PPubMed30 May 2018Cited 4×

Wavelet regression: An approach for undertaking multi-time scale analyses of hydro-climate relationships

Jianhua Xu

Abstract

Title: Graphical abstract

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Wavelet regression combines wavelet analysis and regression to reveal multi‑time‑scale hydro‑climate relationships, performing best at longer time scales.

What’s new

i.Developed an integrated wavelet regression (WR) approach for multi‑time‑scale hydro‑climate analysis.
ii.Applied the WR method to the Yarkand River basin, demonstrating scale‑dependent runoff‑temperature‑precipitation relationships.
iii.Identified Sym8 as a robust wavelet function and used R² and AIC/AICc to evaluate model performance.
iv.Showed that model fit improves with longer time scales, achieving R² up to 0.9999.

How they did it

The study decomposed annual runoff, temperature, and precipitation series using the Sym8 wavelet at six scales (s0–s5). For each scale, linear regression equations relating runoff to temperature and precipitation were fitted and evaluated with the coefficient of determination and Akaike information criterion.

What they found

R² values increased from 0.3666 at s0 (1‑year) to 0.9999 at s5 (32‑year).
AIC values decreased from 400.528 at s0 to -209.172 at s5, indicating better fit at larger scales.
Significance levels were α=0.01 for s0 and α=0.001 for all larger scales (s1–s5).

Caveats

✕Linear regression may be insufficient; nonlinear models are required if the linear fit is poor.
✕Small sample sizes (n/k ≤ 40) necessitate using AICc instead of AIC.
✕Performance varies with time scale, with poorer fits at shorter scales.

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