UC SAN DIEGO LIBRARY
UNIVERSITY OF CALIFORNIA, SAN DIEGO
3 1822 04429 0781
APRIL 1988
ATMOSPHERIC OPTICAL SYSTEMS
TECHNICAL NOTE NO. 209
Offsite
(Annex-jo
rinals)
QC
974.5
. T43
no. 209
THE DETERMINATION OF ATMOSPHERIC VISIBILITY
WITH A DIGITAL, IMAGE-ACQUISITION SYSTEM
Wayne S. Hering
Richard W. Johnson

UNIVERSITY
CALIFORNIA
SAN DIEGO
The material contained in this note is to be considered
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without the prior consent of the Marine Physical Laboratory
and the Air Force Geophysics Laboratory
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UNIVERSITY OF CALIFORNIA, SAN DIEGO
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11
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3 1822 04429 0781
TECHNICAL NOTE NO. 209
THE DETERMINATION OF ATMOSPHERIC VISIBILITY
WITH A DIGITAL, IMAGE-ACQUISITION SYSTEM
Wayne S. Hering
Richard W. Johnson
Marine Physical Laboratory, UCSD
1. Introduction
The potential for fully automated measurements of the visibility of distant objects
has improved substantially with the recent advances in the development of digital,
image-acquisition systems. Dedicated systems which combine solid-state image sensing
capability with microcomputer control and processing functions can handle the
imagery data transfer, processing and storage requirements for real time
measurements. Thus, we are challenged to exploit this capability through the
development of operationally efficient algorithms, which extract the useful information
from the imagery and provide continuously-updated, numerical representations of the
visibility. The purpose of this Technical Note is to review briefly the factors that are
important for the determination of daytime visibility, both instrumentally and by the
human observer, and set forth techniques for objective measurements of prevailing
visibility with the digital imagery system.
2. Basic Concepts: An Overview
The solid-state video camera in combination with a digitizer-processor board
(frame grabber) provides an output of relative image brightness to the microcomputer
for further processing. Each picture element (pixel) in the resultant 2-dimensional
array defines the relative brightness of the corresponding element of the actual image.
With careful radiometric and geometric calibration of the system, each pixel in the
fixed array is transformed to the calibrated apparent radiance of the elemental
fraction of the target or background area in the scene that corresponds with the pixel
location at the instant of recording.
2.1. Expression for Contrast Transmittance
Let us review the procedures involved in the determination of visibility from the
measured radiance distribution through reference to the basic expressions for contrast
transmission in the atmosphere as given by Duntley, Boileau and Preisendorfer (1957).
Reference to these basic concepts is of particular interest for understanding the effects
of simplifying assumptions and for identifying the factors important for the selection
of the best available visibility targets.
The expression for the (monochromatic) apparent spectral radiance L, of a target
t at range r along the path of sight specified by zenith angle 0 and azimuthal angle 0
is
Ly(0,0) = 41.(0,0)T,(0+pL,(0,0)
(1)
where I, is the inherent target radiance and el, is the path radiance generated by the
- 2 -
(3)
scattering of direct sunlight and diffuse light from the surrounding sky, clouds and
terrain into the path of sight. The radiance transmittance of the path, T,(0) is given
by
T (0) = expãr,
(2)
where ā is the average attenuation coefficient.
Similarly, the expression for the apparent spectral radiance of the adjacent
background I, is
Ly(0,0) = 6L.(,0)T,(0) + PL,(1,6),
where el, is the inherent radiance of the background.
Thus the measured pixel radiance is the sum of the residual, image-forming light
from the target (or background) and the path radiance due to aerosol and molecular
scattering throughout the path. Strictly speaking, Eqs. (1) and (3) apply only to
monochromatic radiance and ignore the effects of small scale turbulence on
atmospheric transmission.
Subtracting Eq. (1) from Eq. (3) we have
Lr(0,0) - ,(0,0) = 1,(01,L,(0,6) - 01.(0,)].
(4)
Note that radiance differences are transmitted along atmospheric paths with the same
attenuation as the individual target and background radiances.
The apparent spectral contrast C, of a target with respect to the background is
defined by
C = (L.-L.)/L,
(5)
For convenience the notation with respect to viewing angle has not been continued in
this and following expressions. However, it is important to remember that the
apparent and inherent contrast as well as the spectral radiance have strong directional
dependence.
The corresponding definition of the inherent spectral contrast is given by
Co = (L.-L.)/L..
