Use of Bayesian Statistics to Study Chlorine Decay within a Water Distribution System
Bibliographic record
Abstract
Decay of chlorine residuals within a water distribution system is a result of a number of interacting processes operating at multiple spatial and temporal scales. These processes are not easily combined into a single and simple predictive model. In the past, first-order decay models have been widely adopted to describe chlorine decay. However, as these models only entail two variables (initial chlorine level and time), these models are not representative of many of the important phenomena influencing chlorine residual decay. Numerous other factors have been identified, including pipe wall material, TOC, temperature and pH. As an alternative, multi-component chlorine decay models represent the aggregation of underlying processes contributing to overall chlorine consumption more appropriately. Clark first proposed a two-component second-order chlorine bulk decay model based on the concept of competing reacting substances. The research in this paper extends the two-component second-order model to incorporate recent findings of the involvement of NOM in the chlorine decay process. This model is further applied in the estimation of wall decay coefficients as used in EPANET. A novel procedure, a two-step parameter assignment method which employs a Bayesian statistical method and Monte Carlo Markov Chain (MCMC), is described to evaluate the parameters of both bulk decay and the wall decay components. A study conducted in Goderich, Ontario, Canada is used to demonstrate the application of the two-component second-order chlorine model. The effects of pipe diameter, pipe wall roughness, flow velocity. TOC, initial chlorine concentration on chlorine decay are investigated. This paper was presented at the 8th Annual Water Distribution Systems Analysis Symposium which was held with the generous support of Awwa Research Foundation (AwwaRF).
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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 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| 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".