Psychophysical Interface

Thresholds (plume and landscape) Judgments of visual air quality Value assessment

Different Kinds of Threshold Calculations

fxNNNN

N bmbm 2cos22

The mean square radiance associated with the above equation can be shown to equal 

where m is the modulation contrast, m=(Nm-Nb)/(Nm+Nb), is the average image

radiance, and (1/2) is the mean square radiance fluctuation.

22222/1 NmNN

N22 Nm

Modulation Contrast (mean square radiance is the relative psychophysical variable)

Human Visual System Sensitivity

Wave Types

Sine Wave GratingSine Wave Grating

More complicated one-dimensional images can be represented as weighted sums of light and dark bars of various frequencies and intensities. Mathematically,

where Nr(x) is the one dimensional image radiance

field at an observer image distance r, ao is the

average image radiance, , and an are the

weighting factors associated with various sinusoid frequencies n2πfo. The second term, , is

the modulation of average image radiance ao.

xfinn

onnor

oeaaxN 2

,

N

xfinn

onn

oea 2

,

Superposition Principle

Equivalent Contrast

The mean square radiance associated with the above equation yields

Comparison of two mean square radiance equations suggests that the second term in each of these equations can be set equal to each other to yield

and

222n

nor aaN

2222/1 nn

aNm

N

amC

nn

eq

22

Modulation Transfer Function

The effect of an increase in atmospheric aerosol concentration on a complex scene is 

xnfin

nror

oeaTNTaxN 2

The modulation contrast of any sinusoid is then 

ron NTaTam /

...and the transfer of modulation contrast is  

Ta/N1

1m/mM

oora,tf

The Equation

If the change in scene equivalent contrast is a result of addition or subtraction of atmospheric aerosol, initial and final contrast are related to each other by

where Mtf is the atmospheric modulation

transfer function given by 

itff CMC

TaNM

ortf /1

1

Transfer of Equivalent Contrast

2222 iTif CkCCC

The quadratic detection model stated

mathematically:

Quadratic Detection Model

where

of aC /2

Cross Section of Haze Layer

Power Spectra Without Plume

Power Spectra Without Plume

Substituting and solving for Mtf yields

1/ 22 kCCM iTtf

Modulation Transfer and Equivalent Contrast

Proportionality Constant

Modulation Transfer Function Surface For a One JNC Change

JNC Surface (80% reduction in extinction)

Plume Geometry

Plume Contrast Calculation

Computer Generated Plumes

Contrast Level at Threshold of Detection vs. Plume Length and Edge Type

Probability of Detection of 0.36 Degree Circular Plume vs. Modulation Contrast

Predicted Probability of Detection vs. Modulation Contrast and Plume Width

Modulation Contrasts of 3 Plume Types at a 70% Detection Threshold

Contrast Level at Threshold of Detection vs. Plume Width

Contrast Level at Threshold of Detection of 3 Plume Types vs. Plume Width

Sine Wave GratingSine Wave Grating

Thresholds vs Judgments of Visual Air Quality

Perceived Visual Air Quality (PVAQ) Visual Air Quality Index (VAQI) Scenic Beauty Estimate (SBE)

Perceived Visual Air Quality vs. Particulate Concentration

Perceived Visual Air Quality vs. Sun Angle and Sky Conditions

Perceived Visual Air Quality vs. Distance to Vista

Perceived Visual Air Quality vs. Time of Day

La Sals -- 30km

Perceived Visual Air Quality vs. Height of Plume

Value Assessment of Visual Air Quality

Willingness to pay Utility function (time and dollars) Importance value Visual air quality and behavior Etc.

Time) Waiting(Time) Driving(

)PVAQ()PVAQ()PVAQ(V

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Utility Function for Visual Air Quality