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Evaluating several methods to determine cirrus clouds properties using
lidar measurements in Cuba and Argentina
Evaluación de diversos métodos para determinar las propiedades de los cirrus
utilizando mediciones hechas con lidar en Cuba y Argentina
Mario Lavorato(1,*), Boris Barja(2), Juan Carlos Antuña(2) and Pablo Canziani(3)
1.
División Radar Láser, CEILAP (CITEFA-CONICET), Juan B. La Salle 4397, B1603ALO, Villa
Martelli, Buenos Aires – Argentina.
2. Estación Lidar Camagüey, Centro Meteorológico de Camagüey, Manuel de Quesada No. 1, e/
Idependencia y San Pablo, Camagüey 70100, Cuba.
3. PEPACG, Pontificia Universidad Católica Argentina-CONICET, Cap. Gral. Ramón Freire 183,
C1426AVC, Buenos Aires, Argentina
* Email: [email protected]
Recibido / Received: 20 – Jul – 2007. Versión revisada / Revised version: 27 – Nov – 2007. Aceptado / Accepted: 29 – Nov – 2007.
ABSTRACT:
Lidar measurements provide information to determine the cirrus clouds optical and geometrical
properties. Those quantitative determinations require properly determined backscatter to
extinction ratio coefficients. In this work we analyze and combine different methods used to
obtain the cirrus clouds parameters profiles (optical depth, extinction and backscattering
coefficients). We applied the proposed combined method to several cirrus lidar signal measured
over Buenos Aires, Argentina and we analyze one occurrence over Cuba. We conducted a critical
analysis of the results. We obtain the parameters using the conventional approach, double ended
and Back-TOD partially methods, all based on the Klett method. The goal of this work is to
determine the backscatter to extinction ratio. We analyze and compare the results with old and
recent data.
Keywords: Backscatter to Extinction Ratio, Lidar, Cirrus.
RESUMEN:
Las mediciones hechas con lidar, nos proveen información para determinar las propiedades
ópticas y geométricas de los cirrus. Estas determinaciones cuantitativas requieren una apropiada
evaluación de la relación entre los coeficientes de retrodifusión y extinción. En el presente trabajo
analizamos y combinamos diferentes métodos para obtener los perfiles de los parámetros de los
Cirrus (espesor óptico, coeficientes de extinción y de retrodifusión). Aplicamos el método
combinado propuesto a diferentes señales de cirrus medidas con lidar sobre Buenos Aires,
Argentina y analizamos un caso sobre Camagüey, Cuba; realizando un análisis crítico de los
resultados. Obtuvimos los parámetros buscados, combinando una aproximación convencional y
los métodos ‘double-ended’ y ‘Back-TOD’ en forma parcial; todos ellos están basados en el
método de Klett. El logro del presente trabajo es que se pudo determinar el factor que relaciona
los coeficientes de retrodifusión y de extinción. Analizamos y comparamos los resultados con
datos antiguos y recientes.
Palabras clave: Relación entre Retrodifusión y Extinción, Lidar, Cirrus.
REFERENCES AND LINKS
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Opt. Pura Apl. 41 (2) 191-199 (2008)
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[3] A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, W.W. Michaelis, “Independent measurement of
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cirrus clouds”, Appl. Opt. 35, 1512 (1996).
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[6] J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios”, Appl. Opt. 24, 1638-1643 (1985).
[7] S. Elouragini, “Etude des propiétés optiques et géometriques des cirrus par télédétection optique active
(lidar) et passive (radiométrie)”, These de Doctorat de l’Universitè de Paris 6 (1991).
[8] F. G. Fernald, “Analysis of atmospheric lidar observations: some comments”, Appl. Opt. 23, 653-653
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[11] M. Lavorato, P. Cesarano, E. Quel, P. Flamant, “A dual receiver-backscatter lidar operated in Buenos Aires
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[12] M. Lavorato, M. Pagura, P. Cesarano y P. Flamant, “Monitoreo de la troposfera mediante un lidar de
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[13] M. Lavorato, P. Flamant, J. Porteneuve, M. Pagura, P. Cesarano y P. Canziani, “Monitoring of the
troposphere by backscatter lidar in Buenos Aires (34.6 S / 58.5 W): Overview of the multi year data set and
implementation of new IR channels and depolarization capability”, Proc. 22th ILRC (International Radar
Laser Conference), pp 156-159, Matera – Italy, (2004).
1. Introduction
is necessary to assume or determine a backscatter to
extinction ratio Kp.
