th
Abstract: The water vapor is known as the most important greenhouse gas due to its high concentration in the atmosphere
(parts per thousand) and its chemical property of being. a solvent for mineral and chemical constituents of anthropogenic and natural sources of the atmosphere. Therefore a high interest in obtaining water vapor profiles is manifested in the meteorological and remote sensing scientific world all around the globe. In this paper a set of lidar calibration techniques are presented and compared for validation of the retrievals of multi-wavelength Raman Lidar system. The algorithms are using data fusion from three different sources: Raman Lidar, CIMEL sun photometer and radiosondes to estimate the correct calibration constant and the corresponding technique. The comparisons and errors are then discussed and the calibration constants obtained are validated by independent hygrometere surface readings. Finally the considered calibration constant is used in the retrieval of the water vapor ratio mixing ratio profiles above the CCNY (City College of the City University of
New York) station.
Key words : Water vapor mixing ratio, calibration constant, Raman lidar.
The importance of water vapor as a solvent for mineral and chemical constituents of anthropogenic and natural sources of the atmosphere is crucial to the short and long term global climate.
As the most important greenhouse gas, the water vapor concentration in the atmosphere should be determined along with size, chemical composition and hygroscopic properties of the constituent aerosols of the atmosphere derived from their physical and optical characteristics. To obtain accurate water vapor mixing ratios, the lidar system should be calibrated and the measurements validated by concomitant independent readings of the same gas. This paper will discuss and compare a set of two calibration techniques of the multi wavelength
Raman lidar installed at the CCNY station. The theory that represents the base of the two calibration methods is explained in section 2 and 4. The lidar optical and electronic system design at the CCNY station is described in section 3 and the two calibration techniques are presented section 4. The error analyses and comparisons of the two calibration methods are presented in section 5 and section 6 respectively. Finally the conclusions are drawn in section 7.
The chemical property of water vapor of condensation on different types of aerosols found in the atmosphere is changing the chemical composition, shape and size of this particles, and at the same time it affects their optical properties and the direct radiative forcing[1]. High Cirrus clouds and contrails created by airplanes are formed from amalgams of water or ice crystals suspended in air cooled below the saturation temperature, allowing the moisture to form into small drops on microscopic particles called condensation nuclei that can be water

molecules (homogeneous nucleation) or other metallic nitrogen oxides, carbon dioxide etc
(heterogeneous formation of aerosols)[2]. While the impact of high altitude clouds on global warming is larger than their cooling effect (long waves albedo is
0.4-0.7), the lower altitude clouds in change have an overall cooling effect [1],[3]. Therefore good measurements of water vapor in the atmosphere
(troposphere) are necessary. One of the methods of monitoring the water vapor mixing ratio in the atmosphere is by using a Raman lidar which is based on the Raman effect. When a substance is subjected to an incident exciting wavelength, it exhibits the
Raman effect. It reemits secondary light at wavelengths that are shifted from the incident radiation. The magnitude of the shift is unique to the scattering molecule, while the intensity of the Raman band is proportional to the molecular number density
[4]. The water vapor Raman lidar technique uses the ratio of rotational-vibrational Raman scattering intensities from water vapor and nitrogen molecules, which is a direct measurement of the atmospheric water vapor mixing ratio. The water vapor and nitrogen Raman signals are given by equation 1
P
R
( z )

K s
(
 z 2
R
, z ) n
R
( z )
 d

(

L
, d


R
, z )

(1)
 exp


 
0 z
(


L
( z )
 

R
( z )) dz


 b

R
( z )
P
R is the detected Raman lidar backscatter signal corresponding to nitrogen and water vapor, K s
is a system function that is dependent on the optical transmission and detector efficiency, the overlap function and the area of the collector mirror of the telescope, n
R
is the number density of Raman active molecule,
 d

(

L
, d


R
, z )
is the differential Raman backscatter cross-section, α is the extinction coefficient and b is the background (noise) signal.
By taking the ratio of the two signals one can obtain the water vapor mixing ratio profile in equation 2.
P
H
2
O
( z )
P
N
2
( z )







