Page 1
Temperature sensitivity of differential absorption lidar
measurements of water vapor in the 720-nm region
Edward V. Browell, Syed Ismail, and Benoist E. Grossmann
Recently measured properties of water vapor (H20) absorption lines have been used in calculations to
evaluate the temperature sensitivity of differential absorption lidar (DIAL) H20 measurements. This paper
estimates the temperature sensitivity of H20 lines in the 717-733-nm region for both H20 mixing ratio and
number density measurements, and discusses the influence of the H20 line ground state energies E", the H20
absorption linewidths, the linewidth temperature dependence parameter, and the atmospheric temperature
and pressure variations with altitude and location on the temperature sensitivity calculations. Line parame-
ters and temperature sensitivity calculations for sixty-seven H20 lines in the 720-nm band are given which can
be directly used in field experiments. Water vapor lines with E" values in the 100-300-cm- range were found
to be optimum for DIAL measurements of H20 number densities, while E" values in the 250-500-cm-1range
were found to be optimum for H20 mixing ratio measurements.
1. Introduction
Accurate measurements of atmospheric water vapor
(H20) are needed to aid in the understanding of many
earth system processes including the hydrologic cycle,
the radiation budget, global circulation and dynamics,
and various meteorological processes.
absorption lidar (DIAL) is an active remote sensing
technique that has been used to measure H20 profiles
from ground-based and airborne platforms1-5in the
atmosphere. The DIAL technique can provide long
range measurements of H20 profiles, and it has the
potential for making H20 measurements from space
(see Ref. 6 and references therein). In the DIAL mea-
surement of H20, it is necessary to choose H20 absorp-
tion lines that are insensitive to variations in the atmo-
spheric temperature in the measurement region. This
is done to prevent the uncertainty in the knowledge of
the local temperature from producing a significant
error in the DIAL measurement. Since atmospheric
temperature is a function of altitude, geographic loca-
tion, and season, it is necessary to select the most
temperature insensitive H20 lines for a specific mea-
Differential
When this work was done Benoist Grossmann was with Old Do-
minion University Research Foundation, Norfolk, Virginia 23508;
he is now with Thomson CSF, Activites des Technologies Emer-
gentes, B.P. 55, F-78283 Guyancourt CEDEX, France. The other
authors are with NASA Langley Research Center, Atmospheric
Sciences Division, Hampton, Virginia 23665-5225.
Received 16 February 1990.
surement region. Earlier temperature sensitivity
analyses3 78were applied to some specific DIAL mea-
surements and were based on a H20 line temperature
dependence parameter which is more directly applica-
ble to pure rotational transitions.
In this paper a full discussion and evaluation of the
temperature sensitivity of H20 lines for DIAL mea-
surements of H20 number densities and mixing ratios
are presented. In this analysis it has been assumed
that the off-line cross section aoff is negligible, and
therefore, only the on-line contributes to the tempera-
ture sensitivity of the DIAL measurement. This as-
sumption is valid for the 720-nm band of H20 where
regions of negligible o.ff (<<1/10 Con) can be easily
found.8
In cases where this assumption is not valid,
the temperature sensitivity due to 0-off must be taken
into consideration. The effects of changes in atmo-
spheric pressure and temperature and H20 line pa-
rameters, including the H20 linewidth -y; the energy of
the lower state E"; and the temperature exponent of
air broadening a, on the temperature sensitivity of
H20 lines are evaluated assuming the Voigt9profile
shape for the H20 line. To make this analysis more
useful for DIAL measurements in the 720-nm region,
spectroscopic data from the most recent measure-
ments10 11are presented and used in this analysis.
Temperature sensitivity calculations for sixty-seven
H20 lines are presented which can be directly used in
H20 DIAL field experiments.
II. Temperature Dependence Relationships
The absorption profile of an H20 line can be repre-
sented by a Lorentz profile when atmospheric pressure
20 April 1991 / Vol. 30, No. 12 / APPLIED OPTICS
1517
Page 2
is the dominant broadening process. In this case, the
cross section is a function defined by line strength S
and the Lorentz linewidth YL.7 5
dependence of the line strength is given by
The temperature T
=To3/2
(T )
1- exp[-hcvo/(kT)1 1
{1 -
[exp[-hcv
r 1
1'
TJ'
S(T) =
0/(T0)] J
LT
(1)
where So [cm-1/(mol cm-2)] and To(K) refers to the
initial values; o is the line center position (cm-'); h is
Planck's constant (6.6252 X 10-27 erg s), k is Boltz-
mann's constant [1.38046 X 10-16 erg/(mol K)], c is the
velocity of light in a vacuum (2.99793 X 10'0 cm/s); and
E" is the ground state energy of the transition (cm-').
