Environmental Engineering Reference
In-Depth Information
in terms of energy flux density, such as W/m
2
.
Equation (
2.15
) simply states that the net radia-
tive input at land surface is used to heat the air,
warm the soil, and evaporate water. Energy and
water budgets are directly linked because
ET
is a component in each. Net radiation can be
measured with a net radiometer.
G
is measured
with soil-heat-flux plates and/or soil tempera-
ture probes (Sauer,
2002
). Because of the lim-
ited accuracy with which sensible-heat flux can
be directly measured, attempts to determine
evapotranspiration from Equation (
2.15
) by the
residual method are susceptible to large errors.
Bowen (
1926
) proposed using the ratio
β
=
H/
λ
ET
to solve Equation (
2.15
).
β
can be calculated
as a constant times the vertical gradient in air
temperature divided by the vertical gradient of
water-vapor pressure. Then Equation (
2.15
) can
be rewritten as:
A sonic anemometer, fine-wire thermocouple,
and a krypton hygrometer are commonly used.
These are expensive instruments; recent inno-
vations have substantially improved their dur-
ability and reliability relative to early designs
(Lee
et al
.,
2004
). The eddy correlation method
is the most popular land-based point or ground-
truth method for large-scale regional and global
evapotranspiration and trace-gas flux experi-
ments, such as FLUXNET (Baldocchi
et al
.,
2001
)
and EUROFLUX (Aubinet
et al
.,
2000
). However,
it is well known that direct application of the
method systematically underestimates both
H
and
ET
and that corrections are required to
ensure the closure of the energy budget (Wolf
et al
.,
2008
). Twine
et al
. (
2000
) showed that these
corrections can be as high as 10 to 30% of avail-
able energy,
R
n
- G
.
Additional approaches for measuring eva-
potranspiration include the zero-flux plane
method and lysimeters (both described in
Chapter 5
). Sap-flow meters (Wilson
et al
.,
2001
)
provide estimates of transpiration by sens-
ing water velocity in plant stems. Small static
chambers (Stannard and Weltz,
2006
) can be
used to estimate evapotranspiration rates for
areas of about 1 m
2
.
ET
=− +
(
R
G
) /( (1
λβ
))
(2.16)
n
Measurements of air temperature and vapor
pressure are made at two heights, usually
between 0.5 and 2.0 m above the top of the
vegetation canopy. Measurements are made at
intervals of a minute or less, and Equation (
2.16
)
is applied with values that are averaged over
periods of 15 to 60 minutes. Additional details
on this method can be found in Rosenberg
et al
.
(
1983
) and Brutsaert (
1982
).
The eddy correlation method directly meas-
ures vertical fluxes of heat (
H
) and water (
ET
).
The method is based on the concept that water
vapor is transported in the vertical direction by
the upward and downward movement of small
parcels of air, or eddies (Lee
et al
.,
2004
). The
relevant equations are:
2.3.3 Change in storage
Change in storage and its evaluation should
be considered with respect to the time scale
and spatial scale of interest. Changes occur in
response to daily and seasonal weather pat-
terns. Annual cycles are of interest in many,
if not most, hydrologic studies. Natural hydro-
logic systems typically display little change in
storage from year to year, so the simple assump-
tion that storage change is 0 when averaged
over 1 year may be appropriate for some sys-
tems (Healy
et al
.,
1989
). However, decadal and
longer term changes can occur in response to
changing climates or land use.
Equation (
2.5
) includes change in storage
for four distinct compartments: surface water,
snow, unsaturated zone, and saturated zone.
Change in storage between times
t
1
and
t
2
in
any of these compartments is usually calcu-
lated as the difference in total water storage
in the compartment at the two observation
H
ρ
c wT
p
''
(2.17)
ET
=
w
''
(2.18)
where
ρ
is the density of air,
c
p
is specific heat
of air,
w'
is the deviation from the mean vertical
wind speed,
T'
is the deviation from the mean
air temperature, and
q'
is the deviation from
the mean water-vapor density. Precise and rapid
(10 Hz) measurement of
w
,
T
, and
q
requires
highly specialized instruments (
Figure 2.4
).
