Revisiting Salvucci's semi-analytical solution for bare soil evaporation with new consideration of vapour diffusion and film flow

Bare soil evaporation is controlled by a combination of capillary flow, vapour diffusion and film flow. Relevant analytical solutions mostly assume horizontal flow conditions and ignore gravitational effects. Salvucci (1997) provided a rare example of a semi-analytical solution for ver10 tical bare soil evaporation. However, he did not explicitly represent vapour diffusion and film flow, which are likely to account for a significant proportion of total flow during vertical evaporation from soils. Vapour diffusion and film flow can be incorporated via Salvucci’s desorptivity parameter, which represents the proportionality constant relating Stage 2 cumulative evaporation to the square root of time under horizontal flow conditions. The objective of this article is to implement vapour diffusion and film flow within Salvucci’s semi-analytical solution and test its performance by comparison with isothermal numerical simulation and relevant experimental data. The following important conclusions are drawn. Analyticalsolutions that assume horizontal flow conditions are inadequate for understand18 ing vertical evaporation problems because they overestimate evaporation rates and mostly predict vapour diffusion and film flow to be of negligible influence. Salvucci’s semi-analytical solution is ef20 fective at predicting the order-of-magnitude reduction in evaporation caused by gravitational effects. However, it is unable to identify the correct importance of vapour diffusion and film flow because these processes can only be represented through its desorptivity parameter.