Evaporative water loss equations

For Evaporative Water Loss (VH₂O), the program assumes that due to O₂ consumption and CO₂ production, there are gas volume changes between the part of the system where flow rate is measured (whether upstream or downstream of the chamber) and the point where water content is measured. The 'full' equation is:

EWL = {[ (FeH₂O (1 – FiO₂ – FiCO₂ – FiH₂O) / (1 – FeO₂ – FeCO₂ – FeH₂O]) – FiH₂O } * STP * FR

where EWL is ml H₂O vapor/min; the program applies an appropriate correction for whatever output units are selected. If you only measured O₂ content (and not CO₂), then FeCO₂ is estimated from FeO₂ and RQ:

EWL = {[ (FeH₂O (1 – FiO₂ – FiCO₂ – FiH₂O) / (1 – FeO₂ – RQ*(FiO₂ – FeO₂) – FeH₂O]) – FiH₂O } * STP * FR

In the above equations, VO₂ (and VCO₂ in the first case) are read from a data channel. You can also use a constant VO₂ if your data file contains only humidity data.

These equations (from Withers 2001, Aust. J. Zool. 49) are fairly complex, and figuring out FiH₂O and FeH₂O from typical humidity data is also complicated, because of the non-linear relationship between temperature and the water content of a gas.

Water vapor content is usually measured as either percent relative humidity or dew point temperature (in °C); some instruments can output vapor pressure as Pascals (or kiloPascals), or vapor density as g H₂O vapor / m³ (same as mg H₂O / L or µg H₂O / mL). Select the appropriate units for your humidity sensor's output. For any units, values must be converted into water vapor densities and then into fractional concentrations. The equations for computing water vapor density are arithmetically rather nasty (and therefore the speed of conversion isn't as fast for some EWL calculations as for other kinds of gas exchange). If you use % RH, the algorithms need to know the temperature of the humidity sensor. You can either enter this directly or the value can be obtained from a data channel. In the latter case, and for all analyses of dew point data, vapor density calculations must be repeated for each sample point. That slows the rate of conversion considerably, so a progress bar is shown if the number of samples is high.

The algorithms used to compute vapor density are derived from Properties of Air, by Tracy, Welch, and Porter (1980; University of Wisconsin; you can find a pdf on the Web via Google Scholar). In turn, these are based on the Smithsonian Meteorological Tables. For those interested, the formulae used are as follows:

• Vapor pressure (pw) at temperatures over liquid water (Smithsonian Tables, 1984, after Goff and Gratch, 1946):

Log10 pw = -7.90298 (373.16 T-1)
+ 5.02808 Log10(373.16 / T)
- 1.3816 10^-7 (10^11.344 (1-T / 373.16) -1)
+ 8.1328 10^-3 (10^-3.49149 (373.16 / T-1) -1)
+ Log10(1013.246)
with T in °K and pw in hPa

• Vapor pressure (pi) at temperatures below 0 °C (over ice; Smithsonian Tables, 1984):

Log10 pi = -9.09718 (273.16/T - 1)
- 3.56654 Log10(273.16/ T)
+ 0.876793 (1 - T/ 273.16)
+ Log10(6.1071)
with T in °K and pi in hPa

The Goff-Gratch equation (for air over liquid water) covers a temperature range of -50 °C to about 100 °C, but is mostly theoretical for very low temperatures. Accuracy is probably ±0.5% or better at temperatures between -20 and 70 °C.

• CAUTION: regardless of the accuracy of the equations, technically it is very difficult to avoid condensation or freezing of water vapor when working at subzero temperatures.