Estimating the Uncertain Structure of a Water Balance
Model via Bayesian Data Assimilation
Nataliya Bulygina and Hoshin
Gupta
Department of Hydrology and
Water Resources, the
HWR Department Seminar, Oct 3,
2007
ABSTRACT
To date, most ‘physically based’ models of hydrologic
systems are based on an implicit up-scaling premise that the behavior at
the model scale can be described by the small scale governing equations,
by spatial averaging of the state variables and by use of ‘effective’
parameters. Of course, the
up-scaling assumption may be wrong, and the effective large scale
governing equations for a heterogeneous system
may be different in form, not just different in parameters, from the
equations derived from small-scale physics.
In this work, we assume that the major hydrologic processes in the
system and their interconnections have been identified a priori. We wish to
construct the mathematical relationships in question via data assimilation,
using measurements made on the system inputs and outputs. In this work, as
opposed to assuming fixed mathematical structure, a model is perceived as a
representation of both what we know
and what we do not know about the
structure and behavior of a system. The model is therefore seen as the ‘posterior’ joint probability density
function for the relationships in question, constructed in such a way that data
assimilation helps to correct ‘prior’ belief about the dependences. In regions where no data are available
‘prior’ knowledge about the system can be incorporated and will dominate. The
approach is applied to the problem of estimating a water mass balance model for
the Leaf River catchment,