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to be testedwith additional work in the future. However, their
work does illustrate the power to formulate globally general-
isable relations through a combination of the Newtonian and
Darwinian approaches.
12.3.3 A new unified uncertainty framework for PUB
Traditional uncertainty quantification
The traditional paradigm of uncertainty estimation in
hydrology has been the method of
'
(e.g., Kuczera and Parent, 1998 ; Montanari and Brath,
2004 ; Liu and Gupta, 2007 ), and work on predictions in
ungauged basins has not been an exception. In this
approach, for any prediction method or model, one div-
ides up the sources of uncertainty into (i) measurement
uncertainty (measurement and interpolation errors of pre-
cipitation inputs and runoff measurements that are used
in calibration), (ii) model parameter uncertainty, and
(iii) model structure uncertainty. In a first step, one quan-
tifies these uncertainties individually; e.g., measurement
uncertainty on the basis of known instrument errors and
the spatial statistical analyses, parameters uncertainty by
assuming or inferring distribution functions of the param-
eters, and model structure uncertainty by assuming differ-
ent model structures. In a second step, one then
propagates them through the model to estimate resulting
prediction uncertainty. If there is any additional informa-
tion on the catchment systems (such as groundwater
levels, remotely sensed snow cover data, information
from reading the landscape in the field, or regionalised
runoff signatures), this additional information can be
assimilated to reduce the predictive uncertainty (Wagener
and Montanari, 2011 ). The interest resides in one catch-
ment, even though regional information may be used for
reducing the uncertainty. There are an enormous number
of techniques for this type of uncertainty estimation (see
e.g., Liu and Gupta, 2007 ), and all have the element of error
propagation. This fundamentally mirrors the Newtonian
approach in its execution, and carries with it the same
advantages and disadvantages
'
error propagation
Figure 12.12. (Top) Synthesis of the Newtonian and Darwinian
approaches, Coweeta, USA. (Bottom) A postulated relationship
between vegetation gradient and aridity. Bottom graph redrawn from
Hwang et al . (2012) .
avenue well worth pursuing. In a comparative approach
Hwang et al .(2012) focused on why long-term spatial devel-
opment of forest ecosystems is different in different places.
They sought guidance from regional work done by Troch
et al.( 2009 ), Brooks et al.( 2011 ) and Voepel et al.( 2011 ) ,
with the use of over 400 catchments across continental USA.
This work had shown a strong empirical, co-evolutionary
(Darwinian) relationship between the Horton index (a form
of aridity index focused on vegetation water uptake) and
remotely sensed vegetation at the catchment scale (e.g.,
normalised difference vegetation index, NDVI). Within the
Coweeta experimental catchment in North Carolina, Hwang
et al. additionally found strong correlations between the
Horton index and downslope gradient of the NDVI, and
attributed this to a topographically driven, downslope
groundwater subsidy. They then used extensive local hydro-
logical observations, combined with simulations with a dis-
tributed ecohydrological model, RHESSYs (Band et al.,
1993 ; Tague and Band, 2004 ), to characterise the patterns
of seasonal
the ability to attribute indi-
vidual error sources based on causal relationships, but the
difficulty remains that effects of unknown feedbacks cannot
be identified.
-
ow regimes (Newtonian approach), interpret
them in terms of ecohydrological processes and feedbacks
occurring in forested headwater catchments, and to explore
the role of downslope vegetation gradient in these interacting
processes (Darwinian approach). On the basis of the under-
standing gained in this way, Hwang et al. had the foresight to
postulate a new regional (and possibly global) relationship
between the Horton index and downslope vegetation gradi-
ent that extends beyond the environmental conditions found
in North Carolina (see Figure 12.12 ). Of course, this remains
Uncertainty quantification based on comparative
hydrology
The approach to uncertainty quantification in this topic
has been fundamentally different. Indeed, this topic has
focused on predictive uncertainty measured by cross-
validation performance of the prediction of runoff signa-
tures, in the form of blind testing. This comparative
performance assessment is a Darwinian way of assessing
predictions and estimating model uncertainty through an
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