The term in braced brackets is equal to unity for the
temperature range of 100-500 K in the 720-nm region.7
The Lorentz linewidth is given by
'YL = 0
(2)
where P is the pressure, and a is the linewidth tem-
perature dependence parameter, and yo, Po, and To are
initial values. The most recent measurements" of a in
the 720-nm region show that this parameter varies
widely (0.28-0.88). Earlier analyses3 78have assumed
a constant value of 0.62, which is based on theoretical
calculations for pure rotational lines in the microwave
region.'2The range of a values used in this analysis,
which is applicable for DIAL measurement in the 720-
nm region, is presented in the next section.
The condition that makes the line center absorption
cross section o independent of temperature (tempera-
ture neutral point TN) can be determined by differen-
tiating o with respect to T and setting it equal to zero,
i.e., (doao)/(d77) = 0. Simple analytical expressions for
the temperature neutral points can be obtained in
some special cases. In the limiting case where pres-
sure broadening is dominant, the Lorentz profile can
be used to represent the H20 line absorption profile.
In this case, the line center cross section is given by7
=U S
(3)
A'YL
and using Eqs. (1) and (2) it becomes
aO = B(TO/T)"(1
where A = 1.439 (cm mol K)/s, and B (cm2) is a con-
stant whose value need not be evaluated for tempera-
ture sensitivity calculations. Equation (4) gives a sim-
ple relationship between o, E", and T which can be
used for DIAL measurements from the surface to -2
km in altitude. The temperature neutral point for this
condition can be directly calculated to be
5-a) exp(-AE"/T),
(4)
TN = (I15-
Equation (5) gives the temperature neutral condition
that directly applies to the case of H20 number density
n measurements using the DIAL equation.l3
case of DIAL H20 mixing ratio m measurements, the
quantity p = o nair, where nair is the number density of
(5)
In the
air molecules, is proportional to ao/T. As was shown
by Cahen et al.,3p has to be temperature insensitive for
the mixing ratio to be temperature insensitive in the
region of the measurement. In this case, the tempera-
ture neutral point TN can be shown to be
AE"
(2.5- a)
(6)
It can be easily seen from Eqs. (5) and (6) that, for the
case of a region dominated by pressure broadening, the
temperature neutral points for DIAL H20 number
density and mixing ratio measurements occur at dif-
ferent temperatures, or, conversely, to make these
measurements at the same neutral temperature re-
quires H20 lines with different E" values.
In the other limiting case, where the atmospheric
pressures are very low (as in the mesosphere and
above), Doppler broadening is the dominant line
broadening mechanism, and the line shape of the ab-
sorption cross section a is then defined by the Gaussian
function
r
1n2(v -
a(v)
-I-J expl
'YD
7
L
where v is the wavenumber (cm-'); YD = (o/c)(2kT
ln2/m')12is the Doppler width (HWHM); and m' is the
mass of the H20 molecule. At the line center position,
Eq. (7) becomes
S 1n2\ 1/2
o)21
2
D
7)
J
S /ln2 /2
(12 ),
'YD
00
(8)
and substituting the functional temperature depen-
dence of S and YD into Eq. (8) results in
a = C( 2)exp Q-)AE
(9)
where C (cm2K2) is a constant. The temperature
neutral point for this case, for number density mea-
surements, is given by
AR"
TN =
2E *
(10)
Deviation from the Doppler broadening limit would
cause an increase in the value of TN toward the pres-
sure broadening limit given in Eq. (5). The Doppler
broadening approximation is valid at high altitudes
(>50 km), and the pressure broadening approximation
is applicable at low altitudes (<2 km). In the DIAL
technique, measurements at the on-line'3are normally
made near the absorption line center; in this case, a
composite representation of the line shape is given by
the Voigt profile9V which is a convolution between the
Lorentz and Gaussian profiles. The Voigt profile is
given by the relation
V(x,y)
(
) y ,
2p(
t)2 dt,
(1
where (xy) is the absorption cross section; x = [(v -
vO)/-YD](ln2)"/2; y = (YLbYD)(ln2)1/2; and K = (SI
-YD)(ln2/7r)"/2. Equation (11) represents an integral
relationship and is generally evaluated by numerical
1518
APPLIED OPTICS / Vol. 30, No. 12 / 20 April 1991
Page 3
techniques. In this study, the computer code of Dray-
son9was used for this calculation. Equations (5), (6),
and (10) are useful analytical relationships which can
be used to check the validity of the Voigt calculations
in the limits and for use directly when evaluating con-
ditions clearly indicative of the limiting cases. Equa-
tions (5) and (6) can also be used to derive the variation
of TN with a. These expressions can also be used for
preselecting the range of E" values for a more complete
calculation using Eq. (11). For H20 concentration
measurements, the temperature neutral point in-
creases by -51 K for a +0.1 change in a when a = 0.7
and E" = 200 cm-1, and for H20 mixing ratio measure-
ments TN increases by -19 K for a +0.1 change in a
when a = 0.7 and E" = 400 cm-'. The changes in TN
for the two cases are proportional to the E" values.
