FLOOD06027

• County: Statewide
• Basin: Statewide
• Title: Of Carts and Horses in Hydrologic Modeling
• Date: 4/1/1997
• Floodplain - Doc Type: Educational/Technical/Reference Information

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model on the basis of the new knowledge, and so on. This
process of improvement of the model is schematically illus-
trated in Fig. I (a).
In theory, this method of making a model better applies
equally to theoretical and empirical models because results of
a better theoretical model can, in principle, be summarized in
the form of a better empirical model. However, to paraphrase
George Orwell, in practice it applies "more equally" to the-
oretical models than to empirical ones. This is so because the
overriding purpose of an empirical model is to summarize (the
results of) what is known and give it to a client who may
already be waiting impatiently to use it in his project. So there
is a strong disincentive to go back to the prototype (collect
more data, do experiments and perhaps theoretical research)
even if the result is not fully satisfactory and as long as the
client "can live with it" (after all, it could be an open-ended
exercise-it could take years, there is no guarantee of success
and the need for the project is here and now!). And so, as
Rogers (1983) once matter-of-factly summarized .the typical
situation, the scientist or engineer yields to the various admin-
istrative and legal requirements and tries "to do the best he
can under the situation."
In practice, Hdoing the best", is improving the fit of the
model to the available data. It dries not require going back to
the prototype and gather new information-all it needs is to
have one run the model in a "do loop" a few times and adjust
a parameter here and there to reduce some formal error func-
tion to improve the goodness of fit. This process is schemat-
ically illustrated in Fig. I(b).
On comparing Figs. l(a) and l(b), we see that the first pro-
cess tries to make the model better with respect to the proto-
type while the second does so only with respect to itself: the
first tries to improve the representation of the substance, the
second of the form. Since this form is determined by the pat,
tern of the original data, which, in the second case, is the only
information about the substance that ever enters the picture,
there is no way the second process can improve the model

(a)

(b)

NO

YES
~

YES
~

BETTER

BETTER

MODEL

FIT OF A

MODEL

FIG. 1. Difference between Procedures Aimed at: (a) Improve-
ment of a Model; (b) Improvement of the Fit of a Model

YES

~~

YES
~

BETTER
MODEL

FIG. 2. General Model-Bulldln9 Proeedure

substantially-there is nothing more to be learned about the
prototype, no matter how many times the loop is repeated. It
is the inviolable axiom of the modeling process that the pro-
totype is the horse and the model is the cart it is pulling; thus
the basic message of this essay is that one cannot get ahead
by putting the cart before the horse.
Unfortunately for the advancement of hydrology, this is ex-
actly what the mainstream of hydrological modeling has been
doing for the last 30 years-pretending that a meticulous pol-
ishing of the fits of the various empirical models will trans-
form them into sound theoretical models! No wonder the result
has been stagnation, since, as my friend and colleague (one of
the best hydrologists I have met), Fred Morton, used to say:
"They are spinning the wheels of a car stuck in the mud."
It has to be emphasized that some amount of polishing is
legitimate and usually necessary in every kind of modeling as
it is, for instance, in every kind of writing: it is a rare occasion
that nothing can be improved on a first draft. Thus there is
usually secondary fitting, or calibration, loop within the pri-
mary modeling loop shown in Fig. l(a). Accordingly, under
the magnifying glass, Fig. l(a) would usually appear as shown
in Fig. 2, which illustrates the general process of model build-
ing.

Theoretical-What Does It Mean?

There is a widespread misconception about the meaning of
the notion "theoretical," which reinforces the misconceptions
about modeling discussed earlier. It derives from the fascina-
tion with mathematics. This is a very common phenomenon
among nonmathematicians, who often view mathematics as
the purest and highest theory whose pronouncements have the
final authority about everything in this world and are unchal-
lengeable by definition because, if the mathematics is rigorous,
they are exact. Thus a curve drawn through a few points, if it
can be expressed by a mathematical equation, automatically

JOURNAL OF HYDROLOGIC ENGINEERING / APRIL 1997/45