162
TOP OF MIXING LAYER
1p(4)
Zz
i
- 7
PYRHELIOMETER ON TOP OF BUILDING
t
8
Lal.)
Lgl)
PYRHELIOMETER AT BOTTOM OF BUILDING
Fie, 129.—Measurement of mixing depth with two pyrheliometers and two solar zenith distances. Unfiltered solar radiation used.
L601) = a see
Le(O.) = asec 6.
aschhe
In J»(@.) — In Ia(6.)
sec & — sec #1 ln Ir (@1) — In Lp (1)
Dividing Equation (2) by Equation (4) we have
Ip(O1) — Lo(@r)
Tle) > 7b) oP {pa sec 6,3
(6)
(10)
Technique for Obtaining Mixing Depth with Pairs of
Pyrheliometers at Each of Two Levels Using Two
Wave Bands
Throughthe useof filters, it is possible to measure the
or
— In [Tr(61)/Te(1)]
a
a see 6;
(7)
Dividing Equation (4) by Equation (5) we have
I5(61)/T (60)
_ To( 01)
Ly (02)
(8)
-exp {—ulL((i) + La(ti) — Ls) — La( 62) 1}.
Since [o(@1) = Jo(#2) and L(#:) + La(@i) and L(@2) +
L.(82) are H sec #, and H sec 4 respectively, we have
Tn(6)
" Fy (00)
= —pH (sec 6 — sec és),
(9)
where H is theeffective height of the mixing depth.
Combining Equations (7) and (9) and solving for H
we have
received solar radiation in a prescribed band. With two
pyrheliometers at each of two levels, one operating at
400-450 nanometers and the other at 550-600 nanometers, it is possible to determine the height of the mixing
depth at a single zenith distance of the sun. (See Figure
130.) In other words, nearly instantaneous measure-
ments of the mixing depth are obtained. In selecting
the two bands, it is desired that attenuation in one band
be as large as possible and in the other as smallas possi-
ble so that the difference u(A1) — (do) is at a maximum.
Using an argument similar to that above we have
Tr, 1) = Lo(dr, 01) exp {—wOu) L(O)}.
(11)
Since we are dealing with a single zenith angle the
#’s will be omitted and. we have
Ie(M) = Lo(\x) exp {—pOu)L}.
(12)
The A: refers to the first wave band used. See Figure 130.