There is an increasing interest in identifying soil hydraulic properties from simplified evaporation experiments. However, the conventional simplified evaporation method includes a deficit due to using the linear assumption and not accounting for uncertainty in parameters. A suggested alternative method is assessing the parameter uncertainties through inverse modeling. We examined the combination of a Bayesian inverse method, namely, DREAM_(ZS), and a numerical simulation model, namely, HYDRUS-1D, for parameter inversion with data in simplified evaporation experiments. The likelihood function could be conditioned only on pressure head observations (single-objective (SO)), or on both pressure head and evaporation rate observations (multi-objective (MO)), with different treatments on the top boundary condition. Three synthetic numerical experiments were generated in terms of the soil types of sand, loam and clay to verify the inverse modeling method. The MO approach performed better than the SO approach and linear assumption when the stage 1 evaporation rate was kept constant. However, the SO inversion was more robust when oscillations existed in the potential evaporation rate. Then, the SO inverse modeling was adopted to investigate two real experiments on loamy-sand soils and compared with the linear assumption. The linear assumption could be reliable for wet conditions with stage 1 evaporation but was not always useable for a relatively dry condition, such as that with stage 2 evaporation. The inverse modeling could be more successful in capturing the whole evaporation process of soils when both stage 1 and stage 2 were involved.

Accurate estimation of boundary conditions is essential to the success of numerical schemes for modeling soil water flow processes. The flux‐type boundary condition, which is integration of many boundary fluxes and subsurface conditions, is traditionally estimated from hydrologic and meteorological information. However, such information could be rapidly variable in space and time and difficult to measure and quantify accurately. This study inversely estimates upper flux boundary conditions by calibrating interior observations of soil moisture. Unknown flux boundaries with both spatiotemporal and temporal only variabilities are studied. In the case of spatiotemporal variability, we formulate the inverse model by extending a Tikhonov regularization framework proposed in our previous study, which calibrated a macroscopic root water uptake model in one‐dimensional soil water flow. The developed method is efficient because it takes advantage of the strategy in the previous study that the inversion is transformed to a variational problem, and also because it incorporates locally one‐dimensional operator splitting technique to overcome the computation complexity when dealing with multidimensional flow processes. When flux boundaries vary with time only (special case), we have found that the inversion degenerates into a well‐posed problem and formulated the inversion explicitly without use of regularization. Numerical tests are conducted through both one‐dimensional (well‐posed) and two‐dimensional (ill‐posed) heterogeneous soil profiles to illustrate the effectiveness of the proposed inverse formulation. Particularly, the applicability of the inverse formulation in the special case is further validated in field experiments using in situ measurements in arid and semiarid northern China.