Prediction of low flows in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 178

than regional regression (R² 0.70) but gave no improve-

ment over the top-kriging model (R²

¼ gauging periods. The serial correlation associated with

low flow sequences, however, reduces those gains consid-
erably. Alternatively, a multiplicative scaling approach
has been proposed (Robson and Reed, 1999 ; Laaha and
Blöschl, 2005 ). The approach assumes (i) that low flow
characteristics calculated from a short observation period
will differ from that of the entire observation period by a
scaling factor, and (ii) that the scaling factor of the subject
site can be inferred from an appropriate donor site. The
scaling factor can be weighted to account for the strength
of correlation between the subject and donor sites and the
length of the overlap period between the subject and donor
site. A number of studies compared the performance of
record augmentation with regionalisation methods that do
not use local runoff data. In a study in Austria, Laaha and
Blöschl ( 2005 ) found that record augmentation with one
year of local runoff data gave more accurate low flow
estimates than any other regionalisation method. In a study
in France, Chopart and Sauquet ( 2008 ) found that spot
gauging may also give more accurate low flow estimates
than various regionalisation methods, provided nearby sta-
tions with longer runoff records are available.
Another related technique is record extension, which
simulates an extended runoff record rather than estimating
specific runoff statistics. Hirsch ( 1982 ) compared four
record extension techniques using both Monte Carlo and
jack-knife simulations, and found that linear maintenance
of variance techniques, i.e., those that preserve the mean
and variance of the short record, yielded more accurate
estimates of historic low flow characteristics than regres-
sion techniques. This method was recently applied by Eng
et al.( 2011 ) for the entire USA. Vogel and Stedinger
( 1985 ) proposed a similar estimator, which Ahearn
( 2008 ) used to improve the estimation of low runoff statis-
tics in Connecticut, USA.
In the baseflow correlation (or regression) method a
regression relationship between single runoff measure-
ments at a short-record subject site and synchronous flows
at a long-record donor gauge is used to estimate low flow
characteristics at the subject site ( Figure 8.12 ). Unlike
record augmentation where a substantial record is required,
baseflow correlation can be performed with only a limited
number of runoff measurements at the subject site (about 5 -
15 measurements). The key to this method is that the runoff
at subject and donor sites is under baseflow conditions
when a measurement is taken, meaning that all contribu-
tions to runoff are from groundwater discharge or release
from other large stores, e.g., lakes and glaciers (Reilly and
Kroll, 2003 ). The baseflow correlation method assumes a
linear relationship between the logarithm of the annual
minimum runoff series at the subject and donor sites
(Stedinger and Thomas, 1985 ). Since annual minimum run-
off is not available at the short record site, it is assumed

0.75). An alterna-
tive combination is physiographic space-based
interpolation (PSBI) (Castiglioni et al., 2011 ), which was
originally proposed for floods (Chokmani and Ouarda,
2004 ). The main idea of PBSI is to perform kriging in a
transformed space of catchment characteristics by multi-
variate analysis. Standard point-kriging methods are then
applied for spatial estimation. The method has some simi-
larities with the region of influence approach, where
regional averaging is performed by a weighted mean of
similar stations. In PSBI the weights are estimated from
variograms. The correlations along the stream network
are accounted for

¼

indirectly through the catchment

characteristics.

8.3.4 Estimation from short records
In some instances there may be short runoff records avail-
able for a catchment that is otherwise ungauged. These
runoff records may not be representative of the longer time
period that is normally used for the estimation of low
flows. Methods are therefore needed that relate the low
flow estimates from the short runoff records to the longer
hydrological history of the basin on the basis of regional
information. A number of methods are currently in use.
In record augmentation a relationship is established
between the runoff at the subject site and runoff at a nearby
donor site where a long runoff record is available. Donor
sites are usually selected on the basis of spatial distance,
similarity of catchment characteristics or correlation of
runoff between the sites (Vogel and Stedinger, 1985 ;
Laaha and Blöschl, 2005 ). Laaha and Blöschl ( 2005 ) sug-
gested that choosing an immediate downstream neighbour
may be a better choice than other methods. Early studies on
record augmentation suggested use of regression estima-
tors of the mean and variance of runoff and transformation
of runoff to obtain approximately normally distributed data
(Fiering, 1963 ; Matalas and Jacobs, 1964 ). An augmented
estimator of the low flow statistic at the subject site is then
achieved by linear combination of the statistics estimated
from the short record at the subject site with a regression
estimate from additional record years at a donor site. The
regression relationship used for transferring the low flow
statistics of the donor site to the subject site is established
from the overlapping records of the subject and donor sites.
Vogel and Stedinger ( 1985 ) introduced improved record
augmentation procedures by using a weighting factor to
account for the strength of correlation between the subject
and donor sites. Vogel and Kroll ( 1991 ) tested the
improved record augmentation procedure to minimum
annual low flows and found a substantial decrease in
estimation variance, especially for longer (10 - 15 years)