This manuscript systematically investigates the effects of gravity during soil-limited (Stage 2) evaporation from bare soil. Analytical and numerical solutions to the one-dimensional Richards soil moisture flow equation are developed based on simplified hydraulic functions that depend exponentially on soil water matric potential. Semi-infinite domains with either freely draining or hydrostatic bottom boundary conditions and finite domains with no-flow bottom boundary conditions are considered. Cases with gravity are directly compared to those without. The simplified solutions are verified by comparison to numerical solutions with fully realistic soil hydraulic functions for two soils at the extreme ends of the range of possible soil textures. Cumulative evaporation versus time and soil volumetric water content versus depth at selected times are determined for each case from the simplified solutions. These results are reported in terms of non-dimensional variables that are universal, spanning all soil textures and other conditions. For the semi-infinite domain cases cumulative evaporation with gravity is reduced by several orders of magnitude for very coarse soils at times of practical interest while gravity has a negligible effect for the finest textures at those times. For the finite domain cases gravity is less important because cumulative evaporation is ultimately limited by the fixed amount of water in the profile.

中文翻译：

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土壤受限条件下重力对蒸发的影响

这份手稿系统地研究了裸土在土壤受限（第 2 阶段）蒸发过程中重力的影响。一维理查兹土壤水分流动方程的解析和数值解是基于简化的水力函数开发的，该水力函数以指数方式依赖于土壤水基质势。考虑具有自由排水或静水底部边界条件的半无限域和具有无流动底部边界条件的有限域。有重力的情况直接与没有重力的情况进行比较。通过与具有完全真实的土壤水力函数的数值解进行比较，验证了简化的解，这两种土壤位于可能的土壤质地范围的最末端。从简化的解决方案中确定每种情况下的累积蒸发与时间的关系以及在选定时间的土壤体积含水量与深度的关系。这些结果是根据普遍的无量纲变量报告的，涵盖所有土壤质地和其他条件。对于半无限域的情况，在实际感兴趣的时候，对于非常粗糙的土壤，重力的累积蒸发会减少几个数量级，而在那些时候，重力对最精细的质地的影响可以忽略不计。对于有限域情况，重力不太重要，因为累积蒸发最终受到剖面中固定水量的限制。跨越所有土壤质地和其他条件。对于半无限域的情况，在实际感兴趣的时候，对于非常粗糙的土壤，重力的累积蒸发会减少几个数量级，而在那些时候，重力对最精细的质地的影响可以忽略不计。对于有限域情况，重力不太重要，因为累积蒸发最终受到剖面中固定水量的限制。跨越所有土壤质地和其他条件。对于半无限域的情况，在实际感兴趣的时候，对于非常粗糙的土壤，重力的累积蒸发量减少了几个数量级，而在那些时候，重力对最精细的质地的影响可以忽略不计。对于有限域情况，重力不太重要，因为累积蒸发最终受到剖面中固定水量的限制。