Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Detection of Temporal Variability in U.S. Climate Using Harmonic and Wavelet Decomposition

Thomas Xiao

TL;DR

The paper addresses how temporal variability in U.S. climate—comprising both monotonic trends and nonseasonal oscillations—can be better understood and forecasted by incorporating frequency-domain information. It applies Fourier and wavelet analyses to over a century of NOAA nClimDiv anomalies, then compares a trend-only regression to a harmonic regression that includes dominant periodic components, evaluating performance with RMSE. The study finds dominant periodicities near 1 year and 2–7 years (ENSO-related) and shows that harmonic terms substantially improve predictive skill across many variables and regions, while wavelet analysis reveals time-varying interannual strength and discrete regime shifts detected by change-point analysis. The results support integrating frequency-aware components into seasonal outlooks, drought monitoring, and resource planning, offering a physically grounded interpretation of how variability, not just monotonic change, shapes the U.S. climate system.

Abstract

This study investigates temporal variability in U.S. climate using harmonic decomposition techniques, specifically Fourier and wavelet transforms. Monthly temperature, precipitation, and drought index data from the National Oceanic and Atmospheric Administration (NOAA) U.S. Climate Divisional Dataset (nClimDiv, 1895--2024) were analyzed to detect periodic structures and their evolution over time. By comparing harmonic-based models with linear regression trends, this research evaluates the explanatory power of cyclic components in reproducing and predicting observed variability. Results show that U.S. climate records exhibit dominant periodicities near one year (seasonal) and 2--7 years (associated with the El Nino--Southern Oscillation, ENSO), and that incorporating harmonic terms significantly improves model performance across most states and variables. The findings indicate that U.S. climate fluctuations are characterized by quasi-stationary oscillations rather than purely monotonic trends. Overall, the main implication is that frequency-aware models provide measurably better predictive skill than trend-only approaches and should be incorporated into seasonal outlooks, drought monitoring, and resource planning.

Detection of Temporal Variability in U.S. Climate Using Harmonic and Wavelet Decomposition

TL;DR

The paper addresses how temporal variability in U.S. climate—comprising both monotonic trends and nonseasonal oscillations—can be better understood and forecasted by incorporating frequency-domain information. It applies Fourier and wavelet analyses to over a century of NOAA nClimDiv anomalies, then compares a trend-only regression to a harmonic regression that includes dominant periodic components, evaluating performance with RMSE. The study finds dominant periodicities near 1 year and 2–7 years (ENSO-related) and shows that harmonic terms substantially improve predictive skill across many variables and regions, while wavelet analysis reveals time-varying interannual strength and discrete regime shifts detected by change-point analysis. The results support integrating frequency-aware components into seasonal outlooks, drought monitoring, and resource planning, offering a physically grounded interpretation of how variability, not just monotonic change, shapes the U.S. climate system.

Abstract

This study investigates temporal variability in U.S. climate using harmonic decomposition techniques, specifically Fourier and wavelet transforms. Monthly temperature, precipitation, and drought index data from the National Oceanic and Atmospheric Administration (NOAA) U.S. Climate Divisional Dataset (nClimDiv, 1895--2024) were analyzed to detect periodic structures and their evolution over time. By comparing harmonic-based models with linear regression trends, this research evaluates the explanatory power of cyclic components in reproducing and predicting observed variability. Results show that U.S. climate records exhibit dominant periodicities near one year (seasonal) and 2--7 years (associated with the El Nino--Southern Oscillation, ENSO), and that incorporating harmonic terms significantly improves model performance across most states and variables. The findings indicate that U.S. climate fluctuations are characterized by quasi-stationary oscillations rather than purely monotonic trends. Overall, the main implication is that frequency-aware models provide measurably better predictive skill than trend-only approaches and should be incorporated into seasonal outlooks, drought monitoring, and resource planning.

Paper Structure

This paper contains 11 sections, 7 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Data and Preprocessing
  3. Dataset
  4. Anomaly Computation
  5. Methods
  6. Fourier Transform
  7. Wavelet Transform
  8. Trend and Harmonic Modeling
  9. Change-Point Detection
  10. Results and Discussion
  11. Conclusions

Figures (10)

  • Figure 1: Time series of U.S. national precipitation anomalies, 1895–2024.
  • Figure 2: Fourier amplitude spectrum of precipitation anomalies.
  • Figure 3: Continuous wavelet power spectrum of precipitation anomalies.
  • Figure 4: Linear regression trend in U.S. precipitation anomalies.
  • Figure 5: Detected change points in U.S. precipitation anomalies.
  • ...and 5 more figures