A Unified Flow Resistance Formula for Open‐Channels With Natural and Engineered Submerged Obstacles
Bibliographic record
Abstract
Abstract Stream obstacles, naturally formed like boulders or engineered like weirs, are the major source of flow resistance; however, to quantify their flow resistance, a resistance formula needs to be selected in accordance with the specific obstacle type, that is obstacle type dependency. So far, a unified resistance formula that adequately characterizes the roughness of distinctive obstacle types remains elusive. Here, we conduct flume experiments with various natural and engineered submerged obstacles, including boulders, weirs, log jams, and transverse stones. We combine them with existing data sets containing rigid vegetation, step‐pool, and riffle‐pool to identify a unified metric for a general resistance relation. We test three roughness metrics, the widely used roughness metric D 84 (84th percentile of bed grain size distribution), a bathymetric‐line‐based metric σ z,centerline (the standard deviation of bed centerline elevation), and a 3D‐bathymetry‐based σ z,bed (the standard deviation of elevation of the entire bed) as bed roughness, respectively. σ z,bed is adopted to incorporate the roughness inhomogeneity in the transverse direction which widely exists in both natural and engineered channels, complementing the insufficiency of line‐based metric σ z,centerline . Using 3‐fold cross validation, we show that the resistance formula based on σ z,bed demonstrated a more consistent and superior velocity prediction capacity than those based on D 84 and σ z,centerline in predicting velocity across almost all obstacle types. Interestingly, when applied to channels with submerged rigid vegetation, the resistance formula based on only σ z,bed can compare with those based on multiple vegetation characteristic parameters. This study shows the viability of unifying the flow resistance formula in open‐channels with submerged obstacles, avoiding obstacle‐type dependency.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.001 | 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".