163 Tf), Tol) \ TOP OF MIXING LAYER z PYRHELIOMETER ON TOP OF BUILDING | a Ig(dy) Tg(ha) SAAASSESSALLLALLLLS PYRHELIOMETER AT BOTTOM OF BUILDING Fie. 130.—Measurement of mixing depth with pairs of pyrheliometers at each of two levels. One pyrheliometer of each pair operates in a 500 A band centered at 4, A and the other in a 500 A band centered at : A. Equations corresponding to Equations (3), (4), and (5) are In Pp Q\a)/Le(A2) = In Toda)/Tofr2) — (ws) — #O2)](L + Le) Ep(h2) = Lo{ds) exp | —u(r2)LE} (13) TeQa) = Fo(M1) exp [—w(u)(Z + La} (14) Ip(h2) = Lo(d2) exp {—n(r.)(L + Lay}. (185) Dividing Equation (12) by Equation (14) and taking the logarithm of both sides we have Tru) ‘, In FO) = p(A1) a sec 0 (16) or Eth) Terr) HOM) = ere (17) _ In Tre) /Ta (2) (18) a@ sec 6 where 2 represents the solar radiation in band 2. Dividing Equation (14) by Equation (15) and taking the logarithms of both sides, we have or In Fe (\1)/2Pe(\2) — In Lo(A1)/To(d2) = [u(A2) — w(Ai)] Hf sec 6 (20) Solving for H and making use of Equations (17) and (18) we have — ain FgQu)/IZaQe) — In Lo(A1) /To(A2) ) In IpQe) /ZeQ2) — In FpQa)/Te Qa) (21) Thus H,the effective height is determined from known or measured quantities.The ratio Jo(A1)/Zo(A2) is, of course, the ratio of the energy in the two selected wave bands and is given in Physical Tables. Figure 131 shows a schematie circuit diagram for pro- viding a continuous reading of the mixing depth. Similarly, (ro) (19) LINEAR VARIATION OF POLLUTANT WITH HEIGHT The attenuation coefficient, u, varies directly with the mass of pollutant traversed per unit cross section or the concentration. If the concentration varies linearly with height, then the attenuation coefficient will also vary this way, Let us assume that