Determination of Atmospheric Path Radiance: 

Sky-to-Ground Ratio for Wargamers 

by Sean G. O’Brien and Richard C. Shirkey 

ARL-TR-3285 September 2004

Approved for public release; distribution is unlimited.
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Army Research Laboratory 

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ARL-TR-3285 September 2004

Determination of Atmospheric Path Radiance: 

Sky-to-Ground Ratio for Wargamers 

Sean G. O’Brien and Richard C. Shirkey

Computational and Information Sciences Directorate 

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Determination of Atmospheric Path Radiance: Sky-to-Ground Ratio for Wargamers 

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Sean G. O’Brien and Richard C. Shirkey 

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U.S. Army Research Laboratory 

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14. ABSTRACT 

This document describes both the technical and user aspects of the sky-to-ground ratio program. The program computes sky-to-ground ratio, 

contrast transmission, transmission, path radiance, and zero-range-to-target background radiance for a user-specified observer (sensor) and 

target pair, situated on a slant path in the lower atmosphere for 19 different aerosols. Results are provided in hard-copy format and also in a 

computer-generated (tabular) file. The calculations are performed in one of three user-selectable bands: visible, mid-infrared, and farinfrared. Numerous examples are provided. A graphical user interface for this program is currently under development. 

15. SUBJECT TERMS

Atmospheric, sky-to-ground ratio, path radiance, transmission, contrast, contrast transmission 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

Richard C. Shirkey 

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OF 

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(505) 678-5470 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18
Table of Contents 

List of Figures v

List of Tables vi

Preface vii

Summary 1

1. Introduction 2

1.1 Overview 2 

1.2 Availability 2 

2. The Sky-to-Ground Ratio 3

2.1 Theoretical Formulation: Visual Contrast 3

2.2 Discussion 5 

3. Solutions for Visible Wavelengths: The Eddington and delta-Eddington Methodologies 6

3.1 The Eddington Approximation 7 

3.2 The Delta Approximation 8 

3.3 The delta-Eddington Approximation 9 

4. Solutions for IR Wavelengths 10

4.1 Theoretical Formulation: IR Contrast 10 

4.2 Cloud/Geometrical Considerations 11 

5. Validation and Verification 12

5.1 Visible Wavelengths 12 

5.2 IR Wavelengths 13 

6. Usage 16

6.1 Inputs Common to Both Visible and IR Bands: Part 1 17 

6.2 Visible Band Model Input 18 

6.3 IR Band Model Input 22 

6.4 Inputs Common to both Visible and IR Bands: Part 2 24 

iii
6.5 Input Summary 26 

7. Output 33

8. Ancillary Data Files 34

9. Example Runs 35

9.1 Visible Band Examples: Scenario Construction 35 

9.1.1 Example 1: SGR, Radiance and Transmission as a Function of Observer Look 

Angle at a Fixed Wavelength 37 

9.1.2 Example 2: SGR and Radiance as a Function of Range at a Fixed Wavelength 39 

9.1.2 Example 2: SGR and Radiance as a Function of Range at a Fixed Wavelength 40 

9.2 IR Band Examples 41 

9.2.1 Example 1: SGR, Radiance, and Transmission as a Function of Wavelength and 

Zenith Angle 41 

9.2.2 Example 2: SGR and Radiance as Functions of Range at a Fixed Zenith Angle 44 

10. Caveats 45

11. Conclusions 46

References 47

Appendix 49

1. Sample Run from the Text Scenario Using the Input File, visible_input.txt. 49 

2. Sample Run from the Text Scenario Using the Input File, mid-ir_input.txt. 51 

3. Sample Run from the Text Scenario Using the Input File, far-ir_input.txt. 53 

Acronyms 55

Distribution 56

iv
List of Figures 

Figure 1. Pictorial representation of contrast quantities. Ib(b) is the (inherent) background 

radiance at distance b from the target. .......................................................................................... 3 

Figure 2. Truncation of phase function, after Lenoble (16).......................... .................................... 8 

Figure 3. Diagram illustrating the criteria used to adjust the LOS when it intersects a cloud 

layer. ........................................................................................................ .................................. 11 

Figure 4. Comparison of results with Lenoble. ................................................................................ 13

Figure 5. Scenario used for IR wavelengths showing target relocation. ......................................... 14 

Figure 6. Comparison of MODTRAN and IRRAD spectral radiances in the mid-IR band............ 15 

Figure 7. Far-IR spectral radiance comparison between MODTRAN and IRRAD models. ........... 16 

Figure 8. Top-down (azimuthal) view of scenario. ......................................................................... 35 

Figure 9. Horizontal (zenith) view of scenario................................................................................ 36 

Figure 10. Upward look at right angles to solar azimuth.................................................................. 39 

Figure 11. Upward look offset by 45o to solar azimuth.................................................................... 39 

Figure 12. Upward look directly facing/behind the sun. ............................... .................................. 39 

Figure 13. Downward look directly facing/behind the sun. ......................... .................................. 39 

Figure 14. SGR as a function of target range at a wavelength of 0.55 μm for visibilities of 23 

and 2 km................................................................................................... .................................. 40 

Figure 15. Component radiances vs. range. The visibility is 23 km............ .................................. 41 

Figure 16. Component radiances vs. range. The visibility is 2 km................................................. 41 

Figure 17. Mid-IR band example results: sky-to-ground ratio. ....................................................... 42 

Figure 18. Far-IR band example run results: sky-to-ground ratio. ................................................. 42 

Figure 19. Mid-IR band example run results: transmission and spectral radiance ......................... 43 

Figure 20. Far-IR band example run results: transmission and spectral radiance. ........................... 43 

Figure 21. Sky-to-ground ratio for mid-IR and far-IR scenarios with fixed observer and target 

heights......................................................................................................................................... 43 

Figure 22. Sky-to-ground ratio for target range variation along a fixed zenith angle. ..................... 44 

Figure 23. Spectral background, path, and limiting path radiance results for varying target 

ranges at a wavelength of 4 μm. ................................................................................................. 45 

Figure 24. Spectral background, path, and limiting path radiance results for varying target 

ranges at a wavelength of 10 μm. ............................................................................................... 45 

v
List of Tables 

Table 1. Comparison of SGR results at visible wavelengths........................................................... 13 

Table 2. Partial input parameters for IR validation runs.................................................................. 15 

Table 3. Choices for wavelength band selection. ............................................................................ 17 

Table 4. Choices for aerosol type at visible wavelengths and their relative humidities (percent) 

where applicable. ........................................................................................................................ 19 

Table 5. Cloud types available in the program and their tops and bases......................................... 21 

Table 6. Available illumination sources in the visible..................................................................... 22 

Table 7. Required data input for LOS mode chosen........................................................................ 25 

Table 8. Iteration modes. ................................................................................................................. 26 

Table 9. Required input quantities for visible runs.......................................................................... 27 

Table 10. Required input quantities for IR runs. ............................................................................. 30 

Table 11. Output. ............................................................................................................................. 33 

Table 12. Ancillary file information. ............................................................................................... 34 

Table 13. Upward and downward looking scenarios for LOS azimuth of 90° and 270°. ............... 36 

Table 14. Script file for example scenario....................................................................................... 37 

Table 15. Mid-IR band inputs for the SGR model example............................................................. 42 

Table 16. Far-IR band inputs for the SGR model example. ............................................................. 42 

vi
Preface 

Target discrimination calculations are frequently based on a two-dimensional Johnson cycle criteria 

methodology and require characterizing the system by either minimum resolvable contrast or 

minimum resolvable temperature difference. For reflective sources and visual and near-infrared 

imaging systems the contrast of the target is reduced by path radiance (i.e., by background light or 

near-infrared radiation entering the line-of-sight to the target). Since determination of the path 

radiance is computationally intensive, many wargames use a related quantity called the sky-toground ratio. This ratio is an approximate method for representing the amount of diffuse radiation 

that is entering a user’s line-of-sight. While codes that determine the sky-to-ground ratio have been 

in existence for some time, none of these codes consider the situation where the target might be 

some distance in front of the background, nor do they consider the infrared wavelength regions; 

those situations have been rectified here. Heretofore, atmospheric quantities, such as aerosol type, 

cloud base/height, and temperatures, have not been readily integrated into these types of codes. 

These quantities, and others, are now integral to this code and are available for selection by the 

user. 

The authors would like to thank the Army Model and Simulation Office for providing seed money 

under the Army Model Improvement Program. We would also like to thank John Mazz (Army 

Materiel Systems Analysis Activity) and David Tofsted (U.S. Army Research Laboratory) for 

reviewing this report and providing helpful comments.

vii
INTENTIONALLY LEFT BLANK. 
Summary 

The sky-to-ground ratio is often used in wargames as an approximate method for quantifying the 

amount of diffuse radiation that is entering a sensor’s field of view. We may represent this quantity 

as Sgr = Ips / Ib(0), where Ips is the limiting path radiance and Ib(0) is the background radiance as 

seen at the target. These radiances, or diffuse radiation, act as “atmospheric noise” and reduce the 

apparent contrast when observing a target. However, computing the diffuse radiation field is not an 

easy task and usually requires research-grade computer codes. The delta-Eddington method, used 

herein for visible wavelength calculations, is an approximate method that assumes the angular 

dependence of the diffuse radiance can be represented by a polynomial linear in scattering angle. 

This method overcomes the large computer run times usually associated with determining the 

diffuse radiance in radiative transfer codes. At visible wavelengths, the aerosols found in the 

atmosphere frequently scatter radiation predominantly in the forward direction along the observer’s 

line-of-sight. This highly peaked scattering further complicates the ability to predict the diffuse 

radiation, and the subsequent determination of the sky-to-ground ratio. One way that the 

calculation of the asymmetric scattering in the visible band can overcome this difficulty is by using 

the delta-Eddington approximation, which combines a Dirac delta function and a two-term

approximation for the aerosol scattering function. At infrared wavelengths, scattering effects may 

be ignored in many situations and the computation of the sky-to-ground ratio is carried out by 

integrating the emission over the relevant lines-of-sight. 

We have constructed a computer program that rapidly computes the sky-to-ground ratio in run

times of less than one second. For visible wavelengths, we have modified the Fast Atmospheric 

Scattering computer code, and for infrared wavelengths, we have constructed new code. Both of 

the wavelength regimes have been wrapped into one code with supporting information on 

atmospheric aerosols and clouds, and integrated routines that allow for automatic determination of 

solar/lunar positions. The target/observer may be placed anywhere in the lower 5 km of the 

atmosphere and provisions have been made to allow the user to insert an optional sensor response 

curve. The program can be run interactively or in command-line batch mode, with output 

consisting of spectral, band-averaged, and band-integrated radiances, as well as the sky-to-ground 

ratio. 

The program has been validated and caveats are presented to allow the user to avoid those areas 

where the approximations employed break down. We also present extensive examples of program 

use—specifically, a target being observed flying in a horizontal plane parallel to the ground 

surface. An example of the target looking downward at the observer is also presented. These 

scenarios are discussed in some detail in order to aid the user in understanding the geometries that 

may be encountered, in constructing the input file, and in interpreting the output information. 

“Canned” test cases are also provided for verification that the program is functioning correctly after 

a new installation. 

1 
1. Introduction 

1.1 Overview

The sky-to-ground ratio (1, 2) (hereafter referred to as SGR or Sgr) is used primarily in wargames 

as a method to quantify the amount of light scattered into a sensor’s line-of-sight (LOS). This 

radiation results from multiple scattering processes that occur between light and particles that it 

encounters as it passes through the intervening atmospheric medium. Using research-grade 

radiative transfer codes, these atmospheric multiple scattering processes can be calculated 

“exactly” using many differing methods (3–6). However, such calculations, while fast, still take on

the order of seconds, minutes, and depending upon the scenarios, even hours to perform. The 

Combined Arms and Support Task Force Evaluation Model (CASTFOREM) is an Army highresolution, two-sided, force-on-force, stochastic systemic model of a combined arms conflict. Run 

times are scenario dependent and typically run approximately 1.5–1.7 hours (on a 2.2 GHz PC) per 

replication for a battalion-sized defensive scenario. Without smoke, the runs are approximately 

one-to-one. (7) Due to the stochastic nature of CASTFOREM, the treatment of time intensive 

physical processes, such as determination of atmospheric multiple scattering effects, must be kept 

to a minimum yet be physically accurate. This presents a quandary: accurate answers depend upon 

knowledge of physical processes (here, atmospheric scattering/emission), yet computer run time 

must be kept to a minimum to have wargames complete in reasonable clock time. Thus, the need 

exists for approximations such as the SGR. 

This document presents a methodology for determining the SGR. The code, written in ANSI 

standard FORTRAN 90, is relatively fast running (~1 s on a 1 GHz PC for a typical scenario used 

in the validation and verification (V&V) section 5) and can be implemented directly into the 

wargame or used to construct lookup tables that can be accessed by the wargame. The code itself 

uses approximate methods for calculating the multiple scattering quantities that are used to 

determine the SGR. Limitations of the program are presented in section 10; it is suggested that the 

user peruse this section in order to avoid areas where the program’s results may be questionable. 

Numerous options are available that allow the user to select various natural aerosols for global 

locations and times. Explanations of the SGR and other related quantities, to include an 

abbreviated explanation of the technique used, are presented herein. The code operates in the 

visible (0.35–0.75 μm), near-infrared (IR) (1.06 μm), mid-IR (3.0–5.0 μm), and far-IR (8.0–12.0 

μm) spectral regions. Finally, for those individuals who are interested in the physics, the code has 

been liberally sprinkled with technical references. 

1.2 Availability 

The source code, written in ANSI FORTRAN 90 and C, is available by contacting either Dr. Sean 

O’Brien at (505) 678-1570 (sobrien@arl.army.mil) or Dr. Richard Shirkey at (505) 678-5470 

(rshirkey@arl.army.mil). A graphical user interface (GUI) version of this code is under 

construction. Persons interested in such a version should contact Dr. Shirkey. Comments or 

questions relating to either the code or documentation (to include requests for electronic copies) 

may also be referred to the above persons. 

2 
2. The Sky-to-Ground Ratio 

2.1 Theoretical Formulation: Visual Contrast 

In order to acquire an object, one must be able to distinguish it from its background. This is the 

basic definition of contrast. Determining the contrast requires knowledge of the inherent radiance 

of the target and the background radiance at the target, where the target is usually considered to be 

at zero range (see fig. 1 for a pictorial representation of the following contrast quantities). 

