Constrained two layer models for estimating evapotranspiration
One Layer Models
The least complex model which still provides an adequate model for the processes involved is the one-layer Resistance Energy Balance Model ( REBM) or in a linearized form, the Penman-Menteith formula (Monteith, 1975; 1981), This model treats the surface as a single, composite entity, assumes equilibrium of the fluxes and concentrations, is 'external' in that it only includes fluxes of heat and water vapour external to the effective surface and does not include water balance components.
The flux relationship for the one-layer model are governed by the following equations. The sensible heat flux (H) is modeled using a 'resistance' formulation ( monteith, 1975) by:
H = rCp {(T0-Ta)/ra}------------------------(2)
Where T
0 is an effective temperature for the composite surface, T
a is air temperature at a reference height above the surface and r
a is a term describing the resistance to transport of sensible heat between the surface and the reference height. If a model for this resistance is available and computable then the REBM proceeds by
identifying T
0 with the (remotely) measured surface temperature T
s to obtain H and using equation (1) to compute the ET as:
lE = Rn - G - H-------------------------(3)
Which assumes that G and R
n have been adequately modelled.
The ET can also be expressed in resistance form (see Jupp and Kalma, 1989 for greater details in the notation being used here) as:
lE = (rCp/g){(es (T0) - ea)/(ra + rs)}--------------------------(4)
Where e
s (T
0) is saturated vapour pressure at temperature T
0, e
a is vapour pressure at the reference height and r
s is a composite 'surface' resistance expressing both the intrinsic capacity to extract water through the composite surface and the available water.
The equations above are ideal for combination with remotely sensed data as shown by practical application in Jupp and Kalma (1989). If T
0 is identified with T
s then both
lE and rs are computable. Also computable is a term called the 'moisture availability' (m
a) defined as:
ma = lE / lEpot ------------------------------(5)
Where
lE
pot is the ET that would occur for the same reference meteorological conditions but with no limit on moisture availability through the composite surface. This last condition is assumed equivalent for this work to r
s being zero.
Computing this potential ET, as well as computing ET and T
0 when r
s or m
a are specified rather than t
s, required some care. The equations are nonlinear in that r
s is a function of T
0 and can be numerically difficult in situations of partial cover and unstable and drying meteorological conditions. With an appropriate numerical method, therefore, is possible to derive an effective T
0 corresponding to an input value r
s or m
a and the opportunity this poses for remote sensing of water related effects has been outlined in Jupp et al. (1990). In particular, if the soil wetness (eg the ratio W/W
max) is obtained by mass balance methods and the operating characteristic:
ma + lE / lEpot =
f(W/Wmax)
is known for a cover type, the REBM allows you to combine meteorological data and mass balance data to predict effective surface temperature and therefore bring remote sensing and water balance model into directly comparable form. In Jupp et al. (1990) this temperature Index'.
