Campbell CSAT3B, Product Manual

Page: 81 / 88

Appendix B. CSAT3B Measurement Theory
B-3
C
pd
and C
vd
= specific heat of dry air, respectively (Fleagle
and Businger, 1980)
Substitute Eq. (B-7a) and (B-7b) into (B-6) and ignore the higher order terms.
This yields
c R T R T q
d d s d d
2
1 0 51
= = + γ γ
( . )
(B-8)
where: T
s
= sonic virtual temperature
γ
d
= ratio of specific heat of dry air at constant pressure to
that at constant volume (Fleagle and Businger, 1980; Kaimal
and Gaynor, 1991; Kaimal and Businger, 1963; Schotanus et
al., 1983)
With Eq. (B-8), the effect of humidity, on the speed of sound, is included in the
sonic virtual temperature.
The sonic virtual temperature, in degrees Celsius, is given by Eq. (B-9), where
γ
d
= 1.4 and R
d
= 287.04 JK
-1
kg
-1
.
T
c
R
s
d d
= −
2
273 15
γ
.
(B-9)
B.2 References
Kaimal, J. C. and Businger, J. A.: 1963, “A Continuous Wave Sonic
Anemometer-Thermometer”,
J. Applied Meteorol.
, 2 , 156-164.
Kaimal, J. C. and Gaynor, J. E.: 1991, “Another Look at Sonic Thermometry”,
Boundary-Layer Meteorol. , 56 , 401-410.
Fleagle, R. G. and Businger, J. A.: 1980, An Introduction to Atmospheric
Physics
, Academic Press, Inc., New York.
Liu, H., Peters, G. and Foken, T.: 2001, “New Equations for Sonic
Temperature Variance and Buoyancy Heat Flux with an Omnidirectional Sonic
Anemometer”, Boundary-Layer Meteorol. , 100 , 459-468.
Schotanus, P., Nieuwstadt, F. T. M. and de Bruin, H. A. R.: 1983,
“Temperature Measurement with a Sonic Anemometer and its Application to
Heat and Moisture Fluxes”, Boundary-Layer Meteorol. , 26 , 81-93.
Wallace, J. M. and Hobbs, P. V.: 1977, Atmospheric Science an Introductory
Survey
, Academic Press, Inc., New York.