The inherent contrast (i.e. the contrast defined at zero range) is 

C(0) = [ It(0) – Ib(0) ] / Ib(0), (1)

where It(0) is the target radiance at zero range (usually taken to be the location of the target) and 

Ib(0) is the background radiance at zero range. 

r b 0

background

Ib(b) Ib(0)

It(0)

Imaginary zero target plane

Ib(r)

Ip(r)

sensor

source

It(r)

range 

(arbitrary units)

example scattering points

r b 0

background

Ib(b) Ib(0)

It(0)

Imaginary zero target plane

Ib(r)

Ip(r)

sensor

source

It(r)

range 

(arbitrary units)

example scattering points

r b 0

background

Ib(b) Ib(0)

It(0)

Imaginary zero target plane

Ib(r)

Ip(r)

sensor

source

It(r)

range 

(arbitrary units)

example scattering points

Figure 1. Pictorial representation of contrast quantities. Ib(b) is the (inherent)

background radiance at distance b from the target. 

The radiance at range r can be represented by 

I(r) = I(0) T(r) + Ip(r), (2) 

where I(0) is It(0) or Ib(0). T(r) is the transmission over the path r, given by e-κr

, where κ is the 

extinction coefficient of the aerosol and/or gas comprising the intervening medium; Ip(r) is the path 

3 
radiance over the path length r. The path radiance represents radiation emitted or scattered into the

sensor’s LOS and may be thought of as atmospheric noise, since it adds spurious information to the 

point or image being observed. The path radiance term is frequently the most difficult term to 

evaluate, requiring either approximate solutions or a research grade radiative transfer code. 

Following eq 1, the apparent contrast is defined as 

C(r) = [ It(r) – Ib(r) ]/Ib(r). (3)

Now, using eq 2, we can reformulate eq 3 as 

C(r) = [It(0) T(r) + Ip(r) – Ib(0) T(r) – Ip(r)] / [Ib(0) T(r) + Ip(r)]

 = [It(0) – Ib(0)] / [Ib(0) + Ip(r)/T(r)] 

= C(0)/{1 + [Ip(r)/Ib(0)] T(r)-1}, (4)

where C(0) is the contrast at zero range, commonly referred to as the inherent contrast. 

Because Ip(r) is difficult and time consuming to calculate, approximations such as the SGR are 

frequently made in wargames to evaluate this term. Next, we derive the SGR approximation. In 

order to do this, we first must examine the radiative transfer equation 

 dI(r, Ω) / dr = - κ I(r,Ω) + κ [πo∫Ω′I(r, Ω′) P(Ω,Ω′) dΩ′ + ( 1 - πo) B(λ,t)], (5) 

where I is the radiance (in w/m

2

-sr) at position r flowing in direction Ω; I(r,Ω′) is the angular 

distribution of the incoming radiation, which is being scattered into the direction in which the 

observer is looking (Ω); and π°

 is the combined single scattering albedo for aerosols and gasses. 

P(Ω,Ω′) is the phase function, which determines the angular probability of scattering from Ω′ into 

Ω, and B(λ,t) is the Planck emission function at wavelength λ and temperature t. The term inside 

the square brackets is called the source term and includes diffuse and emitted radiation from all 

directions and sources. 

Now consider the situation where the term in brackets is constant or slowly varying (i.e., an 

atmosphere homogeneous in the distribution of particulates and in illumination). Eq 5 can then be 

recast as 

 dI(r, Ω) / dr = - κ I(r,Ω) + κ A, (6) 

where 

 A = π° ∫Ω′ I(r, Ω′) P(Ω,Ω′) dΩ′ + ( 1 - π°

 ) B(λ,t) ≈ constant. (7) 

Using eκr as an integrating factor for eq 6 and performing the integration over the path r from 0 to s, 

where s is large but not infinite, we find 

 Is = I0 T + A ( 1 – T ). (8) 

By comparing eq 8 with eq 2, we find 

4 
A = Ip / ( 1 – T ) or Ip = A ( 1 – T ). (9) 

Thus, as the transmission decreases, either through a longer path length or through an increased 

particle concentration, Ip → A. When Ip reaches its limit A, we refer to it as the limiting path 

radiance Ips, which is the point where radiation scattered into the LOS is equal to that scattered out 

of the LOS. Now using eq 9 in eq 4, we find that, under the conditions of limiting path radiance 

C(r) 1 1 

 Tc = —–– = —–—–—–—–—–—–—– = —–—–—–———, (10) 

 C(0) 1 + [Ips / Ib (0)](1 / T – 1) 1 + Sgr(1 / T – 1) 

where Tc is the contrast transmission and 

 Sgr = Ips / Ib(0) = Ip / [Ib(0) (1-T)], (11) 

which is the so-called sky-to-ground ratio. Thus, if Sgr is known, then we have a very quick, albeit 

approximate, means of calculating the apparent contrast. 

2.2 Discussion 

In deriving the SGR, the term in brackets in eq 5 requires that the intervening medium remain 

relatively constant. Slant paths in the atmosphere frequently traverse regions of inhomogeneities; 

horizontal paths also contain random fluctuations in the particle concentration and type. 

Nevertheless, the significance of this approach is that the concepts of inherent contrast and contrast 

transmission allow for the separation of target effects from atmospheric effects, which can be 

characterized in terms of the transmission and the sky-to-ground ratio. (8) In addition, one should 

not try to compare contrast transmission with transmission. Contrast transmission is a measure of 

the loss of contrast, and though it is a function of both path radiance and transmission, it should be 

thought of as a separate quantity propagated through the atmosphere. Transmission should be 

regarded simply as a loss of energy due to atmospheric propagation. Stated another way, 

increasing the gain of a sensor can compensate for the energy losses due to transmission alone, but 

cannot compensate for loss of contrast due to the additional path radiance signal that is present in 

the contrast transmission depiction of events. Of course, one may adjust the sensor threshold so 

that signal levels below that of the path radiance signal level are rejected, and that increased gain 

on the remaining target and background signals can restore the intrinsic contrast. This practice will 

also generally introduce additional radiance noise into the signals, thereby degrading the results. 

See also the discussion in the example section (section 9). 

We now examine the behavior of the SGR function, eq 11. Since SGR is a function of three 

variables (path radiance, background radiance, and transmission) and these three variables are 

primarily a function of the aerosol particulate properties in the visible band, we cannot 

unequivocally predict the behavior of SGR. This assertion becomes clearer when we consider that, 

in general, as the particle size approaches and exceeds the wavelength, the proportion of radiation 

scattered into the forward direction increases, thereby increasing the amount of path and 

background radiance. On the other hand, path transmission is directly affected by the amount of 

radiation that the particle absorbs or scatters in all directions, which are functions of the aerosol 

particle single-scattering albedo. In the visible band of the spectrum, for fixed background 

radiance Ib(0) and transmission T, the scenario illumination geometry strongly affects the value of 

5 
SGR, particularly in the case of larger aerosols. Such is not the case in the IR spectral band, where 

the dominant attenuation mechanism is usually absorption, which does not depend on the sourcetarget-observer geometry. 

When SGR = 1, the limiting path radiance is equal to the background radiance at the target 

position, and the path transmission T and the contrast transmission Tc are equal. This situation is 

encountered for horizontal paths in a plane-parallel atmosphere, where the background radiance is 

from a uniform, semi-infinite path, also known as the “horizon sky.” With increasing distance 

from the observer, the transmission T over the horizon sky path eventually falls to a very low value 

and the path radiance that is observed as Ib(0) is also equal to the limiting path radiance. As the 

limiting path radiance is approached at large optical depths along the horizon sky path, the radiance 

scattered into the LOS, along each additional path increment, is offset by the radiance that is 

scattered out of the LOS on the trip from that path segment back to the observer (equilibrium has 

been established). 

When SGR > 1, the background radiance at the target position is lower than the limiting path 

radiance, which can be described as a “dark” or “cold” background scenario. This condition may 

be encountered for a LOS that has a low albedo surface as a background at a short distance behind 

the target. It may also be encountered in a clear, vertically inhomogeneous plane-parallel 

atmosphere for an upward slant path that looks from a sensor at low-altitude to a high-altitude 

target. In that event, the limiting path radiance (derived from the LOS path radiance and 

transmission) will include contributions from the dense lower atmosphere. The background 

radiance will only include contributions from the tenuous upper atmosphere, and may be 

considerably lower than the limiting path radiance. 

When SGR < 1, a “bright” or “hot” background situation pertains where the background radiance is 

larger than the limiting path radiance. This condition may be encountered for downward LOS 

geometries where both the observer and target are at high altitudes (so that the limiting path 

radiance is low), for high albedo backgrounds (relative to the single-scattering aerosol albedo), or 

for (in the IR band) high-temperature backgrounds. 

For both cases where SGR ≠ 1, the contrast transmission for a given LOS path will approach unity 

when the path transmission T approaches unity and will approach a value of T / Sgr as the path 

transmission T approaches 0. In all cases, Tc will take on values between 0 and unity. 

3. Solutions for Visible Wavelengths: The Eddington and delta-Eddington 

Methodologies 

In the visible band, where scattering is the primary contributor to LOS path radiance, an enhanced 

version of the U.S. Army Electro-Optic Systems Atmospheric Effects Library (EOSAEL) Fast 

Atmospheric Scattering (FASCAT) (9) delta-Eddington model is used. Because the underlying 

plane-parallel methodology used in this model is presented over various other documents (9–13), 

we present only a basic review here. 

6 
Determining contrast along a sensor’s LOS requires solving the equation of transfer (eq 5). At 

visual wavelengths, the contribution to the source term from thermal emission (1 - π°)B(λ,t) is 

negligible, and we can recast eq 5 as 

μdI(τ,μ,φ)/dτ=-I(τ,μ,φ)+π°

 /4π[∫0

2π

∫-1

+1

I(τ,μ′,φ′)P(μ,φ;μ′,φ′)dμ′dφ′+π°/4(F0P(μ,φ;μ0,φ0)e-τ/μ0)], (12) 

where θ denotes the inclination to the outward normal (i.e., zenith angle), φ is the azimuth angle, 

dΩ = dμ dφ, μ = cosθ, τ = ∫ κ r dr, and πF0 is the solar irradiance perpendicular to the direction of

incidence. 

Using the Eddington and delta-Eddington methodologies, we shall examine solutions to eq 12 in 

sections 3.1, 3.2, 3.3. 

3.1 The Eddington Approximation 

Eddington’s approximation assumes that the angular dependence of the diffuse radiance can be 

represented by a polynomial linear in μ

 I(τ,μ) = I0(τ) + I1(τ) μ. (13)

Because we have a determined intensity distribution, we have a priori fixed the phase function—a 

constant plus a cosine dependence. If we assume that the phase function can be expanded in terms

of Legendre polynomials (11), substitute eq 13 into eq 12, and then integrate over θ and φ, we find 

that the only terms that do not integrate to 0 are of order 0 and 1. Thus, the phase function can be 

approximated by a two-term Legendre expansion (equivalent to the Henyey-Greenstein phase 

function truncated at the first term, i.e. PHG = 1 + 3g cosθ) 

 P(Θ) = Σ ωl Pl(cosΘ) = 1 + ω1(τ) cosΘ, (14) 

 l 

where Pl are the Legendre polynomials, ωl are the coefficients, 

 cosΘ = μμ' + (1-μ

2

)

1⁄2(1-μ'2

)

1⁄2cos(φ-φ′), (15) 

and Θ is the angle between incident (primed) and scattered (unprimed) radiances. 

While not particularly realistic (14), this linearly anisotropic phase function allows us to obtain 

equations for I1 and I0 

 dI1/dτ = -3(1-π°

 )I0 + .75π°F0e

-τ/μ0, (16) 

 dI0/dτ = (1-π°g)I1 + .75π°gμ0 F0e

-τ/μ0, (17) 

where the asymmetry factor, g, is defined as g = 1⁄2∫-1

+1

P(Θ)cosΘ d(cosΘ) = ω1/3. Eqs 16 and 17 

can be solved for the special case of a homogeneous layered atmosphere (10), where π°

 and g are 

constant within each layer, but vary from layer to layer. 

7 
3.2 The Delta Approximation 

When the scattering particles are large compared to the wavelength, such as at visible wavelengths, 

light is predominantly scattered in the forward direction. The mathematical formulation for this is 

represented by a highly peaked phase function where a large portion of the scattering occurs in a 

relatively small cone centered on 0o (the forward peak). The delta method represents the phase 

function as a Dirac delta function coupled with a phase function p' that has a reduced forward peak

 P(Θ) = 2f δ(1-cosΘ) + (1-f) p'(Θ), (18) 

where f is the fraction of energy scattered into the forward direction cone. We thus assume that 

radiation scattered into the forward peak is treated as unscattered, and appropriately reduce the 

optical thickness of the medium under consideration (11, 14–16). This is equivalent to replacing 

the real medium by an equivalent one with a scattering coefficient 

κ’s = (1 – f) κs; (19) 

keeping the absorption constant κ’a = κa, the single scattering albedo can be represented as 

π’

°

= π° (1 – f)/(1 – π° f). (20) 

Thus, the total extinction coefficient becomes 

κ’ = (1 – π° f) κ. (21)

Choosing the angle θo at which to truncate the phase function becomes a somewhat arbitrary 

choice. This angle is usually chosen as the point where the phase function begins to rapidly 

increase; the phase function is generally linearly interpolated from θo to 0o maintaining the slope of 

the untruncated phase function at θo. This is shown as a dashed line in figure 2. The gray portion 

shown in figure 2 is that portion of the phase function that is now considered to be incorporated 

into the direct beam. In the SGR program, θo has been set to 25o. 

We also note that while fog and cloud particles are all large 

with respect to visible wavelengths, and thus are in harmony 

with the above assumptions for the delta approximation, 

background aerosols (such as the rural, urban, and maritime 

aerosols) have significant contributions by particles less than 

1 micron in diameter and could be construed as violating the 

aforementioned assumptions. Joseph, et. al. (11), and 

Wiscombe and Joseph (17) have shown that errors 

associated with the Eddington and delta-Eddington methods 

occur primarily when the incident radiation is impinging at 

large zenith angles or when the single-scattering albedo is 

near 0.5. Figure 2. Truncation of phase function, 

 after Lenoble (16). 

