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We introduce a systematic method for extracting multivariable universalscaling functions and critical exponents from data. We exemplify our insightsby analyzing simulations of avalanches in an interface using simulations from adriven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize thespatial structure of these avalanches- we report universal scaling functionsfor size, height and width distributions, and also local front heights.Furthermore, we resolve a problem that arises in many imaging experiments ofcrackling noise and avalanche dynamics, where the observed distributions arestrongly distorted by a limited field of view. Through artificially windoweddata, we show these distributions and their multivariable scaling functions maybe written in terms of two control parameters, the window size and thecharacteristic length scale of the dynamics. For the entire system and thewindowed distributions we develop accurate parameterizations for the universalscaling functions, including corrections to scaling and systematic error bars,facilitated by a novel software environment SloppyScaling.

Avalanche Spatial Structure and Multivariable Scaling Functions; Sizes, Heights, Widths, and Views through Windows