Abstract
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 modeling community. Striving for novel uncertainty analysis tools, we present the Bayesian calibration of process-based models as a methodological advancement that warrants consideration in ecosystem analysis and biogeochemical research. This modeling 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 mechanisms improves the confidence in predictions made for a variety of conditions, whereas the statistical methods provide an empirical basis for parameter value selection and allow for realistic estimates of predictive uncertainty. 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. We illustrate some of the anticipated benefits from the Bayesian 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Great Lakes Areas of Concern are designated geographic areas within the Great Lakes Basin that show severe environmental degradation.
- 2.
An impairment of beneficial uses means a change in the chemical, physical or biological integrity of the Great Lakes system sufficient to cause any of the following: Restrictions on Fish and Wildlife Consumption; Tainting of Fish and Wildlife Flavor; Degraded Fish and Wildlife Populations; Fish Tumors or Other Deformities; Bird or Animal Deformities or Reproductive Problems; Degradation of Benthos; Restrictions on Dredging Activities; Eutrophication or Undesirable Algae; Restrictions on Drinking Water Consumption or Taste and Odor Problems; Beach Closings; Degradation of Aesthetics; Added Costs to Agriculture or Industry; Degradation of Phytoplankton and Zooplankton Populations; Loss of Fish and Wildlife Habitat.
References
Alexander RB, Smith RA, Schwarz GE (2004) Estimates of diffuse phosphorus sources in surface waters of the United States using a spatially referenced watershed model. Water Sci Technol 49:1–10
Arhonditsis GB, Adams-Van Harn BA, Nielsen L et al (2006) Evaluation of the current state of mechanistic aquatic biogeochemical modeling: citation analysis and future perspectives. Environ Sci Technol l40:6547–6554
Arhonditsis GB, Qian SS, Stow CA et al (2007) Eutrophication risk assessment using Bayesian calibration of process-based models: application to a mesotrophic lake. Ecol Model 208:215–229
Arhonditsis GB, Papantou D, Zhang W et al (2008a) Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management. J Marine Syst 73:8–30
Arhonditsis GB, Perhar G, Zhang W et al (2008b) Addressing equifinality and uncertainty in eutrophication models. Water Resour Res 44:W01420
Arhonditsis GB, Kim D-K, Shimoda Y et al (2016) Integration of best management practices in the Bay of Quinte watershed with the phosphorus dynamics in the receiving water body: What do the models predict? Aquat Ecosyst Health Manage 19:1–18
Basu NB, Rao PSC, Thompson SE et al (2011) Spatiotemporal averaging of in-stream solute removal dynamics. Water Resour Res 47:W00J06
Bayarri MJ, Berger JO, Cafeo J et al (2007) Computer model validation with functional output. Ann Stat 35:1874–1906
Beck ME (1987) Tectonic rotations on the leading edge of South America: the Bolivian orocline revisited. Geology 15:806–808
Beven K (1993) Prophecy, reality and uncertainty in distributed hydrological modelling. Adv Water Resour 16:41–51
Beven K (2006) A manifesto for the equifinality thesis. J Hydrol 320:18–36
Blukacz-Richards EA, Koops MA (2012) An integrated approach to identifying ecosystem recovery targets: application to the Bay of Quinte. Aquat Ecosyst Health Manage 15:464–472
Charlton MN (2001) The Hamilton Harbour remedial action plan: eutrophication. Verh Internat Verein Limnol 27:4069–4072
Claessens L, Tague CL, Band LE et al (2009) Hydro-ecological linkages in urbanizing watersheds: an empirical assessment of in-stream nitrate loss and evidence of saturation kinetics. J Geophys Res Biogeosci 114:G04016
Dawes RM (1988) Rational choice in an uncertain world. Harcourt Brace Jovanovich, San Diego
Dermott R, Bonnell R (2011) Benthic fauna in the Bay of Quinte. Bay of Quinte remedial action plan: Monitoring Report #20, Kingston, ON, pp 51–71
deYoung B, Barange M, Beaugrand G et al (2008) Regime shifts in marine ecosystems: detection, prediction and management. Trends Ecol Evol 23:402–409
Dietzel A, Reichert P (2012) Calibration of computationally demanding and structurally uncertain models with an application to a lake water quality model. Environ Modell Softw 38:129–146