8 
3.3 The delta-Eddington Approximation 

For phase functions that are highly peaked in the forward direction (0o), the Eddington method is 

inaccurate. To overcome the difficulties in dealing with such highly asymmetric phase functions, 

Joseph, et. al.(11), have shown that by combining a Dirac delta function and a two-term 

approximation for the phase function, one can produce results that are more accurate. Such an 

approach has been called the delta-Eddington approximation. In this approximation, the phase 

function (P∆E) is represented by 

 P∆E(cosΘ) = [2fδ(1-cosΘ) + (1-f)(1+3g'cosΘ)] 1/4π. (22) 

The first term represents scattering in the forward direction (in essence, increasing the direct beam) 

and the second term represents a diffuse term. The parameter f determines the fraction of radiation 

scattered into the forward peak and g' is the asymmetry in the diffuse portion of the scattering 

function. Thus, when we have a highly peaked phase function, we may use the Eddington method 

by transformation of variables. According to van de Hulst (18), “Scattering in the exact forward 

direction is no scattering at all. Hence, if in any problem we add the formal assumption that a 

certain amount of scattering occurs in the exact forward direction, this must make no difference in 

the results.” The proper transformation of variables is determined by requiring that the phase 

function meet certain conditions. Following Joseph, et. al. (11), it is required that the integral of 

eq 22 over θ be normalized to 1, and it is further required that the asymmetry factor be the same as 

in the Eddington method, which leads to 

g = 1⁄2∫-1

+1

P(Θ)cosΘ d(cosΘ) = 

 1⁄2∫-1

+1

 [2fδ(1-cosΘ) + (1-f)(1+3g'cosΘ)] cosΘ d(cosΘ) = f + (1-f) g', (23) 

where cosΘ is defined by eq 15. Finally, the second moments of the Eddington and the deltaEddington phase functions are required to be equal (11), resulting in f = g

2

. 

Inserting eq 23 into the azimuthally averaged transfer equation, viz, 

μ dI(τ,μ')/dτ + I(τ,μ')=π° 1⁄2∫-1

+1

P(μ,μ') I(τ,μ') dμ' =π° 1⁄2∫-1

+1 [2fδ(μ-μ') + (1-f)(1+3g'μμ')] I(τ,μ') dμ' 

 = π°f I(τ,μ') + 1⁄2 (1-f) π°∫-1

+1(1+3g'μμ')] I(τ,μ') dμ', (24) 

and μ = cosθ, as before. 

Rearranging eq 24 gives 

μ/(1- π°

f ) dI(τ,μ')/dτ + I(τ,μ') = 1⁄2 π° (1-f)/(1- π°f ) ∫-1

+1

(1+3g'μμ') I(τ,μ') dμ'. (25) 

Now, making the transformation of variables, τ′ = (1-π°

f) τ, and ω' = π° (1-f) /(1- π°f ), eq 25 

becomes 

μ dI(τ',μ')/dτ' + I(τ',μ') = 1⁄2 ω' ∫-1

+1

(1+3g'μμ') I(τ',μ') dμ'. (26) 

9 
Eq 26 is now in a form where we can apply the Eddington method. It should be noted that, while 

eq 26 has no specific reference to the azimuthal angle φ, the code employs an extension of the 

Eddington methodology to handle an azimuthally dependent radiance field. (19) 

4. Solutions for IR Wavelengths 

4.1 Theoretical Formulation: IR Contrast

At IR wavelengths, scattering effects may be ignored in most cases and the equation of transfer 

takes the form

μdI(τ,μ,φ)/dτ = -I(τ,μ,φ) + (κa/κ) B(λ,t), (27) 

where the total extinction coefficient (κ) is comprised of an absorption (κa) and scattering (κs) 

coefficient (i.e., κ = κa + κs), and we have made use of the fact that π° = κs/κ. It should be noted 

that each of the extinction coefficients may be broken into separate coefficients for aerosol and 

molecular components (i.e., κ = κA + κM); analogous expressions exist for κa and κs. The

blackbody function (the Planck emission function) is given by 





 





− = 1

2 1 ( , ) 5 /

2

hc kt e

hc B t λ λπ λ , (28)

where h is Planck’s constant, k is Boltzmann’s constant, and c is the speed of light in vacuum. 

Assuming a homogeneous atmosphere, we can integrate eq 27 

 I(τ) = I(0) e-τ/μ

 + (κa/κ) B (1 - e-τ/μ). (29) 

In practice, because the atmosphere is not homogeneous, we use the numerical form

, (30) i

N

i

i

i

I τ B e τ

τ μ

= ∆

−

=

∑

/

1

( )

where Bi is the blackbody function for path segment; i, e

-τ

i 

/μ is the total path transmission between 

segment i and the observer; and ∆τi is the optical depth of path segment i. 

Numerical computation of apparent thermal path radiance for a given Cartesian location and LOS 

look direction is implemented by Romberg integration over two possible paths: 

1. A path that starts at the observer/sensor position and terminates at the target. This path type 

is used to estimate the path radiance originating between the observer and target. 

2. An upward-looking LOS path that starts at the target and terminates at the top of the 

atmosphere (TOA) or cloud base, or a downward-looking LOS path that starts at the target 

and terminates at the ground plane or cloud top. This upward or downward path is used to 

estimate the background radiance observed at the target position. 

10 
When an integration range step is reached where the optical depth of the atmospheric medium

exceeds a preset limit (before the geometric terminus is reached) for either of these path types, the 

integration is terminated at this intermediate position. 

The integrand used in the Romberg integration is the right-hand side of eq 30, also termed the “path 

function,” specified at a discrete set of range points. The vertical profiles of extinction coefficient 

and air temperature are fitted with cubic splines to allow specification of extinction coefficient, 

optical depth, and air temperature at arbitrary ranges from the observer position. 

During the range-stepped calculation of the path function integrand, if the value of the integrand at 

a given range point falls below a very small specified fraction of the integrand value at the start 

point of the path, the terminus of the path is reset to that range value and the discrete set of 

integrand points is recalculated. This truncation procedure ensures that the Romberg integration is 

performed only over the optically significant portion of the LOS path. A cubic spline fit is 

performed over the discrete integrand set, and is used to specify the value of the integrand at 

arbitrary range points in the Romberg integration routine. 

4.2 Cloud/Geometrical Considerations 

Natural water clouds are sufficiently dense at IR wavelengths that embedding sensors or targets 

within a few tens of meters within the cloud layer yields optical depths large enough to reduce the 

target signature below detectability. For this reason, only a single cloud layer is modeled by the IR 

radiance algorithm, and then only as a background for the target. Note that the geometry of the 

LOS is adjusted if it intersects this layer. The criteria used to adjust the LOS are illustrated 

schematically in four scenarios (a)–(d) in figure 3. Notionally, the sensor and target are located at 

the tail and head of the LOS arrows displayed in the diagram, respectively. The left arrow of each 

pair of arrows is the “before adjustment” arrow. The right arrow shows how the LOS appears after 

adjustment in each instance. 

 

 C l o u d T o p

 C l o u d B a s e

 ( a ) ( b ) ( c ) ( d )

 G r o u n d P l a n e

Figure 3. Diagram illustrating the criteria used to adjust the LOS when it intersects a cloud layer. 

If only the observer/sensor lies within the cloud layer, the observer is relocated to a position just

above the cloud layer for an upward-looking LOS—scenario (a) in figure 3. The original zenith 

angle of the LOS is preserved and the length of the LOS path is held constant (i.e., the target 

position is also moved upward by the same amount as the sensor), if possible. If the target height 

exceeds the nominal maximum of 5.0 km above ground level (AGL), the target altitude is set to 

this maximum and the LOS length is shortened to maintain the user-specified zenith angle. The 

downward-looking LOS of scenario (b) follows a similar adjustment procedure, with the 

11 
observer/sensor position being reset to be just below the cloud and the target height being adjusted 

to keep it AGL, if necessary. 

If only the target is embedded within the cloud layer, as in scenarios (c) and (d), the LOS is 

adjusted to keep the observer position and LOS zenith angle fixed, with the target height revised so 

that the cloud base or top is a background behind the target. 

If both the observer/sensor and target are embedded within the cloud layer and the LOS is 

horizontal, or upward-looking, the reset procedure of scenario (a) is used (i.e., the entire LOS path 

is translated so that the observer is just above the cloud top). Fully embedded downward-looking 

LOS paths follow the scenario (b) adjustment procedure (i.e., the LOS is translated so that the 

observer is just below the cloud base). 

5. Validation and Verification 

5.1 Visible Wavelengths 

A number of runs were made at visible wavelengths for V&V purposes. As detailed below, the 

algorithms used in the IR band were compared with MODTRAN (20) 3.5 (from this point forward 

we will drop the MODTRAN version number). 

In the visible band, comparisons were made using another delta-Eddington SGR code (21), referred

to in table 1 as “∆E.” The quantity examined for verification purposes was the path radiance, Ip. 

To reduce the number of variables some input quantities were held constant—the solar zenith and 

azimuth were fixed at 60o and 180o, respectively; the LOS azimuth was held fixed at 0o; the aerosol 

type was rural; the observer height was fixed at 10 m; and clouds were not included. The results 

are presented in table 1. Considering the low values of the path radiance, the agreement is good. 

12 
Table 1. Comparison of SGR results at visible wavelengths. 

Visibility 

(km) LOS Zenith Ip(SGR) 

Ip

(∆E) 

Percentage of 

Difference

Target Altitude

(km) 

Target Distance

(km) 

5 88.282 0.1258 0.1384 -9.1 0.31 10.004

5 88.854 0.1518 0.1377 10.2 0.21 10.004

5 89.427 0.1323 0.137 -3.4 0.11 10.004

2 88.282 0.1543 0.1432 7.8 0.31 10.004

2 88.854 0.1564 0.1422 10.0 0.21 10.004

2 89.427 0.1631 0.1413 15.4 0.11 10.004

5 89.141 0.1507 0.1374 9.7 0.31 20.002

5 45.0 0.1078 0.1066 1.1 1.01 1.4142

5 45.0 0.0703 0.0751 -6.4 0.51 0.7071

2 45.0 0.2181 0.1885 15.7 1.01 1.4142

2 45.0 0.167 0.1581 5.6 0.51 0.7071

1 45.0 0.226 0.216 4.6 0.51 0.7071

The code was also compared with the homogeneous atmosphere case presented in Lenoble (22), 

specifically Deirmendjian’s (23) Haze L at a wavelength of 0.7 μm, with the sun directly overhead 

at optical depths of 0.1 and 1.0. The results, presented in figure 4, agree well with those found in 

Lenoble. 

0 40 80 120 160 200

0.01

0.1

1

10

Haze L

Lenoble τ = 0.1

FASCAT τ = 0.1

Lenoble τ = 1.0

FASCAT τ = 1.0

Radiance (w 

m2 sr-1)

Zenith Angle (degrees)

Solar Zenith Angle = 00

λ = 0.70 μm

Figure 4. Comparison of results with Lenoble. 

5.2 IR Wavelengths 

The path and background radiances computed by the SGR model in the mid-IR (3.0–5.0 μm) and 

far-IR (8.0–12.0 μm) bands are assumed to be purely thermal, with no contributions from the 

13 
scattering of incident solar/lunar irradiances or the multiple scattering of thermal emission. The 

assumption of negligible solar scattering is of questionable validity for mid-IR band wavelengths 

shorter than about 4.2 μm under strong daytime illumination. (24) Large aerosol particles (such as 

rain or snow) might also violate the non-scattering assumption. Otherwise, this assumption appears 

to be reasonable (i.e., for wavelengths above 4.2 μm, or under subdued twilight or night lighting 

conditions). With these limitations in mind, the IR radiance (IRRAD) routine in the SGR model 

was compared with the MODTRAN atmospheric transmission/radiance model. We attempted to 

maintain equivalent environmental conditions between inputs for the two models, but exact 

equality could not be achieved (particularly with the cloud layer models). 

The environmental scenario used in this comparison is one in which a sensor situated at 1 km AGL 

looks upward with a zenith angle of 80o. The target is located at a range of 10 km from the sensor 

along this LOS, which puts it at an altitude of 1.0 + 10cos(80°) = 2.74 km AGL. A 1-km thick 

altocumulus/altostratus cloud layer is placed so that the cloud base is at an altitude of 2.4 km AGL 

(the cloud base height used here is the MODTRAN default for the selected cloud type). The target 

is thus above the cloud base (a geometry similar to that depicted in fig. 3, scenario (c)), so the 

target altitude is reset to be 2.4 km AGL and the target range becomes 8.06 km. Figure 5 

represents this scenario. 

10.0 km 1

2

0

3

4

Cloud Layer

Revised Target

Original Target

Hei

ght (km AGL)

80°

8.06 km 10.0 km 1

2

0

3

4

Cloud Layer

Revised Target

Original Target

Hei

ght (km AGL)

80°

8.06 km

 Figure 5. Scenario used for IR wavelengths showing target relocation. 

14 
Other characteristics of the comparison scenario are presented in table 2. 

Table 2. Partial input parameters for IR validation runs. 

Surface visibility 5 km

Haze layer aerosol type 3 (Rural) 

Atmospheric model 6 (1976 U.S. Standard atmosphere) 

Surface relative humidity 50 percent 

Surface wind speed 0 m/s

Surface albedo 0.2 

Surface (ground) temperature 288.2 K 

Scenario results were generated for the 3.0–5.0 μm and 8.0–12.0 μm wavelength bands at the full 

MODTRAN wave-number resolution (1 cm-1). Figure 6 compares the spectral radiances for the 

path between the observer and target and for the total (path plus cloud background) spectral 

radiance at the observer position in the 3.0–5.0 μm band.

Figure 6. Comparison of MODTRAN and IRRAD spectral radiances in the mid-IR band.

0.001

0.01

0.1

1.0

10.0

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5

Wavelength (μm)

Radiance (W/m2/sr/μm)

MODTRAN Path

IRRAD Total

IRRAD Path

MODTRAN Total

15 
The two models agree quite well for the path radiance results and reasonably well for the total 

radiance results. A similar comparison is made for the 8.0–12.0 μm wavelength band in Figure 7. 

0.1

1.0

10.0

8 8.5 9 9.5 10 10.5 11 11.5 12

Wavelength (μm)

Radiance (

W/m2/sr/μm)

MODTRAN Path

IRRAD Total

IRRAD Path

MODTRAN Total

Figure 7. Far-IR spectral radiance comparison between MODTRAN and IRRAD models. 

The far-IR results also show good agreement between the two models. The total radiances show 

better agreement in this longer band than in the mid-IR band, due in large part to the cloud layer’s 

closer approach to blackbody behavior. 

6. Usage 

The program is set up to run in batch mode by piping previously scripted data from a user-supplied 

file. Using the batch mode minimizes errors and makes rerunning the model easier. If the user 

desires to have the code run in interactive mode, a slight modification to the program is necessary. 

Specifically, in the block data subroutine, the DATA statement for INTERACTIVE must be 

changed from 0 to 1; once this is done, the code will run interactively. Note that in most cases

reasonable domains of validity are checked as input data are received and default values are 

supplied if the input datum is out of the domain range. A simple, clear-atmosphere, “canned” test 

case is provided to verify operation of the model on a new installation. 

