Water in the unsaturated zone - Ch. 8
Soil is a mechanical mixture of mineral and organic material, water and air.
Soil volume occupied by water or air is the pore volume
Water table, typically some depth beneath the surface, is the region with all pore volume is filled
with water at pressures greater than atmospheric
Between surface and groundwater table is the unsaturated zone or vadose zone. Zone will vary in
thickness significantly between sites and within a site as the groundwater level rises and falls.
The ability of terrestrial plants to extract water through roots from this region depends on the
ratio of available water/available water capacity in the soil water zone as previously discussed.
The soil water zone is typically defined as the rooting depth of the soil.
Some basic soil variables:
Soil texture refers to the grain size distribution of the mineral soil
Gravels, sands silts: in decreasing order of grain size are products of mechanical
breakdown of rock material
Clays: microscopic grains of secondary minerals, typically with a surface
electronegative charge. Charge on clay particles provides soil with the ability to
hold positively charged ions - cations - providing nutrients for root uptake
Soil texture nomenclature varies by organization/country
Basic soil properties vary by texture class and structure of the soil
Soil porosity,  = pore volume/total soil volume
0<<1
 increases as grain size decreases - pore diameter decreases directly with grain
size but number of pores goes up rapidly as grain size decreases
sand  typically < 40% while clay  can reach 60% or higher
Soil water content,  = water volume/total soil volume
0 <  <  when  =  , soil is saturated
Water held under surface tension to soil particles - smaller the pore size (or radius) the greater
the surface tension. Figure 6.2 shows the characteristic curves relating tension (suction) and
water content for different soil textures. The surface tension provides pressure less than
atmospheric. Atmospheric pressure is used as a datum to measure soil water pressure - values
less than atmospheric are negative pressure, or tension. This tension also referred to as capillary
forces.
Pressure is given in units of pascals (M L-1T-2). Recall that pressure is a force per unit area. If
force = mass x acceleration, it is has units of M L T-2. Dividing by area (L2) gives the units of
pressure. In hydrology, we typically convert pressure into units of pressure head = p/ g, where p
is pressure,  is the density of water and g is the gravitational constant. This gives a measure of
L.
Water table now more formally defined as the level within subsurface (in soil or bedrock) at
which soil water pressure = atmospheric pressure. Water beneath the water table is under
positive pressure, water above is under negative pressure.
In figure 8.1, there is a region above the water table in which water is drawn up from the
groundwater table through capillaries (connected pores) under tension to produce the capillary
fringe - a tension-saturated zone. Sands may be a few to several centimeters thick, in clays it can
be meters thick.
If  <  , soil water is held under negative pressure or tension. Figure 8.4 shows the relation
between tension,  (in units of L), on  . These types of curves are referred to as characteristic
curves. Lower pressure (in drier soils) is represented as larger, negative values.
Because of differences in pore diameters, at same  ,  is progressively smaller for sands, loams
and clays.
Total head, h, is a combination of the pressure head and the elevation head (given simply by the
elevation above an arbitrary elevation datum), h =  + z
h is a measure of the potential energy of the water. Water moves through the soil down a
gradient in h. Thus, water moves in the soil in response to changes in elevation (gravitational
forces) and pressure as a diffusion process.
Darcy's Law (named after Henry Darcy, a French sanitary engineer in the 19th century) gives the
velocity of water flow as
v = -K( ) dh/dl
where v is the velocity (LT-1), dh/dl is the gradient in h or the change in h per unit length in the
flow direction, and K( ) is the hydraulic conductivity (LT-1) of the soil. Note that it is a function
of  , with the function defined as a characteristic of a soil (see figure 8.5 as an example). If we
multiply v by A (cross sectional area of flow) we change the velocity to a volume rate of flow, q.
The conservation law for soil water can be given by (for vertical flow - in the z axis only):
d /dt = -dv/dz
which states that the rate of change of  is positive (increases, gets wetter) if the flow of water
slows in the direction of flow (I > O), and is negative (decreases, dries) if the flow of water
accelerates in the direction of flow (O > I)
substituting in Darcy's Law into the conservation equation gives Richard's Equation:
d /dt = -d/dz(-K( ) dh/dz)
this gives the rate of change of soil moisture,  , at any point in the z profile as a function of the
change in K, and the change in the hydraulic gradient. This means if the hydraulic gradient or K
are zero, there is no flow, or if the hydraulic gradient and K do not change down a profile, there
is no change in  . Where there is the most curvature to the total hydraulic head, h, (greatest
change in the hydraulic gradient) there is the greatest change in  .
Infiltration is the rate of water movement into the soil from above from rainwater, snowmelt or
irrigation. Initially the soil may be dry, so the pressure gradient acts downward into the soil in
the same direction as gravity - so rapid infiltration by Darcy's Law. As  increases in the surface
soil, the pressure gradient decreases so the infiltration rate slows (figure 8.9). Eventually, if  is
saturated everywhere, only the gravitational gradient is non-zero, and since the gravitational
gradient is -1, by Darcy's Law infiltration should assymptote to the saturated hydraulic
conductivity. All this discussion is predicated on a supply of water equal to or greater than what
the velocity could be according to Darcy's Law (the infiltration capacity).
If rainfall or snowmelt (supply rate) < infiltration capacity, infiltration = supply rate,
if supply rate >= infiltration capacity, infiltration = infiltration capacity.
Simpler infiltration equations that make simplifying (and more restrictive) assumptions include
the Green and Ampt infiltration equation and the Phillips Equation. The Green-Ampt infiltration
equation: it = -K( - + Lf)/Lf assumes a sharp wetting front with a uniform, deep soil. it is the
rate of infiltration at time t, while Lf is the depth of the wetting front – the upper saturated soil at
time t. As the saturated storage to the wetting front, Lf, increases, the driving gradient decreases
and the rate of infiltration decreases.
Finally, macropores from root casts, faunal burrowing, etc. are much larger than other pores and
therefore may conduct much larger amounts of water. Since they typically have much higher
pressure (near atmospheric until filled) they will only drain the matrix when the matrix is
saturated, but may conduct large amounts of water from the surface, bypassing matrix storage.