The interpretation of data generated by aerosol backscatter lidars is often facilitated by presentation of RHI and PPI images. These pictures are especially useful in studies of atmospheric boundary layer structure where convective elements, stratifications and aerosol laden plumes can be easily delineated. Procedures used at the University of Wisconsin to generate lidar images on a color enhanced raster scan display are described

Eloranta, E. W.

Forrest, D. K.

English

NASA Technical Reports Server

N87 -10367
GENERATION OF ATTENUATION CORRECTED IMAGES FROM LIDAR DATA
Edwin W. Eloranta and Daniel _. Forrest
Dept. of Meteorology
University of Wisconsin
Madison, WI
The interpretation of data generated by aerosol backscat-
ter lidars is often facilitated by presentation of RHI and PPI
images. These pictures are especially useful in studies of
atmospheric boundary layer structure where convective elements,
stratifications and aerosol laden plumes can be easily delinea-
ted. This paper describes procedures used at the University of
Wisconsin to generate lidar images on a color enhanced raster
scan display.
The generation of RHI and PPI images from lidar data pre-
sents several problems: I) it is a comptter intensive task
because each image consists of 105 to 10 ° separate pixels, 2)
data are acquired in polar coordinates (range, elevation angle)
and thus do not map exactly onto the rectangular raster scan
coordinates of the picture display, 3) attenuation corrections
must be applied to produce a useful image, 4) even after atten-
uation and range-squared corrections the lidar return ampli-
tudes often vary over a factor of 1OO while image displays
typically provide less than 32 distinguishable gray levels, 5)
real-time display of lidar images is normally required to
control data acquisition during experiments.
Different routines are used to form real-time and post-
facto displays. Images prepared for publication or detailed
analysis are generated using a more sophisticated correction
for atmospheric attenuation than is used for the real-time pic-
tures. Except for this difference, which is due to computation
time constraints, the image forming routines are identical.
Real-time displays on the UW lidar are formed using the
procedures described by Kunkel et al. (J. Applied Meteor.,
Vol. 16 #12). Each lidar profile is corrected for variations
in the transmitted laser energy and for the inverse range-
squared signal decrease. The logarithm of the lidar return is
then displayed in an A-scope format. A pair of parallel
straight lines are shown superimposed on the lidar return. The
operator controls the vertical position, the separation and the
slope of the displayed lines pairs. The lower line delineates
the largest corrected return which will be displayed as black
while the upper line indicates the smallest return which will
saturate the displayed intensity. Before the lidar return is
displayed signal values corresponding to the lower line are
subtracted from the signal and the signal values are rescaled
such that the distance between the enhancement lines corre-
sponds to 64 levels. The rescaled signal is now used as an
index to a color enhancement look-up table. Each element of
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the table contains three values corresponding to the mixture of
red, green and blue which is to be projected for each rescaled
input value. A series of computer subroutines to load the
color enhancement tables are available to the operator.
Changing the slope of the enhancement lines corresponds to
providing a correction for a spatially invariant attenuation
coefficient while changing the separation and the vertical
position of the lines provides control of the displayed dynamic
range.
The operator selects range and altitude boundaries of the
displayed image. The program then computes the ranges at which
the last two lidar profiles intersect the near edge of the
display area. The lidar data points nearest in range to the
intersection points are used to specify two pixels in the
image. Any pixels which fall between these two pixels are
filled in by linear interpolation. The program then computes
the ranges at which the two profiles intersect the next ver-
tical column of pixels and repeats the above process. This is
continued until all pixels in the display memory which fall
within the pie shaped sector between the last two lidar firing
directions are specified.
This real-time display algorithm executes in well under
one second per laser shot when run on a digital equipment
PDP-II/40. While the pictures produced are excellent for real-
time control of experiments and scanning of data tapes, careful
examination of the images quickly reveals the limitations of
the constant attenuation assumption. Images consisting of a
well mixed hazy boundary layer under a much cleaner upper layer
force the operator to choose between over-correcting for atten-
uation in the upper layer or under-correcting in the lower
layer. Images containing dense plumes or strong swelling of
hydroscopic aerosols at the top of convective cells occasion-
ally show shadows resulting from variations in attenuation. An
algorithm based on the Bernoulli solution to the lidar equation
is used to improve the attenuation correction when preparing
presentation quality pictures. In order to apply this solution,
a functional relationship between the extinction cross section
and the backscatter cross section must be provided: in addition
the extinction cross section must be provided at one point in the
data interval. The procedure proposed by Klett (Applied
Optics, Vol. 20, #2), where the extinction cross section at
large ranges is estimated, works only in the presence of
substantial extinction. Because the extinction cross section
is usually small in the fair weather boundary layer, the Klett
approach is not applicable.
The RHI attenuation correction algorithm first estimates
the extinction cross-section profile of the lowest elevation
angle shot in the image. In the range interval between I and
7.5 kilometers, a least-squares linear fit is matched to the
logarithm of the range-squared and energy corrected lidar
profile.
292
The extinction at a data point just out of the overlap region
is estimated, for each lidar return in the image, from:
SIGNAL(R,J)
BETA(R,J)= LEkST-SQUARE._T'(R) *SLOPE BETA*EXP(2*(TAU(J)-TAU(1)))
where:
BETA(R,J) - extinction at range, R, for J-th lidar return
SIGNAL (R,J) = energy and range-square corrected lidar return
TAU(J) = optical depth from liflar to range, R, for J-th return
and where: The value of the estimated optical depth, TAU(J),
is set equal to TAU(1) unless it can be estimated from an imme-
diately preceding image.
Equation I provides a first estimate of the extinction
cross section at one point in each of the lidar profiles which
make up the image. The Bernoulli solution to the lidar
equation is then used to generate first guess values for the
extinction at each point in all profiles. In the relatively
uniform, small extinction conditions normally encountered in
clear air boundary layer studies this procedure provides good
initial values and therefore relatively good first estimates of
the extinction field. However because of the well-known insta-
bilty of the Bernoulli solutions small errors in the initial
guesses will cause substantial errors at longer ranges. Images
produced from these corrected profiles show unacceptable fluc-
tuations between successive lidar shots.
The corrected data points are now grouped by altitude and
a median filter is applied to each altitude group so as to pro-
vide a median profile of the extinction as a function of alti-
tude. The median profile is very stable in the presence of
errors in the Bernoulli solutions. The median vertical profile
is then used as a guide to correct the initial guesses for each
lidar shot. For each point along each lidar shot, we compute
the correction to the initial guess which would place the point
exactly on the median vertical profile. The initial guess is
then adjusted by the median of the computed corrections for
that shot and the Bernoulli solution is recomputed. This pro-
cess is very stable in the presence of scattering inhomoge-
neities in the individual lidar return.
The recorrected lidar profiles are once again used to com-
pute a median vertical profile of extinction and the whole pro-
cess is repeated until the maximum change in an initial guess
of any of the returns in the picture is below an operator
supplied threshold value. This procedure converges to produce
an image from 50 lidar returns in ~ 30 seconds of computation
time on the UW lidar VAX 751 computer and attached CSPI mini-
map array processor.
293
The scattering cross section in the hazy mixed layer is
occasionally as much as 100 times as large as it is in the
clear stable layer immediately above. If the contrast range of
the lidar display is adjusted to accommodate this large dynamic
range, small fluctuations in scattering cross section are not
visible in either layer and much interesting image detail is
lost. Most of this detail is restored by displaying the dif-
ference of computed scattering cross section from a background
level computed by fitting a smoothing spline to the median
vertical profile of scattering cross section.
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Generation of attenuation corrected images from lidar data

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