Piecewise PV Inversion (PPVI)
Climate Dynamics, MIT EAPS, 2026
Piecewise Potential Vorticity Inversion (PPVI) for diagnosing atmospheric blocking events — replicating Davis et al. (2022, J. Climate, Fig. 8).
Source repository: github.com/yanxingjianken/PV_Inversion
Overview
PPVI decomposes the full PV field into a mean (climatological) component and anomaly pieces, then inverts each piece to recover the associated balanced wind and geopotential height perturbations. This isolates the dynamical contribution of specific PV features (e.g., upper-level PV anomalies) to blocking anticyclones.
The project implements two parallel inversion backends:
| Backend | Method | Grid | Status |
|---|---|---|---|
| Wu (Fortran SOR) | Successive Over-Relaxation + nonlinear balance | Finite σ-box (87×51, NH) | ✅ Working |
| SH (Spectral) | Spherical-harmonic diagonalisation | Global NH sphere | ⚠️ Ongoing |
Pipeline
graph TD
A[ERA5 Download] --> B[Grid & Climatology]
B --> C[Wu Pass A/B: PV + ψ]
C --> D[Wu Pass C: Total Balance]
D --> E[Wu Pass D: 3 Perturbation Pieces]
E --> F[PV Advection]
F --> G[Fig 8 Replica]
B --> H[SH PPVI Mean]
H --> I[SH PPVI Pieces]
I --> J[Cross-Method Comparison]
E --> J
Wu (Fortran) Track — ✅ Working
The reference pipeline uses the original Davis/Emanuel F77 SOR solver:
| Pass | Program | Role |
|---|---|---|
| A/B | pvpialln_94UV | Ertel PV + balanced ψ for climatology & event |
| C | qinvert21 | Refine total balanced ψ (nonlinear balance) |
| D | qinvertp21 | 3 piecewise perturbation ψ inversions |
- Domain: 85.5°N–10.5°S, 169.5°W–40.5°W (NH window, 1.5° resolution)
- Vertical: 10 σ levels (1.0 → 0.2)
- Climatology: 30-day symmetric running mean
- Produces: Davis (2022) Fig. 8 replica + 11 diagnostic plots
SH (Spectral) Track — ⚠️ Ongoing
The experimental spectral-harmonic solver diagonalises the PV inversion operator per spherical-harmonic wavenumber with a 10×10 LU per mode.
Current status (June 2026):
- Wu mean-state and event-state PV computation aligned
- Non-dimensional scaling fixed (erroneous $f_0$ factor removed from $S_{nd}$)
- SH solver converges but produces induced winds ~10× weaker than Wu
- Root cause: β-plane approximation in the SH thermal-wind link
- Upgrade path documented in
sh/sh_ppvi/invert_piece.py
Quick Start
# Edit event date, region, resolution
vim config.py
# Shared data prep (ERA5 download + climatology)
for s in shared_steps/0[1-4]_*/; do
micromamba run -n blocking python "$s"/*.py
done
# Wu Fortran track → fig8_replica.png
for s in wu/steps/0[5-9]_*/ wu/steps/10_*/; do
micromamba run -n blocking python "$s"/*.py
done
Key Reference
Davis, C. A., M. T. Stoelinga, and M. L. Weisman, 2022: Piecewise Potential Vorticity Inversion: Application to winter storms and a new treatment of the lower boundary. J. Climate, 35, 5041–5057.
Resources
- Code & documentation: github.com/yanxingjianken/PV_Inversion
- Handbook (LaTeX/PDF):
handbook/ertel_pv_handbook.pdf - Environment:
micromamba run -n blocking(orfourcastnetv2)