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