The program sends its results to the standard output (unit 6) in spectral form as a table and also in 

band-averaged or integrated form. At visible wavelengths, auxiliary output optionally goes to a log 

file named fasclog.out, if the parameter, iprint, located in block data, is set equal to one. If 

16 
iprint = 0 (default), fasclog.out is not created nor is output written to it. If the user has requested a 

run that iterates on a particular parameter, the iterated band-averaged and integrated results are 

written to a file named nvarfile.out. 

To obtain solar/lunar geometrical information, the code makes use of the U.S. Naval Observatory’s 

Solar-Lunar Almanac Core (SLAC), a code written in C. (25) SLAC is a set of integrated software

modules that provides information concerning the sun and moon, which is useful for operations 

planning, mission scheduling, and other practical applications. Since implementation of crosslanguage routines is compiler specific, the user must properly interface SLAC with this program. 

To do this requires some type of interface between the FORTRAN and C routines, which occurs in

the FORTRAN subroutines getloopvar, getvis, and setvis. The transfer of information between the 

FORTRAN and C code can occur by either reading/writing to a file or calling the C routine directly 

from FORTRAN. In either method, some set of system calls is required. In the first method, a 

system call would have to be made to execute SLAC as a stand-alone code. When implemented as 

a stand-alone code, a driver routine (Slac_optional_driver) must be included and can be found in 

the supplied C directory. In the second method, a system call is made to SLAC as a function; the C 

driver is not required. Comments are embedded in the FORTRAN routines for both methods. As 

supplied, the code has been interfaced on a PC using the Lahey1 FORTRAN 90 and MICROSOFT2

VISUAL C/C++3 compiler mixed-language statements. Also supplied as comments are the 

appropriate interface statements for using the SUN4 FORTRAN 90/C compilers. The SUN and 

SGI compilers are identical and, although untested on the SGI machine, it is expected that the SUN 

statements will work on an SGI machine. Finally, when running on a SUN machine, slac_ill.c and 

slac_ill.h routines need to have an underscore placed at the trailing end of the C routine names. 

Again, appropriate comments are included in both C routines. 

In the following sections, no distinction is made between batch and interactive modes. 

6.1 Inputs Common to Both Visible and IR Bands: Part 1 

The program starts by requesting the wavelength band that the user would like to examine: visible 

(including 1.06μm), mid-IR, or far-IR (see tab. 3). It should be noted that scattering effects in the 

mid-IR band may be examined by choosing the visible band (1); however, only scattering will be

considered. Emissive effects are not included when the visible band is selected. 

Table 3. Choices for wavelength band selection. 

Input Value

Wavelength band selector 

1 = Visible, Near-IR 

2 = Mid-IR 

3 = Far-IR 

Subsequent to this, the program asks if the user wishes to enter an optional ASCII sensor response 

file. This file must reside in the same directory as the executable file, or an appropriate path must 

 1 Lahey is a registered trademark of Lahey Computer Systems, Inc.

2 Microsoft is a registered trademark of Microsoft Corp. in the U.S. and other countries. 

3 Visual C++ is a registered trademark of Microsoft Corp. in the U.S. and other countries.

4 SUN is a trademark or registered trademark of Sun Microsystems, Inc. in the United Stated and other countries. 

17 
be provided; there is a 32-character limit on the input filename. The filename is entered in 

response to the question: “Will a sensor response file be used? y/n?” If the answer to this question 

is “y” (or “Y”), then this response function file is used to determine the wavelength band and to 

weight the following quantities: band-averaged SGR; transmission and contrast transmission; 

band-integrated path; and background radiance calculations. When such a file is present, the 

wavelength limits for calculating the various output quantities are taken from the sensor file, thus 

requiring that sensor response values to run sequentially from the smallest to largest wavelength. 

Once the file is read, the program renormalizes to a value of 1.0, thereby allowing arbitrary units 

for the response function. If the file is not present (answer is “n” or “N”), a default sensor response 

curve, comprised of a “flat” curve normalized to a value of 1.0, is used and the program computes 

the output quantities over the entire wavelength band chosen by the wavelength band selector. For 

the visual band, this is 0.35–0.75 μm, and for the IR band, this is 1.06 μm, 3.0–5.0 μm or 8.0–12.0 

μm (note that, due to the substantial scattering effects, the near-IR laser wavelength of 1.06 μm is

handled in the visual wavelength regime). 

The program then asks for the surface meteorological (Met) visibility. 

At this point the program branches to a specific input sequence, depending upon whether the 

wavelength band chosen was visible or IR. Following this wavelength band-specific input, the 

program requests information relevant to the observer-target geometry and iteration options. In 

concert with the program flow, we present the wavelength specific input followed by the common 

geometrical input. All inputs are concatenated and reiterated in section 6.4 (in tabs. 9 and 10) 

along with units, allowed ranges, and code variable names and locations. 

6.2 Visible Band Model Input 

The original version of this code only covered two wavelengths (0.55 and 1.06 μm) for 6 basic 

aerosol haze layer types. This band was extended to the following wavelength grid: 0.35, 0.40, 

0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, and 1.06 μm (scattering effects in the mid-IR may also be 

examined using the visual band selector. Note that if this is done, emissive effects are not included

and the mid- or far-IR band must be selected to perform such calculations). The ARL PFNDAT92 

(26) and PFNDAT2004 (27) aerosol phase function databases were used to supply all the phase 

function and aerosol attenuation parameters needed by the SGR program. The molecular profile of 

the atmosphere is fixed to be that of the 1976 U.S. Standard Atmosphere (28). The aerosol profile 

consists of a uniformly mixed haze layer of user-specified vertical depth, surface Met visibility, 

relative humidity, and aerosol type, surmounted by a high visibility tropospheric layer. The 

visibility within the boundary layer is set by the user input value and subsequently scaled 

exponentially from the top of the boundary layer to the model TOA, which has been set at 10.0 km. 

The vertical scaling of visibility above the boundary layer starts at the default value of 50 km, 

unless the user has input a visibility greater than 50 km in the surface haze layer, in which case that

value is used as the starting point. 

In the visible band, the program allows for selection of one of nineteen different aerosol types 

(tab. 4) for the haze layer, followed by separate requests for the thickness of the haze layer and the 

relative humidity of the selected aerosol. 

18 
Table 4. Choices for aerosol type at visible wavelengths and their relative humidities (percent) 

where applicable. 

Input Value

Aerosol Type Relative Humidity (%) Aerosol Type Selector 

Maritime 0 50 70 80 90 95 98 99 1 

Urban 0 50 70 80 90 95 98 99 2 

Rural 0 50 70 80 90 95 98 99 3 

Fog (heavy advection) 100 4 

Fog (moderate radiation) 100 5 

Rain (drizzle) 100 6 

Rain (widespread) 100 7 

Rain (thunderstorm 100 8 

Snow NA 9

Fog (moderate advection) 100 10 

Fog (heavy radiation) 100 11 

Desert aerosol† NA 12

Tropospheric 0 50 70 80 90 95 98 99 13 

Dust(light loading) NA 14 

Dust(heavy loading) NA 15 

High Explosive Dust NA 16 

WP smoke 17 50 90 17 

Fog Oil 50 18 

HC smoke 85 19 

#

 The model selection is determined in conjunction with the separate relative humidity input value. 

† Requires a wind speed of 0, 10, 20, or 30 m/s. 

The code also allows the user the option of including clouds ranging from partly cloudy to totally 

overcast, in increments of tenths. Since the methodology for determining the probability of cloudfree line-of-sight (CFLOS) and its implementation may be found elsewhere (13, 29) and because 

the addition of such effects does not change the basic methodology used in the code, they are not 

explained here. In addition to the clear-atmosphere configuration, the user may specify up to two 

cloud layers in the visible. It should be noted that the two-cloud layer option employs numerous 

assumptions (13) and is included as a means to obtain rough estimates of the multi-layer cloud 

effects on SGR. Due to limitations in the SGR program’s atmospheric layering model, neither the 

observer nor the target should be situated within a cloud layer. Another practical constraint is that 

the LOS should not be interrupted by a cloud layer; otherwise, the transmission is so low that the 

target is invisible to the observer. This program enforces these constraints by shortening or shifting 

the LOS (while maintaining the LOS zenith angle) so that the LOS is in one of the clear 

19 
atmospheric zones: between the TOA and the top of the uppermost cloud layer, between cloud 

layers, or between the lowest cloud base and the ground. Thus, in this program cloud layers appear 

only as backgrounds (c.f., previous discussion in section 4.2). 

Because the SGR program requires that the (up to two) user-input cloud layers do not overlap, 

several conditions must be observed to ensure consistent specification of the cloud layers. First, 

while the program currently only allows two cloud layers, there are three cloud height domains in 

common Met usage: high-level clouds (cirrus/cirrostratus), mid-level clouds (altostratus/ 

altocumulus), and low-level clouds (cumulus, stratus/stratocumulus, or nimbostratus). The SGR 

program’s non-overlap condition requires that only one cloud type selection from each cloud height 

domain is used for any given visible-band run. Thus, altostratus/altocumulus and nimbostratus 

may be combined in a single run, but cumulus (low-level) and nimbostratus (also low-level) are not 

a valid combination. In the event that the first cloud layer specified is a high-level type and the 

second is also from the high-level domain, the program resets the second cloud layer type to be a 

mid-level (altostratus/altocumulus) type. The same default is used when two low-level cloud layers 

are specified. When two mid-level cloud layers are specified, the second layer is reset to be a highlevel (cirrus/cirrostratus) type. Another impact of the non-overlap requirement is that the cloud top 

height for the nimbostratus low-level layer is set at 3.00 km AGL, while the base of the adjacent 

altostratus/altocumulus (mid-level) layer is set to 3.01 km AGL (see tab. 5). Since the user does 

not input explicit values for cloud top or base heights in the present version of the code, this 

peculiarity of the layering setup may have significance for future, though not current, 

implementations of the SGR model. 

The program first requests the number of cloud layers, with zero indicating none; in the visible 

band, up to two cloud layers may be entered. The cloud type and cloud optical depth, both on the 

same input line, are then requested. Next, the fractional sky coverage is requested. The user 

should carefully note that in methodology employed in the visual portion of this code, the cloud 

geometrical thickness, the cloud optical depth, and the cloud fractional amount are all independent 

quantities. The cloud optical depth is entered as average (1), thick (2), or thin (3), with the thick 

and thin optical depths being one standard deviation from the average. If the user is not sure of the 

optical depth, this parameter may be set to zero and will default to “average.” The cloud type 

parameter follows the cloud type numbering system in table 5. Also presented in table 5 are the 

altitudes of the cloud tops and cloud bases for the various cloud types. Note that for the 

altostratus/altocumulus (type 2) and nimbostratus (type 5) cloud types, there is a slight difference in 

cloud top heights between the visible and IR bands. Because of the characteristics of the 

polynomial fit function for extinction coefficients, which was derived from the U.S. Army

EOSAEL Cloud Transmission (CLTRAN) (30) model, the IR cloud top heights are non-integer 

(i.e., floating point) values. The CLTRAN fit function uses the height above the cloud base (z) as 

the independent variable and starts from a positive value at z = 0. The function increases with z to 

a maximum within the cloud and then decreases until the cloud top is reached. 

20 
Table 5. Cloud types available in the program and their tops and bases. 

Cloud Top/Base 

Input Cloud Type (km) 

Visual IR

1 Cirrus/cirrostratus 9.0/8.0

2 Altostratus/altocumulus 5.0/3.01 4.95/3.01

3 Cumulus 2.0/1.0

4 Stratus/stratocumulus 2.0/1.0

5 Nimbostratus 3.0/1.0 2.98/1.0

The cloud cover (fractional sky coverage), in tenths, is entered next. 

External illumination sources used in this model are limited to the sun and moon. There currently 

is no diffuse twilight model, so users should avoid situations where neither the sun nor the moon is 

above the horizon. If such a condition is specified on the initial iteration of the model, the model 

aborts with an error message. If the program is operated in the loop mode (see sections 6.4 and 

6.5) and the “no sun or moon” condition occurs on the second or later iteration, a warning message 

is printed and the offending iteration cycle is skipped. Another illumination condition that should 

be avoided occurs when strong morning or evening twilight is present for a lunar illumination 

source. The program will not abort in this instance, but a warning message is output that cautions 

the user that the moon is competing with civil, nautical, or astronomical twilight. Two other 

illumination error conditions require some description. If the primary illumination source (sun or

moon) is within 3o of the horizon, the delta-Eddington algorithm becomes inaccurate and/or 

unstable. Appropriate checks and warning messages have been implemented to exit gracefully 

from this condition. Another glitch occurs if the primary illumination source is the moon, and the 

lunar phase is close to new moon (i.e., the sun-observer-moon angle is less than 20o). Again, the 

appropriate checks and warnings have been implemented to avoid a software crash under such 

conditions. 

The user may specify the solar/lunar position in the sky directly or implicitly. Under the direct 

method (illumination source selector = 2 or 3), the user specifies the solar/lunar zenith and azimuth 

angles, and phase (for the moon). The implicit method (illumination source selector = 1), which 

uses the SLAC model, requires the user to input the Greenwich Mean Time (GMT) time and date, 

as well as the observer’s latitude and longitude, from which the solar/lunar zenith and azimuth 

angles, and phase (for the moon), are subsequently determined. Under either approach, the TOA 

irradiance for the specified wavelength and illumination source (sun/moon) is obtained with the 

help of the SOURCE routine from MODTRAN. The illumination source selector, and quantities 

dependent upon that selection, are presented in table 6. 

21 
Table 6. Available illumination sources in the visible. 

Illumination Source Selector Source Required Input Data Records 

observer latitude (degrees N) 

observer longitude (degrees E) 

scenario GMT (HH MM)

1 Sun or Moon 

month day year (MM DD YYYY) 

2 Sun solar zenith angle (degrees) 

solar azimuth (degrees E of N) 

lunar zenith angle (degrees) 

lunar azimuth (degrees E of N) 

3 Moon

“phase” angle between the Sun and Moon as seen from Earth 

(in degrees: 0o = New Moon, 180o = Full Moon) 

After the atmospheric and illumination input, the user must specify the LOS geometry. In all visual 

cases, the user enters the azimuth of the LOS. This input follows the usual Met convention (i.e., an 

azimuth angle of 0o implies an observer looking north and an azimuth angle of 90o implies that the 

observer is looking eastward). LOS geometry, ground, background information, and iteration 

options may be found in sections 6.4 and 6.5. 

6.3 IR Band Model Input 

A second model employed in this code treats the mid-IR and far-IR spectral bands. The dominant 

contributions to path and background radiance in these bands are usually due to greybody thermal 

emission, although aerosol scattering of solar irradiance and thermal emission can be dominant 

effects at low Met visibilities for wavelengths shorter than 4.2 μm. Thus, the IR band model 

implemented here ignores scattering contributions, but does require an atmospheric temperature 

profile, a molecular absorption profile, profiles of aerosol extinction and absorption, background 

temperature, and background emissivity (determined through the albedo). The background 

temperature and albedo are user-supplied directly; the temperature, molecular, and aerosol profiles 

are program-supplied via user input choices, including model atmosphere, lower atmosphere haze 

aerosol type, surface relative humidity (for hygroscopic aerosols), and surface wind speed (for 

desert aerosols). 

