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IRGASON Integrated CO

O Open-Path Gas Analyzer and 3D Sonic Anemometer

11.1.2 Temperature

The sonically determined speed of sound can be found from the sum of the

inverses of Eq. (1) and (2). The CSAT3 corrects online for the effect of wind

blowing perpendicular to the sonic path. No additional off-line corrections are

required as suggested by Liu et al., 2001.

⎡

⎣

⎢

⎤

⎦

⎥

(5)

The speed of sound in moist air is a function of temperature and humidity and

is given by:

(

)

cP RTRT q

dv d

1061== = +γργ γ .

(6)

where γ is the ratio of specific heat of moist air at constant pressure to that at

constant volume, P is pressure, ρ is air density, R

is the gas constant for dry

air, T

is virtual temperature, T is the air temperature, and q is the specific

humidity defined as the ratio of the mass of water vapor to the total mass of air

(Kaimal and Gaynor, 1991; Wallace and Hobbs, 1977).

Note that γ is a function of specific humidity. It would be convenient if the

effects of humidity could be consolidated into one term.

The specific heats for moist air at constant pressure and volume are given by:

−

qC q C

pw pd

()1

(.1084q)

(7a)

−

qC q C

vw vd

()1

(.1093q)

(7b)

where C

and C

are the specific heats of moist air at constant volume and

pressure, C

and C

is the specific heat of water vapor, and C

and C

is the

specific heat of dry air, respectively (Fleagle and Businger, 1980).

Substitute Eq. (7a) and (7b) into (6) and ignore the higher order terms. This

yields

(8)

cRTRT

dds dd

1051== +γγ(.

where T

is sonic virtual temperature and γ

is the 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. (8), the effect of humidity, on the speed of sound, is included in the

sonic virtual temperature.

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