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should be at the heart of a modelling process
treated as learning about the responses of the
places at which models are applied, a process that
places emphasis on making data available to
allow the uncertainty in model predictions to be
constrained (Beven, 2007).
One issue to be addressed in the future is
developing guidelines on good modelling practice
and the value of different types of data in con-
straining uncertainty (Pappenberger & Beven,
2006; Beven et al ., 2008). It does seem, however,
that there will be uncertainty about uncertainty
estimation methods for some time to come. Clear
differences of opinion exist between those who
insist that formal statistical methods of uncer-
tainty estimation are the only way to evaluate
model predictions, and those who accept that
epistemic uncertainties undermine the theoreti-
cal rigour of formal statistics, and that conse-
quently it will be worthwhile pursuing other,
more exploratory methodologies.
It should, however, be stressed that uncer-
tainty estimation should not be considered as the
end point of an analysis. Since, when used with
erosion models, it will often reveal the failure of
models to match observations, it demands
improvements in both models and data to check
whether such errors represent Type I, Type II or
Type III modelling errors. Types I and II have been
mentioned earlier, and can be constrained by the
collection of more data to refine the characteriza-
tion of the system and constrain the uncertain-
ties further. Type III errors are the unknown
unknowns, the missing processes, the epistemic
errors that we had not previously considered
important. Addressing Type III errors implies
future creativity from modellers, based on a care-
ful analysis of model failures.
ment, Part I: model development. Journal of American
Water Resources Association 34 : 73-89.
Beven, K.J. (1985) Distributed modelling. In Anderson,
M.G. & Burt, T.P. (eds), Hydological Forecasting . John
Wiley & Sons, Chichester: 405-35.
Beven, K.J. (1989) Changing ideas in hydrology: the case
of physically based models. Journal of Hydrology 105 :
157-72.
Beven, K.J. (1993) Prophecy, reality and uncertainty in
distributed hydrological modelling. Advances in
Water Resources 16 : 41-51.
Beven, K.J. (1996a) Equifinality and uncertainty in geo-
morphological modelling. In Rhoads, B.L. & Thorn,
C.E. (eds), The Scientific Nature of Geomorphology .
John Wiley & Sons, Chichester: 289-313.
Beven, K.J. (1996b) A discussion of distributed model-
ling. In Refsgaard, J.-C. & Abbott, M.B. (eds),
Distributed
Hydrological
Modelling .
Kluwer,
Dordrecht: 255-78.
Beven, K.J. (2001a) Rainfall-Runoff Modelling: The
Primer . John Wiley & Sons, Chichester.
Beven, K.J. (2001b) Dalton Medal Lecture: How far
can we go in distributed hydrological modelling?
Hydrology and Earth System Sciences 5 : 1-12.
Beven, K.J. (2001c) Calibration, validation and equifinal-
ity in hydrological modelling. In Anderson, M.G. &
Bates, P.D. (eds), Model Validation: Perspectives in
Hydrological Science . John Wiley & Sons, Chichester:
43-55.
Beven, K.J. (2002a) Towards a coherent philosophy for
environmental modelling. Proceedings of the Royal
Society London A 458 : 2465-84.
Beven, K.J. (2002b) Towards an alternative blueprint for
a physically-based digitally simulated hydrologic
response modelling system. Hydrological Processes
16 : 189-206.
Beven, K.J. (2006a) A manifesto for the equifinality the-
sis. Journal of Hydrology 320 : 18-36.
Beven, K.J. (2006b) On undermining the science?
Hydrological Processes 20 : 3141-6.
Beven, K.J. (2007) Working towards integrated environ-
mental models of everywhere: uncertainty, data, and
modelling as a learning process. Hydrology and Earth
System Science 11 : 460-67.
Beven, K.J. (2008) On doing better hydrological science.
Hydrological Processes 22 : 3549-53.
Beven, K.J. (2009) Environmental Modelling: An
Uncertain Future? Routledge, London.
Beven, K.J. & O'Connell, P.E. (1982) On the role of phys-
ically-based distributed models in hydrology. Institute
of Hydrology Report , No. 81, Wallingford, UK.
References
Andréassian, V., Lerat, J., Loumagne, C., et al . (2007)
What is really undermining hydrologic science today?
Hydrological Processes 21 : 2819-22.
Arnold, J.W., Srinivasan, R., Muttiah, R.S. & Williams,
J.R. (1998) Large area hydrologic modeling and assess-
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