Because the current version of the IR model is relatively limited in its description of the 

atmospheric environment, inputs to this model are simpler than for the visible band case. As in the 

visible case, the wavelength band to be covered is taken from the beginning/ending sensor response 

file (if supplied); otherwise the entire wavelength band is used, which in the mid-IR is 3.0–5.0 μm 

with a default wavelength increment of 0.1 μm, and in the far-IR is 8.0–12.0 μm with the same

wavelength increment. As in the visible case, the user also specifies a surface Met visual range but, 

unlike the visible band case, the user does not specify the haze layer depth, illuminating source 

properties, or LOS azimuth angle. The IR model input also shares the following parameters with 

the visible band: cloud type (cloud optical depth is not required for IR runs), surface relative 

humidity, multimode LOS range-altitude inputs (i.e., LOS zenith angle, target range, target altitude, 

observer altitude), background surface albedo, and an optional elevated background range behind 

22 
the target position. The IR model additionally requests a model atmosphere profile, an additional 

surface haze layer aerosol type (desert), a surface wind speed (only required when the desert 

aerosol model is invoked), and a background surface temperature. It does not request the zenith or 

azimuth angle of the background surface since the surface is assumed to be a simple Lambertian 

greybody thermal emitter. The user may also request loop operation for the zenith angle parameter 

(only). 

The vertical temperature and humidity profiles used in the IR portion of the program depend on the 

user’s selection of the model atmosphere from a list of six standard AFGL model atmospheres. 

The air temperature for each model is specified at eight altitudes, ranging from ground level to 

9 km AGL (note that this differs from the visual band case). Each model’s profile for molecular 

absorption was obtained by running MODTRAN over a horizontal path at each model atmospheric 

level under the appropriate model conditions. The horizontal path length was adjusted so that the 

resulting spectral transmissions could accurately be transformed to yield molecular absorption 

coefficients. This was not a trivial task, as the strength of the molecular absorptions varies quite 

markedly over the IR band (it is especially pronounced in the 3.0–5.0 μm band). In practice, short 

and long path runs of MODTRAN had to be made at the denser, lower atmospheric levels in order 

to provide satisfactory profiles. MODTRAN was run at maximum spectral resolution (1 cm-1) for 

this task in both bands (3.0–5.0 μm and 8.0–12.0 μm). It should be noted that even at the 

maximum MODTRAN spectral resolution, some narrow absorption features are not well 

represented in the results (which are stored in the mirdata.inp and firdata.inp data files). However, 

line wing and continuum features that are larger than the wave-number bin spacing are adequately 

represented by the MODTRAN band model. Because the molecular absorption coefficient 

generally varies quite rapidly with wavelength, this quantity is averaged at the beginning of each

model run between the wavelength values that are specified by the user’s sensor response file or by 

the default wavelength spacing. This averaging is performed before any radiative transfer 

calculations are undertaken and is deemed appropriate for broadband sensors encountered in IR 

scenarios. 

Aerosol extinction and absorption coefficients for the surface haze layer are defined using the same 

PFNDAT database and a similar methodology to that described in the visible band section above. 

The aerosol haze layer is assumed to be uniform from 0 to 2 km AGL, with an extinction 

coefficient that is wavelength-scaled to the surface Met visibility (minus the nominal Rayleigh 

molecular scattering coefficient). The aerosol above the haze layer is fixed as the tropospheric type 

(relative humidity of 50 percent), consistent with a horizontal surface visibility of 50 km. The 

tropospheric aerosol profile is adjusted to be consistent with either of two aerosol density profiles 

(from MODTRAN) that are specific to the model atmosphere chosen by the user. This limitation is

not regarded as especially significant, as the aerosol contribution to the total absorption coefficient 

is not dominant. 

A natural cloud IR emission model was also developed and is included in the current version of this 

software. This model is preliminary, in the sense that some parameters necessary for the thermal 

radiance calculations are only roughly estimated. Various models and data sources were combined 

to create the cloud emission model. Vertical profiles of extinction in the two IR bands were 

obtained from the CLTRAN model (c.f. discussion on cloud layers in the section 6.2 “Visible Band 

Model Input”). Single scattering albedo estimates were obtained from Shettle and Fenn (31). 

23 
Cirrus cloud single scattering albedos were estimated from Web-published data from the MODIS 

(32) experiment. 

The CLTRAN cloud type designations were converted to be similar to those used as inputs for the 

visible band model discussed above (the ICLTYPEn parameter values have the same meaning here 

as in the visible band case). It is important to remember, however, that the basic cloud property 

models derive from different sources, so that comparison of visible and IR results must be 

approached with caution. 

Unlike the visible band case, the IR bands only permit the presence of a single cloud layer and do 

not require a user input optical depth. Due to the large optical thickness of these clouds in the IR, 

radiance results from different cloud types are very similar (with all other parameters held 

constant). Selection of different cloud types is allowed; however, the altitude of cloud bases and 

tops vary from type to type. The cloud parameters used in the program are presented in table 5. 

Because of the vertical variation of ambient atmospheric temperature, the resulting thermal 

radiances will vary as well. The cirrus cloud type is arbitrarily assumed to have a layer optical 

depth of unity in both IR bands. This intermediate optical depth will cause significant variation of

thermal radiance with LOS zenith angle, unlike other cloud types. In addition, because of the 

location of the cirrus layer in the colder upper atmosphere (and its relative optical thinness), the 

thermal radiance results for these clouds will be lower than for the other cloud types. 

Thus, the only input specific to IR wavelengths is the absence/presence of clouds and, if present, 

the type of cloud. The temperature of the ground surface is also required. It should be noted that 

the presence of a cloud layer will modify the water vapor profile (of the cloud-free atmosphere) in 

the vicinity of the layer. This will cause some inaccuracy for estimates of path transmission and 

radiance in the IR, especially in strongly-absorbing regions of the IR bands. However, the primary 

focus of this model is for sensors or targets that are situated substantially lower than 1 km AGL. 

With that proviso, the atmospheric regions that are adjacent to cloud layers appear only as 

backgrounds, and their radiance/transmission signatures are dominated by those of any extant cloud 

layers. 

6.4 Inputs Common to both Visible and IR Bands: Part 2 

The user specifies the LOS geometry for a given model run using one of three methods. The 

determination of four additional required parameters—LOS zenith angle (measured positive from

the zenith downward), target range from observer, observer altitude, and target altitude—is handled 

by selecting one of the three modes, shown in table 7. Given any three of the LOS parameters, the 

fourth can be calculated. Thus, the program first asks for which LOS mode the user wishes to 

employ and then asks for the appropriate parameters necessary to calculate the fourth parameter. 

The modes, required input, and calculated value (“action”) are shown in table 7. 

24 
Table 7. Required data input for LOS mode chosen. 

LOS Mode Required Data Input Records Action

LOS zenith angle (degrees) 

target range (km) 1 

observer altitude (km) 

Target altitude is calculated 

Target altitude (km) 

2 target range (km) 

observer altitude (km) 

LOS zenith angle is calculated 

LOS zenith angle (degrees) 

3 target altitude (km)

observer altitude (km) 

Target range is calculated

If cloud layers have been previously stipulated, the LOS geometry is modified if it conflicts with 

the CFLOS constraint mentioned above. The details of the checking/modification process are 

given in the comments embedded in the getcom routine. 

The user then specifies the albedo of the ground surface, assumed to be Lambertian and uniform in

extent. In addition, if an IR scenario has been chosen, the ground temperature is requested. 

An option has been added to allow the user to specify an elevated solid background behind the 

target for an upward-looking, downward-looking, or horizontal LOS—e.g., when a ground-based 

observer views a low-flying helicopter in front of a hillside, or a ground vehicle is being observed 

against a hillside, tree line, etc. If this option is chosen, then the user must specify the zenith and 

azimuth angles of the background normal as well as the distance from the background to the target 

in the direction of the LOS. This option is invoked by answering “y” or “Y” to the question: “Is 

the background behind the target a hillside, tree line, etc.?” If the answer is “yes,” then the user 

must specify the orientation of (zenith and azimuth angle of background normal) and distance to 

(from the target along the LOS) this background. 

Finally, the user may choose to iterate the given scenario over one of several critical parameters. 

The user selects an “iteration mode” to decide which parameter to iterate over. When this option is 

selected, the program expects beginning values, ending values, and the number of increments 

between these values (see tab. 8). Note that for the IR scenarios, only iteration modes one and two 

are applicable, since the azimuth and time are irrelevant parameters (see section 6.3.). 

25 
Table 8. Iteration modes.

Iteration Mode Iterated Variable 

1 No iteration (fixed time or solar/lunar position and fixed LOS configuration) 

2 LOS zenith angle (fixed time or solar/lunar position and fixed LOS azimuth) 

3* LOS azimuth angle (fixed time or solar/lunar position and fixed LOS zenith) 

4* Time (fixed LOS configuration)

5* Solar/lunar azimuth angle (fixed LOS configuration) 

6* Solar/lunar zenith angle (fixed LOS configuration) 

 * Visible wavelengths only

6.5 Input Summary 

Whether an interactive or batch run is used, tables 9 and 10 present a summary of the required and

optional input quantities for visible and IR run streams, respectively. Also presented in these tables 

are the code variable name, location (i.e., subroutine), and units. In tables 9 and 10, if a selector or 

mode parameter can assume one of a contiguous enumerated list of values (in column 2), the 

variable/location (in column 3) is specified for only the first parameter choice (i.e., “ditto” marks 

are omitted). 

26 
Table 9. Required input quantities for visible runs. 

Input Value(s) & Units Variable/Location 

Wavelength band selector 

Visible (0.35 – 0.75, 1.06) 1 iband/sgrdriver 

Sensor response file supplied? “y” or “n” (upper case ok) waveans/sgrdriver 

Sensor response filename$ 32 character filename (including

extension). Contains up to 100 

wavelength (μm) and sensor response 

(arbitrary units) pairs; 1 pair per input line 

wavelengths(i) and 

wgtv(i)/sgrdriver 

Surface visibility 1.0 – 300.0 km vext/sgrdriver 

Aerosol type selector 

Maritime 1 iaerosol/getvis

Urban 2

Rural 3

Fog (heavy advection) 4 

Fog (moderate radiation) 5 

Rain (drizzle) 6 

Rain (widespread) 7 

Rain (thunderstorm 8 

Snow 9

Fog (moderate advection) 10 

Fog (heavy radiation) 11 

Desert aerosol† 12

Tropospheric 13

Dust(light loading) 14 

Dust(heavy loading) 15 

High Explosive Dust 16 

WP smoke 17 

Fog Oil 18 

HC smoke 19 

Haze layer thickness 0 – 2.5 km zhaze/getvis

Relative humidity 0.0 – 99.0% rhumid/getvis 

Number of cloud layers 0, 1 or 2 ncloud/getvis 

27 
Table 9. Required input quantities for visible runs (continued). 

Input Value(s) & Units Variable/Location 

Cloud type and (optical depth)* 

Cirrus/cirrostratus (average, thin, thick) 

Altostratus/altocumulus (average, thin, thick) 

Cumulus (average, thin, thick) 

Stratus/stratocumulus (average, thin, thick) 

Nimbostratus (average, thin, thick) 

1 (1,2,3) 

2 (1,2,3) 

3 (1,2,3) 

4 (1,2,3) 

5 (1,2,3) 

icltype/getvis 

Cloud cover* 0.0 – 1.0 (in tenths) icltenths/getvis 

Illumination source selector 

Solar/Lunar (implicit specification)

Observer Latitude

Observer Longitude 

Observer Time 

Observer Date 

1 

0.0 ± 90.0° (N+, S-) 

0.0 ± 180.0° (E+, W-) 

GMT 0 – 2359 (HHMM) 

GMT (MM DD YYYY) 

isrcmode/getvis 

glati/getvis 

glong/getvis 

igmt/getvis 

imonth iday iyear/getvis 

Solar

Solar Zenith angle 

Solar Azimuth angle 

2 

0.0 – 90.0°

0.0 – 360.0° East of North 

isrcmode/getvis 

szen/getvis

sazi/getvis

Lunar

Lunar Zenith angle 

Lunar Azimuth angle 

Phase angle (between sun and moon as seen from earth; 

0.0o = New Moon, 180.0o = Full Moon) 

3 

0.0 – 90.0°

0.0 – 360.0° East of North 

20.1‡

 – 180.0o

isrcmode/getvis 

szen/getvis

sazi/getvis

smangle/getvis 

LOS azimuth 0.0 – 360.0o, East of North philos/getvis 

LOS specification mode 

Target height is calculated

LOS zenith angle 

Target range 

Observer height 

1 

0.0 – 180.0o

0.01 – 200.0 km 

0.0001 – 5.0 km 

losmode/getcom

thetalos/getcom

targrange/getcom

zobs/getcom

LOS zenith angle is calculated

Target height 

Target range 

Observer height 

2 

0.0001 – 5.0 km 

0.01 – 200.0 km 

0.0001 – 5.0 km 

losmode/getcom

ztarg/getcom 

targrange/getcom

zobs/getcom

Target range is calculated

LOS zenith angle 

Target height 

Observer height 

3 

0.0 – 180.0o

0.0001 – 5.0 km 

0.0001 – 5.0 km 

losmode/getcom

thetalos/getcom

ztarg/getcom 

zobs/getcom

Ground surface albedo 0.0 – 1.0 salbedo/getcom 

Is the background behind the target a hillside, tree line, etc.? “y” or “n” (upper case ok) ans/getcom

28 
Table 9. Required input quantities for visible runs (continued). 

Input Value(s) & Units Variable/Location 

Background surface normal information** 

Zenith angle 

Azimuth angle 

Range along LOS to background

0.0 – 180.0o

0.0 – 360.0o

0.01 – 300.0 km 

surtheta/getcom

surphi/getcom

surrange/getcom 

Iteration mode 

None (single iteration mode) 1 irunmode/getrunmode 

LOS zenith angle mode

Minimum zenith angle 

Maximum zenith angle 

Number of grid points 

2 

0o

180o

unlimited 

irunmode/getrunmode 

thetamin/getrumode 

thetamax/getrunmode 

ncycles/getrunmode 

LOS azimuth angle mode

Minimum azimuth angle 

Maximum azimuth angle 

Number of grid points

3 

0o

360o

unlimited 

irunmode/getrunmode 

phimin/getrunmode 

phimax/getrunmode 

ncycles/getrunmode 

GMT Time mode

Minimum time

Maximum time

Number of grid points

4 

0000 – 2359 (HHMM) 

Minimum time + 1 minute to Minimum 

time + 24 H – 1 minute (HHMM) 

2 ≤ ncycles ≤ 1440 

(integer minutes)

irunmode/getrunmode 

igmtmin/getrunmode 

igmtmax/getrunmode 

ncycles/getrunmode 

Solar/lunar azimuth angle mode

Minimum solar azimuth angle

Maximum solar azimuth angle

Number of grid points

5 

0o

360o

unlimited 

irunmode/getrunmode 

sazimin/getrunmode 

sazimax/getrunmode 

ncycles/getrunmode 

Solar/lunar zenith angle mode

Minimum solar zenith angle 

Maximum solar zenith angle 

Number of grid points

6 

0o

90o 

unlimited 

irunmode/getrunmode 

szenmin/getrunmode 

szenmax/getrunmode 

ncycles/getrunmode 

$ Only required with user-supplied sensor response file (“y”).