K
H
2
O
K
N
2





 d d d


 d


H

N
2
O
2






T
H
2
O
T
N
2






* q
H
2
O
( z )
M air
M
H
2
O
where T is the transmission for the two wavelengths through the atmosphere and M represents the mass of water vapor in atmosphere and dry air P
H
2
O
and P
N
2
.
The water vapor profile may be retrieved as expressed in equation 3. q
H
2
O
( z )

K
N
2
K
H
2
O d
 d
 d d



H

N
2
2
O
T
N
2
T
H
2
O
M
H
2
O
M
N
2
O
P
H
2
O
P
N
2
where q is the water vapor mixing ratio in [g/Kg dry air] or in [ppmv].
Hence q
H
2
O
( z )

C *

*



P
H
2
O
P
N
2



where  
T
N
2
T
H
2
O

1 and C is the calibration function.
Due to little aerosol influence on the 407nm and
387nm Raman channels this technique is relatively free of systematic errors (aerosol effects), can be operated from the ground (the radiation is not absorbed by the water vapor itself) and its use is relatively simple. Its main limitation is the relatively small backscatter Raman cross- sections, that result in weak Raman signals compared with the elastic backscatters or the electronic noise induced in daytime by solar radiation (see figures 3 and 12)[5].
As mentioned above one might observe that the method requires the use of a calibration constant towards the retrievals.
C

K
N
2
K
H
2
O





 d d d
 d






N
2



H
2
O
M
H
2
O
M
N
2
O
There have been many calibration techniques proposed and used along time [1], [6-9]. Some methods suggest an approximate external calibration, a one point in situ value, or a calibration based on horizontal lidar measurements. The methods proposed in this paper are presented in diagrams in fig. 7 and 11 (sections 4.2 and 4.3 respectively) and discussed in detail in section 4.
CCNY multi-wavelength Raman lidar is a monostatic system that contains a Quanta-Ray Nd:YAG laser model PRO 230 with a 30 Hz repetition rate. The performances and technical specifications of the

transmitter and receiver along with a schematic of the lidar system are described in detail in Ref.10.
A schematic of the receiver is presented in figure 1.
15VDC Voltage Supply
15VDC Voltage Supply
High Voltage Supply
RM2
IF L
Mie 1064 APD A/D
ND
IF L
BS2
BS1
ND
L
Mie 532 PMT,A/D
BS3 IF
Mie 355 PMT,A/D
BS4
ND
IF
IF
L
Raman 387 PMT,A/D
PMT
L
Raman 407 PMT, A/D
R1527P
L Iris
RM1
Al coating
15VDC Voltage Supply
Si:APD:C30956E
PMT:H6780-20
PMT:R1527P
PMT:R2693P
LICEL
UNIT
COMPUTER
Figure 1. Optical set-up of the receiver
The data acquisition is performed using LICEL transient recorders working at (40 Mega samples
/sec) 40MHz, 12 bit resolution of the recoder in analog (A/D) mode and a discriminator which detects voltage pulses above a selected threshold in the range
0-100mV. Typically an acquisition file contains 1800 shots averaged for each wavelength in A/D and P.C modes of 16000 bins. With an acquisition sampling rate of 40MHz the pulse width is 2.5*10 -8 s which is results in a spatial resolution of 3.75 m resolution/1 bin)
Water vapor and nitrogen profile measurements are thus performed and the obtained profiles are presented in section 3.2. By combining the two profiles one can retrieve the relative humidity or water vapor mixing ratio in the lower troposphere
An example of a Mie / Rayleigh 1064nm signal measured on September 7 th , 2006 is plotted between the hours of 10am and 18pm in fig. 2. This day has been considered for calibration due to the high
PBL(planetary boundary layer) that can be observed in fig.2 and is known to contain most of the atmospheric water.
Logarithm(e) of Pz
2
at 1064-nm, Sep07,2006 CCNY
12
10
8
6
4
2
-4
-6
0
12 13 14 15
Local time (hr)
16 17
Figure 2. Lidar image obtained at CCNY station on the day of September 7 th , 2006
The vertical profiles
Lidar vertical profiles of the multiwavelength Raman lidar installed at CCNY
10
8
6
4
2
0
-2
10
2
10
0
355nm
532nm
1064nm
407nm
387nm
10
-2
10
-4
0 2 4 6
Altitude(Km)
8 10 12
Figure 3. Lidar profile collected at 11:44am averaged over 60min on September 7 th ,2006
During daytime measurements the solar radiation is inducing a high noise in the measurements and this can be noticed in the water vapor and nitrogen
Raman signals where they have low SNR(signal to noise ratio) below 3.5Km and respectively 6.5Km.
The backward trajectories complemented by human observers and Modis satellite data contribute to choosing the right observation days for calibration.

