Representing Richardson Number Hysteresis in the NWP Boundary Layer
Bibliographic record
Abstract
Abstract Turbulence in the planetary boundary layer (PBL) transports heat, momentum, and moisture in eddies that are not resolvable by current NWP systems. Numerical models typically parameterize this process using vertical diffusion operators whose coefficients depend on the intensity of the expected turbulence. The PBL scheme employed in this study uses a one-and-a-half-order closure based on a predictive equation for the turbulent kinetic energy (TKE). For a stably stratified fluid, the growth and decay of TKE is largely controlled by the dynamic stability of the flow as represented by the Richardson number. Although the existence of a critical Richardson number that uniquely separates turbulent and laminar regimes is predicted by linear theory and perturbation analysis, observational evidence and total energy arguments suggest that its value is highly uncertain. This can be explained in part by the apparent presence of turbulence regime-dependent critical values, a property known as Richardson number hysteresis. In this study, a parameterization of Richardson number hysteresis is proposed. The impact of including this effect is evaluated in systems of increasing complexity: a single-column model, a forecast case study, and a full assimilation cycle. It is shown that accounting for a hysteretic loop in the TKE equation improves guidance for a canonical freezing rain event by reducing the diffusive elimination of the warm nose aloft, thus improving the model’s representation of PBL profiles. Systematic enhancements in predictive skill further suggest that representing Richardson number hysteresis in PBL schemes using higher-order closures has the potential to yield important and physically relevant improvements in guidance quality.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".