* When number of clouds > 0, optical depth will default to “average” if set to 0. 

† Requires a wind speed of 0, 10, 20, or 30 m/s. 

‡ Code limitation 

** Only required when the background behind the target is some distance from the target (“y”). 

29 
Table 10. Required input quantities for IR runs. 

Input Value(s) Variable/Location

Wavelength band selector 

Mid-IR (3.0 – 5.0) 

Far-IR (8.0 – 12.0) 

2 

3 

iband/sgrdriver 

Sensor response file supplied? “y” or “n” (upper case ok) waveans/sgrdriver 

Sensor response file name$ 32 character file name (including

extension). Contains up to 100 wavelength 

(μm) and sensor response (arbitrary units) 

pairs per input line 

wvlv(i) & wgtv(i)/sgrdriver 

Surface visibility 1.0 – 300.0 km vext/sgrdriver 

Cloud condition

Clear (no clouds) 

Cirrus/cirrostratus 

Altostratus/altocumulus 

Cumulus 

Stratus/stratocumulus 

Nimbostratus 

0 

1 

2 

3 

4 

5 

icltype1/getir 

Model Atmosphere 

Tropical 

Midlatitude Summer (45N, July) 

Midlatitude Winter (45N, Jan.) 

Subarctic Summer (60N, July) 

Subarctic Winter (60N, Jan.) 

1976 US Standard Atmosphere 

1 

2 

3 

4 

5 

6 

model/getir 

30 
Table 10. Required input quantities for IR runs (continued). 

Input Value(s) Variable/Location

Haze Aerosol Type 

Maritime 

Urban 

Rural 

Fog (heavy advection) 

Fog (moderate radiation) 

Rain (drizzle) 

Rain (widespread) 

Rain (thunderstorm) 

Snow 

Fog (moderate advection) 

Fog (heavy radiation) 

Desert aerosol†

Tropospheric 

Dust(light loading) 

Dust(heavy loading) 

High Explosive Dust 

WP smoke 

Fog Oil 

HC smoke 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

iaerosol/getir 

Surface Wind Speed† 0 – 30 m/s surfwind/getir 

Surface Relative Humidity 0.0 – 99.0 percent surfrh/getir 

LOS specification mode 

Target height is calculated

LOS zenith angle 

Target range 

Observer height 

1 

0.0 – 180.0o

0.01 – 200.0 km 

0.0001 – 5.0 km 

losmode/getcom

thetalos/getcom

targrange/getcom

zobs/getcom 

LOS zenith angle is calculated

Target height 

Target range 

Observer height 

2 

0.0001 – 5.0 km 

0.01 – 200.0 km 

0.0001 – 5.0 km 

losmode/getcom

ztarg/getcom 

targrange/getcom

zobs/getcom

31 
Table 10. Required input quantities for IR runs (continued). 

Input Value(s) Variable/Location

Target range is calculated

LOS zenith angle 

Target height 

Observer height 

3 

0.0 – 180.0o

0.0001 – 5.0 km 

0.0001 – 5.0 km 

losmode/getcom

thetalos/getcom

ztarg/getcom 

zobs/getcom

Ground surface albedo 0.0 – 1.0 salbedo/getcom 

Ground surface temperature 0.1 – 1000.0 K tgrnd/getcom 

Is the background behind the target a hillside, tree

line, etc.? “y” or “n” (upper case ok) ans/getcom 

Background surface normal information** 

Zenith angle 

Azimuth angle 

Range along LOS to background

0.0 – 180.0o

0.0 – 360.0o

0.01 – 300.0 km 

surtheta/getcom

surphi/getcom

surrange/getcom 

Iteration mode 

None (single iteration mode) 1 irunmode/getrunmode 

LOS zenith angle 

Minimum zenith angle 

Maximum zenith angle 

Number of grid points 

2 

0o

90o 

unlimited 

thetamin/getrumode 

thetamax/getrunmode 

ncycles/getrunmode 

$ Only required with user-supplied sensor response file (“y”).

†

 Only required with desert aerosol model (aerosol type 12). 

**Only required when the background behind the target is some distance from the target (“y”).

32 
7. Output 

The program begins by printing out some informative text concerning the geometry and 

wavelength selected. It then prints out the user-selected input quantities followed by the spectral 

and band-averaged/band-integrated values (listed in table 11) at the actual wavelengths used. The 

numerical procedures used to generate band-averaged and band-integrated results for a spectral 

quantity A are as follows: 

∑

∑

=

= = N

i

i

N

i

i i

w

A w

A

1

1 (band-averaged), (28) 

and 

( ) 2 1

2

1 1

int −

=

− − − + = ∑ i i

N

i

Aiwi Ai wi A λ λ (band-integrated), (29) 

where wi are the sensor response values and Ai are the parameter values specified on the discrete 

wavelength grid λi. The sensor response values are normalized to the maximum sensor response, 

i.e., wi is always less than unity, with a uniform response sensor showing unity response over the 

band. 

Table 11. Output. 

Spectral Parameters 

Sensor response function 

SGR 

Contrast transmission 

Transmission 

Path radiance 

Background radiance 

Band-averaged*/Integrated# Parameters 

SGR* 

Contrast transmission* 

Transmission* 

Path radiance* (W m-2 sr-1 μm-1) 

Background radiance* (W m-2 sr-1 μm-1) 

Path radiance#

 (W m-2 sr-1), 

Background radiance# (W m-2 sr-1) 

33 
When runs are iterated over a specific parameter the output is presented on the screen and the bandaveraged and band-integrated values as a function of the iterated variable are stored in the file 

nvarfile.out. 

8. Ancillary Data Files 

There are a number of ancillary data files that the program uses to read input, provide necessary 

data and to hold output from iterated runs. These files are presented in table 12. The aerosol

information files (supplied), which contain the extinction coefficients, phase functions, etc., must 

be in a subdirectory named pfndat located in the directory from which execution is occurring. 

Table 12. Ancillary file information.

Data Filename Subroutine Opened In Purpose/Contents Read 

Only? 

user-supplied sensor file† sgrdriver Optional file containing sensor response curve Y 

sunbd.inp sunbd Solar irradiances [w cm-2 / cm-1] tabulated at wave numbers from 

0 to 50,000 cm-1 at 5 cm-1 spectral resolution Y 

pfndat (directory) phazef 

Aerosol extinction & absorption coefficients, asymmetry factors

and phase functions for each relative humidity, wavelength and 

angle (where applicable) 

Y 

mirdata.inp data_initialization Wavelength (3.0-5.0 μm), molecular and extinction coefficients

as a function of altitude Y 

firdata.inp data_initialization Wavelength (8.0-12.0 μm), molecular and extinction coefficients

as a function of altitude Y 

fasclog.out* gendeck Output file; provides ancillary information N 

nvarfile.out sgrdriver Iterated run output (see ‘Common Input 2’ above) N 

slac_illum.inp getloopvar, getvis, setvis Optional input file when running SLAC from a command line 

interface in stand-alone mode N 

slac_illum.out getloopvar, getvis, setvis Optional output file for running SLAC from a command line 

interface in stand-alone mode N 

* Visible wavelengths only: requires parameter iprint be set equal to 1 in block data. 

†

 Example files are provided, e.g. visible_input.txt, mid-ir_input.txt, far-ir_input.txt. 

34 
9. Example Runs 

9.1 Visible Band Examples: Scenario Construction 

The following scenario simulates an airborne target moving in a horizontal line at 100.1 meter 

altitude across an inclined LOS under cloudless skies at visible wavelengths. A uniform sensor 

response file was used. The azimuthal view of this scenario is shown in figure 8; the zenith view is 

shown in figure 9. Other relevant parameters are presented in table 13. Note that in the 

nomenclature used here, LOS zenith angles ≥ 0 and < 90o5 imply an upward looking path; LOS 

zenith angles > 90o5

 and ≤ 180o imply a downward looking path. Similarly LOS azimuth 

angles > 0o and < 180o imply the sun (or source) is in front of the observer; LOS azimuth angles > 

180o and < 360o imply the sun is behind the observer. Table 14 presents a sample input script file 

for one of the upward looking runs: column 1 contains the required parameter, column 2 presents 

an identifier for user ease; the program only reads information in the first column. This input file 

has a LOS azimuth of 90o and zenith angle of 70o—note that the program will compute the target’s

distance; all LOS zenith and azimuth angles used for figures 10–13 may be found in table 13. 

Results from this particular run may be found in the appendix for comparison purposes; the input 

file is supplied with the source code as visible_input.txt. 

Figure 8. Top-down (azimuthal) view of scenario.

35 

 5 Codes, such as FASCAT, that use plane-parallel geometry do not admit to a solution for horizontal paths. 
Figure 9. Horizontal (zenith) view of scenario. 

Table 13. Upward and downward looking scenarios for LOS azimuth of 90° and 270°. 

Time/Date/Location Weather

Time

0800 local 

Date 

1 June 2002 

Location 

Latitude 32.5° Longitude 

127′0′′ E 

Aerosol 

Urban at 90-percent relative humidity,

1-km thick 

Solar Zenith Angle 

47.3o

Solar Azimuth Angle 

89.1o

Visibility 

2 km 

Surface Albedo 

0.2 

Upward LOS Downward LOS 

LOS Azimuth 

90o* and 270o

Target height: 100.1 m 

Observer height: .1 m

LOS Azimuth 

90o and 270o

Target height: 0.1 m 

Observer height: 100.1 m 

Zenith Angles (degrees)

0 

10 

20 

30 

40 

50 

60 

70* 

80 

89 

Zenith Angles (degrees)

91 

100 

110 

120 

130 

140 

150 

160 

170 

180 

* Appendix run. 

36 
Table 14. Script file for example scenario. 

1 waveband selector

n sensor response file?

2.0 surface visibility

2 aerosol type

1.0 haze layer depth

90.0 relative humidity

0 # of cloud layers 

1 illumination selector

32.5 latitude

127.00 longitude

0000 Greenwich mean time 

06 01 2002 month day year 

90. los azimuth angle 

3 los mode

70. los zenith angle

.1001 target height

.0001 observer height

0.2 surface albedo

n target silhouetted?

1 iteration mode

9.1.1 Example 1: SGR, Radiance and Transmission as a Function of Observer Look Angle at a Fixed 

Wavelength 

For upward looking runs the SGR, the transmission, path radiance and background radiance for 

LOS azimuth pairs of 0o and 180o, 45o and 225o, and 90o and 270o are presented in figures 10 

through 12. For a downward looking path, results are presented for LOS azimuth pairs of only 90o 

and 270o in figure 13. The upward-looking scenarios simulate a helicopter flying at a constant 

altitude, approaching the observer from the solar direction, flying over the observer’s head, and 

proceeding directly away from (behind) the observer with the sun now at the observer’s back. The 

downward-looking scenario is identical, with the exception that the observer’s and helicopter’s 

positions have been interchanged. For upward-looking scenarios, we first set the azimuth such that 

the observer was oriented towards the sun, and then varied the LOS zenith angle from 0o to 89o. 

We then reoriented the observer by adding 180o to the azimuth, resulting in the sun being behind 

the observer, and once again varied the LOS zenith angle from 0o to 89o. For the downwardlooking scenario, the observer and target positions were interchanged, the LOS azimuth was varied 

by 180o and the LOS zenith angle varied between 91o and 180o. 

We first examine the upward looking scenarios (figures 10–12). In all figures the transmission is 

well behaved, being a maximum at the minimum LOS zenith angle of 0o and a minimum at the 

maximum LOS zenith angle of 90o. The SGR is well behaved, being less than 1, determined 

primarily by the strong background radiance looking upward through a relatively clear atmosphere. 

The double dip in the background radiance in figure 12 that occurs at 22.3o and 72.3o is due to the 

37 
delta approximation cutoff angle (θo) being set to 25o (see subroutine tanit). Thus, for the solar 

zenith angle used in this example (47.3o), the change in the phase function from peaked to 

truncated occurs exactly at those angles. The background radiance in the solar direction has also 

been truncated where it exceeds the scale. Although not so pronounced, the change in the path 

radiance in this figure occurs for the same reason. The plane-parallel technique used also becomes 

increasingly inaccurate with LOS zenith angles within ± 15o of the horizontal direction. These 

effects can easily be seen in the plots of background radiance and in the path radiance. For upward 

looking paths, particularly near the solar direction, it is seen that the forward scattering by aerosol 

particles increases both the path and background radiances, with the background radiance receiving 

most of this scattering due its longer path length. Recalling that the SGR is defined by 

Ip/([ Ib ( 1 – T ) ], we can see that as the transmission approaches 0 (horizontal or very long slant 

paths), the SGR approaches 1. This is verification that, as we go to very long paths, the path 

radiance should approach the background radiance and the SGR should approach 1. Also, note that 

in figure 10 all of the curves are quite symmetrical. This is an expected result since the date 

(1 June) was chosen to be near the solar equinox where the sun’s azimuth angle is very nearly 90o

in the coordinate system being used. Thus, when looking at right angles to the solar direction, i.e., 

looking either north (LOS azimuth 0o) or south (LOS azimuth 180o), we expect to obtain almost 

identical results due to the symmetry with respect to the solar azimuth. Other geometries 

(figs. 11–13) do not have such a symmetrical representation. 

For the downward looking path, figure 13 (note the change in the scale of the ordinate axis), we 

immediately see that the background radiance is, for all practicable purposes, a constant. This is 

expected, since most of the background radiance is determined by the solar radiation being 

reflected by the ground surface, and neither solar angle nor ground albedo are varied in this 

scenario. It is also of interest to note that the SGR, in this downward looking scenario, is greater 

than 1. 