th
Figure 5 presents an example of a backward trajectories on the day October 05, 2006.
Another source used in the retrieval algorithm is
AERONET (Cimel sun photometer) that is providing the integrated column water vapor (cm) above the
CCNY campus that in conjunction with the CCNY multi-wavelength Raman lidar measurements at
407nm and 387nm and the radiosounds located in the neighborhood (40º86’north latitude and 72º86’ west longitude) of the CCNY station (40º77’ north latitude and 73º 98’ west longitude) form the bases for the first calibrated technique presented in section 4.2.
The radiosonds deliver information about the pressure, height, temperature, dew point temperature, relative humidity and mixing ratio above the
Brookhaven station in NY.
The second calibration method is based on data retrieved from the Raman Lidar signals at the CCNY station and the radiosonds pressure, temperature and mixing ratio profiles mentioned above and is presented in section 4
The collection of the different data sets is simple and can be obtained in detail from Ref. 10.
An example of an aerial image obtained by MODIS satellite at the time considered of interest for our measurement is presented in fig 6 .
th
Finally analysis of the local measurements of the relative humidity using ground based hygrometers collocated with the CCNY multi wavelength lidar system are used to validate the two methods.
The diagram describing the steps followed in obtaining the calibration constant is presented in fig7.
As one can observe the method is using 3 major sources: CCNY lidar data, collocated aeronet sun photometer retrieved water vapor integrated column and Brookhaven radiosond profiles. The theoretical approach is based on the theory presented in section2
S
407
CCNY
LIDAR
DATA
S
387
S
H
2
O
S
N
2
H
2
O
AERONET
DATA
Total column water vapor pressure
Column water vapor density
RADIOSONDS
DATA
P
T
Density of dry air
Calibration constant
C
Figure 7. Block diagram representing the fusion of the three sources of data in the attempt of calibration constant (technique 1) retrieval.

Starting from the very well known relation of the water vapor mixing ratio given in equation 6
q
H
2
O
z



H
2 air
O
z z
Where

H
2
O
is the water vapor density measured by the sun photometer as an integrated column and multiplied by the water vapor mixing fraction corresponding to the height interval used for analysis
(i.e. calculated fractions for 0.5km to 4km spatial range resulted in water vapor integrated column fractions of 0.82) provided by the water vapor mixing ratio profile measured by the radiosound. The
 air is the air density measured by the radiosounds and integrated over the spatial range of intrest.
Making equation 6 equal equation 3 results in:
 z z
0

