A NEW SKY-TO-GROUND RATIO PROGRAM FOR USE IN

CASTFOREM AND OTHER WARGAMES

Richard ShirkeySean O'Brien

U.S. Army Research LaboratoryComputational & Information Sciences Directorate

Battlefield Environment Division

Contact: US Army Research Lab, Battlefield Environment Division, AMSRL-CI-EE, White Sands Missile Range, NM 88002-5501

Richard Shirkey: Commercial: 505 678-5470; DSN 258-5470; rshirkey@arl.army.milSean O'Brien: Commercial: 505 678-1570; DSN 258-1570; sobrien@arl.army.mil

Wargame Sensor/Target Environment

Scattering

ReducedReducedtargetcontrastcontrast

Smoke/Haze

Emission

Sky-to-Ground Ratio - Motivation

• Sky-to-ground ratio (SGR) is a computational shortcut frequently used in wargames to quantify contrast

• This contrast is degraded by path radiance entering the sensor LOS due to– Multiple scattering of ambient light by atmospheric aerosols and/or

gases – Greybody atmospheric thermal radiance

• Research grade radiative transfer models can compute path radiance with high accuracy

• These calculations take a considerable amount of time; the SGR approximation provides a fast answer with moderate accuracy

0r b

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

0r b

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

0r b

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

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

Contrast Component Definitions

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

SGR Definition

Ips () = I(r, ) P(, ) d

Limiting path radiance:

For a uniform path:

<Sgr> = <Ips >/ Ib(0) = Ip / [Ib(0) (1-T)] For a slant path:

Why SGR?

The SGR provides an approximate, time conservative, method for determining the reduction in contrast due

to LOS in-scattering of light

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

SGR Model IR Products

The SGR model can compute an SGR for the IR bands, using the IR thermal path radiance as a starting point:Ip() = Ib(0) e-/ + (a/) B (1 - e -/)

<Sgr> = Ip() / [Ib(0) (1-T)]

Or, it can calculate a slant path SGR:

Or, the model can compute an IR ΔT by inverting the Planck function for the computed radiances

SGR Code Heritage

• FASCAT– Visible band radiances

• EOSAEL PFNDAT– Aerosol phase functions for upgraded FASCAT

• AFRL MODTRAN– Molecular absorption and aerosol attenuation profiles

• EOSAEL CLTRAN– Optical thickness for cloud layers

• EOSAEL FITTE– IR atmospheric path radiance

SGR Code Assumptions

• General• suitable only for near-earth altitudes ( < 10 km)• narrow absorption features may not well represented• cloud layers will modify the water vapor profile

• At Visible wavelengths• delta-Eddington methodology is employed

• At IR wavelengths • at 3.0 – 5.0 scattering effects are not included • only thermal radiance is considered• numerical path integration

i

N

ii

i

eBI

/

1

)(

SGR Code – Parameter Domain

• Aerosol types• Rural• Maritime• Urban• Tropospheric• Radiation Fog• Advection Fog

• Cloud types• Cirrus/cirrostratus• Altostratus/altocumulus• Cumulus• Stratus/stratocumulus• Nimbostratus

• Atmospheric profiles• Tropical• Midlatitude Summer (45N, July)• Midlatitude Winter (45N, Jan.)• Subarctic Summer (60N, July)• Subarctic Winter (60N, Jan.)• 1976 US Standard Atmosphere

• Geometries• Target height calculated• LOS zenith angle calculated• Target range is calculated

Example Scenario

EW

N

S

89.1°

Upward LOS: helicopter approaches from Sun direction, passes over observer and exits with Sun behind

Downward LOS: position of helicopter & observer interchanges

Lambertian Ground Plane

Upward Looking in Visual

0

0.2

0.4

0.6

0.8

1

Sky-

to-g

roun

d R

atio

/Tra

nsm

issio

n

0

100

200

300

Rad

ianc

es (W

m-2

sr-1

m

-1)

S G RT ra n sm iss ionP a th R ad ian c eB a ck g rou n d R a d ia n ce

Zenith Angle (degrees)

U p w a rd L o o k

L O S A zim u th = 27 0 o L O S A zim u th = 9 0 o

0 30 60 90306090

Downward Looking in Visual

0

1

2

3

4

Sky-

to-g

roun

d R

atio

/Tra

nsm

issi

on

0

100

200

300

Rad

ianc

es (W

m-2

sr-1

m

-1

S G RT ran sm issionP a th R a d ian ceB a ck g rou n d R ad ia n ce

D o w n w a rd L o o k

L O S A zim u th = 2 70 o L O S A zim u th = 9 0 o

Z en ith A n g le (d eg rees )

180 150 120 90120 15090

Upward Looking in Far-IR (10.0 μm)

0

0.2

0.4

0.6

0.8

1

0 30 60 90

Zenith Angle (degrees)

Tran

smis

sion

0.01

0.10

1.00

Spec

tral

Rad

ianc

e (W

m-2

ste

r-1 u

m-1

)

TcTLpLb(0)

Upward Looking LOS at IR Wavelengths

Summary

• SGR code can be added to wargames without imposing prohibitive run speed penalties

• SGR IR sky radiance algorithms have been adapted for use in TDA models such as TAWS

• The new code also treats the problem of upward LOS targets against hillside backgrounds

• Choice of model atmospheres (and temperature profiles) is limited to AFRL MODTRAN set at present, but can be easily expanded

Availability

rshirkey@arl.army.milsobrien@arl.army.milhttp://mel.dmso.mil