Prediction of seasonal runoff in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 119

Scandinavia was interpolated around classified stations,
allowing a map of flow regimes to be developed (Krasovs-
kaia and Gottschalk, 1992 ). The same approach failed for
Western Europe, apparently because catchment character-
istics were not detailed enough to support this mapping
(Krasovskaia et al., 1994 ).
Allocation rules can be developed on the basis of catch-
ment and climate characteristics for a region. For example,
predictions of mean monthly runoff in Switzerland (Sprea-
fico, 1986 ) classified alpine regions based on the mean
altitude of a catchment and proportion of the catchment
area covered by ice (Aschwanden and Weingartner, 1985 ).
The first characteristic is a strong indicator of the signifi-
cance of snow for the seasonal runoff patterns, particularly
the duration of the snow cover in winter and the timing and
intensity of the snowmelt in spring, whereas the second
characteristic indicates the importance of ice melt for the
runoff during summer time. The threshold values for
each flow regime class were determined graphically
( Figure 6.16a ). On the basis of catchment altitude and
ice, regime types can then be assigned to the ungauged
sites ( Figure 6.16b ). Several representative stream gauges
are usually available, again allowing a transfer of monthly
Pardé coefficients to the ungauged site on the basis of the
regime types. There is no strict rule for selecting the
representative stream gauges, which means there is an
inherent subjective component. Similarities in the attribute
space are a first criterion for selection, while a nearest-
neighbourhood approach is an improvement allowing
more objective selection.

representative catchment. Alternatively, a weighted mean
of the Pardé coefficients of several similar catchments
could be used. Andrews ( 1972 ) showed that the area
between two Andrews curves is proportional to the Eucli-
dian distance between points in a k-dimensional attribute
space: the weight can thus be calculated as being inversely
proportional to the area between the Andrews curves for
the gauged and ungauged sites.
Simple interpolation methods such as nearest-
neighbour methods and splines assume that geographical
proximity is the key factor in determining a hydrological
parameter. They have been used by Acreman and Wilt-
shire ( 1989 ) and by Arnell et al.( 1993 ) for the regional-
isation of monthly runoff. They have also been used for
the regionalisation of the Fourier harmonics of the
regime curve (Hermann and Egger, 1980a , b ;Aschwan-
den and Weingartner, 1985 ). These methods should,
however, be applied with caution since river runoff is
generally related to accumulated area and temporal vari-
ation, rather than a simple 2D spatial variation
(Gottschalk et al., 2006 ). Isolines of runoff are therefore
rarely as reliable as plots formed for hydrometeorologi-
cal variables that vary smoothly in space.
Geostatistical methods assume that runoff at the target
site can be estimated as a weighted mean of runoff at the
gauges. The main difference between interpolation
methods and geostatistics is that, in the latter, the runoff
at the target site is considered a random variable. Geosta-
tistical methods account for spatial correlation structure
and de-cluster redundant information from gauging sta-
tions close in space. Kriging (Kitanidis, 1997 ) is the most
commonly used geostatistical method. However, standard
kriging techniques cannot be applied straightforwardly to
estimate runoff characteristics since they are not adapted to
handle variables organised within a network and related
to specific areas rather than to points. Several develop-
ments have been suggested to address these theoretical
issues (see Section 8.3.3 for a discussion). A direct (geo-)
statistical method to estimate the 12 monthly means of the
flow regime is to evaluate them independently, month by
month, in which case a spatio-temporal interpolator has
to be developed. On the other hand, the space-time covar-
iance structure could be incorporated, as for the spatio-
temporal interpolation procedure developed for daily run-
off by Skøien and Blöschl (2007) . Further developments
should incorporate non-stationarity in the space-time cov-
ariance structure.
An instructive example of how to estimate the mean
monthly runoff at ungauged sites is given by Sauquet
et al.( 2008 ). The method combines an application of
empirical orthogonal functions (see below) and an adapted
geostatistical interpolation scheme to match the runoff
data. The procedure is applied in two steps. First,

6.3.3 Geostatistical and proximity methods
Spatial proximity has often been considered the most
important factor in transferring information from gauged
to ungauged catchments. The simplest regionalisation
methods assume that the closer a location of interest is to
a gauging station the more similar the flow regime or the
regime type is (Korzun, 1978 ; Arnell et al., 1993 ). Maps
describing monthly runoff variability can be used to pre-
dict in ungauged regions. Electronic maps allow a broader
range of scales to be addressed through these techniques
(e.g., Lienert et al., 2009 ) and a large number of stations
can be mapped. Mapping procedures are not true regional-
isations but they support the extrapolation of gauged infor-
mation to ungauged sites.
Andrews curves (Andrews, 1972 ; see Section 6.2.2 for
more details of the method) allow nearest-neighbour
approaches to be used to identify gauged locations that
are most similar to ungauged sites of interest (Weingartner,
1999 ). Once the nearest neighbours are determined, Pardé
coefficients can be transferred from the most similar the