Environmental Engineering Reference
In-Depth Information
measuring one or more parameters that are important to the water or chemical
budget. Positive errors often are offset by negative errors, so
R
commonly is smaller
than the error associated with one or more individual terms. A first-order error
analysis takes this into account when determining error as a function of multiple
parameters. When errors are additive, first-order analysis (e.g., Taylor
1982
)
involves calculating the square root of the sum of the squared values of each of
the parameters:
q
δ
2
2
2
2
2
2
2
2
ΔV
δ ¼
P
þ δ
E
þ δ
Si
þ δ
So
þ δ
Gi
þ δ
Go
þ δ
Of
þ δ
(3.54)
where
δ ¼
error,
P
¼
precipitation,
E
¼
evapotranspiration,
Si
¼
surface-water flow to the wetland,
So
¼
surface-water flow from the wetland,
Gi
¼
ground-water discharge to the wetland,
Go
¼
loss of wetland water to ground water,
Of
¼
overland flow,
Δ
V
change in volume of water contained in the wetland (positive for increase in
volume).
¼
First-order error analysis assumes that errors are independent and randomly
distributed. This clearly is a poor assumption. For example, most of the water-
budget parameters are dependent on precipitation. If substantial interdependence is
suspected, a more rigorous analysis can be conducted where covariances between
terms are considered (e.g., LaBaugh
1985
). However, a large percentage of water-
budget studies, if they present error estimations at all, simply assume parameters are
independent and apply an equation similar to
3.54
.
By estimating the error associated with each of the water-budget components of
a wetland, cumulative error,
, can be compared with the residual,
R
, of Eq.
3.53
.
If differences are large, it is likely that at least one of the components has been
determined incorrectly or that errors associated with one or more of the water-
budget components have been poorly estimated.
A common question among wetland scientists is just how large are these errors?
Estimates vary substantially depending on the setting, goals of the study, and
methods of measurements. Errors reported in a selection of publications that
provide error estimates for water-budget components of studies of lakes, wetlands,
and reservoirs generally are smallest for precipitation and largest for groundwater.
Based on values presented in ten such studies in Table
3.1
, median estimates for
error associated with
P
,
E
,
S
,
G
, and
δ
Δ
V
are 9, 10, 10, 36, and 10 %, respectively.