H
2
O dz

C
 z z
0
P
H
2
O
 air dz
P
N
2
Therefore by using the two range corrected and background subtracted lidar signals P
H
2
O
, P
N
2
and the sounding and the corresponding fraction
atmosphere one can retrieve the calibration constant of the lidar system observed.
The measured water vapor mixing ratio in fig 8 was obtained by multiplying the calibration constant to the ratio of the two signals (see equation 5) on the day of September 7 th , 2006.
LIDAR retrieved water vapor mixing ratio compared with radiosondes data
3.5
LIDAR retreived radiosondes
3
2.5
2
1.5
1
0 2 4 6 8 10
Water vapor mixing ratio(kg/kg) x 10
-3
Figure 8. Water vapor mixing ratio profile measured by the CCNY lidar and radiosonde at the Brookhaven station on Sept 7 th ,2006
Comparing the water vapor mixing ratios measured by the two instruments: the multi wavelength Raman lidar and radiosounds one may easily observe there are good agreements between them. There are days when the radiosounds and the lidar measurements do not entirely agree. Analyzing the meteorological conditions at the two locations (Brookhaven and
CCNY) the divergences can be easily justified.
Water vapor mixing ratio retrieved from lidar and radiosonds
4
3.5
Wvmixr technique1
Wvmixr 8am radiosondes
Wvmixr at 8pm radiosondes
3
2.5
2
1.5
1
0.5
0 0.001 0.002
0.003 0.004
0.005 0.006 0.007
0.008 0.009
Water vapor mixing ratio(kg/kg)
0.01
Figure 9. Water vapor mixing ratio measured by the
CCNY Raman lidar and radiosondes on Oct 5, 2006
One example of disagreement is the water vapor mixing ratios measured by radiosonds and the CCNY lidar on October 5 th , 2006 plotted in fig. 9
It is expected to see higher humidity at Brookhaven below 2000m due to the atmospheric currents shown in figure 5 that are pushing the clouds above
Brookhaven and could be seen in the Modis image presented in fig.6 too. An indication of higher humidity above Brookhaven is the plot in fig. 10 that shows temperatures close to the saturation (cloud or fog) up 2.5km in the morning and 1.8km in the evening while the human observers at CCNY indicate no fog or clouds present during the measurements.
Temperature and dew point temperature
4
3
Dew point temperature 8a.m.
Temperature
2
1
-60 -40 -20 0 20 40 60
4
3
2
1
Dew point temperature 8p.m.
Temperature
-60 -40 -20 0 20 40 60
Temperature(C)
Figure 10. Temperature and dew point temperature profiles measured above Brookhaven on Oct5 th ,2006.
As observed from the vertical profiles of the 1064nm and 407nm channels in figure 12, the PBL (planetary boundary layer) is thinner above NY city for the day of October 5 th 2006. The lidar indications of that day’s PBL height is around 1.2km (see 1064nm and
407nm signal in fig.12) with very high sparse clouds in the evening.[9]

The alternative method that is only using the lidar returns and the radiosounds alone as main sources for calibration is presented in the diagram in figure 11.
The assumptions are that the parcels of air over both the radiosound and the lidar location have similar meteorological characteristics at the times of data collection (it can be verified from the hysplit back trajectories if the air circulation to and from the 2 specified location is favorable to calibration) The simplicity of the method consist in choosing a spatial range in the lidar data with very little noise where there are at least 2 or 3 radiosonds readings. By taking the ratio of the water vapor mixing ratio indicated by the radiosondes over the range and the lidar ratio of the 407nm and 387nm channels one can obtain the calibration constant.
CCNY
LIDAR
DATA
S
407
S
387
S
H
2
O
S
N
2
Calibration constant
C(z) z min
<z<z max
C(z) averaged
RADIOSOUND
DATA
H 2 O
Water vapor mixing ratio
Figure 11. Block diagram representing the fusion of the three sources of data in the attempt of alternative calibration constant retrieval (technique 2).
October 5 th , 2006 was one of the days used for calibration. The collected signal is plotted in fig.12
Lidar vertical profiles of the multiwavelength Raman lidar installed at CCNY
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
355nm
532nm
1064nm
407nm
387nm
10
-5
0 0.5
1 2 2.5
3 1.5
Altitude(Km)
Figure 12. Lidar profiles measured at CCNY station on October 5 th , 2006
The retrieved relative humidity from the calibrated signal by use of technique 2 described above is plotted in fig 13.
Relative humidity measured by lidar and radiosonds
4
RH 8am radiosonds
3.5
RH technique2
RH 8pm radiosondes
3
2.5
2
1.5
1
0.5
0 10 20 30 40 50 60
Relative humidity %
70 80 90 100
Figure 13. Relative humidity measured by CCNY lidar and 8a.m. and 8p.m. radiosond on Oct 5 th , 2006
The relative humidity measured by the lidar and calibrated by using the second technique is plotted in fig. 13 is in disagreement with the same profile calibrated by use of technique 1 plotted in figure 9.
Since the second calibration technique is based solely on validation with radiosonde data it is expected to see better conformity between the lidar signal and the radiosond. The concordance of the 2 signals is limited below 1km for the reasons specified in section 4.2 (low clouds above Brookhaven not present and noticed by human observers above
CCNY at the time of measurements)
The correct calibration constant of the lidar system can be obtained only after careful analyses of the errors and validations of the measurements.
In this section error analyses have been performed and discuss for the following days: September 7 th ,
11 th , 21 st , 26 th and October 5 th , 2006. Figure 13 is giving an insight into the percentage errors between the two calibration constants that were retrieved with the formula presented in equation 8.
Percentage error

