Geography Reference
In-Depth Information
a) Top-kriging: q95
c) Top-kriging: sdev
q95 (l/s/km
2
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0 - 1
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> 12
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b) Regression: q95
d) Regression: sdev
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Figure 8.11. Q
95
low flow predictions in ungauged basins by top-kriging (top left) and regression (bottom left) for the Mur River, Austria.
Right panels indicate uncertainty standard deviations. For the main river (ellipses) the estimated uncertainty is lower in the case of top-kriging
but for the headwaters it is higher. The area shown is 100 km across. From Laaha et al.(
2012
).
the problem of nested catchments by integrating the point
variogram over the drainage area and maps the runoff
estimates back to the stream network.
In order to apply geostatistical methods to low flow
indices (i.e., Q
95
), a variogram model is needed. For geo-
statistics on stream networks, the variogram cannot be
directly estimated from sample data because of the differ-
ent catchment sizes and the nested nature of catchments.
A number of methods exist to estimate the variogram
where the variograms valid for different catchment sizes
are estimated from the point variogram by integration and
the parameters are found by optimisation against the
An example of the geostatistical method is presented in
Figure 8.11
. Along with the estimates of the Q
95
low flows,
the figure presents estimates of the uncertainty of the
predictions, expressed as error standard deviations. It is
interesting that the geostatistical method estimates uncer-
tainties that not only depend on the location of the
ungauged basins with respect to stream gauges but also
strongly depend on the catchment size. For the main stream
marked yellow,
uncertainty are much smaller than those of a regression
model for the same reach. For smaller catchment areas,
however, the estimates of the uncertainties are much larger.
It is clear that the performance of the geostatistical
approach will depend on two main factors: the stream
gauge density and the degree of spatial heterogeneity of
the low flow processes. The approach seems to be best
suited for areas with medium or high stream gauge dens-
ities and in areas that are geologically rather homogeneous.
In the case studies summarised in
Section 8.5
, the geosta-
tistical approach tends to outperform global regressions for
low flow predictions.
To account for spatially heterogeneous regions, the
geostatistical method has been extended to combine it with
multiple regression methods, in which the residuals of the
regressions are used for the spatial geostatistical estima-
tion. Predictive accuracy of this method is described in
detail
in
Section 8.5
, and the results suggest
that
the
combined method performed better (R²
¼
0.73) than geo-
statistics alone (R²
0.61), but did not yield an improve-
ment over regional regression (R²
¼
¼
0.74). In Austria, a
for example,
the estimates of
the
spatially adjusted regression (R²
¼
0.75) performed better
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