar
0
≈ βλpar
0
≈ 0.
There is no other method used in the EARLINET consortium than the one described with
Equation (5.1).
226 Optical depth
The optical depth due to aerosol extinction is defined as the integral of the particle extinction
coefficient from ground to the top of the atmosphere (TOA):
Z T OA
τ= αpar (z)dz. (6.1)
0
If stratospheric aerosol load is negligible integration up to the tropopause zTrop is sufficient.
Extinction and backscatter profiles from Raman lidar observations are available in a height
range from zbot, α to ztop, α and from zbot, β to ztop, β , respectively. In general, those boundaries
are located as follows:
0 < zbot, β < zbot, α < zPBL < ztop, α < ztop, β ≈ zTrop . (6.2)
zPBL is the top height of the planetary boundary layer (PBL).
If there is only an extinction profile, it has to be extrapolated from zbot, α down to the ground
using the relation αpar (0 . . . zbot, α ) = αpar (zbot, α ). This leads to an estimation of the optical
depth Z ztop, α
τ = αpar (zbot, α )zbot, α + αpar (z)dz. (6.3)
zbot, α
If an additional backscatter profile is available, then the amount of aerosols above ztop, α can be
estimated to be
Z ztop, β
Z ztop, β β par (z)dz Z ztop, α
z
αpar (z)dz = Z top, α
ztop, α αpar (z)dz. (6.4)
ztop, α par zbot, α
β (z)dz
zbot, α
In this case, also the amount of aerosols below zbot, α can be estimated using the mean lidar ratio
in the upper part of the PBL S(zbot, α . . . zPBL ) and the profile of the backscatter coefficient:
Z zbot, α Z zbot, α
par
α (z)dz = S(zbot, α . . . zPBL ) β par (z)dz. (6.5)
zbot, β zbot, β
The aerosol content within the lowest part of the PBL below zbot, β is considered by
Z zbot, β
αpar (z)dz = S(zbot, α . . . zPBL ) β par (zbot, β ) zbot, β . (6.6)
0
236 Optical depth
Figure 1 illustrates how the particle optical depth can be derived from the combination of a
backscatter and an extinction profile. All terms can be combined to
Z zbot, β Z zbot, α Z ztop, α Z ztop, β
par par par
τ = α (z)dz + α (z)dz + α (z)dz + αpar (z)dz
0 zbot, β zbot, α ztop, α
Z !
zbot, α
par
= S(zbot, α . . . zPBL ) β (zbot, β ) zbot, β + β par (z)dz (6.7)
zbot, β
Z ztop, β
par
Z ztop, α β (z)dz
par ztop, α
+ α (z)dz 1 + Z ztop, α .
zbot, α par
β (z)dz
zbot, α
10 ztop, β
8 0.018
ztop, α
HEIGHT, km
6
0.248
4 0.248
2
zPBL
zbot, α 0.127
zbot, β 0.179 0.046
0
0 1 2 3 0 100 200 0 100 200 0 100 200
BACKSCATTER EXTINCTION -1
-1 -1 -1 EXTRAPOLATED EXT. COEF., Mm
COEF., sr Mm COEF., Mm
Figure 1: Illustration of different methods to derive particle optical depth. Left and center left:
measured backscatter and extinction profiles at 532 nm. Center right: Extinction
profile extrapolated down to the ground. The red line and value correspond to the
first term of the right side of Eq. (6.3), the green curve and value correspond to
the second term. Right: Extinction profile extrapolated to the ground and to the
tropopause using the simultaneously measured backscatter profile. Green: same as
in center right. The black value corresponds to Eq. (6.4). The cyan and red profiles
and values describe Eqs. (6.5) and (6.6), respectively.
247 Ångström exponents
The Ångström exponent å as introduced by Ångström [1929] describes the wavelength depen-
dence of optical depths τ :
å
τ (λ1 ) λ2
= . (7.1)
τ (λ2 ) λ1
From multi-wavelengths Raman lidar observations at 355 and 532 nm we can derive extinction-
related Ångström exponents:
par par
ln [α532 (z)] − ln [α355 (z)]
åα (z) = . (7.2)
ln 355 − ln 532
Profiles of backscatter-related Ångström exponents can be derived from Raman backscatter
coefficients and from Klett backscatter coefficients:
par par
355/532 ln [β532 (z)] − ln [β355 (z)]
å β (z) = , (7.3)
ln 355 − ln 532
par par
532/1064 ln [β1064 (z)] − ln [β532 (z)]
å β (z) = .
ln 532 − ln 1064
There is no other method used in the EARLINET consortium than the one described with
Equations (7.2) to (7.3).
