Non-parametric MTB methodology for producing plausible future scenarios from real rainfall data.

Written by: Dale Mellor (
Date: February 2003
Version: 2.0 (previous version 1.0, December 1996)

Copyright © 1996, 2003 Dale Mellor

All rights are reserved by the author, except that this document may be freely reproduced in full (not in part) in any form, and may be quoted from provided that i) the quotation is attributed to "Dale Mellor, 2003", and ii) the quotation is only used in the context established by the rest of this document.

1. Introduction.

1.1 History.

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).

1.2 Motivation for new method.

1.3 Layout, scope and purpose of this document.

2. The new methodology.

2.1 Description of the model.

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.

2.2 Description of the nowcasting methodology.

  1. Take a succession of radar images. Locate the maximum rainfall intensity in all the images. In the image in which this occurs, obtain the boundary of all points adjacent to the maximum at which the intensity decreases with distance from the point of the maximum. Take the previous image, and within the region identified above, locate the maximum intensity and the corresponding region around that. Repeat for earlier images, and later ones. It will be necessary to define several thresholds (XXX) to prevent this process running out of control. Once the exercise is complete, remove the pixels inside the identified regions, and repeat. This will result in a set of identified artifacts.

  2. Combine data from adjacent artifacts, so they do not 'cut off' abruptly at the edges. This will result in a more realistic set of artifacts, on the assumption that real rainfall fields are obtained as the sum of artifacts where they overlap.

  3. Apply a large moving average to all the radar images. This will result in the identification of an underlying Poisson rate function which explains the distribution of the artifacts.

  4. Compute the lag-1 spatial correlogram from the smoothed images. More particularly, determine the offset from the origin of the nearest maximum in this correlogram.

  5. Convect the details in the most recent smoothed image to future times, according to the displacement of the peak in the above correlogram from the origin.

  6. Using a random number generator, distribute the set of observed artifacts according to a synthesized Poisson process, using the underlying rate obtained above.

  7. Repeat the above step many times to produce a set of plausible future scenarios.

3. Conclusions.

4. References.