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Table 11.5. Summary of modifications made in each model variant as compared to the original
MAC-HBV model (i.e., Model (0))
Change possible ranges of
model parameters
Modify objective function in the
optimisation procedure
Models
Modify model structure
(0)
—
—
—
(1)
Yes
No
No
(2)
Yes
Yes
No
(3)
No
Yes
No
(4)
Yes
Yes
Yes
(5)
No
Yes
Yes
Figure 11.29. Model test results in
gauged basins, including (a) Nash
-
Sutcliffe efficiency (NSE) and
(b) volume error (VE) for baseflow.
Boxes are delimited by the 25th and
75th percentiles, the median is
marked with a thick line inside the
boxes and the whiskers are delimited
by the 10th and 90th percentiles.
From Samuel et al.(
2011b
).
0.9
40
0.64
0.6
20
0.59
0.60
0.58
0.57
0.56
12.7
8.4
5.3
4.6
0.3
0
1.5
1.0
0
-20
(0)
(1)
(2)
Models
(3)
(4)
(5)
(0)
(1)
(2)
Models
(3)
(4)
(5)
(a)
(b)
Figure 11.30. Baseflow estimation
in ungauged basins: (a) NSE and
(b) VE statistics. See
Figure 11.29
for meanings of boxplots.
From Samuel et al.(
2011b
).
regionalisation method for ungauged basins in Ontario
(Samuel et al.,
2011a
). To evaluate confidence intervals
of estimated runoff and baseflow in ungauged basins, a
modified Monte Carlo simulation approach was applied
(see Samuel et al.,
2011a
,
b
for details). Baseflow separ-
ation was done using a recursive digital filter (Nathan and
McMahon,
1990
). The algorithm separates baseflow from
total runoff by passing the filter over the runoff record
three consecutive times (forwards, backwards and for-
wards again). The performance of each MAC-HBV model
variant was assessed using the Nash
model improvement was found using Model (4), which
included all the changes, i.e., changing the linear storage
discharge relationship to a non-linear one; using a wider
range of possible maximum and minimum values of model
parameters, especially for the parameters related to subsur-
face/groundwater flows; and considering the average and
low flows and VE in the objective function in the optimisa-
tion procedure. Model (4) has the highest NSE index (
Figure
11.29a
)andthelowestVE(
Figure 11.29b
) for baseflow.
Model (4) was then used with the combined regionalisa-
tion method to estimate flow in ungauged basins. Ninety
basins that produced NSE index values higher than 0.5
were selected and the IDW-PS approach was applied to
obtain model parameters for ungauged sites.
Figure 11.30
shows Model (4) and Model (0) simulation results for the
111 ungauged basins. About 20% of improvement in NSE
index has been achieved with Model (4) as compared to
Model (0). In terms of VE, the improvement is up to 50%
Sutcliffe model effi-
ciency (NSE) index, and volume error (VE).
-
Results
All the five variants of the model (i.e., Model (1) to Model
(5)) show improvement in baseflow estimates, as compared
to the original MAC-HBVmodel (
Figure 11.29
). The highest
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