Bibliographic record
Abstract
Abstract In this article our goal is to present an overview of the fundamental principles that are the basis of most models used in hydrology. We develop the fundamental principles of mass, momentum, and energy conservation and express them in mathematical form. We first outline the general approach that can be used to develop a mathematical statement of a conservation law, using a so‐called Eulerian framework, where we consider volumes fixed in time and space through which material may flow. We then derive the general conservation equations for mass, momentum, and energy for the case of flowing fluids. We next provide examples from hydrology that illustrate the application of the general conservation principles. We begin with relatively straightforward applications of the conservation equations and progress to more complex and less direct applications. Our first and simplest example is the advection–dispersion equation, which is a relatively transparent application of the conservation of mass principle, augmented with a so‐called gradient‐flux model, Fick's law, which describes the dispersion and diffusion of solute mass within the bulk flowing fluid. Next we present the Navier–Stokes equations, which are the conservation of momentum equations for a Newtonian fluid. The next suite of examples involves flow in porous media, which is described by more than one conservation principle applied simultaneously. Our last example is from engineering hydraulics, the Saint Venant equations, which are gross but practical simplifications of the general conservation statements.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".