On evapotranspiration and eddy covariance measurements corrections

Eddy Covariance (EC) technique is one of the most used technique monitoring Green House Gases (GHG) fluxes such as H2O, CO2, CH4. Water vapor movement and corresponding air density fluctuations were corrected by Webb et al (1980) but not water vapor formation. Classic EC technique supposes mean air vertical speed nullity when it cannot be the case because of water evaporation. Water is falling as a liquid, evaporating directly from soil surface, from shallow soil 10 subsurface or either through vegetation transpiration and becomes a gas which corresponds to a notable volume expansion. Water vapor is mounting through atmosphere, compensating in a cloud and falling as a rain (liquid) again. Evaporation and corresponding volume expansion make mean vertical air speed positive (upgoing) and influence more or less a flux balance following concerned gas or energy. A simple accessing and corresponding correction for the half hourly summation is given and applied to a 11-month real set of data. These corrections allow to explain, in part, most observed eddy covariance 15 discrepancies.

fluctuating part , after simplifications supposing spatial, horizontal homogeneity and air density fluctuations ́ negligibility the flux is given by a relatively simple one-dimensional Eq. (1): 30 With r being the mixing ratio of the gas of interest defined by a density ratio r = Eddy covariance vertical air velocity time-mean nullity assumption = 0 allows to simplify again flux calculation formula and retain only the turbulent part Eq. (2): Neglecting main vertical air speed part (called in this note: correction flow) and given by Eq. (3): However, due to water evaporation, the main air vertical speed cannot be nil and is mainly positive (upgoing) since water is falling on the soil surface as a liquid and is returning to the atmosphere as a gas which is accompanied by more than about 1245-fold volume increase. The only exception is during the dew formation when the vertical mean air speed is negative. 40 Dew formation versus rainfall is not negligible only in arid climates where during dry periods dew may reach up to 50% of rainfall water apport (Hao et al. 2012). For accessing the missing flux part as a rough estimation on can use few generic meteorological values. For 1 mm of precipitation, 1 kg of water fall on 1 m² of soil surface. 1 kg of water is 1000/18=55.5(5) mol of water. After evaporation, supposing water vapor a perfect gas at standard pressure PS = 101.325 kPa and standard temperature TS = 0 °C (273.15 K), volume occupied by the water vapor is 22.414 l by mol then the total volume for 1 kg of 45 evaporated water is 22.414*55.5(5) = 1245 l = 1.245 m 3 . Volume increase is then about 1250-fold initial water volume (real temperature is mainly higher than TS making volume increase even bigger than 1245-fold). This volume increase, for 1 mm evaporated rainfall by year, causes a vertical, upgoing air speed Ve = 1.25 m/year which is rather small (Ve = 0.017 mm/s) and well below the sensibility of any anemometer however, this speed is almost always in the same sense; upgoing, and when calculating correction flux; = * * ̅ (vertical mean air speed contribution to the total flux), we have to 50 multiply by ̅ (time-mean mixing ratio) which is, of course, much bigger than the fluctuating part of the mixing ratio .

Missed carbon dioxide flux part assessing
Carbon dioxide volume mixing ratio follows a diurnal and seasonal pattern especially in the surface layer (less than 20 m from the surface) (Satar et al. 2016) where are implemented most of the eddy covariance towers, but as a minimum for 55 carbon dioxide mixing ratio on can retain 400 ppm-v (volume parts per million). For mass flux measurements, the useful mixing ratio is mass mixing ratio. As carbon dioxide is about 1.67 heavier than air, the mass mixing ratio of carbon dioxide will be 1.67-fold its volume mixing ratio. With 400 ppm-v we get then about 670 ppm-m (mass mixing ratio). As the mean

Eddy Covariance measurements correction
Underestimation of the upgoing fluxes by eddy covariance can be corrected at least on the half hourly time-mean basis. As the mean wind speed is too small to be monitored moreover subject to errors due to any possible vertical misalignment of used anemometer and resulting vertical speed biases, an assessment of Fc should be rather based on the evaporation rate. 70 Since most of the used analyzers for eddy covariance measurements are providing water vapor content, monitoring it along with water vapor turbulent transport allows through few simplifications to deduce water vapor production and then corresponding air volume increase. Indeed, water vapor turbulent flow F measured by eddy covariance setup corresponds to water vapor production P and its stockage S variation under EC level. On a half hourly base, first should be estimated the mean vertical air speed . As this speed results from water vapor 85 formation, assuming water vapor stockage variation negligibility and mean water vapor transport being turbulent, production is equal to water vapor flow . Supposing water vapor being a perfect gas, corresponding mean volume occupied by water vapor with a square meter surface base will have a hight h given by Eq. (5) With R being perfect gas constant, n number of produced water vapor mols, mean air temperature (supposed to be 90 uniform and the same as the formed water vapor temperature) and mean air pressure (supposed to be uniform and the https://doi.org/10.5194/bg-2020-43 Preprint. Discussion started: 28 February 2020 c Author(s) 2020. CC BY 4.0 License. same as the formed water vapor pressure). Supposing air pressure the same at EC level and at evaporation level (soil level for soil evaporation or leaf level for vegetation transpiration) is realistic. The same supposition for air temperature is less realistic but, this is not very important since water vapor, once formed at some temperature, during its trip from evaporation level to EC level, will acquire air temperature expending or collapsing accordingly. Vertical mean air speed is sensible to the 95 whole air volume expansion below EC level and then, supposing water vapor formation at EC level air temperature, or water vapor formed at a different temperature reaching EC air temperature progressively is the same from the volume expansion point of view.
By temporal derivation considering initially water vapor flux as only turbulent (with [ ] = mol/m²/s) we obtain the first pass mean vertical air speed by Eq. (6): 100 With this value using mean water vapor molar density we obtain the correction water vapor flux bay Eq. (7) = * Since is in the rage of 1% of it will not be necessary to recalculate again a new correction by iteration up to reach a stable value for total water vapor flux and for the rest of the assessment we may retain this value given by Eq. (8) With being mean carbon dioxide molar density, being air mass density, being air heat capacity (given by SmartFlux2 computations but can be calculated independently based on dry air and water vapor heat capacities, RH and air temperature), being evaporation water latent heat depending on air temperature and given by Eq. (13), and being water molar mass (18.01528 g/mol): 120 = (3147.5 − 2.372 * ) in J/g or kJ/kg (13) https://doi.org/10.5194/bg-2020-43 Preprint. Discussion started: 28 February 2020 c Author(s) 2020. CC BY 4.0 License.
This time, assuming temperature of the evaporating water being the same as air temperature is not strictly speaking correct but the difference of for a 10 K (or 10°C) temperature difference is only 0.75% wide. Then a committed error equating evaporation temperature to air temperature at EC level is acceptable.
importance when the latter correction is relatively small. However, in EC case, corrections due to water evaporation (evapotranspiration on a vegetated plot) do not invalidate usual corrections that are supposing mean vertical air speed nullity 155 such as Webb-Pearman-Leuning (WPL) correction since instantaneous values of the mean vertical speed are very small and assumed its nullity is used to compare vertical dry air velocity versus vertical water vapor velocity. Only, on the half hourly basis, corresponding corrections have to be applied. 160 Webb et al. (1980) introduced eddy covariance corrections due to the water vapor propagations and resulting air density fluctuations. Supplementary corrections proposed here consist to take into account water vapor formations and resulting air volume expansion. All gas and energies flux can be easily assessed using usual EC measurements and results are matching most of the observed EC discrepancies: underestimation of carbon dioxide flux, underestimation of sensible heat flux, underestimation of Bowen ratio or even energy balance closure leak.