Deterministic Simulation of Mildly Intermittent Hydrologic Records

Abstract

Application of a deterministic geometric approach for the simulation of mildly intermittent hydrologic data, exhibiting a few peaks and displaying relatively slowly rising and falling limbs and yielding slowly decaying autocorrelation functions that reach a zero value at a lag that is at least 5% of the length of the records, is presented. Specifically, adaptations of the original fractal-multifractal (FM) method and an extension, yielding more general attractors instead of fractal functions (and relying on five and eight parameters, respectively), are advanced in order to simulate (1) continuous rainfall events gathered every few seconds or minutes and lasting a few hours, and (2) continuous streamflow records measured at the daily scale and encompassing a year. It is shown, using as case studies one rainfall event in Boston, three storms gathered in Iowa City, and 4 years of streamflow records at the Sacramento River in California, all having distinct geometries, that the (computationally efficient) FM approach is capable of closely preserving either the complete record’s autocorrelation function or the data’s whole histogram (including moments), and even both, resulting in suitable rainfall and streamflow simulations, whose features and textures are similar to those of the observed data sets. The study hence establishes, for the first time, the possibility of parsimoniously simulating hydrologic sets in time in a deterministic manner, as a novel way to supplement stochastic frameworks.