The sensitivity of TN to the knowledge of a and the
associated temperature sensitivity, which is discussed
later, can lead to significant error in DIAL measure-
ments. It is, therefore, necessary to know the tem-
perature exponent of the line used in the DIAL mea-
surement.
Ill.
Spectroscopic Data
High resolution spectroscopic measurements of H20
absorption lines in the 720-nm band were recently
completed.10 11
Temperature dependence exponents
were measured for sixty-seven moderate to strong ab-
sorption lines [S > 2 X 10-24 cm-1/(mol cm-2)] in this
region. Table I presents the temperature exponents
a, E" values, line center absorption cross sections, and
linewidths (HWHM) in air at the pressure of 1 atm and
296 K for these lines. The line center cross-sectional
values were deduced from Refs. 10 and 11 by using Eq.
(3). It should be noted that a could not be measured in
these experiments for weakly absorbing lines in this
region. The average value of a for the lines measured
was found to be 0.67 + 0.15. This is -8% larger than
the value of 0.62 used in earlier temperature sensitivity
calculations.3 78
Figure 1 shows that a linear relation-
ship exists between the linewidth and the temperature
exponent a for the transitions whose upper vibrational
level is v' = 301. Figure 1 can be used, for the weak
lines where a values are not available, to deduce the a
values from their measured linewidths.
IV. Temperature Sensitivity Calculations
To conduct the temperature sensitivity calculations,
the values of E", YL, YD, and a and the range of atmo-
spheric temperatures have to be specified. The varia-
tion of temperature sensitivity with pressure is evalu-
ated using the pressure dependence of the- linewidth
[Eq. (2)]. The Voigt profile was used to represent the
H20 line profile, and the temperature sensitivity for
the number density measurement was calculated by
evaluating the expression
1 da-
-O dT
1
o(2) - a00(T')
[O(T) + ao(T)]
2
T-T
as a function of temperature. Calculations were per-
Table 1. Water Vapor Absorption Line Parameters In the 720-nm Band:
Vacuum Wavenumbers (v), Air Wavelengths (),
(gy), Temperature Exponents (a), and Center Cross Section (a0) Values
at P = 1 atm and T = 296 K
E" Values, Linewidths
V
cm-'
13643. 7105
13659.8743
13660.4826
13662.5022
13665.8201
13671.2417
13677.0331
13686.9947
13688. 8686
13690.0014
13690.8726
13704.1808
13705.4437
13709.5717
137 12.9172
13717.1747
137 18.5762
13728.1798
13736.1186
13737.4161
13738.4401
13738.9949
13739.4403
13741.1540
13745.7853
13751.1356
13759.7148
13761.5888
13774.2119
13775.2987
13783.1795
13783.8760
13784.7849
13788.8892
13794.5580
13797.5367
13801.2788
13801.7317
13806.7821
13807.1435
13815.7375
13818.4083
13819.0491
13823.1814
13832. 2508
13839.6550
13853. 2706
13866.7312
13872.6818
13882.7586
13884.0365
13884.3369
13888.0804
13889.1873
13897.1062
13901.5034
13909.4088
13910.1724
13920.3362
13920.7699
13935.0703
13935.8416
13936.5789
13937.5048
13937.8679
13942.0505
13943.0026
The vacuum wavenumbers and
Ref. 14, and Xare calculated using the air
refractive index value from Ref. 8.
