Wind Dynamics Experiment

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Overview

We apply a UKF-based linearized harmonic oscillator (LHO) estimation pipeline to daily wind speed observations from two meteorological stations in the Sürmeli Depression of eastern Türkiye, spanning nine years (2014-2022, 3287 daily records). The analysis framework evolved through a principled sequence of modeling decisions: an initial Hopf bifurcation approach exhibited systematic frequency collapse to the analysis band boundary, motivating the adoption of a linearized harmonic oscillator model whose second-order damped oscillation physics matches the driven dynamics of synoptic weather systems.

Project Structure

wind_experiment/
├── R/
│   ├── constants.R                  ← UKF numerical constants (domain-independent)
│   ├── ukf_engine.R                 ← UKF core: propagate_model, UKF_dT, UKF_blend
│   ├── sl_models.R                  ← SL models: make_sl_single, make_sl_paired_fixed_aw,
│   │                                  hilbert_analytic, omega_from_phase
│   ├── models.R                     ← Coupled oscillator models: LHO, gLk, abk
│   ├── optim.R                      ← iterative_param_optim, optim_params
│   │                                  These 5 files are from SL-UKF_Neural_Criticality_MDD.
│   ├── wind_config.R                ← NEW: wind-specific SL_BOUNDS, timing, bounds
│   ├── wind_preprocessing.R         ← NEW: wind data loading, cleaning, Hilbert
│   └── wind_logging.R               ← NEW: per-fit CSV logging, session log
├── data/
│   └── wind.csv                     ← USER: place wind data here
├── logs/                            ← Generated: master_log.csv, session_log.txt, etc.
├── plots/                           ← Generated: figures
├── wind_experiment.ipynb            ← Main experiment notebook (R kernel)
└── wind_experiment_supplement.ipynb ← Supplement experiment notebook (R kernel)

Only domain-specific configuration changed:

Parameter	BOLD	Wind	Reason
dT	2.0 s (TR)	1.0 day	Data sampling rate
dt	0.2 s	0.1 day	RK4 sub-step (dT/10)
OM_MIN	0.126 rad/TR	0.017 rad/day	Annual cycle
OM_MAX	1.257 rad/TR	2.094 rad/day	3-day synoptic
T_obs	~260 TRs	~3287 days	Record length

Hypotheses

• H1: Single-station natural frequency & LHO single & $\gamma$
• H2: Inter-station coupling & LHO two-stage & $k$
• H3: Seasonal regime transitions & LHO single & $\gamma$ per season
• H4: Yearly stationarity & LHO single & $\gamma$ per year
• H5: Damping sensitivity & LHO (varied $\zeta$) & $\gamma$ and $k$ vs $\zeta$
• H6: Model comparison (LHO vs pendulum) & Both & $\Delta\chi^2$
• H7: Cross-domain SL comparison & SL fixed - $\omega$ & $a$
• H8: Gamma ceiling fix ($\gamma_{\max}$: $5 \to 20$) & LHO both stages & $\gamma$, $k$
• H9: Cross-signal robustness & LHO two-stage & $k$ per pair
• H10: Full zeta sensitivity (new $\gamma_{\max}$) & LHO both stages & $\gamma$, $k$ vs $\zeta$

Dependencies

R packages: pracma, MASS, Matrix (installed automatically by the notebook)

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Citation

If you use this pipeline or build on this work, please cite:

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LHO derived from a Coupled Oscillator Model · Stuart-Landau normal form · Unscented Kalman Filter · SL-UKF_Neural_Criticality_MDD · SL-UKF_Neural_Criticality_MDDvsHC