Clouds and aerosols play an essential role in the
radiative transfer of the atmosphere, and hence their
correct observation is fundamental for Climate
Change studies. It is very important to know their
optical and geometrical properties to understand and
qualify the effects on the solar and terrestrial
radiation transfer in the atmosphere. In particular the
scientific community have been conducting an
increasing number of observations and modeling
studies of cirrus clouds to understand their role in
climate change [1,2]. Those studies have been
concentrated over northern hemisphere mid
latitudes. Yet few measurements over northern
tropical and subtropical regions and even fewer over
the southern hemisphere have been carried out.
That is the case of the data collected by our Lidar
stations at Buenos Aires, Argentina and Camagüey,
Cuba. The goal of this work is to develop a method
to analyze cirrus lidar measurement acquired with
our systems. We will calculate with this method the
extinction and backscattering coefficients profiles
and backscatter to extinction ratio of cirrus clouds.
The method finally developed is based on doubleended [3] and Back-TOD [4] method; according to
the Klett inversion Lidar method [5,6]. The method
combined the use the standard inversion Lidar
equation for obtaining the acquired extinction
coefficient cirrus clouds [α(R)]. The data signal
must fulfill the following requirements:
Satellite
measurements
provide
valuable
information about cirrus clouds global coverage.
But, there is lack of information about the vertical
distribution of cirrus optical and geometrical
properties. Lidars are a useful and powerful
instrument to provide local measurements with high
vertical resolution. We work with single wavelength
lidar detection, and therefore we have a certain
difficulty to determine the cirrus optical properties
(cirrus extinction and backscattering coefficients). It
Opt. Pura Apl. 41 (2) 191-199 (2008)
- Observe the presence of molecular signal after
cirrus signal (continuity condition).
- The signal to noise ratio (SNR) must be higher
than 2 [7]. Others methods use SNR values above
3 [4] as a condition.
This method lets us obtain the backscatter to
extinction ratio (Kp) of cirrus clouds (like the BackTOD method). It can be applied to analyze both a
single signal and a time series evolution. We do not
employ others methods like Fernald [8] or Russel [9]
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in calculations because they used estimated or real
value of Kp.
was calculated with the same
described for the Back-TOD [4].
In the present paper we apply the method in order
to analyze lidar signals acquired during different
monitoring periods in the last 5 years.
3. Signal-to-noise ratio problem
Lidar measurements carried out in Argentina [11]
contain many lidar signals acquired during the
daytime, where the signal to noise ratio is less than
three. During daytime measurements, the
background noise present at those hours limits the
dynamic range of lidar system. It is an instrumental
limitation to improve in the near future. The spatial
resolution of those signals is normally 6 m [7] and
the total acquisition set the dynamic range up to 30
km (the useful Lidar signal from 300 m to 25 km at
nighttime, decreasing to 20 km at daytime). Outside
these heights only noise is present. One cirrus Lidar
signal is obtained by averaging 20 seconds or more
of signals acquired from laser shots backscattered by
the atmosphere, in order to reduce the electrical
Gaussian noise (200 or more laser shot by profile).
2. Cirrus lidar equations
The single-scattering Lidar equation has the form:
V (R ) = I c
β(R )
R
2
⎡
exp⎢− 2
⎣
∫
R
R0
⎤
α(r )dr ⎥
⎦
(1)
where the main variables are:
V(R) = Received power.
β(R) = Backscatter coefficient.
α(R) = Extinction Coefficient.
R = Range.
R0 = Reference Altitude.
Ic = Instrumental constants.
In order to improve the SNR in the Argentine
cirrus Lidar database, a pass-bass filter is applied in
the obtained signal. If the filtering procedure were
not carried out, many original signals would have to
be discarded because they do not have the
appropriated SNR. On the other hand, in the Cuban
cirrus Lidar database, it is not necessary to apply the
filtering procedure because the 75m vertical
resolution results in an appropriated SNR.
Backscattering and extinction coefficients at each
point of atmosphere are related by the Bernoulli
equation:
β(R ) = K p α(R )
(2)
The stable solutions of the Lidar equation for the
extinction and backscattering coefficient could be
derived considering 100% coupling between the
emitter and the receptor telescope. The solution for
the extinction and backscattering coefficients are
showing in Eqs. (3) and (4) following the Klett [5,6]
inversion method:
α (R ) =
where:
exp[S (R ) − S (R0 )]
R0
1
+2
exp[S (r ) − S (r0 )]dr
R
α( R0 )
∫
(
),
S (R ) = ln (V (R ) ⋅ R ) ,
S (R ) = ln V (R ) ⋅ R 2
0
0
2
0
Three mathematical methods are commonly used
to statistically improve the SNR. Once the Lidar
signals are acquired and recorded we can average
two or more originals signals, increasing the
temporal resolution with the increase in SNR. A
second method applied, reduces the spatial
resolution from 6 m to 30 m or more (30 m is the
spatial resolution used in the most lidar stations
around the world) to improve SNR. The third one
uses a numerical filter technique, i.e. a butterword or
moving average filter. It is very important to note
that in all cases, we loss either spatial or temporal
resolution in the signal. However we accept a few
losses in cirrus quality signal in favor of a SNR
increase, i.e. 30 % or more. The three methods do
not use the similar filter o statistical parameters to
improve SNR, thus they are not able to carry out a
comparison.
