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Spinup Duration for Baroclinic QG Double-Gyre Simulations

TL;DR. For a 2–3 layer baroclinic QG double-gyre at 128²–256² resolution on a ~5000 km basin, the literature spans 2 years (demo-quality) to 40+ years (low-frequency variability studies). There is no single canonical number. somax ships 3 years as the default, with a documented ladder for production (10 yr) and publication-grade (40 yr) work.

Why this matters

The “spinup duration” is the length of integration that is discarded before analysis begins, to let transients from the initial conditions die out. Choosing it wrong means either:

The right choice depends on what you’re trying to measure. somax provides a default that’s defensible for general-purpose use and a ladder for users with stricter scientific requirements.

Physical timescales

For a baroclinic QG double-gyre with basin width $L \sim 5000$ km, mid-latitude $f_0 \approx 10^{-4}~\text{s}^{-1}$, and first baroclinic deformation radius $R_d \sim 30$ km, the relevant adjustment timescales are:

Process Timescale Order of magnitude
Inertial period $2\pi/f_0$ hours hours
Barotropic Rossby wave crossing $L/c_{0}$ days–weeks days
First baroclinic Rossby wave crossing $\tau_R = L/c_1$ months–years ~3 yr for $c_1 \approx 2~\text{m/s}$
Eddy-mean flow equilibration years ~5–10 yr
Decadal intrinsic variability modes decades 5–20 yr

The first-baroclinic Rossby wave crossing time $\tau_R$ is the physical floor for any meaningful spinup. Anything less than $2$–$3 \tau_R$ leaves the basin in a state where the slowest large-scale waves haven’t even propagated across it once.

Phases of spinup

A typical baroclinic QG double-gyre, started from rest with a fixed wind forcing, passes through these phases:

  1. Barotropic adjustment (months to ~1 year): Western boundary current forms, basin fills with Rossby waves. Eastward jet has not yet extended.
  2. First-baroclinic adjustment (1–3 years): Eastward jet extends into the interior, first eddies are shed from the WBC, thermocline tilts. This is when the basic mean flow takes shape.
  3. Mean-flow / eddy equilibration (~5–10 years): Eddy kinetic energy saturates, jet length and recirculation gyres stabilize. Statistical mean state is approximately stationary.
  4. Decadal variability envelope (10–50 years): Required only if you want to average over the intrinsic 5–20 year modes Berloff, Hogg and co-authors identified.

What the literature does

Concrete spinup durations from the canonical references and recent open-source implementations:

Reference Layers / grid / basin Spinup discarded Total run Notes
Holland (1978) 2L, ~20 km, 1000 km informal, ~last few yr multi-year Original wind-driven 2-layer gyre
Berloff & McWilliams (1999) 1.5–2L, eddy-permitting ~10 yr 40–100 yr Low-frequency variability
Hogg, Dewar et al. (2003) 3L, ~10 km (Q-GCM) 10–20 yr 50–100+ yr Q-GCM coupled model
Hogg et al. (2005) 3L, ~10 km 10–20 yr 50+ yr Decadal mode quantization
Berloff, Hogg & Dewar (2007) 3L, ~7.5 km, 3840 km 40 yr 200 yr “Turbulent oscillator”
Karabasov, Berloff & Goloviznin (2009) 3L, 7.5–3.75 km ~10 yr multi-decadal CABARET benchmark
Thiry et al. (2024 JAMES) 3L, 256², 5120 km 40 yr 60 yr 20 yr analysis
MQGeometry-1.0 (Thiry et al. 2024 GMD) 3L, 256², 5120 km 10 yr 50 yr Closest direct analog
louity/qgsw-pytorch 3L, 256², 5120 km 2 yr 10 yr Other direct analog

The two analog repos that match somax’s target configuration most closely (MQGeometry and qgsw-pytorch, both 3-layer, 256², 5120 km basin) bracket the practical range: 2 years on the short end, 10 years on the long end. The Berloff/Hogg variability papers go to 40 years because they’re after intrinsic decadal modes that no shorter run can resolve.

Convergence diagnostics

The QG community typically monitors convergence via:

  1. Basin-integrated kinetic energy (KE) and eddy kinetic energy (EKE) per layer as a time series. Upper-layer EKE is the most sensitive.
  2. Running-mean convergence: the running mean of EKE over a sliding window (typically 1–2 years) should drift by less than a few percent over the previous window. Berloff & McWilliams (1999) and Hogg et al. (2005) use variants of this.
  3. Energy spectrum stationarity: the $k^{-3}$ enstrophy range in the upper layer should be established and stable.
  4. Jet length and WBC separation latitude stabilized within a standard deviation.
  5. EOFs of $\psi_1$ converged (only relevant for the publication-grade tier — needs the long 40+ yr runs).

There is no universal quantitative threshold. “5% running-mean drift per year” is a common informal criterion in QG papers but is rarely stated explicitly.

somax’s three-tier ladder

somax ships configs at three tiers:

Tier spinup_duration_years Use case Wallclock at 128² Justification
Default (CI / demo) 3 Smoke test, “show me a turbulent jet”, reference pipeline minutes Just clears the baroclinic Rossby adjustment time $\tau_R \approx 3$ yr; produces a post-WBC-formation state with the first generation of eddies.
Production 10 “Looks scientifically reasonable”; matches MQGeometry’s n_steps_save = 10 yr; used by qgsw-pytorch’s higher-end recommendation. tens of minutes Approaches statistical equilibrium of mean flow + EKE.
Publication 40 Required for decadal variability statistics (Berloff/Hogg conventions, Thiry et al. 2024). hours Captures intrinsic 5–20 yr modes.

The default of 3 years is chosen because:

For any work beyond demonstration, users should override to 10 or 40 years. The override mechanism is documented in the simulation pipeline guide.

Honest uncertainty statement

There is no single canonical number. The 2–40 year spread in the literature reflects two genuinely different scientific goals:

For a general-purpose open-source reference config, 3 years is the shortest defensible minimum, 10 years is the community mode for routine work, and 40 years is publication-grade for variability studies.

If you are using somax for research that depends on the absolute level of spinup, you should run a convergence study at your specific resolution and parameter set, not rely on the default.

References