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(although the latter will also be affected by the nature of the evapotranspiration over some variable up-
wind fetch length). The method has been shown to provide good estimates of sensible heat fluxes over
both homogeneous (De Bruin
et al.
, 1995; McAneny
et al.
, 1995) and heterogeneous (Chehbouni
et al.
,
1999) surfaces and has been used to ground truth other methods of obtaining large scale estimates of
actual evapotranspiration (e.g. Schuttemeyer
et al.
, 2007).
The evapotranspiration at a point is necessarily affected by the nature of the surrounding surface.
Following original work by Bouchet (1963), Morton (1978) has suggested that pan measurements can
be used to derive estimates of the actual evapotranspiration of the surrounding area since, under given
energy inputs, the lower the actual evapotranspiration of the surrounding area, the drier the air and
the greater the resulting pan measurement will be. This
complementarity approach
has been used in a
number of catchment models and extensively tested by Morton (1983a, 1983b). Venturini
et al.
(2008)
have applied the complementarity approach at large scales for different land uses using satellite data. The
complementarity approach has been criticised as inaccurate (for example by LeDrew, 1979, and Lhomme
and Giulioni, 2006) but has a certain intrinsic appeal and may yet require re-evaluation as the difficulties
of the more physically based but parameter-rich approaches become more widely appreciated. Recent
modifications of the method have been suggested by Crago and Crowley (2005) and Szilagyi and Jozsa
(2008).
3.4 Meteorological Data and The Estimation of Snowmelt
In many environments, snowmelt may be the source of the annual maximum discharge in most years and
may be a major cause of flooding. Meteorological data will also be required in the modelling of snow
accumulation and melt. Again, different types of snow models demand different types of data. The very
simplest snow model is the temperature index or
degree-day method
. This model, in its simplest form,
is based on the hypothesis that snowmelt is proportional to the difference between air temperature and a
threshold melt temperature (Box 3.3). Thus data on air temperature are required as an input; the threshold
temperature is effectively a parameter.
A typical modern variant for snowmelt-runoff modelling, the Swiss SNOW1-ETH4 model, has been
proposed by Hottelet
et al.
(1993, see also Ambroise
et al.
, 1996). This still only requires temperature
as an input but tries to take account of whether precipitation is falling as rain or snow and the heat deficit
of the pack that must be satisfied before significant melt will occur. This variant increases the number of
parameters that must be specified. The degree-day method is applied within the Snowmelt Runoff Model
(SRM) of Rango and Martinec (1995), which has been widely applied in both the USA and Europe
(e.g. Mitchell and DeWalle, 1998). The SRM makes calculations for different elevation bands within
the catchment and takes account of the depletion of the snow-covered area as the melt season proceeds
(see Box 3.3).
The degree-day method is obviously a very simple approach, but has the advantage of demanding
only temperatures as an input. The method is most accurate when melt is dominated by heat input due to
radiation and the pack is ripe at 0
â—¦
C and ready to melt. The method is least accurate when melt is dominated
by heat advected by an air mass (see, for example, Braun and Lang, 1986). A combination energy budget
approach to modelling the snowpack and snow melt, similar to that used for evapotranspiration in the
Penman-Monteith equation, was originally proposed by Anderson (1968). This is much more demanding
in both meteorological data (net radiation, temperatures, humidity and wind speed) and parameter values.
Models of the changing structure of the snowpack as a result of freezing and thawing conditions have also
been proposed (e.g. Morris, 1991), requiring even more parameters. A number of distributed energy budget
models for predicting snowmelt have been developed (e.g. Bloschl
et al.
, 1991; Marks and Dozier, 1992).
However, an intercomparison of snowmelt models carried out by the World Meteorological Organisation