(3)
(4)
(5)
α(R0) is extinction coefficient at R0 (reference), and
β(R ) =
exp[S (R ) − S (R0 )]
2 R0
β(R0 ) +
exp[S (r ) − S (r0 )]dr
Kp R
∫
(6)
Figures 1 to 3 illustrate the results of the
application of three methods described above for
improving the SNR. These figures show the results
of the averaging of time series, digital filtering and
reduction the spatial resolution of the lidar
measurements of cirrus clouds during September 8,
2000. All of them reduce the present noise (red line),
For cirrus clouds it is common to consider Kp
constant at all levels. The signal-to-noise ratio
(SNR) became one of the more important parameters
during the lidar signal processing. The SNR
parameter is very important for error estimation
during the restitution process of cirrus optical and
geometrical parameters [10]. The Kp or lidar ratio
Opt. Pura Apl. 41 (2) 191-199 (2008)
methodology
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4. Calculating methods analysis
but always we can observe the lost of signal level in
comparison to original noisy signal (blue line). We
can see averaged signal in Fig. 1. In Fig. 2 the
Butterworth digital filter is applied over each signal.
Finally the signal shown in Fig. 3 was averaged with
the signals contained in the time series but
decreasing the spatial resolution from 6 m to 30 m.
In the set of figure, as we can see ‘a priori’, the
digital filtered signal and the lowered resolution
signal yield similar results, and are better than the
averaged signal. To improve the SNR in the average
method it is necessary to increase the number of
averaged signals.
For deriving the optical and geometrical parameters
of measured cirrus the ‘Double ended’ [3] and
‘Back-TOD’ [4] techniques were analyzed. Both
methods are based on the stable Klett’s solution of
inversion Lidar equation. The first one assumes a
value of Kp derived with a Raman lidar. In our case
we need to estimate this value from tables or
statistics data from other latitudes because we have
not this kind of measurement. The method calculates
β(R) iterating backward and forward the signal until
the same result is achieved in both directions. In this
case a SNR higher than 2 is necessary [3]. Also the
signals which do not fulfill the stable forward
solution of lidar equation should be discarded.
The second method calculates α(R) assuming as
reference value, the value of cirrus extinction
coefficient derived from the slope method [5,6]
(graphical method). Then, this value is compared
with another one calculated considering a maximum
error (less than 0.01%) in the iterating procedure for
deriving α(R). To be able to apply this procedure,
the SNR value should be higher than 2. This method
allows a valid estimation, to determine a Kp value,
only when the molecular signal is present on top of
the cirrus (continuity condition).
Fig. 1. Averaged time series signal.
Both methods combined assure the best use of the
available signals. We carry out the derivation of
α(R) iterating the values forward and backward
assuming as reference values (αref) the integrated
values in each one of the iterations. This procedure
is conducted until the predefined error value is
achieved, i.e., less than 0.1%.
Because the original signal has been statistically
´improved´ with the filtering procedure, it is possible
to calculate the Kp mean value for cirrus series.
Using these combined methods we can analyze only
one signal and obtain all the results. At the same
time it is possible to derive all the results from a
temporal series.
Fig. 2. Digital filter applied over time series signals.
5. Lidar results
We have currently applied the procedure to several
Lidar signals from both sites. Here we discuss the
preliminary results for four cases from Buenos
Aires, Argentina, and one case from Camagüey,
Cuba, in order to highlight the main results. A paper
in preparation will present the results for both
datasets.
5.1. Cuban data example
Figure 4 shows the results of Camagüey Lidar
Station measurement from June 7, 1994,
Fig. 3. Spartial resolution reduction.
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6. Conclusions
corresponding to mean values series. In alternated
colors (red – blue) we can see the range corrected
filtered signals used in the calculations.
We report a combination of methods to derive the
optical and geometrical properties of cirrus clouds.
