The Water Balance

9.6 The Water Balance

We have discussed infiltration, redistribution, evaporation, and transpira- tion as if they are isolated processes. Of course, they are not, and most go on simultaneously. At any particular time conservation of mass requires that the rate of change in water content in a depth of soil L equal the sum of the inputs and losses. This mass balance equation can be written as

where the terms on the left represent the rate of storage and the terms on the right are for infiltration

deep percolation below depth L

evaporation from the soil surface (E,), and plant transpiration

It is not difficult to solve Eq. (9.23) and obtain a record of water content changes in the soil over time, but the solution is only practical using numerical methods on a computer. The methods are covered in detail in Campbell (1985). The analyses presented here are intended to give insight into the processes and how they operate, but do not lead to a full solution of the water balance equation.

References

Campbell, G. S. (1985) Soil Physics with BASIC: Transport Models for Soil-Plant Systems. New York: Elsevier.

Green, W. H. and G. A. (191 1.) Studies in soil physics: the flow of air and water through soils. J. Agric. Sci. Rawls, W.J., L.R.

and D.L. Brakensiek (1992) Estimating soil hy- draulic properties from soil data. In Indirect Methods for Estimating Hydraulic Properties of Unsaturated Soils. M. th. Van Genucthen, F.J.

and L.J. (eds.) U.C. Riverside Press, Riverside, CA.

Problems

and -1500 kg-' water contents. Assume

9.1. For a sandy

soil, estimate the -33 J

0.45 m 3

a. If the rooting depth is 100 cm, estimate the maximum available water to the plant.

b. If 50 of rain falls on this soil in one estimate the runoff if

the initial volumetric water content of the soil is 0.1 . Use Eq. (9.8) to estimate the total infiltration in an hour. Compute the water potential at the wetting front from Eq.

and assume that the average hy- draulic conductivity of the transmission zone is the geometric mean

Problems 145

of the saturated conductivity and the conductivity at the wetting front (the geometric mean of two numbers is the square root of the product of the numbers). Assume that the potential at the infiltration boundary is zero.

c. If 100 mm of rain falls on this soil in two hours, estimate the runoff if

the initial volumetric water content of the soil is 0.1 m 3

d. What is the depth of wetting for each rainfall case above?

e. Estimate the new average water content for the top 100 cm of soil after each of the above rainfalls.

9.2. If is measured to be 5 mm in the sandy loam soil of problem 9.1 immediately after a rain that wets the upper 0.1 m of a root zone to a uniform water content of

m 3 how long will it take before the transpiration decreases to 2.5

because of water depletion in the top 0.1 m root zone? Assume that no water is available below the depth of wetting from the rain.

Radiation Basics 10

The modes of energy transport discussed so far (conduction, convection, and latent heat) all are somewhat intuitive. Radiative energy transport, on the other hand, is not intuitive at all. Radiant energy is transferred

by photons, discrete bundles of electromagnetic energy that travel at the speed of light (c = 3 x

in vacuum) and behave both as particles and waves. These photons are emitted or absorbed by matter as a result of quantum jumps in electronic energy levels in atoms, or changes in vibrational and rotational energy levels in molecules. The wavelength of the radiation is uniquely related to the photon energy in an equation due to Planck:

where h is Planck's constant (6.63 x J S ) and is the wavelength of the photon. Thus green photons, having a wavelength of

would have an energy

The energy transferred by a single photon is not generally of interest, but often the energy content of a mole of photons is. This is obtained by multiplying the energy per photon by Avagadro's number (6.023 x The energy content of photons at

wavelength is photons

6.023 x 10 --- x 3.6 x

= 2.17 x

mol This kind of calculation allows conversions between amounts of radiant

mol

photon

energy and numbers or moles of photons for a particular wavelength.

The energy of photons could also be expressed as a function of fre- quency of the radiation, since

= c, to give e = h v. Frequency, rather than wavelength is used some treatments of environmental radiation (Gates, 1980). Advantages of using frequency are a more symmetrical presentation of absorption bands and the ability to show both solar and thermal radiation on a single graph. These advantages are offset some- what by the loss of detail in the

portion of the spectrum and the

Radiation Basics

unfamiliar nature of the units to many biologists. In this presentation we continue to use wavelength.