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

Different Kinds of Threshold
Calculations

Modulation Contrast (mean square radiance is the relative psychophysical variable)
N

N m

N b

N m

N b cos

2
 fx

2 2
The mean square radiance associated with the above equation can be shown to equal
N
2 
N
2 
1 / 2 m
2
N
2 where m is the modulation contrast , m=(N m
-N b
)/(N m
+N b
), m
2
N
N is the average image
2 radiance, and (1/2) is the mean square radiance fluctuation.

Human Visual System Sensitivity

Wave Types

Sine Wave Grating

Superposition Principle
More complicated one-dimensional images can be represented as weighted sums of light and dark bars of various frequencies and intensities.
Mathematically,
N
 
 a
  a e in 2
 f o x where N r r o n n , n
 o
(x) is the one dimensional image radiance field at an observer image distance r, a o
N n is the are the weighting factors associated with various sinusoid frequencies n2πf o.
 a n e in n , n
 o the modulation of average image radiance a o.
2
 f o x
The second term, , is

Equivalent Contrast
The mean square radiance associated with the above equation yields
N r
2  a
2 o
  n a n
2
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
1 / 2 m
2
N
2   n a n
2 and
C eq
 m

2
 n a n
2
N

Modulation Transfer Function
The effect of an increase in atmospheric aerosol concentration on a complex scene is
N
 r
 a o
T

N r
 
T
 n a n e i 2
 nf o x
The modulation contrast of any sinusoid is then m
 
Ta n
/
 a o
T

N r


The Equation
...and the transfer of modulation contrast is
M tf , a
 m

/ m

1

N r

1
/ a oo
T

Transfer of Equivalent Contrast
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
C f
 

M tf
C i where M tf is the atmospheric modulation transfer function given by
M tf

1

N r

1
/ a o
T

Quadratic Detection Model
The quadratic detection model stated mathematically:
C f
 
2 
C i
 
2 
C
T
 
2  k
    i
2 where
C f
 

2
  
/ a o

Cross Section of Haze Layer

Power Spectra Without Plume

Power Spectra Without Plume

Modulation Transfer and Equivalent
Contrast
Substituting and solving for M tf yields
M tf

C
T
2
 
/ C i
2
 
 k

1

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 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.

Utility Function for Visual Air Quality
V



4
(

1
( PVAQ
1
Driving
)
 
Time)
2
(

PVAQ
2

)
 
3
( PVAQ
3
5
( Waiting Time)
)