Climate as Music: Why Weather Has a Rhythm ✛

Original: "Detection of Temporal Variability in U.S. Climate Using Harmonic and Wavelet Decomposition"
· Thomas Xiao
arXiv:2511.08627 · 2025-11-09 · CC0 1.0 · 1 min
A scientist broke down 130 years of weather into waves and found that cycles, not straight lines, predict the US climate.

The US climate is not a straight line but an orchestra without a conductor. Each instrument plays its own part, and together they create a pattern of warm and cold, wet and dry years. Scientist Thomas Xiao took 130 years of weather records—temperature, precipitation, and droughts—and broke them down into individual notes, like a musician dissecting a melody.

It turns out that this music has two main motifs. The first is the annual cycle: summer is always warmer than winter. The second is the slow breathing of the ocean, lasting from two to seven years, known as El Niño. These two rhythms explain climate variability better than any straight line.

But the orchestra does not always play the same tune. Sometimes the music changes abruptly, as in the 1930s when the Dust Bowl struck, or in 1976–1977 when the ocean shifted its rhythm. If we can hear these notes, we can predict weather more accurately months in advance and prepare for droughts ahead of time. That means farmers and water managers can plan their work better.

The precipitation spectrum peak at 3 cycles per year means that the strongest precipitation fluctuations in the U.S. occur with a period of about 4 months, not once a year as one might expect. This is because the seasonal cycle was already removed when calculating anomalies, leaving faster modes, such as those related to intraseasonal processes.

The idea of predicting climate through hidden rhythms echoes Isaac Asimov's 'Foundation', where Hari Seldon's psychohistory uncovers cyclical patterns in human history. In both cases, the future is not linear but subject to the superposition of waves of different lengths, and the task is to extract these waves from noise.

A_t = \sum_{k=1}^{N/2} [a_k \cos(2\pi f_k t) + b_k \sin(2\pi f_k t)]
Represents a time series as a sum of oscillations with different frequencies, allowing identification of dominant periods.
W(s, \tau) = \frac{1}{\sqrt{s}} \int A(t) \psi^*\left(\frac{t-\tau}{s}\right) dt
Provides a time-frequency map, showing how the strength of each periodicity changes over time.
RMSE = \sqrt{\frac{1}{N} \sum_{t=1}^{N} (A_t - \hat{A}_t)^2}
Quantifies forecast accuracy: the smaller the RMSE, the better the model reproduces data.
Concepts
natural variability decadal variability seasonal cycle North Atlantic Oscillation ENSO Atlantic multidecadal oscillation climate NOAA CPC seasonal forcing spring predictability barrier wavelet analysis El Niño TAO/TRITON moorings climate network Jin-Timmermann model UAH satellite record La Niña ocean-atmosphere coupling drought mixed mode oscillations