Unsaturated Flow Basics


tree with roots

The unsaturated zone, often called the vadose zone, is the portion of the subsurface above the water table. It contains, at least some of the time, air as well as water in the pores. Its thickness can range from zero, as when a lake or marsh is at the surface, to hundreds of meters, as is common in arid regions.

What happens in the unsaturated zone?

First, there is storage—of water, plant nutrients, and other substances. The unsaturated zone is not always considered a major storage component of the hydrologic cycle because it holds only a minute fraction of the earth's fresh water and this water is usually difficult to extract. But it is of great importance for water and nutrients of the biosphere.

Second, the unsaturated zone is a zone of transmission of water and other substances. This is how it has been seen from some hydrologic viewpoints, as to a large degree it controls the transmission of water to aquifers, as well as to the land surface, to water on the surface, and to the atmosphere. It may be a controlling factor in the amount of water that replenishes an aquifer, or it may yield information that permits this replenishment to be quantified. It is often regarded as a filter, removing undesirable substances before they affect aquifers. This idea contains some truth, but some common unsaturated-zone processes transport water to groundwater and surface water bodies with high efficiency and little removal of contaminants.

Third, the unsaturated zone is a zone of natural and human-induced activity. Its constituents do not passively reside in place or steadily pass through. There are transport processes of various kinds, thermodynamic interactions, and chemical reactions involving both natural and artificial substances. There is the biological activity of plant roots, rodents, worms, microbiota, and other organisms. As a zone of human activity, the unsaturated zone is critical to the cultivation of plants, construction of buildings, and disposal of waste.

The flow rate of water is often directly of interest, for example in estimating how fast water moves down to the water table, that is the aquifer recharge rate. It also is critical in the transport of contaminants, whether dissolved or in the form of a nonaqueous liquid or solid. The usual first step in assessing the rate of spreading of contaminants in the subsurface is to assess the flow rate of water that moves the contaminant along with it.

subsurface illustration

Fundamentals of unsaturated flow

The most basic measure of the water in an unsaturated medium is water content or wetness (commonly symbolized q), defined as the volume of water per bulk volume of the medium. Water is held in an unsaturated medium by forces whose effect is expressed in terms of the energy state or pressure of the water. Various types of pressure may be relevant in unsaturated hydrology, but one called the matric pressure or matric potential ( arising from the interaction of water with the rigid matrix) is of unique interest, as it substantially influences the chief transport processes. Matric pressure (commonly symbolized y) is the pressure of the water in a pore of the medium relative to the pressure of the air. When a medium is unsaturated, the water generally is at lower pressure than the air, so the matric pressure is negative.

Greater water content goes with greater matric pressure. Zero matric pressure is associated with high (saturated or nearly saturated) water content. As matric pressure decreases the water content decreases, but in a way that is nonlinear and hysteretic. The relation between matric pressure and water content, called a retention curve, is a characteristic of a porous medium that depends on the nature of its pores. This relation influences the movement of water and other substances in unsaturated media and controls the work that a plant has to do to extract water from the soil.

The hydraulic conductivity, a measure of how easily water moves through the medium for a given driving force, is a second characteristic that is critical to water movement. The hydraulic conductivity (commonly symbolized K) has a highly sensitive and nonlinear dependence on the water content.

Usually we assume that the flow rate of water is equal to the hydraulic conductivity times the driving force (typically gravity and pressure differences). This relation is known as Darcy's law. Applied to unsaturated conditions, it is often called the Darcy-Buckingham law in recognition of Edgar Buckingham, who developed the concepts of matric pressure and unsaturated hydraulic conductivity that are essential in applying Darcy’s law to unsaturated media. For quantification when the flow is steady, Darcy's law may suffice on its own. The more general case of unsteady or transient flow in unsaturated porous media is a highly dynamic phenomenon, and may be represented quantitatively by a combination of Darcy's law and the continuity or conservation law for water. Richards' equation combines both of these laws in one formula. Use of Darcy's law requires measured or estimated K over the appropriate range of moisture states, and Richards’ equation requires knowledge of the water retention curve in addition to K. Other forces may also drive flow under some conditions, as when temperature or osmotic gradients are significant.

Much unsaturated-zone transport of importance, especially when water is abundant, occurs through a small fraction of the medium along preferential paths such as wormholes, fractures, fingers of enhanced wetness, and contact regions between dissimilar portions of the medium. This flow, for which there is not yet (in 2010) a widely accepted theory, occurs at rates typically some orders of magnitude faster than flow through the remainder of the medium. In many applications, its importance is redoubled because preferentially transported substances are exposed to only a small fraction of the soil or rock and only for limited time, reducing opportunity for adsorption or reactions.<

Types of preferential flow

Three basic modes of preferential flow are (1) macropore flow, through pores distinguished from other pores by their larger size, greater continuity, or other attributes that can enhance flow; (2) funneled (or deflected or focused) flow, caused by flow-impeding features of the medium that concentrate flow in adjacent zones that are highly wetted and therefore conductive; and (3) unstable flow, which concentrates flow in wet, conductive fingers.

Common macropores include wormholes, root holes, and fractures. When macropores are filled with water, flow through them can be fast if there are no significant restrictions along the path to a region where water can freely accumulate. Diffuse flow through the remainder of the medium may be called matrix flow. When completely empty, macropores may conduct essentially no flow, and may also constitute a barrier to matrix flow. Macropores that are partly filled with water provide a variety of possibilities for the configuration and flow behavior of water, such as free-surface film flow along macropore walls.

Funneled flow commonly occurs with contrasting layers or lenses, where flow deflected in direction becomes spatially concentrated. The local increase in matric pressure causes a corresponding increase in hydraulic conductivity and flux, and usually a change in the predominant direction of flow.

Unstable variations in flow and water content, even within a uniform portion of the medium, can increase flow rates considerably. A typical case has a layer of fine material above the coarse material. Downward percolating water builds up significantly at the interface, and breaks through into the coarse medium at a few points. The material near individual points of breakthrough becomes wetter and hence much more conductive. For some time thereafter, additional flow into the coarse material moves in the few fingers that are already wet. Between fingers, the medium can be relatively dry. In addition to textural contrasts, hydrophobicity (water repellency) and air trapping may cause flow instability.

The preferential domain is here considered as the portion of the pore space within which the water flux moves over macroscopic distances through conduits of macroscopic length, conduit being defined as a linearly extended volume through which water can flow faster than can be explained in terms of diffuse flow. In general such a conduit could be a macropore filled with water, or a fraction of the pore volume that is water-filled, or a narrow path composed of many microscopic pores of markedly higher water content than the average water content outside that path.


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  • Nimmo, J.R., 2004a, Porosity and Pore Size Distribution, in Hillel, D., ed., Encyclopedia of Soils in the Environment, Academic Press, London. (PDF)

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  • Nimmo, J.R., and Landa, E.R., 2005, The soil-physics contributions of Edgar Buckingham: Soil Science Society of America Journal, v. 69, p. 328-342. (PDF)

  • Nimmo, J.R., 2008, The Public Fountains of the City of Dijon by H. Darcy--translated by P. Bobeck [Book Review]: Vadose Zone Journal, v. 7, no. 4, p. 1311-1312. (PDF)
  • Nimmo, J.R., 2009, Vadose Water, in Likens, G.E., ed., Encyclopedia of Inland Waters: Oxford, UK, Elsevier, v. 1, p. 766-777. (PDF)


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    Last modified: Jan. 2013