(6)
Finally, the expression for contrast transmittance in its most general form is
obtained by combining Eqs. (4), (5) and (6) to yield
Cr/C= T, LoloL.
Duntley, et al., (1957) state that the above equations
height ang hindi ako
"apply rigorously to any path of sight regardless of the extent to which the
scattering and absorbing properties of the atmosphere or the distributions of
lighting exhibit non-uniformities from point to point", and "the equations
can be used in treating all real atmospheres and all real lighting conditions."
bi
- 3 -
2.2. Visibility and equilibrium radiance
Under computer scan control, the digital image-acquisition system continuously
maps the apparent radiance distribution and the relative apparent contrast of objects
within the view of the observation point. The measurements are immediately
applicable to the determination of the optical and meteorological properties of the
ambient atmosphere. In the case of meteorological visibility, the objective is to
extract numerical estimates which are commensurate with the human perception of
visibility. In this regard, guidance given by the World Meteorological Organization
(1971) to help ensure observation compatibility and representativeness prescribes:
"Meteorological visibility by day is defined as the greatest distance at which
a black object of suitable dimensions, situated near the ground, can be seen
and recognized, when observed against a background of fog or sky."
For both practical and theoretical reasons, the technique for the instrumental
determination of visibility should conform with all elements of the definition. As
discussed in the following paragraphs, strict adherence to these criteria for
target/background selection results in a simple direct relationship between the
numerical representation of visibility, V, contrast transmittance, Cr/Co, and radiance
transmittance, T., greatly enhancing the interpretation of measurements made in
different places at different times.
The basic relationships can be shown by substituting for the path radiance ,L,
such that Eq. (3) may be written
oL= 6L, T, + L,(1-Tr).
where L, is defined as the equilibrium radiance (Duntley, et al., 1957) and is the same
as the incremental source function as given by Chandrasekhar (1960). As the radiance
transmittance decreases with increasing range r between the target (and/or
background) and observer the apparent radiance L, approaches the source function
(8)
Lq:
2.3. Special Case: Objects viewed against horizon background
In the case of a cloudless sky background, the apparent horizon radiance tends to
remain unchanged as the observer backs away from the target. Assuming horizontal
uniformity, the apparent horizon radiance L, at that azimuth is equal to the
equilibrium radiance (source function) for the path of sight as follows,
mL (90,0) = 1,(90,0) = 6L,(90,0) = 5L. (90,0).
(9)
Under these special conditions, Eq. 7 for the contrast transmittance becomes
Cr/Co=T,
(10)
Early on in the development of visual range concepts, Koschmieder (1924)
determined through consideration of the process of light scattering in a uniform
atmosphere that the apparent radiance of a black object at range r viewed against the
horizon sky is given by
Ir = h I(1-exp-or).
(11)
.
- 4 -
In addition, Koschmieder extended the development to the more general case where
the inherent target radiance is not zero, deriving the expression
Le = L,exp-or + y L, (1-exp-or),
(12)
where o is the average scattering coefficient. With respect to objects viewed against a
cloudless or overcast horizon sky, Eq. (12) as determined by Koschmieder is equivalent
to Eq. (8) except that the attenuation due to atmospheric absorption is neglected. In
most instances when reference is made to "Koschmieder's Law" the reference is to the
special case of Eq. (10) for a black object, (C. = -1), viewed against the horizon sky
where
Co = E = T, = exp-OV
(13)
and E is the threshold of apparent contrast needed for the detection of the distant
object, and V is the visual range.
2.4. General expression for visibility determination
Finally in this brief review of the general principles for the determination of
visibility, let us return to the complete expressions for contrast transmittance and
visibility that apply to objects viewed against any background. Solving for the
radiance transmittance in Eq. (7), the expression may be written
T
= Cr bus
= exp-ār.
(14)
COL.
Consistent with the basic definition of visibility, as the distance to the target increases
there is a distance V where the apparent contrast C, becomes numerically equal to the
prescribed threshold contrast E. The corresponding equation for the radiance
transmittance at this range is
1. = Esto exp-āv,
(15)
64,
where L, is the apparent background radiance at distance V.