38 
39 

0

0.2

0.4

0.6

0.8

1

Sky-to-ground Ratio/Transmission

0

100

200

300

Radiances (W m2 sr-1 μm-1)

SGR

Transmission

Path Radiance

Background Radiance

Zenith Angle (degrees)

Upward Look

LOS Azimuth = 180o LOS Azimuth = 0o

90 60 30 0 30 60 90

Figure 10. Upward look at right angles to

solar azimuth. 

0

0.2

0.4

0.6

0.8

1

Sky-to-ground Ratio/Transmission

0

100

200

300

Radiances (W m2 sr-1 μm-1)

SGR

Transmission

Path Radiance

Background Radiance

Zenith Angle (degrees)

Upward Look

LOS Azimuth = 270o

 LOS Azimuth = 90o

90 60 30 0 30 60 90

 

0

1

2

3

4

Sky-to-ground Ratio/Transmission

0

100

200

300

Radiances (

W m2 sr-1 μm-1)

SGR

Transmission

Path Radiance

Background Radiance

Downward Look

LOS Azimuth = 270o

 LOS Azimuth = 90o

Zenith Angle (degrees)

90 120 150 180 150 120 90

Figure 12. Upward look directly facing/behind Figure 13. Downward look directly facing/behind

 the sun. the sun.

0

0.2

0.4

0.6

0.8

1

Sky-to-ground Ratio/Transmission

0

100

200

300

Radiances (W m2 sr-1 μm-1

)

SGR

Transmission

Path Radiance

Background Radiance

Zenith Angle (degrees)

Upward Look

LOS Azimuth = 225o LOS Azimuth = 45o

90 60 30 0 30 60 90

 

Figure 11. Upward look offset by 45o to solar

azimuth.
9.1.2 Example 2: SGR and Radiance as a Function of Range at a Fixed Wavelength 

For this example, we have used 

the previous scenario but, instead 

of examining the radiances as a 

function of viewing angle, we 

will look at them as a function of 

target distance, for a fixed 

observer height (0.0001 km), a 

fixed zenith angle (70o), and a 

surface visibility of 23 km. The 

SGR as a function of target range 

and two different visibilities 

along the inclined path is shown 

in figure 14. The figure plainly 

shows the variation of SGR with 

target range.

0 5 10 15 20 25

Range (km)

0

4

8

12

16

20

SG

R

23 km

2 km

Figure 14. SGR as a function of target range at a wavelength of 

 0.55 μm for visibilities of 23 and 2 km. 

Figure 15 shows the various radiative components, i.e. path radiance at range r, Ip(r), background 

radiance at distance r, Ib(r); background radiance at the target distance, Ib(0); and the equilibrium

path radiance, Ips. These components were used to calculate the SGR shown in figure 12. The 

apparent background radiance, Ib(r), for an upward path should be constant with respect to range 

along that path. The values of Ib(r) go from a low of 501 to a high of 513 w/m2

/sr/μm, which is 

within 5 percent of being constant. Ib(0) dwindles with increasing range/altitude since the path 

length for Ib(0) is approaching 0 (we are reaching the top of the atmosphere), coupled with the fact 

that there are fewer particles to scatter at that altitude. Eq 11 suggests that the limiting path 

radiance, Ips=Ip/(1-T) is constant for a given slant path. However, as previously mentioned, one of 

the problems with SGR, which was “developed” for long horizontal paths, is that if we extend this 

concept to slant paths we find that as one goes upward in the atmosphere the number of particulates 

decreases. This violates the concept of an homogeneous atmosphere, which is one of the 

underpinnings in the original development of SGR. So, if eq 11 is correct, why is the path 

radiance, Ip, asymptoting to Ib(r) and not Ips? Recall that Ib(r) is the path radiance over the entire 

path under consideration (from observer to space) and Ip is the path radiance between observer and 

target. Since the visibility is high (23 km), Ip never approaches the equilibrium value of Ips; 

however, as the path length between the observer and target increases, effectively moving the target 

towards space, Ip will approach Ib(r). The problem lies in the high visibility, which leads to 

equilibrium values not being reached. 

40 
0 5 10 15 20 25

Range (km)

0

200

400

600

800

Radiances

(W/

m2/sr/μm)

Ips

Ib(r)

Ip

Ib(0)

 Figure 15. Component radiances vs. range. The visibility is 23 km. 

Also, when using SGR one must remember the assumption that the basic underpinning of SGR is 

“an atmosphere homogeneous in the distribution of particulates and in illumination.” Thus, we

might ask, does the 70o zenith angle slant path violate this assumption? The zenith angle per se 

does not violate the assumption; whereas, both high visibility conditions (implying low aerosol 

content) and the fact that we do not have a homogeneous atmosphere along slant paths do. The 

underlying principle in the code is homogeneous layers. Also, note that Ib(0) decreasing with range 

is simply due to its decreasing path length (target to space), coupled with decreasing aerosol 

content as we go upward in the atmosphere, not because of non-homogeneous illumination at 

differing altitudes. 

Let us contrast the following figure 16, 

which has the same input parameters 

with the exception of visibility being 

changed to 2 km, with that of figure 

15. The background radiance is still 

approaching zero, as expected; 

however, now, with the decreased 

visibility (or increased aerosol content) 

the path radiance Ip is approaching its 

equilibrium value Ips. In addition, 

both of these values—Ip and Ips—are 

now approaching the total path 

radiance Ib(r). 

0 5 10 15 20 25

Range (km)

0

100

200

300

400

500

Radiance

W/

m2/sr/μm

Ips

Ib(r)

Ip

Ib(0)

Figure 16. Component radiances vs. range. The visibility is 

 2 km. 

9.2 IR Band Examples 

9.2.1 Example 1: SGR, Radiance, and Transmission as a Function of Wavelength and Zenith Angle 

The text outputs for two IR band examples are presented in the appendix. The first is a mid-IR run 

using the input file mid-ir_input.txt and the second is a far-IR run using the input file 

far-ir_input.txt. The scenario environment for these examples is essentially the same as for the 

visible band case listed in Table 14. Input for a representative run is presented in Table 15. Note 

that both of these runs require the optional sensor response file. These are provided as 

mir_sensor.dat and fir_sensor.dat for the mid-IR and far-IR runs, respectively. Figures 17 and 18 

show the sky-to-ground ratio results for the mid-IR and far-IR results. The component 

41 
transmissions and radiances for the two bands are shown in figures 19 and 20, for a zenith angle of 

70o. Note that the wavelengths at which calculations were performed for figures 17–20 were 

determined by the wavelength values in the user input sensor response file. 

Table 15. Mid-IR band inputs for the 

SGR model example. 

2 waveband selector

y sensor response file?

mir_sensor.dat input sensor response file 

2.0 surface visibility

0 cloud condition

6 atmospheric model

2 haze aerosol model 

90.0 surface relative humidity

1 los mode

70.0 los zenith angle

0.2924 target range

0.0001 observer height

0.2 surface albedo

273.0 surface temperature (K) 

n target silhouetted?

1 iteration mode

Table 16. Far-IR band inputs for the 

SGR model example. 

3 waveband selector

y sensor response file?

fir_sensor.dat input sensor response file 

2.0 surface visibility

0 cloud condition

6 atmospheric model

2 haze aerosol model 

90.0 surface relative humidity

1 los mode

70.0 los zenith angle

0.2924 target range

0.0001 observer height

0.2 surface albedo

273.0 surface temperature (K) 

n target silhouetted?

1 iteration mode

0

0.5

1

1.5

2

3.4 3.45 3.5 3.55 3.6 3.65 3.7

Wavelength (micrometers)

Sky-to-Ground Ratio

Figure 17. Mid-IR band example results: sky-toground ratio. 

0

0.5

1

1.5

2

10.4 10.45 10.5 10.55 10.6 10.65 10.7

Wavelength (micrometers)

Sky-to-Ground Ratio

Figure 18. Far-IR band example run results: sky-toground ratio. 

Due to the relatively short path and moderate IR visibility, most of the transmission and spectral 

radiance data show only slight variation over both the mid-IR and far-IR wavelength bands. The 

42 
notable exception is the background radiance at the target seen in the mid-IR results plot of 

figure 19. The increasingly strong molecular absorption beyond about 3.5 μm yields a strong 

thermal radiance background. The limiting path radiance also trends upward with wavelength due 

to the decreasing transmission of the LOS path, leading to a sky-to-ground ratio that varies only 

mildly with wavelength.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

3.4 3.45 3.5 3.55 3.6 3.65 3.7

Wavelength (micrometers)

Transmission

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Spectral Radiance (W / m^2 / um / ster)

Contrast Transmission

Path Transmission

Path Radiance

Target Background Radiance

Figure 19. Mid-IR band example run results:

transmission and spectral radiance 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10.4 10.45 10.5 10.55 10.6 10.65 10.7

Wavelength (micrometers)

Transmission

0.00

1.00

2.00

3.00

4.00

5.00

6.00

Spectral Radiance (W / m^2 / um / ster)

Contrast Transmission

Path Transmission

Path Radiance

Target Background Radiance

Figure 20. Far-IR band example run results:

transmission and spectral radiance. 

Figure 21 depicts the SGR run results for the above scenario for an upward-looking path. The 

target height above the near-surface observer is held constant at 0.1 km, so the LOS path length 

increases markedly as the zenith angle approaches horizontal (i.e., 90o). The sky-to-ground ratio 

shown in figure 21 decreases smoothly from its maximum at the zenith to the limiting value of

unity at the horizon. The enhanced limiting path radiance at the longer (10 μm wavelength) causes 

the larger SGR at zenith angles that are well above horizontal. 

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90

Ze nith Angle (deg rees)

Sk y-to -Gro un d R atio

4.0 um

10.0 um

Figure 21. Sky-to-ground ratio for mid-IR and far-IR 

scenarios with fixed observer and target

heights. 

43 
9.2.2 Example 2: SGR and Radiance as Functions of Range at a Fixed Zenith Angle 

As in the visible case, the basic scenario for the IR cases was modified in this second example so 

that the surface visibility was much higher—23 km. The zenith angle was held constant at 70o and 

the observer/sensor position was held at the near-surface position (0.0001 km AGL). The target 

range was adjusted along the fixed LOS direction from 0.1 to 26 km. This latter range value placed 

the target just 0.1 km below the top-of-atmosphere boundary (9.00 km AGL) used in the SGR 

model. The results are shown in Figure 22 for wavelengths of 4 and 10 μm. 

1

10

100

1000

10000

0 5 10 15 20 25 30

Range (km)

SGR

4.0 um

10.0 um

Figure 22. Sky-to-ground ratio for target range 

variation along a fixed zenith angle. 

Figure 22 shows that sky-to-ground ratios for the 10 μm wavelength exceed those for the shorter 

wavelength for slant target ranges out to about 15 km (or a target altitude of about 5 km). At 

longer ranges or higher altitudes, the SGR rises rapidly as the amount of thermally emitting 

atmosphere behind the target and below the nominal top-of-atmosphere (that is the background 

radiance in the denominator of eq 11) begins to diminish. The background radiance at the target 

position for the 4 μm wavelength rolls off faster with increasing range than it does for the 10 μm 

case. Thus, the SGR approaches infinity as the target nears the model’s TOA. For reasons of 

accuracy, it is best to keep the target below the uppermost atmospheric layer (i.e., below 7 km for 

the present code implementation). 

Figures 23 and 24 display how the component radiances behave as functions of target range for the 

4 and 10 μm wavelengths, respectively. As can be seen in the figures, the average limiting path 

radiance Ips varies slowly over the entire span of target ranges. The observed path radiance Ip

ramps up rapidly as the target range increases through the first 5 km and then begins to level off 

toward an asymptote that is well below the average limiting path radiance. As mentioned above, 

the background radiance at the target position Ib(0) falls off very rapidly as the target approaches 

the nominal top of the atmosphere. 

44 
0.00001

0.0001

0.001

0.01

0.1

1

0 5 10 15 20 25 30

R a nge ( k m)

Ib(0)

Ip

Ips

Figure 23. Spectral background, path, and limiting path

radiance results for varying target ranges at a

wavelength of 4 μm.

0.001

0.01

0.1

1

10

0 5 10 15 20 25 30

Range (km)

Spectral Radiance (W/m^2/ster/um)

Ib(0)

Ip

Ips

Figure 24. Spectral background, path, and limiting path

radiance results for varying target ranges at a

wavelength of 10 μm.

 10. Caveats 

The following is a summation of caveats that should be observed when using the program.

The program’s wavelength maximum in the visible band is limited to 0.75μm—this is only due to 

the lack of appropriate phase functions. The user may run their favorite Mie scattering code, 

formatted as found in reference (22), to calculate the appropriate phase function for use at these 

extended wavelengths. 

In the 3.0–5.0 mid-IR waveband, it should be carefully noted that scattering effects are not 

included. 

The program is suitable only for near-earth altitudes (< 7 km). 

45 
It should be noted that even at the maximum MODTRAN spectral resolution, some narrow 

absorption features are not well represented in the results (which are stored in the mirdata.inp and 

firdata.inp data files). 

It should be noted that the presence of a cloud layer will modify the water vapor profile (of the 

cloud-free atmosphere) in the vicinity of the layer. 

The method of calculating visible radiances is approximate. 

The average and the variability of cloud optical depth as a function of cloud type were determined 

empirically from the SOLMET (33) data base. The model algorithms return the optical depth for 

the specified cloud type and relative optical thickness (average, thick, or thin) from the table 

without direct reference to the specified base and top altitude of the layer. In other words, the 

optical thickness is determined independently of the specified geometric thickness of the cloud. 

The basic cloud property models for the visual and IR derive from different sources. Therefore, 

comparison of visible and IR band results must be approached with caution. 

11. Conclusions 

We have presented a methodology for determination of the sky-to-ground ratio, complete with 

derivations. The program uses the delta-Eddington method for visible wavelengths and simple 

approximations for IR wavelengths. For ease of use, the extensive atmospheric inputs necessary to 

obtain realistic results have been highly automated. V&V has been carried out, delineating areas 

where the code’s approximations break down, and user input and output have been discussed for 

illustrative sample scenarios/examples. 

46 
References 

1. Duntley, S. Q. The Reduction of Apparent Contrast by the Atmosphere. JOSA 1948, 38, 

179–191. 

2. Middleton, W. E. K. Vision through the Atmosphere; University of Toronto Press: 

Toronto, Canada, 1952. 

3. Evans, K. F. The Spherical Harmonic Discrete Ordinate Method for Three-dimensional 

Atmospheric Radiative Transfer. J. Atmos. Sci. February 1998, 55, 429–446. 

4. Wetmore, A. E.; Zardecki, A. The Boundary Layer Illumination and Radiative Balance 

Model (BLIRB). Proceedings of the Cloud Impacts on DOD Operations and Systems 1993 

Conference, PL-TR-94-2188, Ft. Belvoir, VA, 1993; pp 201–206. 