A
nm
732. 7365
731. 8695
731.8369
731. 7287
731.5510
731.2609
730.9513
730.4193
730.3193
730.2589
730. 2124
729.5033
729.4361
729.2164
729.0385
728. 8122
728.7378
728.2280
727.8071
727.7384
727.6841
727.6541
727.6312
727.5404
727.2953
727.0123
726. 5590
726.4601
725.7943
725. 7371
725.3221
725.2855
725.2376
725.0218
724.7238
724.5674
724.3709
724. 3471
724.0822
724.0632
723. 6128
723.4730
723.4394
723. 2231
722. 7490
722.3623
721. 6523
720.9518
720.6425
720. 1195
720.0532
720.0376
719. 8435
7 19.7862
719.3760
719. 1485
718.7397
718.7003
718. 1755
718. 1532
717.4162
717.3765
717.3385
717. 2909
717.2722
717.0570
717. 0080
E"
cm-'
648.9790
586.2430
586.4790
552.9120
134.9020
508.8120
446.5100
447.2520
399.4580
610.3410
416.2090
382.5170
399.4580
315.7790
325.3480
275.4970
300.3620
136.7620
222.0520
224.8380
222.0520
224.8380
224.8380
212. 1560
173. 3650
325.3480
136.7620
142. 2790
95. 1760
610.3410
70. 09 10
508.8120
79.4960
173.3650
383.8430
382. 5170
285.4190
285. 2190
212. 1560
23.7940
136.1640
134. 9020
206.3010
300.3620
37. 1370
79.4960
.0000
37. 1370
23. 7940
79.4960
134. 9020
79.4960
70. 09 10
136. 1640
142. 2790
136. 7620
224.8380
382.5170
326.6250
325.3480
508. 8120
552.9120
586.2430
648.9790
399.4580
399.4580
744. 1630
YL,
cm-
a
00
cm' (E-24)
.0817
.0737
.0758
.0833
.0908
.0870
.0893
.0824
.0925
.0711
.0891
.0849
.0900
.0922
.0935
.0967
.0928
.0912
.0975
.0946
.0949
.0919
.0812
.0953
.0976
.0750
.1031
.0980
.1030
.0717
.1089
.0879
.1027
.1018
.0864
.0843
.0822
.0813
.0945
.1039
.0946
.0919
.0942
.0957
.1041
.1043
.1045
.1002
.0985
.0973
.0937
.0961
.0949
.0914
.0908
.0920
.0822
.0788
.0801
.0777
.0866
.0727
.0551
.0770
.0892
.0891
.0460
E" values are from
.660
.430
.280
.740
.770
.640
.790
.720
.750
.520
.630
.600
.610
.570
.690
.710
.740
.620
.880
.790
.750
.700
.610
.680
.760
.530
.730
.760
.730
.560
.850
.610
.790
.790
.710
.620
.680
.680
.750
.780
.660
.700
.620
.760
.680
.790
.840
.880
.780
.720
.750
.800
.650
.610
.760
.750
.600
.540
.570
.570
.690
.580
.440
.370
.590
.590
.300
14.433
37.117
11.030
26.325
16.835
21.404
39.315
55.604
47.238
8.125
13.324
22.114
6.825
17.891
72.375
23.849
51.290
15.690
18.868
80.297
13.395
11.532
13.863
46.601
86.405
11.369
92.798
34.672
22.653
23.136
30.675
17.333
72.092
17.530
14.720
45.830
105.718
36.207
57.106
61.963
42.364
131.844
18.978
22.771
28.913
37.829
22.571
28.873
113.245
108.031
59.517
18.858
31.763
20.743
45.189
131.580
131.876
36.447
29.399
97.680
21.331
23.864
54.366
14.049
30.343
23.386
23.040
formed over the temperature interval of 100-500 K at 1
K intervals.
As discussed earlier, the range of E" values for tem-
perature insensitive number density and mixing ratio
measurements are different. It was found from a pre-
liminary estimate, using Eqs. (5) and (6), that E" val-
ues in the 70-300-cm-1range (thirty-one lines in Table
I) are more suitable for number density measurements
20 April 1991 / Vol. 30, No. 12 / APPLIED OPTICS
1519
.
Page 4
0.9
0.8
0.7
.6 0.9
., 0.5
0.4
0.2
0.2
0.04
0.08
0.08
0.1
UNEWIDTH cm1
a:
0
a:
o
U,
0
Fig. 1. Systematic dependence of the linewidth temperature de-
pendence exponent a on linewidth YL for the v' = 301 band of H20.
The straight line is a linear least-squares fit to the data points.
.9
.7
.6
.4
.3
.2
.1
0
0 100
200
300
400
00
600
El' :Cm-
1
700
900
900
1000
Fig. 2. Systematic dependence of a on ground state energy E".
The straight line is a linear least-squares fit to the data points.
