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The MTB model is a stochastic model of rainfall fields which operates in the continuum of time and (two dimensional) space. It was originally developed by Mellor, 1993. It has eighteen model parameters, and makes very strong assumptions, based on an extensive literature review, about the nature of real rainfall events (such as sinusoidal banded structure, parabolic raincell profiles, constant raincell velocity and lifetime, identical raincells).
The original work saw the development of software to numerically realize the model given a parameter set, and developed a set of ad hoc methods for the estimation of the various parameters.
Subsequent works by this author, cited in the reference section below, developed a methodology for the strong conditioning of the model on real data (determining realizations of the model which exactly reproduced observed data at a point in time or a point in space), and then generating stochastic future scenarios based on the strong conditioning. These have been fed into a catchment response model (XXX) to produce a set of runoff scenarios, and these in turn used to derive probability envelopes in which the actual outcome of the physical event is expected to fall (XXX).
The rainfall field is assumed to be composed of a collection of artifacts, each contributing rainfall over a finite volume of time and space, and each characterized by a single maximum and monotonic falloff from this peak in time and space. These artifacts are distributed such that their maxima coincide with the occurrences of points of an unobserved inhomogeneous Poisson process. Depending on the nature (scale) of the observations, the artifacts may be interpreted as raincells or cluster potential regions. Note that any velocity the artifacts may be deemed to have is implicit in the three-dimensional (two spatial and time) shape of the artifacts; there are no explicit parameters to the model.