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