Identification of effective process formulations for evaporation of water from bare soil

• Applicant: Professor Dr. Wolfgang Durner
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 66234063

• Final Report Year: 2017

Final Report Abstract

The Richards equation as process model is currently the standard concept for the simulation of variably-saturated water flow in soils. However, measurements and theoretical considerations suggest that the local equilibrium between water content and pressure head, assumed by the Richards equation, is violated under some conditions which leads to so-called “dynamic effects”. Another situation in which the Richards equation can fail to describe variably-saturated flow correctly is the process of evaporation. In dry soil, numerical simulations with the Richards equation often suffer from instabilitities and lead to results which are not in agreement with measured fluxes and/or the observed temporal dynamics of state variables. Our aim in SP4 was to explore the limits of the Richards’ equation as a tool to simulate transient water flow in soil. Specifically, we investigated (i) the ability of the Richards model to model “dynamic non-equilibrium phenomena” in variably-saturated flow and (ii) its ability to predict coupled water, vapor and heat flow in near surface soil under atmospheric forcing. We used different laboratory experiments with homogeneously packed soils and conducted inverse simulations to investigate theses questions. Furthermore, we studied how an improved conceptualization of pore space properties influences upscaled hydraulic properties on the continuum scale. Specifically, the effect of a angular pore shape and a varying liquid-solid contact angle was considered. As expected, we found that the standard Richards equation with the currently used parametrizations for hydraulic properties cannot be used to accurately simulate the observed water regimes. However, it was possible to adapt the Richards equation to improve this. Non-equilibrium water flow could be simulated with an effective dual porosity model (DUAL-DNE), which combines the Richards equation with a first-order non-equilibrium model. The modified model described a broad variety of non-equilibrium phenomena, observed in experiments with different boundary conditions, adequately. To the best of our knowledge, no effective non-equilibrium model concept has been shown to be successful in describing such a broad spectrum of DNE phenomena before. Upscaling of the angular pore-bundle model with varying contact angle led to closed-form equations for soil water retention, unsaturated hydraulic conductivity, and liquid-air interfacial area. The model was validated using imbibition and drainage data of ethanol and water measured in our lab and soil hydraulic property data from the literature. It directly explained how macroscopic hysteresis depends on pore-space geometrical features and differences in wettability during imbibition and drainage. To adequately describe the time series of pressure head in transient laboratory evaporation experiments under different boundary conditions, we had to change the standard parametrizations of the soil hydraulic properties. We improved standard models in the dry range by incorporating film and corner flow and ensuring a water content of zero at oven-dryness. In addition, we improved the prediction of hydraulic conductivity by constraining the pore-size in capillary bundle models to a physically plausible maximum value. The model concepts were successfully tested under lab conditions and finally applied to data measured in a large weighing lysimeter in a desert. We identified effective soil hydraulic properties at the lysimeter scale and validated a coupled model of water, vapor, and heat flow which was driven by meteorological data and coupled to the atmosphere by an aerodynamic resistance approach. The model-predicted cumulative actual evaporation differed by only 5% from the lysimeter-derived fluxes. Summarizing, the Richards equation with a suitable extension to describe non-equilibrium and improved parametrizations of the constitutive relationships was shown to be capable of simulating variably-saturated water dynamics in agreement with experimental data for a broad variety of experiments.

Publications

• (2013): Physically-based model of soil hydraulic properties accounting for variable contact angle and its effect on hysteresis, Advances in Water Resources 59, 169-180
  Diamantopoulos, E., and W. Durner
  
• (2014): Comment to “Simple consistent models for water retention and hydraulic conductivity in the complete moisture range” by A. Peters, Water Resour. Res., 50, 7530-7534
  Iden, S.C., and W. Durner
  
• (2015): Closed-form model for hydraulic properties based on angular pores with lognormal size distribution, Vadose Zone Journal, 14(2)
  Diamantopoulos, E., and W. Durner
  
• (2015): Improving prediction of hydraulic conductivity by constraining capillary bundle models to a maximum pore size, Advances in Water Resources 85, 86-92
  Iden, S.C., A. Peters, and W. Durner
  
• (2015): Modelling dynamic non-equilibrium water flow observations under various boundary conditions, Journal of Hydrology 529, 1851-1858
  Diamantopolous, E., W. Durner, S.C. Iden, U. Weller, and H.-J. Vogel
  
• (2015): Revisiting the simplified evaporation method: Identification of hydraulic functions considering vapor, film and corner flow, Journal of Hydrology 527, 531-542
  Peters, A., S.C. Iden und W. Durner
  
• (2016): Prediction of capillary air-liquid interfacial area vs. saturation function from relationship between capillary pressure and water saturation, Advances in Water Resources
  Diamantopoulos, E., W. Durner, and T. Harter