A random cascade disaggregation of spatial rainfall is incorporated into the one‐dimensional hydrological component of the UK Meteorological Office Surface Exchange Scheme (MOSES) used in their general circulation model (GCM). The results of several simulations using exponentially distributed, disaggregated and evenly distributed rainfall are compared. The changes in the water balance—in particular the throughfall and the evaporation from the canopy—are assessed. It is shown that a disaggregation using random cascades gives closer values to the reference simulation of canopy evaporation and throughfall variables than the conventional approach. Copyright © 2000 Royal Meteorological Society

We calculate the box-counting dimension of a self-affine version of the Sierpiński triangle. This is done by investigating the singular values of the affine transformations. We also investigate multifractal features of self-affine measures supported by certain generalized Sierpiński triangles.(1.2)Here we will discuss self-affine fractals in R 2 . A self-affine fractal F is the attractor of an IFS consisting of a set of affine contractions S i :for i = 1, 2, . . . k, where a i ∈ R 2 is a translation vector, and T i ∈ L(R 2 , R 2 ) is the linear part of the 31 Fractals 1998.06:31-41. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 02/03/15. For personal use only.

We discuss the relationship between the multifractal functions of a plane measure and those of slices or sections of the measure with a line. Motivated by recent mathematical ideas about the relationship between measures and their slices, we formulate the "slice hypothesis," and consider the theoretical limitations of this hypothesis. We compute the multifractal functions of several standard self-similar and self-affine measures and their slices to examine the validity of the slice hypothesis. We are particularly interested in using the slice hypothesis to estimate multifractal properties of spatial rainfall fields by analyzing rainfall data representing slices of rainfall fields. We consider how rainfall time series at a fixed site and slices of composite radar images can be used for this purpose, testing this on field data from a radar composite in the USA and on appropriate time series. Fractals 2000.08:337-348. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/09/15. For personal use only. Fractals 2000.08:337-348. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/09/15. For personal use only. Fractals 2000.08:337-348. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/09/15. For personal use only.