Prediction of seasonal runoff in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 123

from gauging stations in west central Virginia. Missing
values were estimated from the pattern of auto- and
cross-correlation among standardised residual log-flow
records. Investigation of the sensitivity of estimation to
data configuration showed that, when observations were
available within two months of a missing value, the esti-
mation was improved by accounting for correlation. Bakke
et al. 1999 ) adjusted short-term estimates at poorly
gauged basins based on regional relationships between
the long-term mean monthly runoff and the mean monthly
runoff computed for the short period of records established
for each month on a data set of nearby stations.

Milly and Wetherald ( 2002 ) made inferences about the
roles of each filter through analysis of observations and
output from a global model of the ocean

land
system. They found that the first filter causes a snowmelt-
related amplification of high-frequency variability in those
basins that receive substantial snowfall. The second filter
causes a relatively constant reduction in variability across
all frequencies and could be predicted well using the
Budyko curve. The third filter, associated with ground-
water and surface water storage in the river basin, causes
a strong reduction in high-frequency variability of many
basins. The strength of this reduction can be quantified by
an average residence time of water in storage, which is
typically on the order of 20

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50 days. The residence time is
demonstrably influenced by freezing conditions in the
basin, fractional cover of the basin by lakes, and runoff
ratio (ratio of mean runoff to mean precipitation). The
purpose of this modelling framework was to synthesise
the observed and modelled data; it has not been used for
prediction in ungauged basins.
Derived distribution methods can be used to apply pro-
cess descriptions such as those suggested by Milly and
Wetherald ( 2002 ) to convert the monthly variation in cli-
mate into monthly variation in runoff. As noted above,
although several methods have been suggested for using
this approach to prediction of seasonal flow regimes, only
incomplete results are available at present. For example,
using an analytical model of climate, snow accumulation
and melt, Woods ( 2009 ) presented predictions of snowmelt
timing and magnitude, as a component of ungauged pre-
dictions of seasonal snowpack evolution. The method pro-
duced reliable ungauged predictions of snowpack in six
different geographic regions of the western USA (see
Figure 6.19 ), and so could potentially be used as a basis
for ungauged prediction of seasonal runoff from catch-
ments in snow-dominated regions.
Similarly, analytical soil water balance models with a
seasonal component have been developed; see, for
example, Milly ( 1994a , b ), Laio et al.( 2002 ) and Woods
( 2003 ), though none of them have been used for estimating
seasonal runoff regimes in ungauged basins. Only the latter
explicitly predicts the time variation of runoff within a
year. These models all use an idealised representation of
the climate forcing, with storm events modelled as a Pois-
son process, and seasonal variation in rainfall and potential
evaporation modelled as sinusoidal curves. Snow pro-
cesses are not included, and nor are lakes; McDonnell
and Woods ( 2004 ) suggested that these both need to be
included in a general treatment of the water balance. Inter-
ception by plants is modelled using either a fixed loss from
each storm or a simple stochastic storage model. Soil water
storage is modelled using variations on the

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6.4 Process-based methods of predicting seasonal
runoff in ungauged basins
The statistical approaches to regionalising runoff regimes
described in the previous sections depend on the existence
of runoff data that capture adequately the diversity of
regimes at multiple spatial scales, from headwater catch-
ments to major river basins. Since many regions are
sparsely gauged, even in developed countries, an alterna-
tive approach involves the use of process-based methods to
regionalise seasonal flow regimes. Process-based methods
may be the most promising to determine the seasonal run-
off variation at ungauged sites. This is especially so when
there is considerable inter-annual variability, which is the
case in semi-arid regions, or those parts of the world
impacted by monsoons. Process-based models also offer
more flexibility in the evaluation of the seasonal variation,
e.g., aspects such as inter-annual variability can be incorp-
orated directly. A further benefit of process-based models
is that they are better adapted to accounting for changes in
climate and land use than statistical methods.

6.4.1 Derived distribution methods
To apply a derived distribution approach requires parsimo-
nious models of both the climate and the processes that
transform climate inputs into seasonal runoff. Milly and
Wetherald ( 2002 ) conceptualised the effects of land pro-
cesses on variability of monthly river runoff, taking a
spectral approach. The power spectrum of monthly runoff
can be interpreted as the product of the power spectrum of
monthly catchment total precipitation (which is typically
white or slightly red) and several filters that have physical
significance. The filters are associated with (i) the conver-
sion of total precipitation (sum of rainfall and snowfall) to
effective rainfall (liquid flux to the ground surface from
above), (ii) the conversion of effective rainfall to soil water
excess, and (iii) the conversion of soil water excess to
runoff.

model
(for a comparison, see Milly, 2001 ). The conversion of soil

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