Donner SD, Kucharik CJ, Oppenheimer M (2004) The influence of climate on in-stream removal of nitrogen. Geophys Res Lett 31:L20509
Doyle MW, Stanley EH, Harbor JM (2003) Hydrogeomorphic controls on phosphorus retention in streams. Water Resour Res 39:1147
Edwards AM, Yool A (2000) The role of higher predation in plankton population models. J Plankton Res 22:1085–1112
Gudimov A, Stremilov S, Ramin M, Arhonditsis GB (2010) Eutrophication risk assessment in Hamilton Harbour: system analysis and evaluation of nutrient loading scenarios. J Great Lakes Res 36:520–539
Gudimov A, Ramin M, Labencki T et al (2011) Predicting the response of Hamilton Harbour to the nutrient loading reductions: a modeling analysis of the “ecological unknowns”. J Great Lakes Res 37:494–506
HH RAP (2003) Hamilton Harbour Remedial Action Plan, Report Stage 2 Update. Hamilton Harbour Technical Team. Burlington, ON
Hall JD, O’Connor K, Ranieri J (2006) Progress toward delisting a Great Lakes Area of Concern: the role of integrated research and monitoring in the Hamilton Harbour Remedial Action Plan. Environ Monit Assess 113:227–243
Hall JD, O’Connor KM (2016) Hamilton Harbour remedial action plan process: connecting science to management decisions. Aquat Ecosyst Health Manage 19:107–113
Harmel D, Qian S, Reckhow K, Casebolt P (2008) The MANAGE database: nutrient load and site characteristic updates and runoff concentration data. J Environ Qual 37:2403–2406
Hiriart-Baer VP, Milne J, Charlton MN (2009) Water quality trends in Hamilton Harbour: two decades of change in nutrients and chlorophyll a. J Great Lakes Res 35:293–301
Hiriart-Baer VP, Boyd D, Long T et al (2016) Hamilton Harbour over the last 25 years: insights from a long-term comprehensive water quality monitoring program. Aquat Ecosyst Health Manage 19:124–133
Kim D-K, Zhang W, Rao Y et al (2013) Improving the representation of internal nutrient recycling with phosphorus mass balance models: a case study in the Bay of Quinte, Ontario, Canada. Ecol Model 256:53–68
Kim D-K, Zhang W, Watson S, Arhonditsis GB (2014) A commentary on the modelling of the causal linkages among nutrient loading, harmful algal blooms, and hypoxia patterns in Lake Erie. J Great Lakes Res 40:117–129
Kim D-K, Kaluskar S, Mugalingam S, Arhonditsis GB (2016) Evaluating the relationships between watershed physiography, land use patterns, and phosphorus loading in the Bay of Quinte, Ontario, Canada. J Great Lakes Res 42:972–984
Kim D-K, Kaluskar S, Mugalingam S et al (2017) A Bayesian approach for estimating phosphorus export and delivery rates with the SPAtially Referenced Regression On Watershed attributes (SPARROW) model. Ecol Inform 37:77–91
Kinstler P, Morley A (2011) Point source phosphorus loadings 1965 to 2009. Bay of Quinte remedial action plan: monitoring report #20. Kingston, ON, pp 15–17
Leisti KE, Doka SE, Minns CK (2012) Submerged aquatic vegetation in the Bay of Quinte: Response to decreased phosphorous loading and Zebra Mussel invasion. Aquat Ecosyst Health Manage 15:442–452
Long T, Wellen C, Arhonditsis G, Boyd D (2014) Evaluation of stormwater and snowmelt inputs, land use and seasonality on nutrient dynamics in the watersheds of Hamilton Harbour, Ontario, Canada. J Great Lakes Res 40:964–979
Long T, Wellen C, Arhonditsis G et al (2015) Estimation of tributary total phosphorus loads to Hamilton Harbour, Ontario, Canada, using a series of regression equations. J Great Lakes Res 41:780–793
McDowell RW, Srinivasan MS (2009) Identifying critical source areas for water quality: 2. Validating the approach for phosphorus and sediment losses in grazed headwater catchments. J Hydrol 379:68–80
McMahon G, Alexander RB, Qian S (2003) Support of total maximum daily load programs using spatially referenced regression models. J Water Res 129:315–329
Moore RB, Johnson CM, Robinson KW, Deacon JR (2004) Estimation of total nitrogen and phosphorus in New England streams using spatially referenced regression models. US Department of the Interior, US Geological Survey, New Hampshire, p 42
Morgan MG, Henrion M, Small M (1992) Uncertainty: a guide to dealing with uncertainty in quantitative risk and policy analysis. Cambridge University Press, New York
Nicholls KH, Heintsch L, Carney E (2002) Univariate step-trend and multivariate assessments of the apparent effects of P loading reductions and zebra mussels on the phytoplankton of the Bay of Quinte, Lake Ontario. J Great Lakes Res 28:15–31
