Complexity and scaling descriptors as diagnostic predictors of heliophysical indices across solar-cycle timescales

Abstract

Heliophysical variability emerges from a coupled, multiscale system in which changes in the solar atmosphere and heliospheric plasma translate into measurable signatures in widely used activity indices. Operational space-weather workflows often summarize this variability through amplitudes and a small set of bulk solar-wind covariates, yet important dynamical information may also reside in the evolving \emph{morphology} of the signals. We examine whether shape descriptors computed from heliophysical time series provide information beyond classical amplitude summaries and standard bulk solar-wind covariates. Using daily OMNIWeb-era records spanning 1964--2025, we compute ten sliding-window descriptors under a past-only convention, designed to capture complementary aspects of temporal morphology such as irregularity, roughness, and long-range dependence. The descriptor set combines entropy measures, fractal-dimension estimators, the Hurst exponent, and Lempel--Ziv (LZ) complexity, yielding a compact representation of time-series structure that is not reducible to amplitude alone. The window length is treated as a methodological hyperparameter and selected through a target-specific sensitivity analysis that jointly favors competitive out-of-sample RMSE and stable permutation-importance rankings across neighboring windows. Two complementary learners, gradient boosting and a multilayer perceptron, are used as diagnostic probes to quantify permutation-based feature relevance under chronological splitting and training-only preprocessing. Across three targets (F10.7, Sunspot Number, and Dst), shape descriptors consistently rank among the most informative predictors, often matching or exceeding the relevance of standard solar-wind inputs. The most robust signals arise from LZ complexity and a compact subset of entropy/fractal measures, whose windowed trajectories track solar-cycle phases with characteristic lead--lag behaviour. Correlation analyses on both levels and standardised first differences expose redundancy within descriptor families and reduce spurious associations driven by shared nonstationarity, motivating a family-level interpretation of relevance rather than causal attribution. Overall, the results indicate that heliophysical time-series morphology encodes dynamical information complementary to amplitude- and bulk-plasma descriptions, suggesting compact, instrument-light features for augmenting future space-weather modelling pipelines.