Geoscience Reference
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2008, 2009; Wong, 2008; Kleidon
et al.
, 2010; and Zehe
et al.
, 2010) and it has been suggested that
this should be a guiding principle in constraining the model representation of hydrological processes
(Schaefli
et al.
, 2011).
There are a number of optimality principles that might be invoked. These include maximising the
net primary productivity of the vegetation cover, maximising entropy production, minimising energy
expenditure, maximising Helmholtz free energy dissipation, maximising water use, minimising water
or oxygen stress, and maximising net carbon profit (see review by Paik and Kumar, 2010). Different
principles might be appropriate over different time scales and there might be conflicts between different
optimality constraints. The question that then arises is whether such concepts might be useful constraints
on appropriate model structures in future, especially when there will be continuing uncertainty in the
forcing data.
In fact, nearly all rainfall-runoff models implement one such principle already: the principle of mass
balance. The input precipitation to a model is partitioned into discharge, evapotranspiration and change
of storage such that, in the model, no water is lost or gained. A check on mass balance is commonly
programmed into a model, because a modeller would be worried if mass was being lost or gained, for
example as the result of an approximate numerical solution to a partial differential equation (this was a
problem with my own early finite element model of hillslope hydrology Beven, 2001).
The problem that then arises is that the data available on the different elements of the water balance
might be subject to sufficient uncertainties that the net mass balance should not actually be zero. This
might arise if the monitoring network for precipitation was not adequate to always give accurate estimates
of the inputs. There might be a non-stationary bias because the raingauge sites under-represent the rain and
snow inputs in high elevation zones, or because they cannot adequately capture local convective raincells
relative to synoptic frontal patterns. There might be inadequate rating curve information such that the
total volume of discharge is not accurately estimated. Similarly estimates of actual evapotranspiration
and storage changes (if available at all) are subject to uncertainties.
The result is that it can be difficult to be sure that the data driving the model are consistent with the
water balance principle. This is one reason why a number of studies have tried to estimate rainfall and
discharge errors as part of the calibration process (see Section 7.8). Similar issues arise in the application
of energy and momentum balances and establishing optimality principles. Even if the vegetation is really
acting optimally in all conditions (and it is not clear how much information would be required about
water status, root growth, nutrient status, health of the plants, and other external forcings such as fire, land
management, insect infestations, etc. to verify this), then the forcing data actually might not be consistent
with the application of the principle. The propensity to change and sensitivity to new forcing events
might also depend on the particular sequence of events (e.g. Beven, 1981b). However, that is not to say
that this approach might not sometimes be valuable. For example, Hwang
et al.
(2009) show that, in an
application of the RHESSys model, the rooting depth parameters that produce an optimal fit to observed
discharges also maximise net primary productivity in fitting vegetation leaf area index data. Schymanski
et al.
(2008, 2009) start with the principle that plants maximise their net carbon profit and implement
a “vegetation optimality model” (VOM) that constrains the number of parameters to be calibrated in
hydrological modelling. They also show how this can be tested as a hypothesis, at least during the dry
season when the vegetation is constrained by the availability of water. This type of hypothesis testing can
be used within an uncertainty framework. Mitchell
et al.
(2011), for example, show how a forest growth
model is not consistent with a set of observations for a site in Oregon, even allowing for uncertainty in
measured fluxes.
In fact, a general principle for the hydrological modeller should be to invoke all prior knowledge
and principles in trying to improve the representation of catchment processes. It may, however, be very
difficult to verify the application of such principles in practical applications. Indeed, it might be the case
that the imposition of a principle might constrain a model in a misleading way, in much the same way as an
incorrect representation of a flow process (treating subsurface flows as purely Darcian; treating overland