Dividing Eq. (15) by Eq. (14), we have the general expression for the
determination of visibility from digitally acquired imagery,
V - Cookies
(16)
Thus, the ratio of the apparent to the inherent background radiance is an important
factor in the determination of visibility from the apparent contrast of objects in the
scene that are viewed against backgrounds other than the clear horizon sky. For
further analysis of this aspect, let us consider yet another form of Eq. (7) obtained by
substituting from Eq.(8) to obtain
L. (1-T.)]-
= 1 +
(17)
6L, T
- 5 -
Here we note that the contrast transmittance is related to the radiance transmittance
by the ratio Lelo L, which is termed the "sky-ground ratio", S, by Duntley (1948), so
that
S(0,0) = L9(0,0)/6L. (0,0).
(18)
Sky refers to the fact that the clear-sky horizon radiance for the horizon path having
the same scattering angle with respect to the sun as the path to the target is to a
good approximation equal to the equilibrium radiance or source function for that path
of sight. Ground refers to the inherent radiance of the background adjacent to the
target, and the term therefore is dependent upon the reflectance and orientation of the
surface as well as the downwelling irradiance. The directional notation is retained for
this expression to emphasize the importance of the directional dependence, particularly
with respect to the variations with sun angle as a function of time of day.
Now substituting Eq. (18) in Eq. (16), we have
- in { SE MI - 1-s} , und 1 - - sy}
(19)
U
which is the general equation expressed in terms of sky-ground ratio.
Fig. 1 is a graphical representation of Eq. 19, and shows the dependence of the
visibility/target-range ratio on the measured apparent contrast for the normal range
of sky-ground ratio that is observed in clear-sky conditions. Low values of S near 0.25
are associated with a surface covered with freshly fallen snow, whereas values near 4.0
correspond, for example, with forest canopy backgrounds. Large fractional changes in
the calculated visibility ratio result as the inherent terrestrial background radiance
departs from the horizon radiance, particularly when the measured apparent contrast
is rather high (i.e. nearby targets in good visibility conditions). The disparity
becomes significantly less when the apparent target contrast is near the limit of
detectability. It is important to note that in overcast sky conditions, the range of
values for the sky-ground ratio increases substantially to near 20 for forest cover
backgrounds and about 1 for fresh snow surface backgrounds.
It is evident from Fig. 1 and Eq. (19) that one must be careful in the
interpretation of visibility observations where the human observer finds it necessary to
depart from the guidelines as given in Section 2.2, and selects non-standard targets
with backgrounds other than the adjacent horizon. Although digital imagery offers
added opportunity to extract information with respect to the optical properties of the
ambient atmosphere, considerable sophistication must be built into algorithms that
diagnose effectively the detection range of many non-standard targets against variable
backgrounds. On the other hand, the wealth of information generated by repetitive
horizon scans with a digital imagery system enables straightforward determinations of
prevailing visibility and visual range from a hierarchy of targets. The resultant
measurements can be designed to conform in accuracy and representativeness with the
highest standards of current practice."
3. Determination of prevailing visibility
The preferred approach for instrumental determinations of visibility from
radiometrically calibrated imagery follows directly from the discussion of the factors
that govern image transmission in the atmosphere. First and foremost it is important,
- 6 -
insofar as possible, to direct attention to the measured apparent contrast between the
horizon sky and objects in the scene. It is desirable but not strictly necessary that the
objects stand above the horizon as viewed from the ground observation point. The
major consideration is that the extinction and directional scattering properties along
the paths of sight to the object and horizon correspond closely. As discussed in the
previous section, with the horizon sky as the background, the sky ground ratio is 1
and Eq. (19) simplifies to
V11 = ln
V/c
=
In
/ in San
(20)
With careful selection of visibility targets on or near the horizon, Eq. (20) becomes
the basic expression for the determination of visibility from the horizon scan imagery.
Criteria for target selection and the specification of inherent contrast C, and threshold
contrast E as input variables to Eq. (20) are reviewed in the following sections.
3.1. Target selection
The prime requirement for reliable determination of prevailing visibility is an
ample supply of suitable targets, well distributed in range and azimuth. On the one
hand it is important to make use of all objects in the horizon scan imagery that may
serve as visibility targets. On the other hand, because of their intrinsic properties,
potential targets are not equal in a given situation as effective determinants of the
prevailing visibility. The basic properties of individual targets must be predefined by
the input variables to Eq. (20). In addition to the target distance from the
observation point, the input variables are the inherent contrast of the target and the
contrast threshold for detection. Stability in the input variables over the full range of
atmospheric conditions is the major consideration in the selection of specific objects to
be included in the accepted group of visibility targets.
