PROFILING OF POORLY STRATIFIED ATMOSPHERES WITH SCANNING LIDAR
C.E. Wold, V.A. Kovalev, A.P. Petkov, and W.M. Hao
U.S. Forest Service, RMRS Fire Sciences Laboratory, Missoula, MT 59808, USA
Abstract: The direct multiangle solution may allow inversion of the scanning lidar data even
when the requirement of the horizontally stratified atmosphere is poorly met. The solution is
based on two principles: (1) The signal measured in zenith is the core source for extracting
the information about the atmospheric aerosol loading, and (2) The multiangle signals are
used as auxiliary data to extract the vertical transmittance profile from the zenith signal.
However, there may exist a level of horizontal heterogeneity of the atmosphere when no
reliable information about the optical properties can be retrieved with multiangle solution
Elastic lidar in scanning mode
Theoretical solution for horizontally homogeneous atmosphere:
h
ln Pi (h)
sin
2
A(h)
i
2
,90
(0 , h )
sin
i
SIMULATED DATA FOR THE ELASTIC LIDAR
Actual formula for heterogeneous atmosphere:
Range
sin
i
(0 , h )
1
i
A
,90
i
(0,h),
Pi(h) – The signal of the elastic lidar in the slope direction, i.
τΣ,90(0,h) – The total molecular and aerosol vertical optical depth.
i – The searching elevation angle.
A90(h)
(a)
0.8
6
300
0.6
200
0.4
A'(
5
(h) (a. u.)
Lidar
A(h)
2
400
1.0
C
h
ln Pi (h)
sin
2
(0,h) sin
h
ln [Pi(r) r2]
Height
A(h)
4
100
3
0
2
h)
0.2
0.0
0
DIRECT MULTIANGLE SOLUTION FOR ELASTIC LIDAR
20
40
i
60
0
80
The estimate of the product C
[1],
C
,90(h)
, 90
(a)
400
ln [Pi(r) r2]
0.4
4.8
4.6
0.2
A(h)
200
0.0
exp ln P90 (h)h
2
b( h)
,
(2)
where b(h) and A (h) are the slope and a shifted intercept of the linear fit , respectively .
1. V. Kovalev, C. Wold, A. Petkov, and W.M. Hao, “Direct multiangle solution for poorly stratified atmospheres,”
Appl. Opt. 51, 6139-6146 (2012).
4.4
0
0
exp A' (h)
(b)
A'(h)
, is found from the set of multiangle data obtained by the same lidar
h
5
A90(h)
600
i
(0,h) sin
(0,h),
T (0, h)
4
5.0
(h) (a. u.)
2
90
P90 (h)h
. (1)
C ,90 (h)
3
x
C
2
2
(degree)
0.6
The solution determines the total two-way vertical transmittance T902 (0, h) versus height h using the square range -corrected backscatter signal, P90(h)h2, measured in zenith, and the estimate d product of the lidar
solution constant, C, multiplied by the total backscatter coefficient,
,90(h), that is,
1
20
40
60
i
(degree)
80
0
100
1
2
3
4
5
x
(a) The black-filled and empty triangles are the slope optical depths, (0, h) and the corresponding vertical
optical depths, (0, h)sin i; i, are the slope angles, selected for the numerical experiment. The data
points, C , (h) are shown as the filled red squares. (b) Dependence of the data points, yi(h) = ln [P(r)r2]
(the blue-filled circles) and their linear fit (the dashed line) on x = 1/sin i. The actual intercept A90(h) for
the zenith direction is shown on the Y-axes as the empty circle. The intercept points of the linear fit, A(h)
and A (h) are shown as the black filled triangles and the red filled squares, respectively.
EXPERIMENTAL DATA
15
17
19
22
24
33
39
46
52
SYS
61
71
80
28
T90(hmin, h)
2
6
5.5
ln Pr^2
5
5000
1.5
4000
1.0
0.36 - 0.66 km-1
height (m)
14
h)
13
1.0
90(hmin,
6.5
12
0.5
3000
2000
0.5
4.5
1000
4
3.5
0
1000
2000
3000
4000
5000
6000
7000
height
Fig. 1. Logarithms of the square-range corrected signals at
532 nm versus height for seventeen elevation angles
retrieved from the lidar data in a smoke polluted
atmosphere in Montana on August 8, 2012.
0
0.0
0.0
0
2000
4000
6000
height (m)
Fig. 2. The thin dashed curve represents the
vertical two way transmission, <T90(hmin,h)>2 ,
extracted from the data in Fig. 1 and distorted
within the polluted layer; the solid red line
represents the corrected two-way transmission.
SUMMARY: The direct multiangle solution allows extracting the vertical profiles
of the optical parameters of the atmosphere directly from the lidar zenith signal
while using the multiangle signals to obtain auxiliary information on backscattering.
0
2000
4000
height (m)
6000
0.0
0.1
0.2
0.3
p(h)
Fig. 3. The estimates of the total vertical
optical depths within the polluted layer
corresponding to the transmission functions
shown in Fig. 2.
0.4
0.5
0.6
0.7
(km-1)
Fig. 4. The vertical profile of the particulate
extinction coefficient extracted from data
shown in Fig. 1 using the direct multiangle
solution. The gray box covers the polluted
region where the extinction coefficient can only
be approximately estimated.
There may exist a level of horizontal heterogeneity within the scanned
region where the multiangle method can provide, at best, only
restricted information about the atmosphere’s optical properties.