Unsaturated flow theory is one of the cornerstones of hydrology. For nearly a century, the Richards equation has provided a mathematical framework for describing how water moves through partially saturated soils. At its core lies a powerful simplification: the hydraulic state of soil can be described by water content alone.
Yet decades of experiments tell a different story.
Across laboratories, field sites, and scales, soil water exhibits behaviors that contradict this assumption in systematic ways. These contradictions have become known, implicitly if not always explicitly, as paradoxes of vadose zone hydrology. They persist not because of experimental error, but because they expose limits in the classical conceptual model.
Below, we review five such paradoxes that continue to shape how hydrologists think about unsaturated flow.
1. Hysteresis
The same water content, different hydraulic states
Observation
During wetting, soils follow a different relationship between water content and matric potential than during drying. Hydraulic conductivity likewise differs between wetting and drying paths, even at identical water content.
Why this is paradoxical
Classical theory assumes a unique retention curve and unique conductivity function. Hysteresis directly violates this assumption and implies that soil retains memory of its past.
2. Rate Dependence
Why infiltration speed changes soil properties
Observation
Fast infiltration experiments routinely yield hydraulic conductivities several times larger than values obtained under slow, quasi-static conditions, even in the same soil.
Why this is paradoxical
Hydraulic conductivity is assumed to be a material property. If that were true, it should not depend on how quickly water is applied.
3. Scale Dependence
Why field conductivities exceed laboratory values
Observation
Field-scale saturated or near-saturated hydraulic conductivities are often one to two orders of magnitude larger than laboratory measurements on the same soil material. The discrepancy increases with measurement scale.
Why this is paradoxical
If conductivity is intrinsic to the soil, it should not depend on the size of the experiment.
4. Persistence of Compaction Effects
Why soils don’t recover hydraulically
Observation
Mechanical compaction reduces hydraulic conductivity dramatically. Even after bulk density and porosity appear to recover, conductivity often remains suppressed for years.
Why this is paradoxical
If conductivity depends primarily on porosity, it should recover once porosity does.
5. Non-Commutativity of Wetting and Drying
Why the order of processes matters
Observation
Wetting followed by drying does not lead to the same hydraulic state as drying followed by wetting, even if final water content is identical.
Why this is paradoxical
In classical physics, state variables are path-independent. Soil water violates this expectation.
A Shared Message from Five Paradoxes
Each paradox has often been addressed with a separate modeling fix—hysteresis rules, dynamic conductivity, macropore domains, or empirical memory terms. Taken together, however, they point to a single conclusion:
Water content alone is insufficient to describe the hydraulic state of soil.
Soils exhibit memory, path dependence, and sensitivity to forcing because internal processes do not instantaneously equilibrate.
Why Hydrologists Should Care
These paradoxes affect:
infiltration and runoff prediction
groundwater recharge estimates
irrigation efficiency assessments
land–surface and Earth system models
transfer of parameters from lab to field
They remind us that the vadose zone is not a passive filter but a dynamic system with internal states and history.
References
Haines, W. B. (1930). Studies in the physical properties of soil: V. The hysteresis effect. Journal of Agricultural Science, 20(1), 97–116. DOI: 10.1017/S002185960008864X
Mualem, Y. (1974). A conceptual model of hysteresis. Water Resources Research, 10(3), 514–520. DOI: 10.1029/WR010i003p00514
Smiles, D. E., Vachaud, G., & Vauclin, M. (1971). A test of the uniqueness of the soil moisture characteristic during transient, nonhysteretic flow. Soil Science Society of America Journal, 35, 534–539. DOI: 10.2136/sssaj1971.03615995003500040007x
Beven, K., & Germann, P. (1982). Macropores and water flow in soils. Water Resources Research, 18(5), 1311–1325. DOI: 10.1029/WR018i005p01311
Hamza, M. A., & Anderson, W. K. (2005). Soil compaction in cropping systems: A review. Soil and Tillage Research, 82, 121–145. DOI: 10.1016/j.still.2004.08.009
Philip, J. R. (1964). Similarity hypothesis for capillary hysteresis. Soil Science, 97(3), 155–164. DOI: 10.1097/00010694-196403000-00001
Kool, J. B., & Parker, J. C. (1987). Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties. Water Resources Research, 23(1), 105–114. DOI: 10.1029/WR023i001p00105
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