3.2. Inherent contrast
For visibility determination using Eq. ( , we must prescribe the relative contrast
between the inherent radiance of the selected object and the adjacent horizon sky
radiance. In the case of the ideal, non-reflecting, black target the relative contrast is
always -1. (Note that the measured apparent contrast of a given target-background
does not change sign with increasing path length so that the absolute value of contrast
can be used for calculation purposes). However, the reflectivity of even natural dark
targets is seldom zero so that careful attention must be given to the estimates of
inherent contrast and the vulnerability of the target to fluctuations in C, due to
changes in the directional distribution of lighting reaching the target from the sun, sky
and surrounding terrain.
The sensitivity of visibility determinations to the uncertainties in the estimates of
the inherent contrast as an input variable is illustrated in Fig. 2. Trial calculations
were made of the visual-range/target-range ratio as a function of measured apparent
contrast for selected values of assumed inherent contrast. Shown here are the
disparities in V/r associated with departures from an assumed inherent contrast of 0.8
for natural dark targets in the acquired imagery. The range of assumed values, -0.6 to
-1.0, is representative of this class of targets. Note in particular that the visibility
determinations are not sensitive to errors in the input values of C, when the object is
-
.
7
near the maximum distance at which it can be seen so that the apparent contrast is
close to the threshold detection contrast. However, the error sensitivity increases
substantially for nearby targets in good visibility conditions when the measured
apparent contrast is relatively large. Thus, the relative accuracy of visibility as
determined from a given non-standard target is in part a function of the visibility
itself. Most weight in a given situation should be applied to the fraction of preselected
targets where the measured contrast transmittance of the intervening path is
relatively low.
3.3. Threshold contrast
Experiments by Taylor (1964) have shown that the visual contrast threshold does
not vary significantly with background luminance over the normal range of daylight
conditions. However, the contrast threshold does vary markedly with the angular
subtense of the target at the point of observation. With dwell times commensurate
with normal visual search (1/3 sec), the minimum contrast for confident detection by
the human eye is about .025 for objects with an angular size greater than 0.5 deg, as
determined from the laboratory experiments. Based upon general field experience,
Douglas and Booker (1977) recommend ".--a recognition contrast threshold value of
about 0.05 when measurements of transmittance are used for determining the visual
range equivalent to that reported by meteorologists and the use of a value of E in the
region of 0.035 to 0.04 for the detection contrast threshold under field conditions".
The sensitivity of the visibility determinations to the assumed value of threshold
contrast is illustrated in Fig. 3.
3.4. Overcast sky conditions
As in the case of a cloudless horizon sky, the apparent horizon radiance of an
overcast sky tends to remain unchanged as the observer backs away from the target.
Thus, Eq. (9) also holds for the overcast horizon case, and the resultant
determinations of visibility using Eq. (20) are commensurate with the fundamental
definition of meteorological visibility given in Section 2.2 above. However, the inherent
contrast of dark objects with the overcast horizon is normally greater than the
corresponding inherent contrast with the cloudless horizon, yielding an overestimate of
the visibility to the extent indicated in Section 2.2, unless proper adjustment is made
in the input values of inherent contrast.
3.5. Partly cloudy horizon sky conditions
Horizon sky backgrounds with variable cloud conditions introduce additional
uncertainty into the visibility determinations. Shown in Figs. 4 and 5 are the results
of trial calculations illustrating the errors in V associated with the presence of isolated
clouds on the horizon when a cloudless horizon is assumed for the calculations. Key
factors are the distance of the cloud background relative to the target and the
brightness of the cloud relative to the corresponding clear sky horizon radiance. Again
we see that the resultant disparities are small when the contrast transmittance of the
path of sight is small, regardless of the cloud position or brightness. The errors
increase substantially in the case of targets having a range much less than the existing
visual range.
- 8 -
As shown in Fig. 4, without an appropriate change in C, the presence of a dark
cloud results in progressively larger underestimates of visual range with increasing
apparent contrast. The errors due to clouds much brighter than the corresponding
clear sky horizon radiance are opposite in sign and more severe. The comparison in
Fig. 4 gives results for horizon cloud radiances equal to twice and one-half the
cloudless horizon radiance. The assumed inherent contrast with the clear-sky horizon
is -.85 and the assumed cloud/target range ratio is 2.
