sient flow of water in a stable and uniform zone

of soil. The root system is considered as a diffuse

sink for water that permeates each depth of soil

depth increments

layer uniformly, though not necessarily at the

same root length density through the root zone.

depth *z*

Macroscopic models are derived from Darcy's

∆*x *= distance between roots at position

law, expressed in hydraulic head terms

where *H * (z,t) and *S*(z,t) are mea-

(1)

sured

∆*z *= soil depth increment.

where *J*w = flux of water (L3 L2 t1)

The major drawback of these models is that they

utilize a gross spatial average of matric and os-

motic potentials and neglect the decrease in water

potential and change in the salt concentration at

the soil/root interface as well as the rhizosphere.

Incorporating the soil water diffusivity term,

Microscopic models consider the diffusion of

(2)

water towards a single root (Gardner 1960). The

models assume that liquid flow resistance in soil

The vertical flow through a thin layer of soil

is dependent on root geometry, rooting length,

where water content changes with time and dis-

and the hydraulic conductivity of the soil. Under

tance can be solved with Richards (1931) continu-

steady-state conditions, the rate of water uptake

ity equation

per unit root length, *q*r, from the soil at a uniform

equilibrium water content can be estimated as

θ/ *t *= / *z K*w H/ *z *+ *K*w/ *z*

(6)

= / *z D *θ/ *z *+ *K*w/ *z*.

(3)

where *K*w = soil hydraulic conductivity

Equation 3 is further modified for water ex-

traction by the plant roots

tal leaf water potential

θ/ *t *= θ/ *z *(*K*w H/ *z*) + *A*(z,t)

(4)

root

where *A*(z,t) is the root water extraction in refer-

ence to soil depth, *z*, and time, *t*.

Several workers assumed that *A*(z,t) is a func-

Root water uptake of a specific soil volume can

tion of root activity. None, however, has assumed

be estimated by multiplying the *q*r with root

that root activity is a function of water potential

length density, *L*v. The transpiration rate, *T*, is as-

difference between plant and soil, distance be-

sumed to be equal to uptake rate and can be cal-

tween the uniformly spaced roots, and some

culated as

measure of conductivity in the rootsoil system.

The root water uptake model of Nimah and

1

(7)

Hanks (1973) can be written as

Taylor and Klepper (1975) proposed the follow-

ing equation

(5)

θfinal = θinitial (*q*r) (*L*v) (*H*p *H*s)

(8)

where *H*roots = effective water potential in root at

where θfinal and θinitial are the volumetric water

contents at the end and beginning of a measuring

period.

dinal resistance in xylem

Water uptake rates of species differ even when

7