Persistence without Multifractality in Tropical Atlantic SST Indices: Scaling-Range Artefacts and a Reappraisal of the ENSO Association

Abstract

We investigate the scaling properties of three weekly tropical Atlantic sea-surface-temperature indices (SAT, TSA and the interhemispheric gradient TASI) over 1981--2025 using multifractal detrended fluctuation analysis and its sign-preserving cross-correlation extension. Exponents are estimated over $s\in [18,100]$ weeks, bounded by $s_{\min }\gtrsim 6(m+1)$ for second-order detrending and a crossover near 100 weeks. On these scales all three indices are strongly persistent and locally non-stationary ($h(2)=1.32$--$1.35$). Comparison with shuffled and phase-randomised surrogates shows that none of the indices are multifractal within record resolution. SAT ($\Delta h=0.077$) and TASI ($\Delta h=0.054$) are fully consistent with both null models. Although TSA yields a larger width ($\Delta h=0.217$), its increasing $h(q)$ implies the unphysical condition $f(\alpha )>1$, indicating a crossover rather than a multiplicative cascade. At the available record length ($N\approx 2300$), apparent multifractal widths are not identifiable because confidence intervals overlap and rankings remain sensitive to analysis choices. The increments are only mildly leptokurtic, excluding heavy tails as the source of the apparent widths. Pairwise couplings reveal strong positive cross-correlations between the regional indices and anticorrelation of the gradient with both, all described by a single cross-scaling exponent, consistent with monofractal behaviour. A lagged analysis further shows that the previously reported TASI--ENSO association disappears after surrogate testing accounting for multiple lags. These results substantially revise downward previous estimates of multifractal strength in tropical Atlantic SST and show that reported widths should not be interpreted without verifying both the sign of $h^{\prime }(q)$ and the stability of the scaling range.