Why Bayesian inference?

The scientific methodology of mathematical models and their credibility to form the basis of public policy decisions have been frequently challenged. The development of novel methods for rigorously assessing the uncertainty underlying model predictions is one of the priorities of the modelling community [1]. Striving for novel uncertainty analysis tools, I present the Bayesian calibration of process -based models as a methodological advancement that warrants consideration in ecosystem analysis and biogeochemical research [2]. This modelling framework combines the advantageous features of both process -based and statistical approaches; that is, mechanistic understanding that remains within the bounds of data- based parameter estimation. The incorporation of mechanism improves the confidence in predictions made for a variety of conditions, whereas the statistical methods provide an empirical basis for parameter value selection and all ow for realistic estimates of predictive uncertainty [3]. Other advantages of the Bayesian approach include the ability to sequentially update beliefs as new knowledge is available, the rigorous assessment of the expected consequences of different management actions, the optimization of the sampling design of monitoring programs, and the consistency with the scientific process of progressive learning and the policy practice of adaptive management. I illustrate some of the anticipated benefits from the Bayes ian calibration framework, well suited for stakeholders and policy makers when making environmental management decisions, using the Hamilton Harbour and the Bay of Quinte – two eutrophic systems in Ontario, Canada – as case studies [4]. REFERENCES: 1. Arhonditsis, G.B., Brett, M.T., 2004. Evaluation of the current state of mechanistic aquatic biogeochemical modelling. Mar. Ecol. Prog. Ser. 271, 13- 26. 2. Arhonditsis, G.B., Qian, S.S., Stow, C.A., Lamon, E.C., Reckhow, K.H., 2007. Eutrophication risk assessment using Bayesian calibration of process -based models: Application to a mesotrophic lake. Ecol Model. 208, 215-229 . 3. Arhonditsis G.B., Kim, D -K., Kelly, N. , Neumann, A. , Javed , A., 2017. Uncertainty Analysis by Bayesian Inference , in Recknagel , F. , Michener , W. , (Eds) , Ecological Informatics. 3 rd Edition Springer. , Cham, pp. 215-249. 4. Recknagel F., Arhonditsis, G.B. , Kim, D -K ., Nguyen H.H. , 2017. Strategic Forecasting in Ecology by Inferential and Process -based Models . in Recknagel , F., Michener , W. , (Eds), Ecological Informatics. 3 rd Edition Springer. , Cham, pp. 341-372

Mass Flux Calculations Show Strong Allochthonous Support of Freshwater Zooplankton Production Is Unlikely

Many studies have concluded terrestrial carbon inputs contribute 20–70% of the carbon supporting zooplankton and fish production in lakes. Conversely, it is also known that terrestrial carbon inputs are of very low nutritional quality and phytoplankton are strongly preferentially utilized by zooplankton. Because of its low quality, substantial terrestrial support of zooplankton production in lakes is only conceivable when terrigenous organic matter inputs are much larger than algal production. We conducted a quantitative analysis of terrestrial carbon mass influx and algal primary production estimates for oligo/mesotrophic lakes (i.e., TP≤20 µg L−1). In keeping with the principle of mass conservation, only the flux of terrestrial carbon retained within lakes can be utilized by zooplankton. Our field data compilation showed the median (inter-quartile range) terrestrial particulate organic carbon (t-POC), available dissolved organic carbon (t-DOC) inputs, and in-lake bacterial and algal production were 11 (8–17), 34 (11–78), 74 (37–165), and 253 (115–546) mg C m−2 d−1, respectively. Despite the widespread view that terrestrial inputs dominate the carbon flux of many lakes, our analysis indicates algal production is a factor 4–7 greater than the available flux of allochthonous basal resources in low productivity lakes. Lakes with high loading of t-DOC also have high hydraulic flushing rates. Because t-DOC is processed, i.e., mineralized or lost to the sediments, in lakes at ≈0.1% d−1, in systems with the highest t-DOC inputs (i.e., 1000 mg m−2 d−1) a median of 98% of the t-DOC flux is advected and therefore is not available to support zooplankton production. Further, advection is the primary fate of t-DOC in lakes with hydraulic retention times <3 years. When taking into account the availability and quality of terrestrial and autochthonous fluxes, this analysis indicates ≈95–99% of aquatic herbivore production is supported by in-lake primary production

