Reconciling Arctic sea ice roughness across four observing platforms: a resolution transfer function and the stability of spectral shape over six decades

Abstract. Sea ice roughness is measured by platforms whose spatial resolutions differ by two orders of magnitude, and the resulting estimates disagree by a factor of four, which has prevented the assembly of a consistent long-term record. Here we analyse ice topography from four platforms within a single broken power law spectral framework: submarine upward-looking sonar (5470 profiles, 43 cruises, 1960–2005), MOSAiC airborne laser scanning (55256 transects), under-ice remotely operated vehicle (ROV) multibeam (52264 transects from 36 dives), and ICESat-2 altimetry (25740 segments). The fourfold spread in the slope-to-amplitude ratio z₂/z₁ collapses onto a single resolution degradation curve, z₂/z₁ = 0.218 Δx^-0.46 (R² = 0.92), whose exponent follows analytically from the observed spectral shape rather than being fitted freely; the curve provides a transfer function for inter-calibrating roughness estimates between platforms with effective footprints of 0.5–20 m. The resolution-independent spectral parameters (β₁ ≈ -0.5, β₂ ≈ -2.2, λ_break ≈ 99 m) are consistent across all four platforms and both ice surfaces, and show no significant trend over the 45-year submarine record despite a halving of mean ice thickness, although that record can only exclude changes larger than about 160 % of the median exponent at 80 % power. Eighty-five paired surface–bottom observations spanning a full MOSAiC year show that the isostatic approximation holds at the derivative level (z₂/z₁ surface-to-bottom ratio 0.99 ± 0.14, against 0.28 for the amplitude z₁), so under-ice morphology can be inferred from satellite surface measurements. That fidelity is seasonal: the ratio is 0.94 ± 0.07 from October to May but reverses to 1.14 ± 0.10 from June to September, when surface melt and basal melt together leave the surface sharper than the underside. Roughness amplitude and spectral shape therefore respond to forcing on different terms: z₁ varies sevenfold over the seasonal cycle and has declined with the ice cover, while the shape parameters remain stable to within the tested bounds.