Journal Paper Reading Notes
Literature Review, MIT EAPS, 2026
Reading notes and reproduction status for atmospheric blocking, Rossby wave breaking (RWB), and related machine-learning methods. All code, simulations, and notes live in the unified repository:
github.com/yanxingjianken/blocking_rwb_literature_review
Status legend: ✅ Reproduced 🔧 In Progress 📖 Literature Review (GIFs generated) 📋 Planned
1. Blocking Theories — 11 Canonical Mechanisms
Each subdirectory contains a Python spectral-model simulation with animated GIFs. See the blocking README for the inheritance diagram of the common barotropic solver.
| # | Experiment | Key Reference | Status |
|---|---|---|---|
| 1 | Energy Dispersion | Yeh (1949) — Rossby wave group velocity & energy trapping | 📖 |
| 2 | Hydraulic Jump | Rex (1950) — 1-D shallow-water hydraulic jump analogy | 📖 |
| 3 | Multi-Equilibria (CdV) | Charney & DeVore (1979) — 3-mode ODE, S-curve bifurcation | 📖 |
| 4 | Modon / Equivalent Barotropic | McWilliams (1980), Haines & Marshall (1987) — Dipole vortex, resonant forcing in Dedalus | 🔧 |
| 5 | Wave Resonance | Tung & Lindzen (1979) — Stationary wave amplitude peaks near $\bar{U}_c = 15.8$ m/s | 📖 |
| 6 | Eddy Straining | Shutts (1983), Wang & Kuang (2019) — Eddy straining dipole convergence | 📖 |
| 7 | Deterministic Chaos | Legras & Ghil (1985) — 25-mode strange attractor with blocking/zonal regimes | 📖 |
| 8 | Wave Accumulation & AWB/CWB | Swanson (2000, 2001) — Anticyclonic vs cyclonic wave breaking diagnosis | 📖 |
| 9 | Selective Absorption | Yamazaki & Itoh (2013) — Same-sign eddies absorbed, opposite expelled | 📖 |
| 10 | NLS Soliton / Envelope | Luo et al. (2014, 2019) — Blocking envelope as localized soliton | 📖 |
| 11 | FAWA / Traffic Jam | Nakamura & Huang (2018) — Finite-amplitude wave activity “traffic jam” | 📖 |
Common library:
blocking/common/— pseudospectral barotropic solver (RK4) + GIF maker.
2. Rossby Wave Breaking (RWB) — Idealized Life-Cycle Experiments
Canonical baroclinic-wave experiments run with three different models (MPAS-Atmosphere, SpeedyWeather.jl, Dedalus).
| Experiment | Engine | Reference | Status |
|---|---|---|---|
| Jablonowski & Williamson Dycore Test | MPAS-A (x1.40962, ~240 km) | JW2006, QJRMS 132, 2943–2975 | ✅ |
| Thorncroft LC1 / LC2 | SpeedyWeather.jl (T42, 15σ) | Thorncroft et al. 1993, QJRMS 119, 17–55 | 🔧 |
| Polvani & Plumb Stratospheric RWB | Dedalus | Polvani & Plumb (1992) | 📋 |
| Vallis Barotropic Decay | SpeedyWeather.jl (barotropic) | Vallis (2004) | 📋 |
| Schemm COSMO Diagnostics | COSMO-LM archive | Schemm et al. (2013) | 📋 |
JW06 — What’s reproduced ✅
16-day hydrostatic baroclinic wave on the x1.40962 Voronoi mesh (64 ranks, no physics). Validated against the published reference: 850 hPa temperature at day 9 (cold/warm fronts), 250 hPa zonal wind (jet streak), surface pressure minimum evolution, Ertel PV on isentropic surfaces. Lat-lon regridding via convert_mpas barycentric interpolation.
Thorncroft LC1 / LC2 — In progress 🔧
LC1 (anticyclonic, equatorward wave breaking) and LC2 (cyclonic, poleward wave breaking) life cycles in SpeedyWeather.jl. LC1 uses J&W basic state with ∇⁶ hyperdiffusion; LC2 adds a barotropic cyclonic perturbation. Diagnostics in development: EKE(t), PV on θ surfaces, EP-flux cross-sections.
3. SFNO — Spectral Fourier Neural Operator
| Item | Details |
|---|---|
| Paper | Spectral Fourier Neural Operator — arXiv: 2306.03838 |
| Status | 🔧 Training infrastructure ready (PyTorch + torch-harmonics) |
| Contents | Checkpoints, literature PDF, training scripts for SFNO weather prediction |
Spherical-harmonic neural operator that leverages the convolution theorem on the sphere to achieve equivariance without explicit spherical-harmonic transforms in every layer.
4. Spherical Attention — Equivariant Transformers on S²
| Item | Details |
|---|---|
| Paper | Attention on the Sphere — Bonev, Rietmann, Paris, Carpentieri, Kurth (NVIDIA, 2024; arXiv: 2505.11157) |
| Status | 🔧 Training ready |
| Key Result | Quadrature-weighted geodesic attention reduces pole errors vs Euclidean attention on lat-lon grids |
| Experiments | (i) Shallow-water 6-h forecast; (ii) ERA5 Z500 6-h real-data forecast, 128×256 Gaussian grid |
| Contents | S² vs R² Transformer implementations, checkpoints, MP4 animations, training data |
5. Hilbert Transform — ERA5 Scale Decomposition & Analytic Signals
| Item | Details |
|---|---|
| Paper | The Analytic Signal and Hilbert Transform — Huang et al. (1998) |
| Status | ✅ Complete (all 15 phases of plan.md) |
| Data | ERA5 Z500, Oct–Nov 2012, 61 days, 1464 hourly snapshots |
| Pipeline | Zonal wavenumber + temporal frequency filtering → 9 bands (3 spatial × 3 temporal) → Hilbert analytic signal → complex PCA |
| Outputs | 3.3 GB NetCDF, 9 PNG snapshots, 5.6 MB MP4 (9-panel animation) |
| Contents | Download scripts, main pipeline, extended animation stitcher, literature PDFs |
Related Repositories
- PV_Ertel_Computation — Ertel PV on sigma levels (ERA5-validated)
- PV_Inversion — Piecewise PV inversion (Wu SOR + SH spectral dual-track)