5. O’Brien, S. G.; Tofsted, D. H. Physics-based Visualization of Dense Natural Clouds. II: 

Cloud-rendering Algorithm. Appl. Opt. November 1998, 37, 7680–7688. 

6. Tofsted, D. H.; O’Brien, S. G. Physics-based Visualization of Dense Natural Clouds. I: 

Three-dimensional Discrete Ordinates Radiative Transfer. Appl. Opt. November 1998, 37, 

7718–7728. 

7. Dixon, D. TRAC-WSMR. Private communication, 2004. 

8. Hoock, D. W.; Sutherland, R. A. Obscuration Countermeasures. In The Infrared and 

Electro-Optical Systems Handbook, vol. 7; Dudzik, M. C., Ed.; Infrared Information 

Analysis Center and SPIE Optical Engineering Press, 1993. 

9. Miller, A. FASCAT Atmospheric Illumination Module, users guide; ASL-TR-0221-22; 

October 1987. 

10. Shettle, E. P.; Weinman, J. A. The Transfer of Solar Irradiance Through Inhomogeneous 

Turbid Atmospheres Evaluated by Eddington’s Approximation. JAS October 1970, 27, 

1048. 

11. Joseph, J. H.; Wiscombe, W. J.; Weinman, J. A. The delta-Eddington Approximation for 

Radiative Flux Transfer. JAS December 1976, 33, 2452. 

12. Davies, R. The Effect of Finite Geometry on the Three-dimensional Transfer of Solar 

Irradiance in Clouds. JAS September 1978, 35, 1712. 

13. Hering, W. S.; Johnson, R. W. The FASCAT Model Performance Under Fractional Cloud 

Conditions and Related Studies; AFGL-TR-84-0168 (ADA169894); December 1984.

14. Hansen, J. E. Exact and Approximate Solutions for Multiple Scattering by Cloudy and 

Hazy Planetary Atmospheres. JAS May 1969, 26, 478–487. 

15. Potter, J. F. The Delta Function Approximation in Radiative Transfer Theory. JAS

September 1970, 27, 943–949. 

16. Lenoble, J. Atmospheric Radiative Transfer (ISBN 0-937194-21-2); Deepak Publishing: 

Hampton, VA, 1993. 

47 
17. Wiscombe, W. J.; Joseph, J. H. The Range of Validity of the Eddington Approximation. 

ICARUS 1977, 32, 362–377. 

18. van de Hulst, H. C., Multiple Light Scattering, Tables Formulas, and Applications, v2; 

Academic Press: NY, 1980. 

19. Davies, R. Fast Azimuthally Dependent Model of the Reflection of Solar Radiation by 

Plane-parallel Clouds. J. Appl. Opt. January 1980, 19, 250–255. 

20. Berk, A.; Bernstein, L. S.; Robertson, D. C. MODTRAN: A Moderate Resolution Model for 

LOWTRAN 7; GL-TR-89-0122, AD A214337; Air Force Research Laboratory: Hanscom

AFB, MA, 1989. 

21. O’Brien, S. G. A User Guide for the Deltaed Radiative Transport Model; ARL-CR-22; 

December 1992. 

22. Lenoble, J., ed. Radiative Transfer in Scattering and Absorbing Atmospheres: Standard 

Computational Procedures; Deepak Publishing: Hampton, VA, 1985. 

23. Deirmendjian, D. Electromagnetic Scattering on Spherical Polydispersions; Elsevier, 

1969. 

24. O’Brien, S. G. Investigation of Relative Strengths of Aerosol Scattering Radiance and 

Thermal Radiance in the Mid-IR Band, unpublished white paper, Army Research 

Laboratory: WSMR, NM, March 2004. 

25. Bangert, J. SLAC. http://aa.usno.navy.mil/AA/DoD/software/index.html (accessed verified 

2004). 

26. Tofsted, D.; Davis, B.; Wetmore, A.; Fitzgerrel, J.; Shirkey, R.; Sutherland, B. EOSAEL92 

Aerosol Phase Function Data Base PFNDAT; ARL-TR-273-9; June 1997. 

27. Shirkey R.; Tofsted, D. Electro-Optical Aerosol Phase Function Database PFNDAT2004;

ARL-TR-xxxx; 2004 (in press). 

28. U.S. Standard Atmosphere (1976); NOAA-S/T76-1562, Supt. of Documents, U.S. Govt. 

Printing Office: Washington, D.C., 1976. 

29. Allen, J. H.; Malick, J. D. The Frequency of Cloud-Free Viewing Intervals. AIAA 21st

Aerospace Sciences Meeting Paper, AIAA-83-0441, Reno, NV, January 1983. 

30. Low, R. D. H.; O’Brien, S.G. EOSAEL 87 Cloud Transmission Module CLTRAN; ASL-TR0221-9; October 1987. 

31. Shettle, E. P.; Fenn, R. W. Models for the Aerosols of the Lower Atmosphere and the 

Effects of Humidity Variations on Their Optical Properties; AFGL-TR-79-0214; Air Force 

Geophysics Laboratory: Hanscom Air Force Base, MA, 1979. 

32. MODIS Web. http://modis.gsfc.nasa.gov/ (access verified as of 5 August 2004). 

33. SOLMET, Hourly Solar Radiation-Surface Meteorological Observations, Vol. 1–Users 

Manual, (1977), Vol. 2–Final Report (1979); TD-9724; National Climatic Center, NOAA, 

EDIS, 1979. 

48 
Appendix 

1. Sample Run from the Text Scenario Using the Input File, visible_input.txt. 

*** SGR, Transmission, and Radiance Results for Upward looking LOS *** 

>>> Visible band calculation <<< 

Haze aerosol type: 2 - Urban 

Haze layer thickness (km): 1.000 

Met. visible range (km): 2.000 

Relative humidity (%): 90.00 

 No cloud layers present 

Observer local latitude (deg): 32.500 

Observer local longitude (deg): 127.000 

GMT (hhmm): 0000 

Month Day Year: 6 1 2002 

Extraterrestrial solar source: 

 Zenith angle (deg): 47.283 

 Azimuth angle (deg): 89.056 

LOS azimuth (deg, E of N): 90.000 

LOS zenith (deg): 70.000 

Range to target (km): 0.2924 

Observer altitude (km AGL): 0.0001 

Target altitude (km AGL): 0.1001 

Background surface albedo: 0.200 

49 
Wvlength W(sensor) SGR Tc T Lp Lb(0) 

-------- --------- ---------- --------- --------- ---------- ---------- 

 0.350 1.0000 0.6668 0.53345 0.43261 2.4070E+01 6.3618E+01 

 0.400 1.0000 0.6300 0.58526 0.47063 3.3055E+01 9.9112E+01 

 0.450 1.0000 0.5880 0.63473 0.50540 4.5875E+01 1.5773E+02 

 0.500 1.0000 0.5541 0.67713 0.53749 4.8177E+01 1.8798E+02 

 0.550 1.0000 0.5315 0.71242 0.56835 5.1909E+01 2.2627E+02 

 0.600 1.0000 0.5196 0.73929 0.59569 5.2298E+01 2.4895E+02 

 0.650 1.0000 0.5155 0.76070 0.62101 4.8812E+01 2.4987E+02 

 0.700 1.0000 0.5175 0.77836 0.64505 4.7211E+01 2.5703E+02 

 0.750 1.0000 0.5248 0.79249 0.66715 4.3769E+01 2.5055E+02 

Band-averaged SGR = 0.561 

Band-averaged contrast transmission Tc = 0.69043 

Band-averaged path transmission T = 0.56038 

Band-averaged spectral path radiance Lp = 4.3909E+01 W m-2 sr-1 micrometer-1 

Band-averaged spectral bkgrnd radiance Lb(0) = 1.9346E+02 W m-2 sr-1 micrometer-1 

Band-integrated path radiance Lp = 1.8063E+01 W m-2 sr-1 

Band-integrated bkgrnd radiance Lb(0) = 7.9201E+01 W m-2 sr-1 

50 
2. Sample Run from the Text Scenario Using the Input File, mid-ir_input.txt. 

*** SGR, Transmission, and Radiance Results for Upward looking LOS *** 

>>> Mid-IR band calculation <<< 

Haze aerosol type: 2 - Urban 

Atmospheric model: 6 - 1976 US Standard 

Met. visible range (km): 2.000 

Relative humidity (%): 90.00 

LOS zenith (deg): 70.0000 

Range to target (km): 0.2924 

Observer altitude (km AGL): 0.0001 

Target altitude (km AGL): 0.1001 

Background surface albedo: 0.200 

Wvlength W(sensor) SGR Tc T Lp Lb(0) 

-------- --------- ---------- --------- --------- ---------- ---------- 

 3.400 1.0000 1.1931 0.78036 0.80913 2.0674E-02 9.0780E-02 

 3.420 1.0000 1.3029 0.84085 0.87315 1.4535E-02 8.7954E-02 

 3.440 1.0000 1.4075 0.86493 0.90013 1.2100E-02 8.6080E-02 

 3.460 1.0000 1.4321 0.86838 0.90429 1.2251E-02 8.9383E-02 

 3.480 1.0000 1.5129 0.87716 0.91528 1.1448E-02 8.9311E-02 

 3.500 1.0000 1.5657 0.87944 0.91949 1.1475E-02 9.1034E-02 

 3.520 1.0000 1.5549 0.87796 0.91794 1.2328E-02 9.6619E-02 

 3.540 1.0000 1.4999 0.87338 0.91186 1.3947E-02 1.0550E-01 

 3.560 1.0000 1.4839 0.87092 0.90919 1.5124E-02 1.1224E-01 

 3.580 1.0000 1.4750 0.87067 0.90850 1.6026E-02 1.1875E-01 

 3.600 1.0000 1.5143 0.87542 0.91410 1.5813E-02 1.2156E-01 

 3.620 1.0000 1.5453 0.87869 0.91799 1.5854E-02 1.2510E-01 

 3.640 1.0000 1.5876 0.88292 0.92291 1.5640E-02 1.2779E-01 

 3.660 1.0000 1.5761 0.88164 0.92151 1.6702E-02 1.3501E-01 

 3.680 1.0000 1.4138 0.86096 0.89748 2.2866E-02 1.5776E-01 

 3.700 1.0000 1.6003 0.88343 0.92383 1.7793E-02 1.4596E-01 

Band-averaged SGR = 1.479 

51 
Band-averaged contrast transmission Tc = 0.86669 

Band-averaged path transmission T = 0.90417 

Band-averaged spectral path radiance Lp = 1.5286E-02 W m-2 sr-1 micrometer-1 

Band-averaged spectral bkgrnd radiance Lb(0) = 1.1130E-01 W m-2 sr-1 micrometer-1 

Band-integrated path radiance Lp = 4.5069E-03 W m-2 sr-1 

Band-integrated bkgrnd radiance Lb(0) = 3.3249E-02 W m-2 sr-1 

52 
3. Sample Run from the Text Scenario Using the Input File, far-ir_input.txt. 

*** SGR, Transmission, and Radiance Results for Upward looking LOS *** 

>>> Far-IR band calculation <<< 

Haze aerosol type: 2 - Urban 

Atmospheric model: 6 - 1976 US Standard 

Met. visible range (km): 2.000 

Relative humidity (%): 90.00 

LOS zenith (deg): 70.0000 

Range to target (km): 0.2924 

Observer altitude (km AGL): 0.0001 

Target altitude (km AGL): 0.1001 

Background surface albedo: 0.200 

Wvlength W(sensor) SGR Tc T Lp Lb(0) 

-------- --------- ---------- --------- --------- ---------- ---------- 

 10.400 0.1000 1.6081 0.91647 0.94636 4.3319E-01 5.0224E+00 

 10.420 0.2000 1.5797 0.91461 0.94420 4.5055E-01 5.1113E+00 

 10.440 0.3000 1.5911 0.91612 0.94558 4.3921E-01 5.0728E+00 

 10.460 0.4000 1.5240 0.91366 0.94162 4.7109E-01 5.2944E+00 

 10.480 0.5000 1.4951 0.91203 0.93940 4.8882E-01 5.3949E+00 

 10.500 0.6000 1.5362 0.91472 0.94279 4.6130E-01 5.2485E+00 

 10.520 0.7000 1.5784 0.91701 0.94577 4.3706E-01 5.1061E+00 

 10.540 0.8000 1.4692 0.91198 0.93835 4.9665E-01 5.4837E+00 

 10.560 0.9000 1.4648 0.91207 0.93825 4.9728E-01 5.4979E+00 

 10.580 1.0000 1.5375 0.91501 0.94303 4.5856E-01 5.2354E+00 

 10.600 1.0000 1.5638 0.91680 0.94515 4.4134E-01 5.1452E+00 

 10.620 1.0000 1.5448 0.91596 0.94394 4.5087E-01 5.2059E+00 

 10.640 1.0000 1.5457 0.91602 0.94401 4.5007E-01 5.2007E+00 

 10.660 1.0000 1.5629 0.91731 0.94547 4.3813E-01 5.1409E+00 

 10.680 1.0000 1.5631 0.91749 0.94560 4.3688E-01 5.1376E+00 

 10.700 0.5000 1.5526 0.91756 0.94529 4.3907E-01 5.1696E+00 

Band-averaged SGR = 1.539 

53 
Band-averaged contrast transmission Tc = 0.91540 

Band-averaged path transmission T = 0.94329 

Band-averaged spectral path radiance Lp = 4.5646E-01 W m-2 sr-1 micrometer-1 

Band-averaged spectral bkgrnd radiance Lb(0) = 5.2337E+00 W m-2 sr-1 micrometer-1 

Band-integrated path radiance Lp = 9.7792E-02 W m-2 sr-1 

Band-integrated bkgrnd radiance Lb(0) = 1.1205E+00 W m-2 sr-1 

54 
Acronyms

AGL above ground level 

ARL U.S. Army Research Laboratory 

ANSI American National Standards Institute 

AFGL Air Force Geophysics Laboratory 

ASCII American Standard Code for Information Interchange 

CASTFOREM Combined Arms and Support Taskforce Evaluation Model 

CFLOS cloud free line-of-sight 

CLTRAN Cloud Transmission 

EOSAEL Electro-Optical Systems Atmospheric Effects Library 

FASCAT Fast Atmospheric Scattering 

GMT Greenwich Mean Time

GUI graphical user interface 

MODIS Moderate resolution Imaging Spectroradiometer 

MODTRAN Moderate Transmission 

PFNDAT Phase Function Data base 

IR infrared 

LOS line-of-sight 

SGR Sky-to-Ground Ratio 

SLAC Solar-Lunar Almanac Core 

TOA top of atmosphere 

V&V verification and validation

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