COMPENDIUM OF EQUATIONS, CONVERSION FACTORS, AND RELATIONSHIPS USED WITH
THE SJVAQS91 DATA.
1. 1 J s-1 = 1 Watt
2. degree K = degree C + 273.15
3. Standard atmosphere = 101.3 kPa
4. Stefan/Boltzman relationship.
The black body radiation assumes an emissivity factor of 1.0
Emitted energy = 5.67 * 10**-8 * T**4
(W m-2) = (W m-2 degreeK -4)(degreeK)
Emitted energy = 5.67 * 10**-8 * (Ta+273.15)**4
5. The correction for the temperature effects for the longwave radiometers is
given by:
LWO = pyg.out.rad
- (3.5 * 5.67*10**-8)(pyg.out.dome**4 - pyg.out.case**4)
LWI = pyg.in.rad
- (3.5 * 5.67*10**-8)(pyg.in.dome**4 - pyg.in.case**4)
6. The sensible heat flux is calculated using the data from the U of W
sonic and the AIR fast temperature at 5 meters on the metflux tower.
Hs is generated in units of deg m s-1
H is required in units of W m-2 and may be obtained from Hs
Hs * rho * Cp = H
where rho = p/RT
where p is pressure in Paschals = P * 10**3 KPa
where R is the gas constant = 287.01 J Kg-1 degreeK-1
where T is the absolute temperature = Ta + 273.15
where Cp is constant pressure heat capacity = 1005 J Kg-1 degreeK-1
therefore:
Hs * rho * Cp = H
Hs * p/RT * Cp = H
Hs * P * 10**3 * (287.01 * (Ta5+273.15))**-1 * 1005 = H
Hs * P * 10**3 * 3.50 * (Ta5+273.15))**-1 = H
USAGE:
H <- Hs * P * 10**3 * 3.50 * (Ta5+273.15))**-1
THIS IS MORE ACCURATE THAN THE SIMPLER EXPRESSION WHICH COULD BE USED:
Hs * 1.17 * 10**3 = H
(deg ms-1)(J m-3 deg-1)=(J s-1 m-2)=(W m-2)
7. The friction velocity, ustar, is calculated using the data from the
U of W sonic at 5 meters on the metflux tower.
8. The stability parameter, zoL, is calculated
zoL = -kgz (Hs + 0.61 E (Ta5+273.15)/rho)/(ustar**3 (Ta5+273.15))
= -19.62*(Hs + 0.61 E (Ta5+273.15)/rho)*(ustar**-3)*((Ta5+273.15)**-1)
where rho is in mg m-3
USAGE:
zoL <- -19.62*(Hs + 0.61 E (Ta5+273.15)/rho)*(ustar**-3)*((Ta5+273.15)**-1)
Nota Bene: for more precise usage rho can be defined:
rho = p/RT = P * 10**3 * (287.01 * (Ta5+273.15))**-1
and calculated for each period.
9. The water vapour flux is calculated using the data from the Campbell
Krypton hygrometer and ATI 1-D sonic at 5meters on the chemflux tower.
E is required in units of mg m-2 s-1. The output is in g m-2 s-1,
and so it must be multiplied by 10**3
LE is required in units of W m-2. This is obtained from E
E * 1.91846 * T**2 / (T - 33.91)**2 = LE
where T is in degreeK
E * 1.91846 * (Ta5+273.15)**2/(Ta5+273.15 - 33.91)**2 = LE
E * 1.91846 * (Ta5+273.15)**2/(Ta5+239.24)**2 = LE
(mg m-2 s-1)(J mg-1) = (J s-1 m-2)=(W m-2)
USAGE:
LE <- E * 1.91846 * (Ta5+273.15)**2/(Ta5+239.24)**2
THIS IS MORE ACCURATE THAN THE SIMPLER EXPRESSION WHICH COULD BE USED:
E * 2.42 = LE
(mg m-2 s-1)(J mg-1) = (J s-1 m-2)=(W m-2)
10. For the calculation of water vapour pressure, ea, in KPa, twet and tdry
must be expressed in degrees K
ea = (2.1718 * 10**7 * exp(-4157/twet-33.91))
- (8.42 * 10**-4 * ((twet-33.91)/twet)**2 * P * (tdry-twet))
USAGE:
ea <- (2.1718 * 10**7 * exp(-4157/twet-33.91))
- (8.42 * 10**-4 * ((twet-33.91)/twet)**2 * P * (tdry-twet))
