Campbell Scientific CSAT3B CSAT3B Three-Dimensional Sonic Anemometer - Page 79

B.2 References

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Appendix B. CSAT3B Measurement Theory Substitute Eq. (B-7a) and (B-7b) into (B-6) and ignore the higher order terms. This yields c2 = γ dRdTs = γ dRdT(1+ 0.51q) (B-8) where: Ts = sonic virtual temperature γd = 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 γd = 1.4 and Rd = 287.04 JK-1 kg-1. c2 Ts = γ dRd − 273.15 (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. B-3

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Appendix B.
CSAT3B Measurement Theory
Substitute Eq. (B-7a) and (B-7b) into (B-6) and ignore the higher order terms.
This yields
c
RT
RT
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.
B-3