Rethinking fractal scaling of sea ice deformation: the dominant role of signed-gradient cancellation

Abstract. We use synthetic sea ice velocity fields to assess the robustness and physical interpretation of first-order scaling diagnostics, commonly associated with spatial localization in the sea ice modeling community. The synthetic fields are constructed to reproduce a wide range of RADARSAT Geophysical Processor System (RGPS)-derived deformation statistics while providing full control over signal-to-noise ratio, divergence-to-shear ratio, lead density, orientation and spatial localization. Results show that spatial scaling arises from the cancellation of signed velocity gradients in the coarse-graining procedure rather than from localization. For instance, dirac-delta deformation field mimicking idealized fracture lines does not show scaling in the absence of signed-gradient cancellation, and smoothly varying (non-localized) deformation fields yield scaling exponents comparable to observations when they contain both positive and negative velocity gradients. We further demonstrate that the standard fractal diagnostic is not invariant under rotation: a pure shear (non-divergent) deformation field exhibits different scale dependence when expressed in a rotated frame. These conclusions derived from synthetic deformation fields when applied to real sea ice deformation from RGPS and sea ice models from the Sea Ice Rheology Experiment (SIREx) show that observed scaling is similarly dominated by cancellation between positive and negative strain rates rather than geometric localization, and therefore are largely determined by PDFs of deformations. These findings reveal key limitations in current scale-invariance-derived diagnostics and call for physically interpretable and robust metrics.