Prediction of flow duration curves in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 154

several catchments in the USA and Europe (Botter et al.,
2010 ). Although the stochastic dynamic framework (e.g.,
Botter et al., 2007a , b , 2009 , 2010 ) is capable of providing
insights into the climatic and catchment controls of the
FDCs, its potential for application to ungauged basins is
constrained by the assumptions made in the work done to
date (e.g., Poisson precipitation arrivals). In circumstances
where there is strong seasonality in the climate inputs,
constant (but different) parameter values have been
adopted for each season. The routing of runoff in the river,
the associated time delays and, in particular, the carryover
of soil moisture storage between seasons has been neg-
lected, so that the method works best in places where
seasonality is low. This highlights the need for a more
general framework, one for the entire year that captures
within-year variations in climate and soil moisture storage,
especially in the light of the strong role that seasonality
plays in controlling the middle part of the FDC, the role
played by hydrogeology and long flow pathways that
control low flows, and the role played by high precipitation
events that govern high flows.
Yokoo and Sivapalan ( 2011 ) proposed a conceptual
framework to reconstruct FDCs by disaggregating the
FDCs of total runoff into two components, i.e., fast flow
duration curves and slow flow duration curves, similar to
the earlier work of Botter et al. (2007a, b) and Muneepeer-
akul et al . (2010) . The approach of Yokoo and Sivapalan
( 2011 ) was formulated on the basis of numerical simula-
tions of the water balance of hypothetical catchments with
the use of a physically based rainfall

7.4.2 Continuous models
Long-term numerical simulations of the soil water balance
equation coupled to some routing scheme to reproduce the
movement of water in soils and streams are greatly benefi-
cial to explore the dependence of the features of the FDC
on the underlying hydrological and climatic processes, as
all the driving processes (precipitation, soil moisture
dynamics, transport in channels and hillslopes) may be
described in much more detail than may be possible with
analytical models. An example of continuous model simu-
lations to describe FDC is described in the following; it
refers to the approach developed by several authors using
the Pitman ( 1973 ) monthly rainfall runoff model, which

has been used extensively in Southern Africa, particularly
in ungauged catchments. The most recent description of
the model is provided in Hughes ( 2006 ). This conceptual
model includes the primary processes that are responsible
for the magnitude and shape of the FDC: surface runoff
(based on a triangular distribution of catchment absorption
rates and monthly precipitation total) and a non-linear
drainage function dependent on the soil moisture storage
level partitioned into rapid (interflow) and slow (ground-
water) components, the latter accounting for groundwater
recharge and runoff components. The balance between the
contributions of the three components (surface runoff,
interflow and groundwater discharge) determines the shape
of the FDC, and this balance is clearly a reflection of the
climate and catchment characteristics (as represented by
the model parameters). The model can also simulate the
effects of anthropogenic impacts (abstractions, reservoir
storage, impacts of different vegetation cover, etc.) on
FDCs (Hughes and Mantel, 2010 ).
One way of assessing the model performance is to
compare simulated FDCs to either FDCs derived from
gauged data or regionalised estimates of the FDCs for
ungauged situations. Figure 7.16 shows results for two
dry catchments in Botswana and Zimbabwe. For the
ephemeral river in Botswana, while most of the FDC can
be simulated, the frequency of zero flow is much more
difficult to capture even after calibration. This may be
related to poor precipitation definition in semi-arid areas,
but may also be related to some processes not being
adequately represented by the model (e.g., dynamic vege-
tation changes, see Mostert et al., 1993 ). For the perennial
(but relatively dry) river in Zimbabwe ( Figure 7.16b ) , the
results indicate poor agreement in the case of low flows;
part of the reason for this can be attributed to upstream
development

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runoff model, and
driven by artificial precipitation inputs generated by a
stochastic rainfall model. These simulations by Yokoo
and Sivapalan ( 2011 ) revealed a clear relationship between
the fast flow FDC and the duration curve of precipitation
(PDC) and between the slow flow FDC and the catch-
ment

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s runoff regime curve (mean seasonal runoff). In
doing so Yokoo and Sivapalan ( 2011 ) proposed a new
conceptual framework for the estimation of FDCs in
ungauged basins, through building bridges between the
fast and slow flow parts of total runoff as precipitation
variability cascades through the catchment system, and
through recourse to understanding the respective process
controls. Yokoo and Sivapalan ( 2011 ) carried out prelimin-
ary analyses on a few selected catchments within the USA
to demonstrate the feasibility of their approach. However,
their approach has not been applied and tested in ungauged
catchments. Nevertheless, there is promise that, through a
combination of the stochastic dynamic approach of Botter
et al. (2007a, b) and Muneepeerakul et al . (2010) , and the
numerical simulation approach of Yokoo and Sivapalan
( 2011 ), one can make considerable advances in the area
of process-based approaches to the predictions of FDCs in
ungauged basins.

'

impacts (small farm dams, etc.) on the

observed runoff data.
While all of the results given above, and also those
extracted from a related report (Hughes, 1997a , b ), include
model calibrations, and are therefore not applications in
ungauged basins, one of the conclusions was that