rT”
163
Io Ig Ip
TOP OF MIXING LAYER
wihL
L
Zz
=@
H
TAVit
a
a?
|
L
2 La
MA
T = PYRHELIOMETER AT TOP OF BUILDING
IM//La M=PYRHELIOMETER HALF WAY UP BUILDING
B
B= PYRHELIOMETER AT BOTTOM OF BUILDING
Fic. 132.—Three pyrheliometers at one wave band and one zenith distance to provide mixing depth information where pollutant concentration is distributed linearly with height.
Ip = Iy exp {a — : {cos 6)(L + 1.)
(27)
Iu = Iy exp (2 — ; (cos 6) (« + zy
(28)
Ir
k
2
In =5 (cos O)(2L-La + La) = P
(29)
In FE = 5 (eos 6) (11. +% = @Q
(30)
(cos 8)(2E-L, + 13) = P
(31)
5 (0s 0)(4L-Le + L2) = 4.
(32)
Solving Equations (31) and (32) for k we have
__ 4P — 8Q
~ eos 6 L2 *
(33)
4Q — P
.
4 In I7/Iy — InT,/TIz
“4 In Ir/ls
or
As previously, we shall assume that the wave bands
At and 2 are 400-450 and 550-600 nanometers. The
same notation as aboveis used.
I ef{h1)
= LoQa) exp {- a— pO) Lv cos |
Tr{h2) = Ig(A2) exp (- a— Ps) L’ cos |
(38)
(39)
= [o(\1) exp {= a— ew (L + La)’ cos |
(40)
4inI7/Iy
k(d2)
= I)(\2) exp \- a—
(35)
From Equations (38) and (39)
2
(L + L,)° cos a.
(41)
—_ 8 In Ir/luy
Tp(da) Lo(r2)\ kOe) — FOn)
2
In Ge Oe) =
5
(cos BL.
—
InTy/Tp
o 9 Fin Le/Ts — 8Ir/Tue
H=z+ax-a+ta
Two Pairs of Pyrheliometers at Two Levels and Two
Wave Bands
(34)
But L = zsecéand LZ, = asec 6
_
All of the quantities are measurable.
Tp(r2)
L = leap 3G
L=L
(37)
Ta(h1)
Andsolving for Z we have
_
_ a3inIs/Ig — 41lnIr/ly
i= 4 In Ip/Ig — 2nIe/Tu
4|n Ie/ly — In Iy/Tp
4 ln Lo/LT»
—_ 8 In Ir/Iu
(36)
(42)
Irom Equations (40) and (41)
TQM) Loe) — kO2) — On) cos@(L + L,).
Ta(h2) Lo)
2
Dividing Equation (42) by Equation (43) we have
(43)