Regularity Based Functional Streamflow Disaggregation. I. Comprehensive Foundation
An integrated, largely non-probabilistic, calibration-free approach is proposed to identify, estimate, evaluate and attribute conceptual components of a streamflow time series. We assess its gross functional aggregation from the signal structure alone by consistently exploiting elementary constraints. Starting from the separability concept of linear operator theory, cross-connections are revealed of such a blind functional streamflow disaggregation (FSD) to qualitative dynamics. The algorithm is initialized by a first guess of regular behaviour using Singular–system Analysis (SSA). To approach the regular/singular borderline of the data and to separate a fast flow from total runoff, this (probabilistic) SSA mode is transformed into a lower envelope to the series via iterative cubic spline interpolation (CSI). Repeated CSI yields a hierarchy of lower envelopes that piles up part of a transient component and converges into a slow one. A lower bound is constructed as an instantaneous low flow (ILF), using the leading SSA eigenvector. We demonstrate the method for highlands river stations, compare its results with those from distributed hydrologic models, and discuss attributions to overland, inter- and base-flows. For independent evaluation we resort to singularity based multifractal analyses.
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