258 Backscatter coefficients from elastic
signals only
There are two different methods used in the consortium to calculate the aerosol backscatter
coefficient from elastic signals only:
Method A: Iterative method
The iterative method is described e.g., by Di Girolamo et al. [1999] and Masci [1999]. The
particle backscatter coefficient
!
g
P par
(z) K λ
i par λ0
− 1 βλmol
0
βλ0 (z) = (z) (8.1)
d
iP mol
(z)
0
λ0
is calculated in the ith iteration step from the measured, pre-processed, overlap-corrected signal
d
Pλ0
Pg
par
λ0 (z) = (8.2)
O(z)
and an estimated molecular signal
Z z
d
iP mol
βλmol par (i−1) par
λ0 (z) = 0
(z) exp −2 S (ζ) βλ0 (ζ)dζ . (8.3)
0
i
Kλ0 is a calibration factor and can be determined in an aerosol-free region zref :
iPdmol
i λ0 (zref )
Kλ0 = . (8.4)
Pgpar
λ0 (zref )
A proper profile S par (z) or a height-independent value S par of the lidar ratio has to be assumed.
d
In an initial step the molecular signal 0 P mol par
λ0 (z) is estimated with the assumption of βλ0 (z) = 0
and is then used to derive an initial value of 0 βλpar 0
(z). In the following iteration steps i the
i par
backscatter coefficient βλ0 (z) is calculated from a molecular signal which is estimated from
the previous backscatter profile (i−1) βλpar
0
(z). This procedure is repeated until the difference
(i) par (i−1) par
between βλ0 (z) and βλ0 (z) is smaller than a certain threshold. Di Girolamo et al. [1999]
describe that not more than three iterations steps are needed to derive the final profile.
26Method B: Klett-Fernald solution
As an example one variant of the Klett-Fernald solution [Klett, 1981; Fernald , 1984] is described
below:
A(z, zref )
βλpar = −βλmol
0
(z) + R zref par , (8.5)
0
B(zref ) + 2 z Sλ0 (ζ)A(ζ, zref )dζ
with Z
zref
2
A(x, zref ) = Pλ0 (x)x exp 2 Sλpar
0
(ξ) −S mol
βλmol
0
(ξ)dξ , x = z, ζ
x
and
2
Pλ0 (zref )zref
B(zref ) = .
βλpar
0
(zref ) + β mol
λ0
(zref )
S mol = 8π/3 is the molecular lidar ratio, the particle lidar ratio Sλpar
0
(z) has to be assumed
properly.
General considerations concerning both methods
The sources of uncertainties
The sources of uncertainties in the retrieval of the backscatter coefficient from elastic signals
only are the same for both methods. They are the same as in the retrieval from the combination
of elastic and Raman signals (see Chapter 4) plus two additional large sources of uncertainty:
• uncertaity due to the assumption of a particle lidar ratio (profile); this error can easily
exceed 20% [Sasano et al., 1985],
• uncertainty in the lowest part of the profile (below zovl ) due to the incomplete overlap
between laser beam and receiver field of view and the necessity to correct measured signals
with the overlap function O(z).
Critical calculus subsystems
Critical calculus subsystems of the retrieval of the backscatter coefficient which might be dif-
ficult to handle or for which different algorithms are used within EARLINET are the same as
discussed in Chapter 4. Additional critical points are:
• the assumption of the unknown profile of the particle lidar ratio,
• the determination of zovl and of the overlap function O(z) itself (discussed in Sec. 3.3).
278 Backscatter coefficients from elastic signals only
8.1 Assumption of a lidar-ratio profile S par(z)
8.1.1 Documentation of the existing algorithms
There are several methods used in the consortium to assume a lidar ratio profile:
• Some groups implemented an algorithm to process height-dependent lidar ratios (e.g.,
two different values for the aerosol layer and cirrus clouds).
• Some groups use fixed default values for all observations, others use variable lidar ratio
values, estimated from external constraints.
• The possible range of lidar ratios can be estimated, if there are Raman measurements
available during the previous or following night.
• For daytime lidar observations, radiometer (sun photometer) measurements can provide
additional constraints for the solution of Eq. (8.5). This method is explained below. The
same information could be obtained from nighttime star photometer observations, but
this option is not used in the EARLINET consortium.
• Multi-angle measurements can be used to estimate the lidar-ratio profile.
• Lidar-ratio values according to the actual meteorological condition (derived from clima-
tological observations with Raman lidar in the same region or from the literature) can be
applied. In the EARLINET consortium the following publications are used: Collis and
Russell [1976], Barnaba and Gobbi [2001, 2004], and Amiridis et al. [2005].