Also the preliminary results showed very
encouraging performances. Results from Cuban
measurement data process are consistent with former
calculations.
The parameters calculated with the combined
method proposed in this work are the extinction
coefficient, optical depth and backscatter to
extinction coefficient mean values of temporal
series:
Optical depth distributions from four Argentine
measurements cirrus processed data have the
expected characteristics. The figures illustrate three
Gaussian-exponential distribution cases and only
one case with Gaussian distribution. We can see that
the backscatter to extinction ratio can have very
different values. We will derive a real statistical
distribution after we finish processing more than 200
time series acquired since 2000 to the present.
αm = 0.72*10-4 m-1 ------ ODm = 0.2
Kp = 0.043 sr-1 or Lidar ratio = 23.1 sr
Acknowledgments
This work has been supported by the Cuban
National Climate Change Research Program grant
01303177 and by the grant CU/PA04-UXIII/014
from Scientist – Technology Cooperation Program
between SECYT (Argentina) and CITMA (Cuba).
This work was carried out with the aid of a grant
from the Inter-American Institute for Global Change
Research (IAI) CRN II 2017 supported by the US
National Science Foundation (Grant GEO-0452325).
Fig. 4. Progressive lidar data from Camagüey Lidar
Station.
5.2. Argentine data base examples
We present the results of four time series evolutions
corresponding to: March 13, 2003; October 28,
2004; May 27, 2005 and September 10, 2006.
The figures 5 to 9, 10 to 14, 15 to 19 and 20 to 24
show calculated parameters time series evolution for
each sample respectively. We can see at first the
time series evolution with the corrected data range
[P(R)⋅R2] (Figs. 5, 10, 15 and 20) for each sample.
Subsequently, the optical depth evolution (Figs. 6,
11, 16 and 21), and optical depth distribution
(determine the cirrus clouds characteristics of each
region) (Figs. 7, 12, 17 and 22) are shown.
Furthermore, in Figs. 8, 13, 18 and 23 we can see the
extinction coefficient evolution. Finally the
backscatter to extinction coefficient (Figs. 9, 14, 19
and 24) is shown. The last of the parameter
mentioned gives us an important microphysical
characterization of cirrus clouds in our region.
Backscatter to extinction coefficient (Kp) or the lidar
ratio coefficient (1/Kp) is a very sensitive parameter
for the mixing of ice crystals versus vapor water
present inside cirrus.
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5.2.1. March 13, 2003. Lidar data
Fig. 5. Cirrus evolution (13/03/2003).
Fig. 6.Optical Depth evolution (13/03/2003).
Fig. 7. Optical Depth distribution (13/03/2003).
Fig. 8. Extinction Coefficient (13/03/2003).
Fig. 9. Kp - (13/03/2003)
Table I. Results (March 13, 2003).
0.057 sr-1
17.39 sr.
1.17×10-4 m-1
0.42
Kp (series averaged)
Lidar ratio equivalent
αm
ODm
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5.2.2. October 28, 2004. Lidar data.
Fig. 10. Cirrus evolution (28/10/2004).
Fig. 11 -.Optical Depth evolution (28/10/2004).
Fig. 12. Optical Depth distribution (28/10/2004).
Fig. 13. Extinction Coefficient (28/10/2004).
Fig. 14. Kp - (28/10/2004)
Table II. Results (October 28, 2004).
0.042 sr-1
23.80 sr
1.02×10-4 m-1
0.39
Kp (series averaged)
Lidar ratio equivalent
αm
ODm
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5.2.3. May 27, 2005. Lidar data
Fig. 15. Cirrus evolution (27/05/2005).
Fig. 16. Optical Depth evolution (27/05/2005).
Fig. 17. Optical Depth distribution (27/05/2005).
Fig. 18. Extinction Coefficient (27/05/2005).
Fig. 19. Kp - (27/05/2005)
Table III. Results (May 27, 2005).
0.056 sr-1
17.85 sr.
0.94×10-4 m-1
0.47
Kp (series averaged)
Lidar ratio equivalent
αm
ODm
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5.2.4.September 10, 2006. Lidar data.
Fig. 20. Cirrus evolution (27/05/2005).
Fig. 21. Optical Depth evolution (10/09/2006).
Fig. 22. Optical Depth distribution (10/09/2006).
Fig. 23. Extinction Coefficient (10/09/2006).
Fig. 24. Kp - (10/09/2006)
Table III. Results (May 27, 2005).
0.08 sr-1
12.5 sr.
1.12×10-4 m-1
0.45
Kp (series averaged)
Lidar ratio equivalent
αm
ODm
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