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)