Environmental Engineering Reference
In-Depth Information
Table 3.13 Water-budget terms of Whatta Wetland, including percent of input our output terms,
maximum percent error, and maximum error in m
3
per year
Water-budget term Volume (m
3
/year) Percent of input or loss Percent error Error (m
3
/year)
P
18,200
26 %
5 %
910
2,345
S
i
46,900
68 %
5 %
G
i
4,250
6 %
25 %
1,063
ET
6,540
10 %
15 %
981
S
o
49,730
79 %
5 %
2,487
G
o
6,940
11 %
25 %
1,735
R
6,140
Δ
V
700
10 %
70
If we can justify making two simple assumptions, we can estimate our cumula-
tive error with far less uncertainty. First, we assume our errors are distributed
normally. Given that measurements were made approximately biweekly, making
our number of measurements around 26, this assumption appears reasonable.
Second, we assume that errors in our measurements are independent. Given that
precipitation is measured with a rain gage, streamflow with a flow-velocity meter,
evaporation with a suite of sensors, and groundwater with a tape measure of some
sort, there is small possibility that any of our sources of measurement error are
dependent on another. Assuming errors are normally distributed and independent,
cumulative error is reduced based on an equation similar to Eq.
3.54
, but without
the
Δ
V
term:
q
ε
2
2
2
2
2
2
Go
ε ¼
P
þ ε
ET
þ ε
Si
þ ε
So
þ ε
Gi
þ ε
(3.65)
Using
ε
as a measure for the cumulative error, Eq.
3.64
indicates that
Δ
V
¼
R
ε
.
Based on the above information, answer the following questions:
1. How does
R
compare with
V
? Are these values reasonably close? If not,
suggest a reason for why they are different.
2. What is the additive error associated with determination of
R
(what is
R
Δ
ɛ
?)
What is the error associated with
R
based on Eq.
3.65
? Based on
determined
with Eq.
3.65
, are you comfortable with stating that
R
is different from
ɛ
V
?
3. What if our weir failed and we had to use floating oranges all year to make
estimates for the
S
i
term. Recalculate the maximum error for
S
i
assuming an
error of 20 %. How does this affect
R,
Δ
,
and your assessment of the water budget
ɛ
V
?
4. What if the weir was fine but, instead, we had only air temperature data and were
forced to estimate evaporation using the Thornthwaite method, which we
decided had a maximum error of 50 %. How would increasing the error
associated with evaporation from 15 to 50 % affect the determination of
R
relative to
relative to
Δ
Δ
V
?
