Kipp&Zonen Brewer MkIII - Manual (Page 113)

MKIII OPERATOR'S MANUAL 110
COMPENSATING FOR DEADTIME
Poisson statistics are assumed so that for any observation at a true count rate F0 (counts/second)
the observed rate F will be
e T F
F F 1 0
0
⋅ −
⋅ ←
where T1 is the deadtime of the photon-counting system (as determined by the deadtime test, DT,
run as part of the Brewer setup procedures).
This equation is solved for F0 by iterating 9 times on the (rearranged) expression:
e T F
F F 1 0
0
⋅
⋅ ←
This compensation is performed for each of the five operational wavelengths.
The deadtime-compensated count rates are normalized by computing the base-ten logarithm, then
scaled by 104, thus allowing integer arithmetic.
COMPENSATING FOR TEMPERATURE
The count rates are corrected for the temperature-dependent bandpass characteristics of
various filters inside the spectrometer assembly:
( ) 6 .. 2 ,
= + ⋅ + + ←
i AF TE TC PC F F
p i i i
where
PC is the constant part of the temperature coefficient
TCi are the wavelength-dependent temperature coefficients read from the
spectrophotometer's Constants File (stored on disk)
TE is the instrument temperature in degrees Celsius
AFp is the attenuation value of the neutral-density filters at position p (the array AF
of attenuation values is also read from the instrument Constants File).
COMPENSATING FOR RAYLEIGH SCATTERING (DS ONLY)
If the reading is of the direct sun, the count rates are adjusted by compensating the effect of
Rayleigh-scattering attenuation for the airmass calculated for the time of the observation:
6 .. 2 ,
1013
3
=
Ч Ч
+ ←
i
PZ M BE
F F i
i i
where
BEI are the Rayleigh coefficients.
PZ is the atmospheric pressure at the site of the instrument (in millibars)
1013 is standard atmospheric pressure (millibars)
M3 is the airmass (also referred to as the path-lengthening factor) for a layer of
height 5 km above the earth.
M3 is recalculated prior to each solar observation:
)]) sin( [ sec(arcsin 3 A k M
⋅ ←
where
A is solar zenith angle
k = R / (R + Z)
R is radius of earth (6370 km)
Z is layer height (5 km)