Mathematical models are a way to represent
"reality" through the development of mathematical
relationships. This conceptualization of reality
has been attempted for things such as the modeling
of stock market behavior, population growth, weather
forcasting, etc., and can be applied (with varying
success) to any process which can be decribed by
a mathematical expression.
However, models are not the "real thing" and always
involve some degree of simplification and
approximation. Exclusion of processes or elements known
to be functioning in a system is often excused by assumptions
that these things have negligible or insignificant effects
on the system as a whole. The development of mathematical
models also involves the assumption that people understand
the various processes well enough to be able to translate
system behavior into mathematical expressions.
Because models are developed from mathematical expressions, there are parts of the equation which must be known (input), and parts which are being solved (output). Parameters are the elements which the user must input into the model and can be universal constants, measurements, etc. To parameterize a model often means choosing input which will best describe the given system. Variables are the elements which the model calculates and turns into output. It is possible for a variable to become a parameter when feedback cycles are included in the model.
Hydrologic models are simply a variation on this
theme. Mathematical expressions are developed by
scientists to describe the relationships between
various hydrologic parameters and variables.
One could argue that the water balance equation, which
is based on the conservation of mass principle, is itself a
hydrologic model. Yet, although this equation
is at the heart of many hydrologic models, we often
associate "modeling" with more complex mathematical
equations which require computer processing capabilities
to solve them.
There are basically two classes of environmental models:
Results of physically based model: "Chaotic Advection":
Contact Mark Williams at firstname.lastname@example.org with questions or comments.
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