A Field-Based Evaluation of the Reliability of Empirical Formulae for Quantifying the Longitudinal Dispersion Coefficient in Small Channels
Bibliographic record
Abstract
The majority of formulae for predicting in-channel mixing by longitudinal dispersion are based on empirical evidence from medium to large rivers, whereas small creeks and streams are under-represented despite their hydrological and ecological importance. In this study, twenty-six formulae for predicting the longitudinal dispersion coefficient (Kx) were evaluated for their applicability to small channels using field measurements and hydraulic modeling. Predicted values for Kx, following guidelines recommended in the original publications for the formulae, were compared to measured dispersion coefficients obtained from sodium-chloride plumes injected into two small channels (a concrete-lined, trapezoidal channel and a small, natural stream) based on fitting the Hayami solution to the one-dimensional advection-dispersion equation (ADE) to each plume. The predicted Kx coefficients from the formulae were also utilized to create model-simulated plumes, which were compared to those measured well downstream of the point of injection. The findings demonstrate that the predictive accuracy of the twenty-six formulae was extremely variable; none were able to predict the dispersion process in the small channels with better than ± 50% accuracy. These results show that “universal” formulae are plagued with a large degree of uncertainty and should be used with caution when applied to small channels, although more robust predictions are possible with some formulae if site-specific data are available for calibration.
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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 | 0.012 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".