100
200
200
400 500
600
700
800
900 1000
E" c-
Fig. 3. Systematic dependence of linewidth YL onE". The straight
line is a linear least-squares fit to the data points.
100
Z0
300
400
500
TEMPERATURE (K)
Fig. 4. Temperature sensitivity of DIAL number density measure-
ment errors at 1-atm pressure for a range of E" values.
and that E" values in the 220-550-cm-1range (thirty
lines in Table I) are more suitable for mixing ratio
measurements. Using the data in Table I, it was de-
termined that the average value of a suitable for num-
ber density measurements is 0.72, and for mixing ratio
measurements the value of a is 0.66. There is a sys-
tematic dependence of a on E, as shown in Fig. 2.
The associated average linewidth (-y) values are 0.095
cm-l for the number density measurements and 0.088
cm-' for the mixing ratio measurements. There also
appears to be a systematic relationship between E"
and y, as can be seen in Fig. 3. Even though the
relationship between E" and y can be inferred (Fig. 3)
using the relationships between y and a and between
E" and a (Figs. 1 and 2, respectively), Fig. 3 is given
here to enable one to estimate one parameter from
another directly. The data presented in Figs. 2 and 3
show that both a and y appear to be correlated with E",
and that if a range of E" is selected, the appropriate a
and y values must be used in the calculations. An
average value of a and y cannot be used for all the
values of E", as has been done in the past.
A. Number Density Measurement Errors
The temperature sensitivities of H20 lines for DIAL
number density measurements at sea level pressure
and for E" values in the 0-300-cm-1range are shown in
Fig. 4. It shows only those profiles whose temperature
sensitivity is less than +0.4%/degree K of temperature
change. It also shows that lines with E" values near
zero can lead to large errors (-0.3 to -0.4%/degree of
temperature deviation between actual and assumed)
in the atmospheric temperature range 200-300 K, and
that lines with E" 2 300 cm-' can also lead to large
errors at temperatures <250 K.
An expanded view near the temperature neutral
points at the pressure levels of 1.0, 0.5, and 0.25 atm,
1520
APPLIED OPTICS / Vol. 30, No. 12 / 20 April 1991
InE
I II
I
I I
l~~ a
[
s
1B\
_
~~~~~~~~~~~~~B
_
l
l l l
l l
l n
.LI
.. L4 I
I
.
I
.
.
.
I
In
.
.
.
.
.
.
..
i
i
I1
-T-
1 -
I
Page 5
2
0
a:
Ea
zw
0
200 300 400
500
TEMPERATURE (K)
200
300
400
500
TEMPERATURE (K)
representing atmospheric altitudes of sea level, 5.5,
and 11 km, respectively, are shown in Figs. 5(a), (b),
and (c). E" values in the 50-300-cm'1 range were used
to generate these error profiles. The ordinates of the
plots are limited to +0.1% error/degree K, and a •10 K
error in knowledge of the temperature will, therefore,
lead to a •1% error in DIAL measurements for lines
with the E" values in the plotted area. As expected,
when the pressure is decreased (from 1.0 to 0.5 or 0.25
atm) the error profiles shift to lower neutral tempera-
tures for the same E" value. Specifically, when the
pressure is changed from 1.0 to 0.25 atm the tempera-
ture neutral point changes from 333 to 250 K for the
temperature sensitivity profile related to the E" value
of 200 cm-'. For DIAL measurements in a region
(altitude and geographic) where the variability of the
atmospheric temperature is known, the temperature
500
300
TEMPERATURE (K)
Fig. 5. Temperature sensitivity of DIAL number density measure-
ment errors at atmospheric pressure levels of (a) 1 atm, (b) 0.5 atm,
and (c) 0.25 atm.
insensitive H20 lines for the measurements can be
selected from the large number of lines available in the
720-nm region."
The choice of lines becomes more
limited if only those temperature insensitive lines are
selected that can be used over widely varying atmo-
spheric temperatures and for measurements over sev-
eral seasons, as will be needed for spaceborne DIAL
investigations.
The consistency of these calculations can be exam-
ined by comparing the results in Fig. 5 with the limit-
ing value determined from Eq. (5). First, from Fig.
