Decadal- and Annual-Scale Interactions Between the North Atlantic Oscillation and Precipitation over Northern Algeria: Identifying Suitable Wavelet Families for Nonlinear Analysis

The North Atlantic Oscillation (NAO) represents the dominant atmospheric mode governing climate variability across the Northern Hemisphere, particularly influencing precipitation regimes in regions such as northern Algeria. This study investigates the nonlinear linkage between monthly NAO indices and rainfall over northern Algeria for the period 1970–2009 using a cross-multiresolution analysis framework based on seven wavelet families—Daubechies, Biorthogonal, Reverse Biorthogonal, Discrete Meyer, Symlets, Coiflets, and Fejer–Korovkin—comprising a total of 106 individual mother wavelets. More than 700 cross-correlations were computed per NAO–rainfall pair to identify wavelet families that yield stable and physically coherent teleconnection structures across seven decomposition scales (D1–A7). The maximum decomposition level (27 = 128 months, ≈10.6 years) captures intra-annual to decadal variability without extending into multidecadal regimes, ensuring temporal representativeness relative to the 40-year record length. The results reveal that short-term scales (D1–D3) are dominated by noise, masking weak correlations (≤±0.20), while stronger and more coherent relationships emerge at longer scales, reaching ±0.4 at the annual and ±0.75 at the decadal bands. These findings confirm the pronounced influence of low-frequency NAO variability on regional precipitation. Unlike previous studies limited to a few Daubechies wavelets, this work systematically compares 106 wavelet forms and evaluates robustness through reproducibility across scales, consistency among wavelet families, and physical coherence with known NAO periodicities (2–4 and 8–12 years). By emphasizing stability and physical plausibility over statistical significance alone, this approach minimizes the risk of spurious correlations due to multiple testing and highlights genuine scale-dependent teleconnection patterns. The application of discrete wavelet transforms thus enhances signal clarity, isolates meaningful oscillations, and provides a robust diagnostic framework for understanding NAO–rainfall dynamics in northern Algeria.