A Stochastic Closure for Two-Moment Bulk Microphysics of Warm Clouds: Part I, Derivations
Bibliographic record
Abstract
We propose a mathematical methodology to derive a stochastic parameterization of bulk warm cloud micro-physics properties. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size distribution, all parameters have physical meanings which are recoverable from data, and the resultant parameterization has the flexibility to utilize a variety of collision kernels. Our strategy is a new two-fold approach to modelling the kinetic collection equation. Partitioning the droplet spectrum into cloud and rain aggregates, we represent droplet densities as the sum of a mean and a random fluctuation. Moreover, we use a Taylor approximation for the collision kernel which allows the resulting parameterization to be independent of the collision kernel. To address the two-moment closure for bulk microphysical equations, we represent the higher (third) order terms as points in an Ornstein-Uhlenbeck-like stochastic process. These higher order terms are aggregate number concentration, and aggregate mixing ratio, fluctuations and product fluctuations on regions of a 2D space of pre-collision droplets. This 2D space is naturally partitioned into four domains, each associated with a collision process: cloud and rain self-collection, auto-conversion, and accretion. The stochastic processes in the solution to the kinetic collection equation are defined as the sum of a mean and the product of a standard deviation and a random fluctuation. An order of magnitude argument on the temporal fluctuations of the evolving cloud properties eliminates the terms containing a standard deviation and a random fluctuation from the mean evolution equations. The remaining terms form a coupled set of ODE's without any ad-hoc parameters or any assumed droplet size distributions and flexible enough to accept any collision kernel without further derivations.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".