Comparing Corrosion Control Treatments for Drinking Water Using a Robust Bayesian Generalized Additive Model

Abstract

Pipe loop studies are used to evaluate corrosion control treatment, and updated regulatory guidance will ensure that they remain important for drinking water quality management. But the data they generate are difficult to analyze: nonlinear time trends, nondetects, extreme values, and autocorrelation are common attributes that make popular methods, such as the t- or rank-sum tests, poor descriptive models. Here, we propose a framework for describing pipe loop data that accommodates all of these challenging attributes: a robust Bayesian generalized additive model with continuous-time autoregressive errors. Our approach facilitates corrosion control treatment comparisons without the need for imputing nondetects or special handling of outliers. It is well suited to describing nonlinear trends without overfitting, and it accounts for the reduced information content in autocorrelated time series. We demonstrate it using a 4-year pipe loop study, with multiple pipe configurations and orthophosphate dosing protocols, finding that an initially high dose of orthophosphate (2 mg P L–1) that is subsequently lowered (0.75 mg P L–1) can yield lower lead release than an intermediate dose (1 mg P L–1) in the long term. Water utilities face difficult trade-offs in applying orthophosphate for corrosion control, and better models of pipe loop data can help inform the decision-making process.

Evaluating Sentinel Pipe Racks for Monitoring Lead Release and Optimizing Corrosion Control

“…Although lead solubility is predicted to increase with a decrease in orthophosphate, the effect on particulate lead is unclear: an established lead-phosphate scale, for instance, may be no less durable after a decrease in the orthophosphate dose. Passivation/maintenance dosing has the potential to conserve phosphorus, but it should be evaluated carefully to avoid unwanted increases in lead release at the maintenance dose or excess particulate lead at an unnecessarily high passivation dose. , Here though, the dose–response of lead release to orthophosphate was qualitatively similar to that predicted by solubility: lead release decreased when orthophosphate was increased and increased when orthophosphate was decreased.…”

“…Lead in pipe rack effluent, y t , was modeled using a robust hierarchical Bayesian generalized additive model (GAM) with continuous-time first-order autoregressive errors. ,− The model is specified in eq , where T denotes the Student t-distribution with time-varying mean μ t , standard deviation σ, and degrees-of-freedom parameter ν. The mean is modeled as the sum of the smooth functions of time f j ( t ).…”

“…Lead in pipe rack effluent, y t , was modeled using a robust hierarchical Bayesian generalized additive model (GAM) with continuous-time first-order autoregressive errors. ,− The model is specified in eq , .25ex2ex righttrue likelihood : log false( y t false) ∼ T false( μ normalt , σ , ν false) model for μ t : μ t = α pipe i + ∑ j = 1 n f j false( t false) + ϕ s r t − s f j false( t false) = X j β j + Z j b j r t − s = log false( y t − s false) − α pipe i − ∑ j...…”

“…47 The instantaneous rate of change in mean log lead concentration was estimated using finite differences, as described in a recent paper. 20 Briefly, we generated posterior predictions of the global or location-level multiyear trend along a regular time sequence spanning the range of the data. Then, we repeated this process after adding a small constant�δ�to each value in the sequence.…”

“…We present data from three separate racks, located at three sites within Halifax Regional Municipality, a medium-sized Canadian city. We used a robust hierarchical Bayesian generalized additive model with continuous-time autoregressive errors 20 to estimate the effect on lead release of a dose increase from 1 to 2 mg PO 4 L −1 . Then, we used this estimate as a prior probability for the same effect in nine sentinel homes.…”