SPARROW Applications Using Bayesian Inference Techniques

The parsimonious model structures of semi -empirical conceptual watershed models (e.g., SPARROW, GREEN) offer considerable advantages over physically -based watershed models to incorporate stream water monitoring data and effectively accommodate rigorous error analysis. Nonetheless, even these model structures demonstr ate intrinsic equifinality problems due to multicollinearity of model parameters. Bayesian inference techniques offer a robust and formal statistical calibration methodology to address model equifinality issues with watershed inverse analysis. In our presentation, we first summarise known case- studies of Bayesian inference implementation for semi -empirical watershed models (USA, Canada, China). We then provide an overview of relevant Bayesian statistical formulations to explicitly consider watershed spatial heterogeneity, serial correlation, and inter - and intra- annual dynamics. Finally, we outline the strengths and weaknesses of inverse watershed models within a Bayesian inference context for recursive calibration and data assimilation, including hotspot identification, loading source apportionment, representation of legacy nutrients, and quantification of all major sources of uncertaint

Is it appropriate to composite fish samples for mercury trend monitoring and consumption advisories?

Monitoring mercury levels in fish can be costly because variation by space, time, and fish type/size needs to be captured. Here, we explored if compositing fish samples to decrease analytical costs would reduce the effectiveness of the monitoring objectives. Six compositing methods were evaluated by applying them to an existing extensive dataset and examining their performance in reproducing the fish consumption advisories and temporal trends. The methods resulted in varying amount (average 34-72%) of reductions in samples, but all (except one) reproduced advisories very well (96-97% of the advisories did not change or were one category more restrictive compared to analysis of individual samples). Similarly, the methods performed reasonably well in recreating temporal trends, especially when longer-term and frequent measurements were considered. The results indicate that compositing samples within 5 cm fish size bins or retaining the largest/smallest individuals and compositing in-between samples in batches of 5 with decreasing fish size would be the best approaches. Based on the literature, the findings from this study are applicable to fillet, muscle plug and whole fish mercury monitoring studies. Overall, compositing fish samples for mercury monitoring could result in a substantial savings (approximately 60% of the analytical cost) and should be considered in fish mercury monitoring, especially in long-term programs or when study cost is a concern

Are fish consumption advisories for the great lakes adequately protective against chemical mixtures?

Background: The North American Great Lakes are home to \u3e 140 types of fish and are famous for recreational and commercial fishing. However, the presence of toxic substances has resulted in the issuance of fish consumption advisories that are typically based on the most restrictive contaminant. Objectives: We investigated whether these advisories, which typically neglect the existence of a mixture of chemicals and their possible additive adverse effects, are adequately protective of the health of humans consuming fish from the Canadian waters of the Great Lakes. Methods: Using recent fish contaminant monitoring data collected by the government of Ontario, Canada, we simulated advisories using most-restrictive-contaminant (one-chem) and multi-contaminant additive effect (multi-chem) approaches. The advisories from the two simulations were compared to determine if there is any deficiency in the currently issued advisories. Results: Approximately half of the advisories currently issued are potentially not adequately protective. Of the four Great Lakes studied, the highest percentage of advisories affected are in Lake Ontario if an additive effect is considered. Many fish that are popular for consumption, such as walleye, salmon, bass and trout, would have noticeably more stringent advisories. Conclusions: Improvements in the advisories may be needed to ensure that the health of humans consuming fish from the Great Lakes is protected. In this region, total polychlorinated biphenyls (PCBs) and mercury are the major contaminants causing restrictions on consuming fish, whereas dioxins/furans, toxaphene, and mirex/photomirex are of minor concern. Regular monitoring of most organochlorine pesticides and metals in fish can be discontinued. © 2017, Public Health Services, US Dept of Health and Human Services. All rights reserved

A commentary on the modelling of the causal linkages among nutrient loading, harmful algal blooms, and hypoxia patterns in Lake Erie