5(a) the temperature neutral point is found to be at
180.5+0.5KforE" = 100cm-1. FromEq. (5),aTN=
186.2 K is obtained which is based on the pressure
broadening limit. As expected, the Voigt calculation
gives a lower value of neutral temperature because it
includes a small Doppler broadening influence. To
20 April 1991 / Vol. 30, No. 12 / APPLIED OPTICS
1521
0.1
0.05 -
C-
-0.05
-0.1
100
C
a-
0
a:
a)
U,
en
z
0
-0.1IL
100
Page 6
Table 11. Temperature Neutral Points (TN) and Lower (TL) and Upper (Tu) Limits of Temperature Insensitive
Regions for DIAL Water Vapor Concentration and Mixing Ratio Measurements
V
A
nm
EM
a
Concentration
TN(K) TL(K) TU(K)
Mixing ratio
TN(K) TL(K) TU(K)
cm-'
cm-,
cm2(E-24)
13643. 7105
13659.8743
13660.4826
13662.5022
13665.8201
13671.2417
13677.0331
13686.9947
13688.8686
13690.0014
13690.8726
13704.1808
13705.4437
13709.5717
13712.9172
13717.1747
13718.5762
13728.1798
13736.1186
13737.4161
13738.4401
13738.9949
13739.4403
13741.1540
13745.7853
13751.1356
13759.7148
13761.5888
13774.2119
13775.2987
13783.1795
13783.8760
13784.7849
13788.8892
13794.5580
13797.5367
13801.2788
13801.7317
13806.7821
13807.1435
13815.7375
13818.4083
13819.0491
13823.1814
13832.2508
13839.6550
13853.2706
13866.7312
13872.6818
13882.7586
13884.0365
13884.3369
13888.0804
13889.1873
13897.1062
13901.5034
13909.4088
13910.1724
13920.3362
13920.7699
13935.0703
13935.8416
13936.5789
13937.5048
13937.8679
13942.0505
13943.0026
732.7365
731.8695
731.8369
731. 7287
731.5510
731.2609
730.9513
730.4193
730. 3193
730.2589
730.2124
729.5033
729.4361
729.2164
729.0385
728.8122
728.7378
728.2280
727.8071
727.7384
727.6841
727.6547
727.6312
727.5404
727.2953
727.0123
726.5590
726.4601
725.7943
725. 7371
725.3221
725.2855
725.2376
725.0218
724.7238
724.5674
724.3709
724.3471
724.0822
724.0632
723.6128
723.4730
723.4394
723.2231
722.7490
722.3623
721.6523
72n.9518
720.6425
720. 1195
720.0532
720.0376
719.8435
719. 7862
719.3760
719. 1485
718.7397
718. 7003
718. 1755
718.1532
717.4162
717.3765
717. 3385
717.2909
717.2722
717.0570
717.0080
648.9790
586.2430
586.4790
552.9120
134.9020
508.8120
446.5100
447.2520
399.4580
610.3410
416.2090
382.5170
399.4580
315.7790
325.3480
275.4970
300.3620
136.7620
222.0520
224. 8380
222.0520
224.8380
224.8380
212.1560
173.3650
325.3480
136. 7620
142.2790
95. 1760
610.3410
70.0910
508.8120
79.4960
173.3650
383.8430
382.5170
285.4190
285.2190
212. 1560
23. 7940
136.1640
134.9020
206.3010
300.3620
37. 1370
79.4960
.00
37. 1370
23. 7940
79.4960
134.9020
79.4960
70.0910
136. 1640
142.2790
136.7620
224.8380
382.5170
326.6250
325.3480
508.8120
552.9120
586.2430
648.9790
399.4580
399.4580
744. 1630
14.4331
37. 1169
11.0302
26.3250
16.8353
21.4045
39. 3149
55.6043
47.2379
8.1246
13.3237
22. 1139
6.8251
17.8914
72.3746
23.8488
51.2899
15.6901
18.8676
80. 2972
13.3948
11.5325
13.8635
46.6015
86.4054
11.3686
92. 7980
34.6718
22. 6527
23.1355
30.6754
17.3328
72.0923
17.5298
14. 7199
45.8299
105.7178
36.2075
57. 1065
61.9628
42.3640
131.8442
18. 9779
22. 7710
28.9132
37. 8291
22.5712
28.8729
113.2455
108.0314
59.5166
18. 8577
31. 7631
20.7432
45.1885
131.5799
131.8763
36.4474
29. 3991
97. 6802
21.3306
23.8636
54.3656
14.0493
30.3426
23.3861
23.0399
490.0
469.0
247.0 201.0
481.0
466.0
451.0
430.0
420.0
390.0
405.0
337.0
430.0
476.0 365.0
426.0 330.0
460.0
214.0 181.0
410.0
384.0 299.0
369.0 289.0
356.0 282.0
326.0 265.0
336.0 268.0
306.0 243.0
417.0
242.0
258.0
173.0
354.0
313.0
332.0
198.0
209.0
147.0
152.0
