QSignature as a Diagnostic for Atmospheric Oscillations: Asymmetric Amplitude Trends in Seven Years of Qatari Climate Data

We apply the QSignature framework to characterize amplitude trajectories in oscil-
latory climate time series from Qatar spanning January 2018 to December 2024. The
framework uses two model-free estimators: the signed centroid τs and the unsigned cen-
troid τu , from which we compute the diagnostic ratio Rsu = τs /τu and the oscillation
strength ∆su = Rsu − 1. Through systematic simulations over a range of damping ratios,
initial phases, and waveform shapes, we establish that for oscillations with fixed phase,
Rsu < 1 corresponds to decaying amplitude and Rsu > 1 corresponds to growing am-
plitude. However, Rsu is sensitive to the initial phase, and therefore we do not interpret it
in isolation. Instead, we validate all classifications using an independent envelope-based
growth rate Λ computed from peak detection on the detrended absolute signal. The perfect
agreement between Rsu and Λ for all five climate variables provides empirical validation
for this dataset. Maximum and minimum temperatures together with mean wind speed
yield Rsu < 0 and Λ < 0, placing them in the weakly damped regime with decaying
seasonal amplitude. Relative humidity and mean sea level pressure yield Rsu > 1 and
Λ > 0, indicating growing amplitude. Direct comparison of early and recent periods con-
firms a 0.9◦ C reduction in seasonal temperature range driven primarily by winter warming.
These findings are consistent with recent regional literature identifying weakening Shamal
winds and intensifying pressure anomalies as drivers of accelerated Arabian Gulf warm-
ing. The framework requires no model fitting, no detrending, and no phase alignment,
computing directly from raw time series in O(N ) time. All code is available open-source
at https://github.com/1030ahmad1030/Qtheory.