To: delany@atd.ucar.edu
Subject: influence of sawhorse shadow
Cc: militzer@atd.ucar.edu, oncley@atd.ucar.edu

Tony:

The relative influence of a patch of surface dA to the upwelling
radiation measurements is

(dA/pi)*cos(theta)^2/(z^2 + r^2) =

(dA/pi)*z^2/(z^2 + r^2)^2 =

dA/(pi*z^2)*cos(theta)^4,

where z is the height of the radiometer, r is the (horizontal) radial
distance from the radiometer to the location dA, and theta is the nadir
angle of dA from the radiometer.  You could use this to estimate the
influence of the sawhorse shadow on the radiation measurments.

The integrated influence of a circular area of radius ro below the
radiometer is 1/[1 + (z/ro)^2], so that for example: 
50% of the measurement is influenced by an area of radius ro=z,
80% from an area of radius ro=2z,
90% from an area of radius ro=3z,
96% from an area of radius ro=5z, and
99% from an area of radius ro=10z.

Assuming that the Campbell box casts a circular shadow of radius
ro=25cm directly below a radiometer at a height of 200cm, its
influence is 0.015.

The area of a shadow with a width=w and a length=L centered below a
radiometer at height=h has an influence equal to

w/(2*pi*h)*{ (L/h)/[1 + (L/2h)^2] + atan(L/2h) }

                       = 0.014 for w=10cm, h=200cm, L=400cm

Tom


The area of a shadow with a width=w and a length=L centered below a
radiometer at height=h has an influence equal to

w/(pi*h)*{ (L/2h)/[1 + (L/2h)^2] + atan(L/2h) }

                       = 0.02 for w=10cm, h=200cm, L=400cm

Tom