In this study, our primary aim is to evaluate the capacity of past and current modelling efforts to depict the causal relationships between major water quality indicators (e.g., chlorophyll a, harmful algal blooms, dissolved oxygen) and nutrient loading in Lake Erie. We first conduct a review of nearly all the modelling projects documented in the pertinent literature, and then evaluate the performance of six of these models applied over the past thirty years. We examine the strengths and weaknesses of the different modelling strategies, their adequacy in representing the processes underlying plankton dynamics, and their ability to reproduce the spatiotemporal variability in hypoxia or harmful algal blooms. Our analysis shows that these models have mainly offered heuristic tools to examine different ecological hypotheses and dictate future data collection efforts. Our study critically discusses the most appropriate next steps to improve the reproduction of the spatiotemporal patterns of major phytoplankton groups, e.g., cyanobacteria, the functional role of dreissenid mussels, and the relative importance of diagenesis processes on the manifestation of hypoxia in Lake Erie. Finally, we advocate the standpoint that a single &quot;correct&quot; strategy does not exist, and therefore we should strive for a synthesis of multiple modelling approaches which can contribute to an integrative view on the functioning of the system. © 2014 International Association for Great Lakes Research. Published by Elsevier B.V. All rights reserved. Introduction Environmental modelling has been an indispensable tool for addressing lake eutrophication. A variety of data-oriented and processbased models have been used to examine the impact of nutrient loads to ecosystem integrity and to set water quality goals. The dataoriented (or empirical) models are mainly steady-state, mass-balance approaches that predict lake total phosphorus (TP) concentrations as a function of lake morphometric/hydraulic characteristics, such as the areal phosphorus loading rate, mean depth, fractional phosphorus retention, and areal hydraulic loading, which are then associated with the chlorophyll a and/or hypolimnetic dissolved oxygen (DO) concentrations An alternative to these empirical strategies has been the development of process-based models which can be used to understand ecological processes, to predict aquatic ecosystem responses to external nutrient loading changes, to evaluate management alternatives, and to support the policy making proces

Implementation of the Water Framework Directive: Lessons Learned and Future Perspectives for an Ecologically Meaningful Classification Based on Phytoplankton of the Status of Greek Lakes, Mediterranean Region

The enactment of the Water Framework Directive (WFD) initiated scientific efforts to develop reliable methods for comparing prevailing lake conditions against reference (or nonimpaired) states, using the state of a set biological elements. Drawing a distinction between impaired and natural conditions can be a challenging exercise. Another important aspect is to ensure that water quality assessment is comparable among the different Member States. In this context, the present paper offers a constructive critique of the practices followed during the WFD implementation in Greece by pinpointing methodological weaknesses and knowledge gaps that undermine our ability to classify the ecological quality of Greek lakes. One of the pillars of WDF is a valid lake typology that sets ecological standards transcending geographic regions and national boundaries. The national typology of Greek lakes has failed to take into account essential components. WFD compliance assessments based on the descriptions of phytoplankton communities are oversimplified and as such should be revisited. Exclusion of most chroococcal species from the analysis of cyanobacteria biovolume in Greek lakes/reservoirs and most reservoirs in Spain, Portugal, and Cyprus is not consistent with the distribution of those taxa in lakes. Similarly, the total biovolume reference values and the indices used in classification schemes reflect misunderstandings of WFD core principles. This hampers the comparability of ecological status across Europe and leads to quality standards that are too relaxed to provide an efficient target for the protection of Greek/transboundary lakes such as the ancient Lake Megali Prespa

A multi-lake comparative analysis of the General Lake Model (GLM): Stress-testing across a global observatory network

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required

A problem-structuring model for analyzing transportation–environment relationships

This is the post-print version of the final paper published in European Journal of Operational Research. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2009 Elsevier B.V.This study discusses a decision support framework that guides policy makers in their strategic transportation related decisions by using multi-methodology. For this purpose, a methodology for analyzing the effects of transportation policies on environment, society, economy, and energy is proposed. In the proposed methodology, a three-stage problem structuring model is developed. Initially, experts’ opinions are structured by using a cognitive map to determine the relationships between transportation and environmental concepts. Then a structural equation model (SEM) is constructed, based on the cognitive map, to quantify the relations among external transportation and environmental factors. Finally the results of the SEM model are used to evaluate the consequences of possible policies via scenario analysis. In this paper a pilot study that covers only one module of the whole framework, namely transportation–environment interaction module, is conducted to present the applicability and usefulness of the methodology. This pilot study also reveals the impacts of transportation policies on the environment. To achieve a sustainable transportation system, the extent of the relationships between transportation and the environment must be considered. The World Development Indicators developed by the World Bank are used for this purpose