Prediction of runoff hydrographs in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 238

hydraulic conductivity), accompanied also by increasing
topographic slope. The net effect of this is that increasing
group numbers mean that the fraction of runoff by satur-
ation excess decreases (from about 80% of total runoff to
less than 20%), while the fraction of subsurface stormflow
increases from about 20% to more than 80%). The catch-
ment groups are also nested subcatchments within the large
catchment, and the grouping is used to explore the effects
of changing dominant processes on the runoff routing
behaviour within the river network.

weighted average of surrounding observations, the weights
must take into account not only the spatial distance
between the target catchment and the neighbours, and asso-
ciated correlation coefficient, but, in the case of nested
catchments, also the particular topology of streams and
rivers that possibly link them.

10.3.1 Regression methods
The use of regression to directly transfer the full hydro-
graph to ungauged locations is rather unusual. There are
some historical examples though that focused on infilling
missing runoff time series by transferring information from
other gauged locations using regression. For example,
Kritski and Menkel ( 1950 ) developed a method for hydro-
graph estimation of natural runoff for a catchment affected
by construction of a reservoir using regression-based trans-
formation of hydrographs measured in an unchanged ana-
logue catchment. Martin ( 1964 ) related monthly runoff of
one basin to those of a nearby basin with different regres-
sions and showed that including information on the
monthly time series of precipitation generally improved
the results. A very similar method was proposed by Raman
et al.( 1995 ) for extending short records. The fact that
precipitation inputs are used makes these procedures look
like extremely simplified models, such as those discussed
in Section 10.4 , but without physical or conceptual inter-
pretation of the obtained relationships. The most common
approaches for hydrograph transfer are variants of the
index method, which is discussed in the next section.

10.3 Statistical methods of predicting runoff
hydrographs in ungauged basins
Statistical methods use available runoff time series data
from neighbouring catchments (donor catchments) to esti-
mate runoff hydrographs at ungauged locations based on
one or more of the similarity measures and/or grouping
methods discussed above. In this topic, statistical methods
of predicting runoff hydrographs in ungauged basins refer
to methods that do not use precipitation or do so in a
statistical way. Methods that use precipitation based on
balance equations are dealt with in Section 10.4 .
The main advantage of statistically based runoff simula-
tion methods is that they avoid the use of uncertain input
variables such as precipitation and potential evaporation.
For several of the methods that will be described here
catchment characteristics are also unnecessary. The disad-
vantage is that most of these methods are data intensive,
i.e., can only be applied in medium to densely gauged
regions, and they are not applicable when one is interested
in the causal relationship between precipitation and runoff,
as in the case of runoff forecasting. Even when consider-
able data exist, there are several challenges to the applica-
tion of statistical methods for predictions of runoff time
series in ungauged locations. This has to do with the nature
of the spatially random field that is runoff. There are
several challenges to the application of statistical methods
for predictions of runoff time series in ungauged locations.
As described in Section 10.2 , the runoff field has the
imprint of the river network, and therefore, even though
it is a spatially correlated random field, its correlation
structure is very different from that of the rainfall point
process that produced it ( Skøien and Blöschl, 2006b ,
2006c ). Therefore the spatial dependency and correlation
structure have to be expressed not in terms of Euclidean
distance but distance measured along the river network in a
hierarchical manner (Skøien et al., 2006 ) , and must include
the scale effects due to the relative catchment sizes on the
runoff variability, including along a river network in the
case of nested catchments. While a possible approach for
continuous runoff prediction is to predict the runoff as a

10.3.2 Index methods
Index methods work on the principle of similarity, i.e., the
assumption that the nature of (temporal) variability in the
ungauged catchment is in some sense similar to that of
the donor catchment(s). This section discusses three differ-
ent index methods to estimate continuous runoff at an
ungauged location, assuming varying degrees of similarity.
In all cases, estimated continuous runoff time series at the
ungauged or recipient catchment spans the whole period of
observed record at the donor catchment(s) and require
regionalised estimates or direct measurements of key stat-
istics of runoff at both the ungauged and donor catchments.
The simplest form of similarity is to assume that the time
series of runoff, once normalised by the mean flow, is iden-
tical between the donor catchment and the ungauged catch-
ment. This, when combined with a regionalised relationship
between mean flow and catchment size, enables one to
regionalise observed runoff. For example, the drainage area
ratio method (Stedinger et al., 1993 ) assumes that the runoff
at the donor and recipient ungauged catchments only differ