Fundamentals Of Visibility

WILLIAM C. MALM

1 INTRODUCTION

A definition of visibility, as it relates to management of the many visual resources found in national parks, wilderness areas, and urban centers, is a complex and difficult concept to address. Should visibility be defined in strictly technical terms that concern themselves with exact measurements of illumination, threshold contrast, and precisely measured distances? Or is visibility more closely allied with value judgments of an observer viewing a scenic vista?

Historically, visibility has been defined as the greatest distance at which an observer can just see a black object viewed against the horizon sky. An object is usually referred to as at threshold contrast when the difference between the brightness of the sky and the brightness of the object is reduced to such a degree that an observer can just barely see the object. Much effort has been expended in establishing the threshold contrast for various targets under a variety of illumination and atmospheric conditions. An important result of this work is that threshold contrast for the eye, adapted to daylight, changes very little with background brightness, but it is strongly dependent upon the size of the target and the time spent looking for the target.

However, visibility is really more than being able to see a black object at a distance for which the contrast reaches a threshold value. Coming upon a mountain such as one of those shown in Figures 1 a and 1 b, an observer does not ask, "How far do I have to back away before the vista disappears?" Rather, the observer will comment on the color of the mountain, on whether geological features can be seen and appreciated, or on the amount of snow cover resulting from a recent storm system. Approaching landscape features such as those shown in Figures 1 c

Handbook of Weather, Climate, and Water: Atmospheric Chemistry, Hydrology, and Societal Impacts, Edited by Thomas D. Potter and Bradley R. Colman. ISBN 0-471-21489-2 © 2003 John Wiley & Sons, Inc.

Figure 1 Photographs (a) through (d) show that, from a visual resource point of view, visibility is not how far a person can see but rather the ability of an observer to clearly see and appreciate the many and varied scenic elements in each vista, (a) The farthest scenic feature is the 130-km distant Navajo Mountain, as seen from Bryce Canyon National Park, (b) The La Sal Mountains, as seen from the Colorado River, are a dominant view from the distant horizon, (c) This view in Canyonlands National Park shows the highly textured foreground canyon walls against the backdrop of the La Sal Mountains. The La Sals are 50 km from the observation point, (d) Bryce Canyon as seen from Sunset Point, Notice the highly textured and brightly colored foreground features. See ftp site for color image.

Figure 1 Photographs (a) through (d) show that, from a visual resource point of view, visibility is not how far a person can see but rather the ability of an observer to clearly see and appreciate the many and varied scenic elements in each vista, (a) The farthest scenic feature is the 130-km distant Navajo Mountain, as seen from Bryce Canyon National Park, (b) The La Sal Mountains, as seen from the Colorado River, are a dominant view from the distant horizon, (c) This view in Canyonlands National Park shows the highly textured foreground canyon walls against the backdrop of the La Sal Mountains. The La Sals are 50 km from the observation point, (d) Bryce Canyon as seen from Sunset Point, Notice the highly textured and brightly colored foreground features. See ftp site for color image.

1 INTRODUCTION 287

1 INTRODUCTION 287

Figure 1 Continued

and 1 d, the observer may comment on the contrast detail of nearby geological structures or on shadows cast by overhead clouds.

Visibility, in the context of viewing scenic vistas, is more closely associated with conditions that allow appreciation of the inherent beauty of landscape features. It is important to be able to sec and appreciate the form, contrast detail, and color of near and distant features. Therefore, visibility includes psychophysical processes and concurrent value judgments of visual impacts, as well as the physical interaction of light with particles in the atmosphere.

Whether we define visibility in terms of visual range or in terms of some parameter more closely related to how visitors perceive a visual resource, the management of visibility depends on the scientific and technical understanding of:

• How aerosols are dispersed across land masses and into local canyons and valleys

• How they transform from a gas into particles that impair visibility

• How they interact with light

• The psychophysical processes involved in viewing scenic landscape features

Scientific understanding of some of these issues is more complete than others. The focus of this discussion is on developing a basic understanding of the interaction of light with aerosols and the psychophysical properties of the eye-brain system as they relate to visibility.

2 THEORY OF RADIATION TRANSFER AND VISIBILITY

The response of the human eye to radiant energy of different wavelengths is shown in Figure 2. The maximum response to a unit of energy is at 0.55 |im. When radiant energy is discussed in terms of the response of the human eye, photometric concepts and units are conventionally used. Conversely, when the entire radiation field of the sky is modeled or measured, radiometric units are employed. Usually, but not always, photometric parameters are derived from the more fundamental radiometric variables. Table 1 lists the various radiometric and corresponding photometric variables typically employed in radiation transfer calculations.

100n

4000 5000 6000 7000 8000 Wavelength in Angstroms

Figure 2 Spectral response of the human eye.