128.0
477.0
134.0
157.0
316.0 249.0
409.0
393.0
328.0
327.0
279.0
417.0
416.0
356.0
222.0
230.0
311.0
469.0
186.0
191.0
252.0
359.0
157.0 134.0
143.0
243.0
159.0
116.0
211.0
256.0
245.0
324.0
483.0
433.0
429.0
125.0
199.0
135.0
105.0
179.0
208.0
201.0
264.0
377.0
342.0
340.0
489.0
490.0
478.0
402.0
402.0
>500.0
>500.0
>500.0
>500.0
411.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
304.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
412.0
457.0
242.0
>500.0
220.0
>500.0
219.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
331.0
353.0
>500.0
>500. 0
220.0
102.0
185.0
400.0
222.0
139.0
296.0
432.0
403.0
>500. 0
>500.0
>500.0
>500. 0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
>500.0
460.0
384.0
365.0
411.0
111.0
370.0
351.0
338.0
312.0
410.0
307.0
279.0
293.0
230.0
251.0
216.0
238.0
103.0
193.0
186.0
179.0
176.0
168.0
165.0
141.0
230.0
110.0
116.0
416.0
366.0
144.0
294.0
281.0
219.0
219.0
171.0
105.0
106.0
155.0
241.0
393.0 >500.0
337.0
323.0
355.0 >500.0
105.0
322.0 468.0
306.0
297.0
275.0
357.0 >500.0
272.0
250.0
261.0
209.0
226.0
197.0
215.0
483.0
449.0
120.0
442.0
420.0
385.0
373.0
331.0
352.0
265.0
296.0
250.0
280.0
111.0
223.0
211.0
203.0
198.0
186.0
184.0
156.0
263.0
119.0
126.0
176.0
170.0
165.0
163.0
156.0
153.0
133.0
210.0
105.0
110.0
361.0 >500.0
319.0 462.0
135.0
261.0
252.0
200.0
199.0
159.0
159.0
356.0
335.0
252.0
252.0
193.0
101.0
102.0
146.0
217.0
113.0
115.0
172.0
284.0
109.0 104.0
118.0
102.0
116.0
111.0
167.0
270.0
236.0
235.0
377.0
384.0
376.0
415.0
290.0
290.0
443.0
110.0
106.0
156.0
243.0
215.0
214.0
328.0
335.0
332.0
361.0
259.0
259.0
386.0
110.0
126.0
120.0
185.0
317.0
273.0
270.0
481.0
483.0
463.0
>500. 0
347.0
347.0
>500.0
A + 10K error in the knowledge of the atmospheric temperature will
a + 1% DIAL measurement error in this region.
test the calculations at higher pressures, TN values
were evaluated for E" = 100 cm-1at a 5-atm pressure
and 293 K and obtained a value of TN = 185.5 ± 0.5 K
using the Voigt profile representation; this result is in
excellent agreement with the Lorentz profile limiting
value of 186.2 K. To check the calculations at low
1522
APPLIED OPTICS / Vol. 30, No. 12 / 20 April 1991
lead to only
Page 7
0.I
N
0.05_
a)
0,
0
w
0
cr
a)
a:
C
zx
E -005_
-0.1 _
100
200
300
400
TEMPERATURE (K)
300
TEMPERATURE (K)
pressure approaching the Doppler limit, the model was
evaluated in the mesospheric region.15
of 60 km (pressure of 2.685 X 10-4 atm), a temperature
of 247 K, and with E" = 200 cm-1, a neutral tempera-
ture value of 143.5 + 0.5 K was obtained. This com-
pares well with the Doppler limit value of 143.9 K
calculated from Eq. (10). These calculations cannot
be directly compared with those of Ref. 8 because of
the uncertainties associated with the assumptions
used in those calculations. The neutral temperature
value identified in Ref. 8 (Fig. 1) for E" = 100 cm-1, a =
0.62 (assumed), 'YL = 0.1 cm-', 293 K, and sea level
pressure is -142 K. This value is significantly differ-
ent from the Lorentz limit value of 163.5 K [Eq. (5)].
Using the Voigt model along with the above noted
assumptions about the parameters, a value of TN = 159
+ 0.5 K was obtained. However, excellent agreement
was found with Fig. 1 in Ref. 8 when a value of YL = 0.05
At an altitude
N
i!
a)
0r
0
z
x)
500
500
300
TEMPERATURE (K)
X
Fig. 6. Temperature sensitivity of DIAL mixing ratio measurement
errors at atmospheric pressure levels of (a) 1 atm, (b) 0.5 atm, and (c)
0.25 atm.
