Partial wavelet coherence analysis for understanding the standalone relationship between Indian Precipitation and Teleconnection patterns

Hydro-meteorological variables, like precipitation, streamflow are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. Efficient water resources management requires an understanding of the effects of climate indices on the accurate predictability of precipitation. This study aims at understanding the standalone teleconnection between precipitation across India and the four climate indices, namely, Ni~no 3.4, PDO, SOI, and IOD using partial wavelet analysis. The analysis considers the cross correlation between the climate indices while estimating the relationship with precipitation. Previous studies have overlooked the interdependence between these climate indices while analysing their effect on precipitation. The results of the study reveal that precipitation is only affected by Ni~no 3.4 and IOD and a non-stationary relationship exists between precipitation and these two climate indices. Further, partial wavelet analysis revealed that SOI and PDO do not significantly affect precipitation, but seems the other way because of their interdependence on Ni~no 3.4. It was observed that partial wavelet analysis strongly revealed the standalone relationship of climatic factors with precipitation after eliminating other potential factors. Keywords: Indian Precipitation, wavelet coherency, partial wavelet coherence, teleconnections patterns.

💡 Research Summary

This paper investigates the independent influence of four major climate teleconnection indices—Niño 3.4, the Indian Ocean Dipole (IOD), the Southern Oscillation Index (SOI), and the Pacific Decadal Oscillation (PDO)—on Indian precipitation using partial wavelet coherence (PWC). The authors begin by highlighting a methodological gap: conventional correlation and standard wavelet coherence (WC) analyses ignore the inter‑dependence among climate indices, potentially attributing spurious influence to an index that is merely correlated with another dominant driver.

To address this, the study employs monthly precipitation records from 30 Indian sub‑divisional stations covering 1901‑2002, together with contemporaneous monthly indices for Niño 3.4, IOD, SOI, and PDO. Preliminary homogeneity tests (Kruskal‑Wallis, Friedman) confirm the suitability of aggregating the stations, while simple Pearson correlations reveal largely non‑significant relationships, underscoring the need for a non‑stationary, time‑frequency approach.

The authors first apply continuous wavelet transform (CWT) with a Morlet mother wavelet to each precipitation series, identifying dominant low‑frequency oscillations (≈5–10 yr, 64–128 months) across most locations. Standard WC between precipitation and each index shows that all four indices exhibit some degree of coherence with precipitation at various scales, suggesting a multi‑factorial control. However, a correlation matrix of the indices (Table 2) reveals strong inter‑relationships, especially between Niño 3.4 and both SOI and PDO, raising concerns that the observed WC may be confounded.

Partial wavelet coherence is then introduced as a frequency‑domain analogue of partial correlation. By mathematically removing the contribution of Niño 3.4, the authors recompute PWC for precipitation‑PDO, precipitation‑SOI, and precipitation‑IOD pairs. The results are striking: after accounting for Niño 3.4, PDO’s PWC collapses to near‑zero across virtually all stations, and SOI’s PWC is similarly diminished, persisting only in isolated locations (e.g., Chennai, Madurai) at the ~10‑year scale. In contrast, IOD’s PWC remains robust, especially for periods >10 years, indicating that IOD exerts an independent influence on Indian rainfall that is not mediated by ENSO.

Spatial analysis shows that the combined effect of Niño 3.4 and IOD varies regionally—Southern Peninsular and North‑East India exhibit stronger joint signals, whereas Central and Western regions are more dominated by IOD. The authors further decompose precipitation into band‑limited components corresponding to the significant scales identified in the wavelet spectra, and correlate these components with the analogous band‑limited Niño 3.4 and IOD signals. This confirms that Niño 3.4 primarily drives the 4‑8 year variability, while IOD governs the longer 10‑16 year fluctuations.

In conclusion, the study demonstrates that, once the inter‑dependence among climate indices is properly accounted for, only Niño 3.4 (ENSO) and IOD emerge as genuine, independent drivers of Indian precipitation variability. PDO and SOI appear influential only because of their statistical coupling with Niño 3.4. The methodological contribution—application of partial wavelet coherence to climatological time series—offers a powerful tool for disentangling overlapping teleconnections. The findings have practical implications for seasonal forecasting, water‑resource planning, and the development of more accurate climate prediction models that need to prioritize ENSO and IOD signals while treating PDO and SOI with caution in the Indian context.