C technique 1

C technique 2
C technique 2
* 100 % (8)
The percentage errors plotted in fig 17 show only the data presenting percentage errors bellow 30% or very stable over time. The selection of the valuable calibration constant that should be considered on the days presenting stable calibration constants with percentage errors below 15% is easy and any of the above presented techniques can be used for lidar

system calibration. But as one can observe there is a high variability between the calibration constants over time and especially towards the evening.
Therefore there is a high difficulty in selecting the correct calibrating method during the days when there is little stability in the constants (fig 14 a),c) and d)) and/or high percentage errors between the two calibration constants(figure 14 e)).
Percentage error a) September 7, 2006
30
20
10
0
0 50 100 150 200 250
b) September 11, 2006
300 350
30
20
10
0
0 50 100 150 200 250 300
c) September 21, 2006
350 400
30
20
10
0
0 50 100 150 200 250 300
d) September 26, 2006
350 400
30
20
10
0
0 50 100 150 200 250
October 5, 2006
300 350 400
Percentage error
Averaged percentage error 100
50
0
0 50 100 150
Calibration constant index
200 250
Figure 14. Percentage errors estimated on a)
September 7, 2006, b) September 11, 2006 c)
September 21, 2006, d) September 26, 2006, e)
October 5, 2006
One of the main reasons for this high variability can be the use of a single radiosound reading for the whole day of measurements and therefore the determination of the true calibration constant requires not only careful analyses of the weather at the two stations but also statistical analyses of the two calibrating methods. Correlation coefficients and regression analyses were performed and are available in Ref. 10
In this section a set of comparisons and validations
(over three different days) of the two techniques are presented and discussed.
As seen in fig 15 the two calibration methods result in very good agreements between the water vapor mixing ratio measured by lidar and the radiosounds measurements.
Water vapor mixing ratio retrieved from lidar and radiosonds
3.5
3
2.5
Wvmixr technique1
Wvmixr 8am radiosondes
Wvmixr technique2
Wvmixr at 8pm radiosondes
2
1.5
1
0.5
0
0 2 4 6 8 10 12 14
Water vapor mixing ratio(g/kg)
Figure 15. Water vapor mixing ratio measured by lidar and calibrated by the two techniques and compared with the morning and evening radiosonds readings on Sept 7 th , 2006
A hypothesis testing on the means of the two calibration constants confirm the averages of the two calibration constants to be within the 99% confidence interval of each other. The days observed when the two constants lead to big discrepancies in the relative humidity profile but very stable over time (figures 14 and 16) have been carefully analyzed. The local measurements of the relative humidity using ground based hygrometers collocated with the CCNY lidar system lead to the conclusion that technique 1 is providing the accurate measurement of the relative humidity at the surface (see table 1). The GPS system indicates a relative humidity of approximately 51% which corresponds to the lidar profile calibrated by use of technique 1.
Relative humidity measured by lidar and radiosonds
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
RH 8am radiosonds
RH technique1
RH technique2
RH 8pm radiosonds
0.2
0 10 20 30 70 80 90 100 40 50 60
Relative humidity %
Figure 16. Relative humidity retrieved by CCNY lidar and Brookhaven radiosounds on October 5 th ,
2006
The degree of disagreement of the two calibration techniques vary proportionally with the meteorological differences between the two locations
(Brookhaven and CCNY). The water vapor mixing