11. The specific humidity is derived from the water vapor pressure.
q = (R/Rw) * ea / P
where R is the gas constant for air = 287.01 J Kg-1 degreeK-1
Rw is the gas constant for water vapor= 461.5 J Kg-1 degreeK-1
ea is the water vapor pressure in kPa
P is the atmospheric pressure in kPa
q = 287.01/461.5 * ea / P
(Kg Kg-1)= (J Kg-1 degreeK-1)(J Kg-1 degreeK-1)**-1 (kPa)(kPa)**-1
q = 287.01/461.5 * 10**3 * ea / P
q = 6.22 * 10**2 * ea / P
(g Kg-1)
USAGE:
q <- 6.22 * 10**2 * ea / P
12. Conversion factor for water vapor flux
ie the amount of energy required to evaporate a mass of water.
1.0 W m-2 = 2.42 MJ kg(H2O)**-1
1.0 kg = 2.42 MJ
1.0 kg s-1 = 2.42 MJ s-1
= 2.42 * 10**6 W
13. The conversion for ppmv and mg m-3 for CO2
Molar volume = 22.414 liter (stp)
= 2.2414 * 10**-2 m3(stp).
= 2.2414 * 10**-2 * (101.3/P) * (T/273.15) m3(ambient)
where P in kPa and T in degreeK
= 2.2414 * 10**-2 * (101.3/P) * ((Ta5 +273.15) /273.15) m3
Molecular weight of CO2 = 44.01 g
Therefore:
44.01 g CO2 = 2.2414 * 10**-2 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 g CO2 = 2.2414/44.01 * 10**-2 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 mg CO2 = 2.2414/44.01 * 10**-5 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 m3 CO2 = (2.2414/44.01*10**-5*(101.3/P)*(Ta5+273.15/273.15))**-1 mg
1 m3 CO2 m-3 = (2.2414/44.01*10**-5*(101.3/P)*(Ta5+273.15/273.15))**-1 mg m-3
= 10**6 ppmv
1 ppmv CO2 = 10**-6 * (1 m3 CO2 m-3)
= 10**-6 *
(2.2414/44.01*10**-5*(101.3/P)*(Ta5+273.15/273.15))**-1 mg m-3
= 5.29 * P/(Ta5+273.15) mg m-3
and conversely
1 mg m-3 CO2 = 1.89 * 10**-1 * (Ta5+273.15)/P ppmv
To use these factors
CO2V = CO2M * 1.89 * 10**-1 * (Ta5+273.15)/P
ppmv mg m-3
14. The carbon dioxide concentration, CO2M, is required in units of mg m-3.
The output is in g m-3. Multiply by 10**3
15. The mass flux of carbon dioxide, FCO2M is required in units of mg m-2 s-1
Output is in g m-2 s-1. Multiply by 10**3
The equivalent energy flux of carbon dioxide, FCO2E, is required in units
of W m-2. This may be obtained
FCO2M * 11.3 = FCO2E
(mg m-2 s-1)(J mg-1) = (J s-1 m-2)
16. The flux of ozone, FO3V, is required in units of ppbv mms-1
The output is in ppbv ms-1. Multiply by 10**3
17. The conversion for ppbv and ug m-3 for O3
Molar volume = 22.414 liter (stp)
= 2.2414 * 10**-2 m3(stp).
