The use of a deterministic fractal‐multifractal (FM) representation to model high‐resolution rainfall time series via projections of fractal interpolating functions weighed by multifractal measures is reported. It is shown that the intrinsic shape and variability of an 8‐hour Boston storm recorded every 15 s on October 25, 1980, may be encoded wholistically, employing the fractal geometric methodology. It is illustrated that the FM methodology provides very faithful descriptions of both major trends and small (noisy) fluctuations for this storm, resulting in preservation of not only classical statistical characteristics of the records but also multifractal and chaotic properties present in them. These results, and those for other storms, suggest that a stochastic framework for rainfall may be bypassed in favor of a deterministic representation based on projections.

In order to understand processes causing soil crusting and to optimize sampling schemes, improved understanding of crust spatial characteristics is needed. For this purpose, statistical and fractal analyses of soil surface strength, as measured by a 1.59‐mm‐diam. flat‐tipped micropenetrometer, were carried out for a variety of soils and under a variety of sampling schemes. Specifically, this work considered maximum penetration forces sampled at intervals of 0.005, 0.01, 0.05 and 0.5 m along four parallel transects 0.25 m apart, for nine different sites within California's Central Valley. Force measurements were non‐homogeneous in space. For eight of the nine sites, both the mean and the variance were non constant; and for all sites, the range and nugget variance of fitted semivariograms were scale dependent. Fractal analysis of the measurements allowed qualitative discrimination among soils, despite small variations across scales. For all sites, fractal dimensions of sampled series at alternative scales were similar, but the smallest deviations across scales were observed on high‐strength silt loam, and the largest on low‐strength loamy sand soils. Multifractal spectra (for data sets normalized and interpreted as probability measures) gave similar entropy dimensions for all sampling schemes, with very small deviations across scales for silt loam soils and largest again for loamy sands. Results suggest that the fractal attributes (fractal and entropy dimensions), being scale‐independent attributes, may be relevant qualifiers of the intrinsic variability of penetration measurements and that this variability can be modeled as a fractal process.

A method based on an optimal nonlinear filtering technique is proposed and tested for the determination of the hydraulic conductivity function from a field drainage experiment. Simplifications to Richards's equation lead to a Langevin type differential equation to describe the redistribution of stored water as a function of drainage flux excited by a random initial condition and state forcing. The derived equation is then utilized in an optimal estimation scheme that explicitly accounts for the formulation and observation uncertainty in determining the hydraulic conductivity parameters. A field drainage experiment was carried out to study the usefulness of the proposed method for routine in situ hydraulic conductivity function estimation.

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