ratios obtained on August 12th, 2006 show slight disagreement between the water vapor mixing ratios obtained by the two calibrated lidar techniques.
Relative humidity measured by lidar and radiosonds
2
1.8
1.6
1.4
1.2
RH technique1
RH technique2
1
0.8
0.6
0.4
0.2
10 20 30 80 90 100 40 50 60
Relative humidity %
70
Figure 17. Water vapor mixing ratio profile measured by the CCNY lidar and calibrated using technique 1 at 11:45am on August 12 th ,2006
The relative humidity measured by the CCNY collocated hygrometer confirms once again the accuracy of the first calibration technique by indicating an approximately 28% relative humidity and not 32% as retrieved by the profile calibrated using the second technique on August12th, 2006 and plotted in figure 17.
The first conclusion that has to be studied in more details is that calibrating the lidar by use of radiosounds alone is not a reliable method due to the high horizontal variability of the water vapor in the atmosphere that can lead to big discrepancies in estimations. One can use the temperature profile of the day (less horizontal variability) to determine for example air density but not water vapor mixing ratio for stations that are approximately 70 miles away. To overcome the high variability of the calibration constants over the day of measurements (see section 5) sources providing meteorological vertical profiles at shorter time intervals and collocated with the CCNY lidar system should be used. Since an NOAA ARL (national oceanographic and atmospheric administration) meteorological predictive model (EDAS40
Sounding ) develops values at bihourly intervals above CCNY and other locations, then future work of incorporating this predictive data into the retrieval algorithms and statistical analyses should confirm the accuracy of the technique and provide the system with a mean calibration constant that can be used for the times when the complementary data sources are not available.
References
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Politechnique Federale de Lausanne, These No 2975, 2004
2. J.M. Wallace, P.V. Hobbs, Atmospheric Science An introductory survey , Second edition, Academic Press
Elsevier 2006
3. A. Ansmann, U. Wandinger, M. Riebesell, C Weitkamp and W Michaelis, Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar, Applied
Optics, Vol. 31, No. 33, November 20 th , 1992
4. J. I. Steinfeld, Molecules and Radiation An Introduction to Modern Molecular Spectroscopy, MIT, Cambridge,
Massachusetts (1993)
5. D.N.Whiteman, S.H.Maelfi, and R.A. Ferrare, Raman lidar system for the measurement of water vapor and aerosols in the Earth’s atmosphere Applied Optics, Vol.
31, No. 16, June 1 st , 1992
6. E.J.O’Connor, A.J. Illingworth, and R.J Hogan, A technique for Autocalibration of Cloud Lidar, American
Meteorological Society, May 2004
7. J.A. Reagan , Fellow, IEEE , X. Wang, and M. T.
Osborn, Spaceborne Lidar Calibration From Cirrus and
Molecular Backscatter Returns IEEE Transactions on
Geoscience and Remote sensing, vol. 40, No.10, Oct 2002
8. D. N. Whiteman@ all, Scanning Raman Lidar Error
Characteristics and Calibration For IHOP , NASA/HQ
9. C. Weitkamp, LIDAR range-resolved optical remote sensing of the atmosphere , Springer 2005
10. D. V. Vladutescu, Yonghua Wu, Leona Charles, Barry
Gross, Fred Moshary, Samir Ahmed, Water vapor mixing ratio used in lidar calibration technique, WSEAS,
Tenerife, Spain, December, 2006