Similarity Equations for Wind and Temperature Profiles in the Radix Layer, at the Bottom of the Convective Boundary Layer
Bibliographic record
Abstract
In the middle of the convective boundary layer, also known as the mixed layer, is a relatively thick region where wind speed and potential temperature are nearly uniform with height.Below this uniform layer (UL), wind speed decreases to zero at the ground, and potential temperature increases to the surface skin value.This whole region below the UL is called the radix layer (RxL), and is of order hundreds of meters thick.Within the bottom of the RxL lies the classical surface layer (order of tens of meters thick) that obeys traditional Monin-Obukhov similarity theory.The RxL depth is shown to depend on friction velocity, Deardorff velocity, and boundary layer depth.The wind RxL is usually thicker than the temperature RxL.Using RxL depth, UL wind speed, and UL potential temperature as length, velocity, and temperature scales, respectively, one can form dimensionless heights, velocities, and temperatures.When observations obtained within the RxL are plotted in this dimensionless framework, the data collapse into similarity curves.This data collapse is tightly packed for data collected over singlelocation homogeneous surfaces, and shows more scatter for data collected along 72-km flight tracks over heterogeneous surfaces.Empirical profile equations are proposed to describe this RxL similarity.When these profile equations are combined with the flux equations from convective transport theory, the results are new flux-profile equations for a deep region within the bottom of the convective boundary layer.These RxL profile similarity equations are calibrated using data from four sites with different roughnesses: Minnesota, BLX96-Lamont, BLX96-Meeker, and BLX96-Winfield.The empirical parameters are found to be invariant from site to site, except for the profile shape parameter for wind speed.This parameter is found to depend on standard deviation of terrain elevation, rather than on the aerodynamic roughness length.The resulting parameter values are compared with independent data from a forested fifth site, Koorin, and it is found that displacement height must be subtracted from all the heights in the RxL profile equations.The resulting profile equations could be useful for calculating wind loading on bridges, wind turbine power estimation, air pollutant transport, or other applications where wind speeds or temperatures are needed over the bottom hundreds of meters of the convective boundary layer.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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".