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In the Fall of 1987, I was invited by Dr. Hanif Chaudhry
to participate in the International Seminar on Physical and Mathematical Modeling of Hydraulic Structures,
in Lahore, Pakistan. As part of the visit, the six-member U.S. delegation toured Tarbela Dam, on the Indus river, the largest
earth-filled dam in the world.
One evening, after dinner at the guest house, one of the members of the team posed the following question to me:
"Could you tell us what the difference is between deterministic and stochastic modeling?"
I said: "It is simple: If you have a signal, the process should be modeled deterministically; on the other hand,
if all you have is noise,
the process should be modeled stochastically."
In fact, it would be a mistake to handle a signal-driven process such as flood wave routing
with a stochastic model.
On the other hand, daily flows in upland watersheds usually lack enough diffusion to develop a signal;
therefore, they are better handled with a stochastic approach. Both deterministic and stochastic models are useful tools in applied
hydrology.
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