An advective‐diffusive isotopic evaporation‐condensation model

Abstract

Abstract.A one-dimensionM advective-diffusive model is developed for the evaporation process across an evaporating surface, providing a general theory of fractionation during evaporation and condensation. The model configuration is based on the Craig-Gordon linear evaporation model. We improve the model by allowing advection and diffusion to exist in the skin layer beneath the evaporating surface. The model is based on two fundamental physical principles, Henry's law and Fick's law. The model solutions show that diffusion of isotopes in both the atmosphere and the condensed phase plays an essential role in controlling the isotope flux ratio 5F, which is a measurable quantity. There are several dimensionless parameters that control the isotopic fractionation during evaporation. The most important parameter is N, which takes into account the evaporation rate and the depth of the advective-diffusive layer and represents the relative magnitude of the rate of advection versus the rate of diffusion. Assuming rapid surface exchange, the water vapor is always in isotopic equilibrium with the liquid water at the interface. Under the slow evaporation limit, i.e., N -• 0, the back flux from the atmosphere to the liquid water reservoir is not negligible compared with the upward flux; hence the net flux ratio must take into account information from the atmosphere such as the mixing ratio and the isotope ratios of water vapor. When N is large, the back flux becomes negligible, so the upward flux dominates the net flux and brings only the information of the liquid water reservoir into the net flux; therefore the flux ratio approaches the isotope ratio of the liquid water reservoir. The model also justifies itself by matching with independent theoretical results from earlier studies. Vapor condensation onto ice is also included as a special case in the model.

Experimental observation of transient <i>δ</i><sup>18</sup>O interaction between snow and advective airflow under various temperature gradient conditions

“…The results also support the statement that an interplay occurs between theoretically expected layer-by-layer sublimation and deposition at the icematrix surface and the isotopic content evolution of snow cover due to mass exchange between the snow cover and the atmosphere (Sokratov and Golubev, 2009). The specific surface area of snow exposed to mass exchange (Horita et al, 2008) and by the depth of the snow layer exposed to the mass exchange with the atmosphere (He and Smith, 1999) plays an important role. Our results support the interpretation that changes in surface snow isotopic composition are expected to be significant if large day-to-day surface changes in water vapour occur in between precipitation events, wind pumping is efficient and snow metamorphism is enhanced by temperature gradients in the upper first centimetres of the snow (Steen-Larsen et al, 2014a).…”

Air parcel trajectory analysis of stable isotopes in water vapor in the eastern Mediterranean

“…Whereas equilibrium fractionation is well understood theoretically [ Bigeleisen , 1961] and in laboratory experiments [ Majoube , 1971; Horita and Wesolowski , 1994], the situation for nonequilibrium effects is less clear. In particular, there are several models describing evaporation of water from the sea [ Craig and Gordon , 1965; Merlivat and Jouzel , 1979], based upon the theory of one‐dimensional advective‐diffusive systems [ He and Smith , 1999], but there is only very little isotope data available which can be used to validate these models. Hence, it is not clear if some of the assumptions are oversimplified and if all critical physical processes are properly represented.…”

Snow isotopic content change by sublimation

“…The empirical equilibrium fractionation factors corresponding to this mass exchange are not directly linked to the overall evolution of the isotopic content of snow. The latter is affected at least by the specific surface area of snow exposed to mass exchange (Horita and others, 2008) and by the depth of the snow layer exposed to the mass exchange with the atmosphere (He and Smith, 1999). Several centimeters of snow are a source of sublimation from snow, partly because of interconnection of pores and partly due to observed sublimative cooling resulting in temperature gradient formation (Golubev and Sokratov, 1991).…”