500
cm-1was used along with a = 0.62. Therefore, the
calculations presented in Ref. 8 are believed to be
applicable to the region where yL values are 0.05
cm1, which occurs at -0.5-atm pressure or near 5-km
altitude.
Table II presents neutral temperatures and atmo-
spheric temperature ranges for the •0.1% DIAL mea-
surement error/degree atmospheric temperature un-
certainty for the measurement of H20 number density
at sea level pressures for sixty-seven H20 lines in the
717-733-nm region. Inference about the results at
higher altitudes can be made from Figs. 5(a) and (c).
B. Mixing Ratio Measurement Errors
The temperature sensitivities for mixing ratio mea-
surements at the pressure levels of 1.0, 0.5, and 0.25
atm are shown in Figs. 6(a), (b), and (c), respectively,
for E" values in the 250-550 cm1range. Compared to
20 April 1991 / Vol. 30, No. 12 / APPLIED OPTICS
1523
Page 8
number density measurements, the shape of the error
profiles changes less rapidly with changes in E" and
with altitude. For the mixing ratio measurement, the
temperature neutral points agree more closely with the
pressure broadening limit. For example, from Fig.
6(a) the neutral temperature for E" = 250 cm-1is at
192.5 ± 0.5 K, and the value obtained using the pres-
sure broadening approximation [Eq. (6)] is 195.8 K.
E" values in the 250-350-cm-1range are more suitable
for measurements in the mid-to-upper troposphere
(>5 km), and E" values in the 350-550-cm-1range are
more suitable for measurements in the boundary layer.
The temperature neutral points and the temperature
insensitive regions with <0.1% error/degree K for mix-
ing ratio measurements near the ground are also shown
in Table II.
In the above temperature sensitivity calculations for
both density and mixing ratio measurements, the in-
fluence of two second-order effects was not addressed.
First, because most DIAL measurements are never
exactly at the line center position, the influence of
detuning the laser line from the line center must be
considered. Calculations using a detuning of +0.5 pm
from the line center at sea level pressure showed a
negligible influence in the temperature sensitivity for
this degree of detuning. Second, the effect of the
temperature dependence exponent of the pressure
shift reported in Ref. 11 has to be evaluated. Using
the analysis presented in Ref. 6, it was estimated that
at low altitudes (<2 km), using a large temperature
exponent value of 1.0, the additional temperature sen-
sitivity is <0.003%/degree at H20 line center and
-0.01% if the line is tuned off-center by 0.5 pm. This
estimate can also be evaluated at higher altitudes by
using Figs.11(a)-(c) in Ref. 6. In general, these errors
are smaller by an order of magnitude.
V. Conclusion
This paper has discussed in detail the temperature
sensitivity of DIAL H20 measurements in the 720-nm
region using the most recent H20 spectroscopic data.
Temperature sensitivity calculations are given for six-
ty-seven moderate-to-strong H20 absorption lines
whose linewidth temperature dependence has been
measured. The analysis presented can also be used to
estimate the temperature sensitivity of other weaker
lines. The sensitivities for both H20 number density
and mixing ratio measurements have been evaluated.
Effects of variations in atmospheric pressure and H20
line parameters, including a, TYL, and E", have been
discussed. Assuming that the DIAL measurements
are to be made in the 200-300 K atmospheric tempera-
ture range, the optimum E" values for H20 number
density measurements are in the 100-300-cm-1range,
and, furthermore, the lines in the 125-225-cm-1range
are the most insensitive to both altitude and atmo-
spheric temperature variations. For H20 mixing ratio
measurements, lines with E" values in the 250-350-
cm-' range are most suitable in the mid-to-upper tro-
posphere, and lines in the 350-500-cm-1E" range are
optimum in the mid-to-lower tropospheric region. It
should be noted, however, that a comprehensive tem-
perature sensitivity calculation should take into con-
sideration all the parameters associated with the laser
line, the absorption line, and the atmospheric condi-
tions where the DIAL measurements are to be made.
The analysis and data presented here will be useful for
field selection of H20 lines in the 720-nm region for
DIAL measurements and for compensating for DIAL
systematic error effects caused by known atmospheric
temperature variations.
Syed Ismail was with ST Systems Corp., Hampton,
VA, when this research was conducted, and he was
supported under NASA contract NAS1-18460. Ben-
oist Grossmann was supported under NASA grant
NCCI-32.
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