Literature Review
I) Meteorological methods of evaporation estimation
b) Methods to predict unsaturated hydraulic conductivity
Mathematical models of soil water movement frequently use unsaturated hydraulic conductivity (K) as a function of soil water matric potential (VIm)' The determination of this relation by direct measurement is desirable but difficult because: (i) The K(Vlm) function is soli specific and its measurement is time-consuming; (ii) The soil variability is such that the amount of data required to represent the hydraulic properties accurately is enormous; (Iii) The values of hydrauliC
conductivitylo~08f'I
vary by several orders of magnitude within the water content range of interest and most measurement systems cannot effectively cover such a wide range (Alexander and Skaggs, 1986;Mualem, 1986). Furthermore, different methods of K( VIm) determination yield different results and it is unclear which method best represents the hydraulic characteristics of the site (Dane, 1980). Methods have been developed to approximate K(Vlm) from the relationship between volumetric water content (8v) and VIm' These have been reviewed by Alexander and Skaggs (1986) and by M.ualem (1986).
where N is an empirical constant involving some function of windiness, eo Is the vapour pressure at the surface, and ea is the actual vapour pressure at some point above the surface. This method is not easily applied because of difficulty in determining eo (Rosenberg et al., 1983). An analysis of errors In Dalton type equations was given by Hage (1975).
II) Aerodynamic method
Thornthwalte and Holzman (1942) applied an aerodynamic approach to ET estimation. Gradients of specific humidity and the logarithmic wind profile were
included. At their present stage of development, aerodynamic methods are not suitable for routine applied uses such as irrigation scheduling (Rosenberg et al., 1983). Further information on aerodynamic methods is given by Kanemasu et al. (1979).
iii) Resistance methods
The transport of sensible heat from surface to air (H) is at a rate directly proportional to the temperature gradient and inversely proportional to the aerial resistance to heat transfer (r a):
T - T a •
J: a
• •• (2.14)
where Pa is the density of air, Cp is the specific heat of air and T a and Ts are air and surface temperature respectively. Similarly, the transport of vapour is directly
proportional to the gradient In vapour pressure from the evaporating surface to the air and inversely proportional to aerial resistance to the transport of water molecules.
Resistance models estimating lovE have been proposed by Monteith (1963) and by Brown and Rosenberg (1973).
b) Climatological methods
i) Air temperature based formulas
Thornthwaite (1948) proposed an empirical index for measuring monthly potential evapotranspiration which Is sucpessful on a long-term basis because both temperature and ET are similar functions of net radiation and are therefore correlated over long time periods. Other air temperature based formulas are those of Blaney and Criddle (1950), Hargreaves (1974) and Linacre (1977).
Ii) Solar radiation formulas
ET is correlated with solar radiation (Rs) and potential ET (ET p) is linearly and strongly dependent on solar radiation (Aslyng, 1974). The relationship,of ET p and Rs has been established empirically and can be described by simple linear regression.
Regression models are simple to use but have only a limited range of applicability due to their empirical ~ature.
ill) Combination formulas
Methods which consider both the energy supply to, and the turbulent transport of water vapour away from an evaporating surface are known as combination models. In combination models lyE is calculated as the residual in the energy balance equation.
Sensible heat flux is estimated by means of an aerodynamic equation. One form of the combination equation'is (Rosenberg et aI., 1983):
L B= -
[a
+s
+ P C(T. - Tal]
v n a p r
a
... (2.15)
where all terms have been previously defined. The method has been shown to provide reliable estimates of lyE fluxes when surface temperature is measured directly by infra- red thermometry both under advective and non-advective conditions, as well as on both a short period and a daily basis (Verma et aI., 1976; Blad and Rosenberg, 1976; and Heilman and Kanemasu, 1976). Any combination solution assumes that the turbulent transfer coefficients for water vapour and sensible heat are equal (Rosenberg et al., 1983).
When T s cannot be measured directly) T a-T s can be eliminated by application of the Clauslus-Clapyron equation. Kanemasu et al. (1979) give detailed descriptions of the transformations Involved. It Is from this application of the Clauslus-Clapyron
equation that the combination methods of Penman, van Bavel, and Slatyer and Mcilroy are derived. These methods were described by Rosenberg et al. (1983).
van Bavel and Hillel method
Van Bavel and Hillel (1976) proposed a method for evaporative flux determination that required only the following common weather variables: global radiation, air
temperature, air humidity and windspeed. The model (called CONSERVB) is a combination method in that the surface energy balance is combined with the
simultaneous transport of heat and water vapour in the air above the surface, as well as the simultaneous transport of heat and liquid water in the soil below the surface. This approach Is a further extension of the original combination or Penman formula, but is much more comprehensive and accounts for soil properties a~d changes therein as evaporation proceeds. Similarly it reflects changing surface properties and atmospheric stability (refer to Chapter 6). This model represents one example of a comprehensive simulation modelling approach for predicting evaporation (see Chapter 6 for others).
Following satisfactory verification studies, such models might make possible the evaluation of the net affects of various specific processes or parameters on the overall soli water and thermal regimes. The development and verification of such models is seen as a research priority.
c) Water balance method
Evapotranspiration (ET) can be determined using a water balance approach. This hydrologic approach for ET estimation is widely used. Errors associated with the water balance approach invalidate it for estimating ET on a daily basis however (Rosenberg et al.,1983).