Differential Cooling of a Freshwater Body below the Temperature of Maximum Density
Bibliographic record
Abstract
We propose a simplified model for the time rate of change of average basin temperature for a freshwater lake which has two connected basins: a shallow littoral zone of depth D1, and a deeper main basin of depth D2. This system is cooled below the temperature of maximum density (Tmd) with a constant and uniform outgoing surface heat flux, Ho. The differential cooling that is established via this set-up gives rise to an exchange flow between the two basins which we approximate as a time dependent heat flux controlled by the strength of the time dependent density difference between the two basins. Our model is a coupled system of two ordinary differential equations which allows for a process based investigation into the importance of exchange on the timing of ice-onset for a lake with a shallow littoral zone. While basin geometry plays a role in the overall timing of ice-onset for the system, it is the relative strength of Ho to the exchange flow related heat flux due to the density anomaly of fresh water, ρ*, which dictates the behaviour of the cooling system. We show that at sufficiently large values of the heat flux ratio, Φ, the difference in timing of ice onset between the littoral zone and main basin becomes insensitive to the initial conditions in the lake. We use data from Base Mine Lake, Canada, to both verify our model assumptions and evaluate the predictions made by our simple model.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 teacher head, 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".