TABLE 1 Radiometric and Photometric Concepts and Units

Radiometric

Symbol

Units

Photometric

Symbol

Units

Radiant energy

U

joule

Luminous energy

Q

Talbot

Radiant flux

P

watt

Luminous flux

F

lumen

Radiant intensity

J

watt/steradian

Luminous intensity

I

lumen/steradian

Radiance

N

watt/m2

Luminance

B

lumen/m2

steradian

steradian

Irradiance

H

watt/m2

Illuminance

E

lumen/m2

Atmospheric Scattering and Extinction

The alteration of radiant energy as it passes through the atmosphere is due to scattering and absorption by gases and particles. The sum of scattering and absorption is referred to as the extinction coefficient. The effect of the atmosphere on the visual properties of distant objects theoretically can be determined if the concentration and characteristics of air molecules, particles, and absorbing gases are known throughout the atmosphere and most importantly along the line of sight between the observer and object. The extinction coefficient is made up of particle and gas scattering and absorption:

where s, a, g, and p refer to scattering, absorption, gases, and particles, respectively.

Light scattering by gases is described by the Rayleigh scattering theory (vande-Hulst, 1981). Important characteristics of Rayleigh scattering are:

• Its proportionality to molecular number density (bsg = 12 Mm-1 at sea level and at 0.55 |im).

• The amount of scattered light varies as 1 //.4 where I is the wavelength of light.

• Equal amounts of light are scattered in forward and backward directions.

• Light scattered at 90° is nearly completely polarized.

The only gas that is normally found in the atmosphere which absorbs light is nitrogen dioxide, N02. Absorption by N02 at 550 nm is bag = 330[N02], where the units of bag are Mm-1 and the units of [N02] are ppm (Nixon, 1940; Hodkinson, 1966). Furthermore, N02 absorbs more in the blue portion of the spectra than in the red portion. Therefore, N02 appears brown or yellowish if viewed against a background sky.

In most instances, particle scattering and absorption are primarily responsible for visibility reduction. Single-particle scattering and absorption properties can, with a number of limiting assumptions, be calculated using Mie theory (vandeHulst, 1981; Mie, 1908). However, before such calculations are carried out, appropriate boundary conditions must be specified. Typically aerosol models assume:

External Mixtures Particles exist in Ike atmosphere as pure chemical species lhai are mixed without interaction.

Multicomponent Aerosols Single particles are made up of two or more species.

Transfer of Radiant Energy

Visibility involves more than specifying how light is absorbed and scattered by the atmosphere. Important factors involved in seeing an object are outlined iti Figure 3 and summarized below:

• Illumination of the overall scene by the sun, which includes illumination resulting from sunlight scattered by clouds and atmosphere as well as reflections by ground and vegetation

• Scene characteristics that include color, texture, form, and brightness

• Optical characteristics of intervening atmosphere:

Figure 3 Important factors involved in seeing a scenic vista are outlined. Image-forming information from an object is reduced (scattered and absorbed) as it passes through (he atmosphere to the human observer. Air light is also added to the sight path by scattering processes. Sunlight, light from clouds, arid ground-reflected light all impinge on and scatter from particulates located in the sight path. Some of this scattered light remains in the sight path, and at times it can become so bright that the image essentially disappears. A final important factor in seeing and appreciating a scenic vista arc the characteristics of the human observer. Sec ftp site for color image.

Figure 3 Important factors involved in seeing a scenic vista are outlined. Image-forming information from an object is reduced (scattered and absorbed) as it passes through (he atmosphere to the human observer. Air light is also added to the sight path by scattering processes. Sunlight, light from clouds, arid ground-reflected light all impinge on and scatter from particulates located in the sight path. Some of this scattered light remains in the sight path, and at times it can become so bright that the image essentially disappears. A final important factor in seeing and appreciating a scenic vista arc the characteristics of the human observer. Sec ftp site for color image.

• Image-forming information (radiation) originating from landscape features is scattered and absorbed (attenuated) as it passes through the atmosphere toward the observer.

• Sunlight, ground-reflected light, and light reflected by other objects are scattered by the intervening atmosphere into the sight path.

• Psychophysical response of the eye-brain system to incoming radiation

Image-forming information is lost by the scattering of imaging radiant energy out of the sight path and absorption within the sight path, while ambient light scattered into the sight path adds radiant energy to the observed radiation field. This process is described by:

where Nr(0, (p, r) is the apparent radiance at some vector distance, r, from a landscape feature, MJO, (p, r) (referred to as the path function) is the radiant energy gain within an incremental path segment, and bextNr(9, cp, r) is radiant energy lost within that same path segment. The atmospheric extinction coefficient (bext) is the sum of both atmospheric scattering (bs) and absorption (ba). Although not explicitly stated, it is assumed that each variable in, and each variable derived from, Eq. (2) is wavelength dependent. The parenthetical variables (0, q>, r) indicate that Nr and are dependent both on the direction of image transmission and on the position within the path segment. For the sake of brevity, the parenthetical variables will be dropped in following equations. When the postscript r is appended to any symbol, it denotes that the quantity pertains to a path of length r. The subscript 0 always refers to the hypothetical concept of any instrument located at zero distance from the object—as, for example, in denoting the inherent radiance of a surface. Prescripts identify the objects; the prescript b referring to background and I to landscape feature.

When Nr has some special value, N , such that bextNq = then dNq/dr = 0; Nq is independent of r and is commonly referred to as the equilibrium radiance. Therefore, for every path segment dNr(9, (p, r)

0 0

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