= 2.2414 * 10**-2 * (101.3/P) * (T/273.15) m3(ambient)
where P in kPa and T in degreeK
= 2.2414 * 10**-2 * (101.3/P) * ((Ta5 +273.15) /273.15) m3
Molecular weight of O3 = 48.00 g
Therefore:
48.00 g O3 = 2.2414 * 10**-2 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 g O3 = 2.2414/48.00 * 10**-2 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 ug O3 = 2.2414/48.00 * 10**-8 * (101.3/P) * (Ta5 +273.15 /273.15) m3
1.00 m3 O3 = (2.2414/48.00*10**-8*(101.3/P)*(Ta5+273.15/273.15))**-1 ug
1 m3 O3 m-3 = (2.2414/48.00*10**-8*(101.3/P)*(Ta5+273.15/273.15))**-1 ug m-3
= 10**9 ppbv
1 ppbv O3 = 10**-9 * (1 m3 CO2 m-3)
= 10**-9 *
(2.2414/48.00*10**-8*(101.3/P)*(Ta5+273.15/273.15))**-1 ug m-3
= 5.77 * P/(Ta5+273.15) ug m-3
and conversely
1 ug m-3 O3 = 1.73 *10**-1 * (Ta5+273.15)/P ppbv
To use these factors remember that FO3V is reported in ppbv MILLEMETER s-1
O3M = O3V * 5.77 * P/(Ta5+273.15) ug m-3
ug m-3 ppbv
FO3M = FO3V * 5.77 * P/(Ta5+273.15) ug m-3
ug m-2 s-1 ppbv ms-1
18. Gravimetric soil moisture is calculated for each day by collecting
surface to 8 cm depth soil samples weighing them fresh,
drying the samples in an oven at 110 degrees C,
and after 24 hours reweighing them.
wf = (mass of fresh soil - mass of dry soil)/mass of dry soil
19. Soil heat capacity is derived by determination of the mineral fraction,
the organic fraction and the water fraction of the soil.
For the cotton site during the SJVAQS deployment the soil heat capacity was:
Csoil = (1.070 + 6.12 wf) * 10**6
(J degK-1 m-3)
(wf is listed in file gravmoist and logbook entry 167)
20. The soil temperatures corresponding to the depths
of 1cm, 3cm, 5cm, and 7cm
are obtained by demultiplexing the output of the three multiplex
sensor arrays. One set each corresponds to the north furrow, the ridge
and the south furrow.
The temperatures are weighted to generate weighted means for the
north furrow, the ridge and the south furrow. This is only done for
the 30 minute averaging time, not for individual 5 minute averaging times.
The following example is for the North furrow:
TsoilNf = (Tsoil1Nf + 3 * Tsoil3Nf + 3 * Tsoil5Nf + Tsoil7Nf)/8
21. The surface heat flux is obtained from the heat flux at 8cm, G8, and the
time varying soil temperature. The equation given here is for Nf, the north
furrow sensor array. Equivalent equations are appropriate for r, the ridge
sensor array, and Sf, the south furrow array.
GNf(i) = G8Nf(i)
+ Csoil*(0.08)*(TsoilNf(i+1)-TsoilNf(i-1))/(t(i+1)-t(i-1))
where (i-1) refers to data recorded at t(i-1)seconds
and (i+1) refers to data recorded at t(i+1)seconds
The interval involved is 30 * 60 = 1800 seconds. Thus:
(t(i+1)-t(i-1)) = 3600
OBJECT GENERATION
LWO <- pyg.out.rad - (3.5 * 5.67*10**-8)(pyg.out.dome**4 - pyg.out.case**4)
LWI <- pyg.in.rad - (3.5 * 5.67*10**-8)(pyg.in.dome**4 - pyg.in.case**4)
H <- Hs * P * 10**3 * 3.50 * (Ta5+273.15))**-1
zoL <- -19.62*(Hs + 0.61 E (Ta+273.15)/rho)*(ustar**-3)*((Ta5+273.15)**-1)
LE <- E * 1.91846 * (Ta5+273.15)**2/(Ta5+239.24)**2
ea <- (2.1718 * 10**7 * exp(-4157/twet-33.91))
- (8.42 * 10**-4 * ((twet-33.91)/twet)**2 * P * (tdry-twet))
q <- 6.22 * 10**2 * ea / P
CO2V <- CO2M * 1.89 * 10**-1 * (Ta5+273.15)/P
FCO2E <- FCO2M * 11.3
O3M <- O3V * 5.77 * P/(Ta5+273.15) ug m-3
FO3M <- FO3V * 10**-3 * 5.77 * P/(Ta5+273.15) ug m-3
TsoilNf <- (Tsoil1Nf + 3 * Tsoil3Nf + 3 * Tsoil5Nf + Tsoil7Nf)/8
Csoilf <- (1.070 + 6.12 wf) * 10**6