Environmental Engineering Reference
In-Depth Information
Short Exercise 13: Influence of Error on the Water Budget
Whatta Wetland is a hypothetical 1.5-ha wetland situated in a humid environment
where annual precipitation is nearly three times larger than evaporation
(Table
3.13
). The stage of Whatta Wetland is controlled by a small dam that
increases the water level about 0.3 m. As such, it has a well-defined outlet channel,
which allows accurate measurement of surface-water flow from the wetland using a
weir. A weir also is used to measure surface-water flow to the wetland. In fact, great
care was taken to measure all input and loss terms of the Whatta water budget.
Based on a report from the wetland observer indicating that she has never seen
overland flow at this sandy location, we assume that overland flow, if any, is
insignificant. Maximum errors associated with individual components of the
water budget are estimated to be:
Precipitation
P
5%
Evapotranspiration
ET
15 %
Streamflow into the wetland
S
i
5%
Streamflow from the wetland
S
o
5%
Groundwater flow to the wetland
G
i
25 %
Wetland flow to groundwater
G
o
25 %
Change in lake volume
ΔV
10 %
We can write our water-budget equation as
R
ε ¼
P
þ
O
f
þ
S
i
þ
G
i
ET
S
o
G
o
(3.64)
where
R
is the sum of all of the water-budget components (except change in wetland
volume) and
is the cumulative error associated with all of the water-budget terms
on the right hand side.
We are interested in determining how
R
compares with our measured value for
ɛ
Δ
V
, which will tell us if we have any bias in our water budget or whether there are
some unknown or missing terms. Ideally,
R
will be very close to
Δ
V
. If this is not
the case, we want to know if the difference between
R
and
V
can be attributed to
measurement error or if there really is a missing component or some substantial bias
in our estimates of one or more of the water-budget terms.
The uncertainty associated with determination of each term also is presented
in Table
3.13
. After quick calculation, you can confirm that the sum of all the
input and loss terms,
R
, is more than eight times larger than our measured annual
change in wetland volume,
Δ
V
. If we make the worst-case assumption that all
errors are at the positive extreme and then sum all of the error terms, the value
based on a summation of the positive error terms is so large that it encompasses
the measured value for
Δ
V
. Alternately, manipulating the sum to obtain a
minimal cumulative error cannot be supported either. Thus, simple sums of the
error values do not provide a means of discriminating whether
R
is a valid
measure of the residual.
Δ