• Lidar-ratio information can be extrapolated from measured S values at the same time at
another wavelength.
Combination with Sun photometer observations
Some groups in the EARLINET consortium use the simple iterative method by Landulfo et al.
[2003] to use additional information from sun photometer observations for the estimation of a
height-independent lidar ratio.
A. Chaikovsky, BISIP.SMO provided the following algorithm:
If sun photometer measurements are carried out in conjunction with the lidar sounding, addi-
tional information is available:
τR aerosol optical thickness at the sounding wavelength and
SR = τBR column mean lidar ratio as ratio between
τR and the integrated backscatter coefficient B.
In this case, a calibration procedure by integral parameters of the aerosol layer estimated from
radiometric observations can be used. The algorithm to implement the above procedure is
easily combined with the usual algorithm for calculating β par (z) on the base of Eq. (8.5). But
the parameters β par (zref ) and S are determined as the ones minimizing the below functional.
288.1 Assumption of a lidar-ratio profile S par (z)
It characterizes the deviation of integral aerosol parameters calculated by the retrieved β par (z)
value from the integral parameters estimated by the radiometer observations.
2
n(ztop, β )
X
τR − S β(S, β(zref ), i) + β(zovl ) n(zovl ) δz !
i=n(zovl ) (SR − S)2
W = + C1 exp (8.6)
τR2 ∆SR2
where:
β(S, β(zref ), i) is the aerosol backscatter coefficient retrieved by means
of Eq. (8.5) with parameters S and β(zref ),
β(zovl ) n(zovl ) δz is an estimation of the integral backscatter coefficient
below zovl in the “dead space” of lidar,
ztop, β is the top height of the retrieved backscatter coefficient
profile.
The parameters τR and SR are available from radiometer measurements. The parameters C1 ,
∆SR , zovl , and ztop, β are determined by operator.
8.1.2 Assessment and implication for the automated single-chain
software
Since the variability of the lidar ratio is very high, even at a single lidar site, it cannot be
recommended to use a fixed S value to process all measurements. It is strongly suggested to
support the estimation of an appropriate lidar ratio by additional external information like:
• multi-angle observations, which are limited to horizontally homogeneous conditions,
• Raman lidar measurements during nighttime, which can be applied to neighboring day-
time observations only in case of stationary meteorological conditions,
• correlative Sun-photometer observations under cloud-free conditions.
Since all of those methods are limited to certain meteorological conditions, it is strongly rec-
ommended to implement Raman channels in all lidar systems wherever it is possible and to
increase the daytime capability of existing Raman channels.
299 Vertical smoothing and temporal averaging In general, the noise of lidar raw signals (especially Raman signals) is high and prohibits the direct retrieval of optical aerosol properties. The statistical uncertainty of raw signals can be reduced by temporal averaging, vertical smoothing, or both. If the noise of the signals is reduced by temporal averaging, then the vertical resolution remains high and the resulting profiles of optical properties are very useful for climatological studies. In the opposite way, vertically smoothed profiles have a high temporal resolution and are useful for process studies. The vertical smoothing in case of backscatter coefficients is realized by smoothing the raw signals (or signal ratios) before the retrieval procedures are performed. In case of extinction retrievals, the degree of vertical smoothing is defined by the length of the fit window. The effective height resolution of the backscatter retrieval and of the several methods to derive extinction profiles is not equivalent to the length of the smoothing window/fit window and can differ significantly between the different methods. Pappalardo et al. [2004] describe a method to determine the relation between the length of the used smoothing/fit window and the resulting effective height resolution in dependence of the applied retrieval algorithm. Synthetic lidar signals with a step structure are generated. Each step corresponds to an extinction peak with one height bin width. After applying the retrieval analysis it is checked, if the retrieved peaks are resolved according to the Rayleigh criterion. This procedure is repeated for different distances between the simulated peaks and for different window lengths. For each tested window length the minimum peak distance which can be resolved corresponds to the effective vertical resolution of the retrieved profile. This procedure can also be used to determine the effictive height resolution of backscatter profiles. In general, all groups first average their raw signals and then apply height-dependent and/or noise-dependent vertical smoothing. But there is no algorithm in the consortium to determine automatically the required smoothing length in dependence on height and/or signal uncertain- ties. Turner et al. [2002] report a formula to estimate the required height-dependent length of the fit window in order to derive a height-independent level of uncertainty of the calculated extinction profiles. This relation cannot directly be applied to lidar signals measured with other systems or to other meteorological conditions (e.g., low clouds which increase the noise level in the free troposphere dramatically). 30
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