Prediction of flow duration curves in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 153

completely on any regional model, which should be used
to provide a first-order approximation of FDCs. The prac-
tical utilisation of the estimated FDC for design purposes
should be supported through additional, perhaps ad-hoc,
measurement campaigns.

In recent times there have been several efforts that have
begun to approach FDCs from a process perspective. The
focus so far has been on developing understanding of the
climatic and catchment controls on the FDCs, very similar
to the steps that were made in the early days of the derived
flood frequency work (e.g., Eagleson, 1972 ; Sivapalan
et al., 1990 ). These methods have not yet matured to the
point that they can be used to predict FDCs in ungauged
basins, but they show considerable promise. Therefore, in
the sections below a brief summary is given of these
approaches, to highlight their main strengths and weakness
(so far) with a view to recognising the importance of
such work for predictions of FDCs in ungauged basins,
and to complement the significant advances made through
statistical methods. As in all other chapters, this review is
organised into two parts: (i) derived distribution
approaches that aim to capture the process controls on
the FDCs in an analytical or quasi-analytical way so as to
provide process insights into the regional patterns that arise
from statistical methods, and thus improve regionalisation
efforts, and (ii) continuous rainfall

7.4 Process-based methods of predicting flow
duration curves in ungauged basins
Deciphering the separate controls of both climate processes
(e.g., precipitation, temperature, radiation or potential
evaporation) and catchment characteristics (e.g., soil, top-
ography, vegetation type and functioning, catchment size,
human impacts) on the shape of FDCs represents a key
issue for hydrologists. This issue can be best addressed by
using process-based approaches that link the drivers (input
fluxes of water and energy), the state of the system (storage
terms) and its response (output fluxes). To be most effect-
ive, process-based methods need to include, as a basic
ingredient, the time variability of precipitation inputs to a
catchment at all time scales extracted from available obser-
vations. They need to describe how this variability is
propagated through the catchment system and is finally
manifest in the catchment

runoff simulation
methods that generate continuous runoff time series, from
which FDCs can be constructed, but nevertheless enable
sensitivity studies that will again provide insights to
observed patterns.

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s FDC. In this way, process-
based methods provide an excellent basis to interpret (or
reinterpret) and evaluate the results from application of
well-established statistical methods, as well as evaluate
possible changes in the FDC induced by observed or
predicted changes to the climatic drivers (e.g., precipita-
tion) or landscape characteristics (e.g., land uses).
Work on predictions of FDCs, especially in ungauged
basins, has been mostly statistical and empirical, which
has gained strength in the last two decades. However,
application of process-based approaches has lagged
behind, no doubt due to the difficulties of merging the
statistical and dynamical aspects of runoff variability,
especially over a wide range of time scales, as is required
in the case of the FDCs. Indeed, in this respect, the
comparison with derived distribution methods in flood
frequency (see Chapter 9 ) is quite stark. If the FDCs are
brought up at all in the context of process-based model-
ling, they appear to be just one outcome or by-product of
continuous rainfall

'

7.4.1 Derived distribution methods
Flow duration curves may be derived from precipitation
analytically in a way similar to the derived flood frequency
method of Eagleson ( 1972 ) with a number of simplifica-
tions. Botter et al.( 2007a ) adopted a stochastic-analytical
model that consists of (i) a simple lumped (deterministic)
model subsurface drainage (slow flow), governed by a
field capacity threshold and a characteristic residence
time; and (ii) stationary sequences of random precipitation
events, whose arrival times are Poisson distributed, and
precipitation depths are gamma distributed. The rainfall -

runoff model enabled them to estimate slow flow volumes
analytically which, when combined with the statistical
characterisation of the precipitation, enabled them to
derive the probability density function of slow flow
volumes, which represents a form of the slow flow com-
ponent of the FDC. The analytical formulation also
enabled them to relate the runoff variability to the under-
lying catchment properties and key precipitation event
characteristics.
Subsequently, the earlier model of Botter et al.( 2007a ,
b ) has been extended by Muneepeerakul et al. (2010) to
include a fast flow component as well, and by Botter et al.
( 2009 ) to include non-linearities in the subsurface storage

runoff models. For example, FDCs
are used as one of the signatures of runoff variability
(Farmer et al., 2003 ), or are used in the calibration or
performance assessment of rainfall

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runoff models (Wes-
terberg et al., 2011 ). Only in rare instances is the estima-
tion or prediction of the FDCs the actual goal of the
modelling (Mostert et al., 1993 ; Tshimanga et al.,
2011 ), and even then these applications are in gauged
catchments and applications in ungauged catchments are
conspicuously absent.

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runoff relationship. The ability of the stochastic dynamic
model to reproduce observed FDCs has been tested in