The sensitivity with respect to relative cloud distance is shown in Fig. 5. A
cloud/clear-sky brightness ratio of 2.0 and C. equal to -0.85 was assumed. For this
bright cloud example, the error increases well beyond 50% for a cloud positioned at a
range less than 1.5 times the target range when the apparent contrast is greater than
0.3. The error diminishes significantly for cloud ranges more than twice the target
range, and of course for cloud brightness closer to that of the clear sky horizon
brightness.
4. References
Douglas, C. A. and R. L. Booker (1977), "Visual Range: Concepts, Instrumental
Determination and Aviation Applications," U. S. Department of Transportation,
Federal Aviation Administration, Systems Research and Development Service, Report
No. FAA-RD-77-8, Washington, D.C. 20590.
Duntley, S. Q. (1948), "The Reduction of Apparent Contrast by the Atmosphere," J.
Opt. Soc. Am. 38, 179-191.
Duntley, S. Q., A. R. Boileau, and R. W. Preisendorfer (1957), "Image Transmission by
the Troposphere I," J. Opt. Soc. Am. 47,499-506.
Koschmieder, II. (1924), "Theorie der Horizontalen Sichtweit," Beitr. Phys. freien Atm.
12, 33-53, 171-181.
World Meteorological Organization (1971), Guide to Meteorological Instrument and
Observing Practices. Fourth Ed. Secretariat of the World Meteorological Organization,
Geneva, Switzerland WMO-No 8. TP. 3.
VISIBILITY / TARGET RANGE
SENSITIVITY TO SKY-GROUND RATIO

SKY-GROUND RATIO = 4
0.25
o o voo co
A
W
VISIBILITY / TARGET RANGE
DARK FOREST
CLEAR HORIZON SKY
_
FRESH SNOW
ta
0.6
0.2
0.4
APPARENT CONTRAST
Fig. 1 Calculated values of the visibility/target range ratio as a function of the observed
apparent contrast. Relationships are illustrated for the typical range of sky-ground ratio.
The sky-ground ratio is 1 for objects viewed against the cloudless horizon sky. Low
values of sky-ground ratio are associated with bright backgrounds such as snow covered
terrain, wheras high ratios are observed with dark backgrounds such as forest cover.
For these calculations, the assumed values for the inherent contrast and the threshold
contrast were 0.85 and 0.05, respectively.
VISIBILITY / TARGET RANGE
SENSITIVITY TO INHERENT CONTRAST
OOONO

Co=-0.6/
-0.8
+
~
VISIBILITY / TARGET RANGE
ol
0.2
0.4
APPARENT CONTRAST
Fig. 2. Calculations of visibility/target range ratio using Eq. 20, illustrating the sensi-
tivity of the resultant values to the assumed inherent contrast.
VISIBILITY / TARGET RANGE
SENSITIVITY TO THRESHOLD CONTRAST
OOO
ГТ ТТТТ
0 20

~
VISIBILITY / TARGET RANGE
THRESHOLD
CONTRAST
0.02
0.05 +
0.1.
0.6
0.2
0.4
APPARENT CONTRAST
Fig. 3. Calculations of visibility/target range ratio using Eq. 20, illustrating the sensi-
tivity of the resultant values to the assumed threshold contrast.
VISIBILITY ERROR FROM HORIZON CLOUD
VS APPARENT CONTRAST AND CLD BRIGHTNESS

Co=-.85
CLD/TARGET RANGE = 2
BRIGHT CLOUD
PERCENT ERROR IN VISIBILITY
DARK CLOUD
0.2
0.4
MEASURED APPARENT CONTRAST
Fig. 4. Sample calculations illustrating the percent error in the determination of
visibility due to existing cloud obscuring the horizon sky. Results are shown for
a dark cloud with a brightness of one-half the clear-sky horizon brightness, and
for a bright cloud with a brightness equal to twice the clear-sky horizon bright-
ness. The assumed range was twice the target range.
VISIBILITY ERROR FROM HORIZON CLOUD
VS APPARENT CONTRAST AND CLOUD RANGE

Co= -.85
CLD / HORIZON SKY
RADIANCE RATIO = 2
BRIGHT CLOUD RANGE
TARGET RANGE
1.5%
PERCENT ERROR IN VISIBILITY
TTTTTTTTTO
2.07
0.6
0.2
0.4
MEASURED APPARENT CONTRAST
Fig. 5. Sample calculations illustrating the percent error in the determination of
visibility due to existing cloud obscuring the horizon sky. Results are shown for a
ud with a range equal to 1.5 times the target range, and for more distant
clouds with assumed ranges of 2.0 and 2.5 times the target range.