Nicholls KH, Carney EC (2011) The phytoplankton of the Bay of Quinte, 1972–2008: point- source phosphorus loading control, dreissenid mussel establishment, and a proposed community reference. Aquat Ecosyst Health Manage 14:33–43
Pappenberger F, Beven KJ (2006) Ignorance is bliss: or seven reasons not to use uncertainty analysis. Water Resour Res 42:W05302
Ramin M, Stremilov S, Labencki T et al (2011) Integration of numerical modeling and Bayesian analysis for setting water quality criteria in Hamilton Harbour, Ontario, Canada. Environ Modell Softw 26:337–353
Ramin M, Labencki T, Boyd D et al (2012) A Bayesian systhesis of predictions from different models for setting water quality criteria. Ecol Model 242:127–145
Reichert P, Omlin M (1997) On the usefulness of overparameterized ecological models. Ecol Model 95:289–299
Reichert P, Schuwirth N (2012) Linking statistical description of bias to multi-objective model calibration. Water Resour Res 48:W09543
Rode M, Arhonditsis G, Balin D (2010) New challenges in integrated water quality modelling. Hydrol Process 24:3447–3461
Schwarz GE, Hoos AB, Alexander RB, Smith RA (2006) The SPARROW surface water-quality model: theory, application and user documentation. U.S. Geological Survey Techniques and Methods Report, Book 6, Chapter B3; USGShttps://pubs.usgs.gov/tm/2006/tm6b3/PDF/tm6b3_part1a.pdf
Shimoda Y, Watson S, Palmer ME (2016) Delineation of the role of nutrient variability and dreissenids (Mollusca, Bivalvia) on phytoplankton dynamics in the Bay of Quinte, Ontario, Canada. Harmful Algae 55:121–136
Soldat DJ, Petrovic AM, Ketterings QM (2009) Effect of soil phosphorus levels on phosphorus runoff concentrations from turfgrass. Water Air Soil Pollut 199:33–44
Stow CA, Reckhow KH, Qian SS (2007) Approaches to evaluate water quality model parameter uncertainty for adaptive TMDL implementation. JAWRA 43:1499–1507
Watson SB, Borisko J, Lalor J (2011) Bay of Quinte harmful algal bloom programme phase I – 2009. Bay of Quinte remedial action plan: monitoring report #20. Kingston, ON, pp 27–50
Wellen C, Arhonditsis GB, Labencki T, Boyd D (2012) A Bayesian methodological framework or accommodating interannual variability of nutrient loading with the SPARROW model. Water Resour Res 48:W10505
Wellen C, Arhonditsis GB, Labencki T, Boyd D (2014a) Application of the SPARROW model in watersheds with limited information: a Bayesian assessment of the model uncertainty and the value of additional monitoring. Hydrol Process 28:1260–1283
Wellen C, Arhonditsis GB, Long T, Boyd D (2014b) Accommodating environmental thresholds and extreme events in hydrological models: a Bayesian approach. J Great Lakes Res 40:102–116
Wellen C, Arhonditsis GB, Long T, Boyd D (2014c) Quantifying the uncertainty of nonpoint source attribution in distributed water quality models: a Bayesian assessment of SWAT’s sediment export predictions. J Hydrol 519:3353–3368
Wellen C, Kamran-Disfani A-R, Arhonditsis GB (2015) Evaluation of the current state of distributed watershed nutrient water quality modeling. Environ Sci Technol 49:3278–3290
Winter JG, Duthie HC (2000) Export coefficient modeling to assess phosphorus loading in an urban watershed. JAWRA 36:1053–1061
Yerubandi RR, Boegman L, Bolkhari H, Hiriart-Baer V (2016) Physical processes affecting water quality in Hamilton Harbour. Aquat Ecosyst Health Manage 19:114–123
Zhang W, Arhonditsis GB (2008) Predicting the frequency of water quality standard violations using Bayesian calibration of eutrophication models. J Great Lakes Res 34:698–720
Zhang W, Kim D-K, Rao Y et al (2013) Can simple phosphorus mass balance models guide management decision? A case study in the Bay of Quinte, Ontario, Canada. Ecol Model 257:66–79
Acknowledgements
George Arhonditsis wishes to acknowledge the continuous support of his work on model uncertainty analysis from the National Sciences and Engineering Research Council of Canada (Discovery Grants). The Hamilton Harbour modeling project has received funding support from the Ontario Ministry of the Environment (Canada-Ontario Grant Agreement 120808). The Bay of Quinte modeling project was undertaken with the financial support of the Lower Trent Region Conservation Authority provided through the Bay of Quinte Remedial Action Plan Restoration Council.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Arhonditsis, G., Kim, DK., Kelly, N., Neumann, A., Javed, A. (2018). Uncertainty Analysis by Bayesian Inference. In: Recknagel, F., Michener, W. (eds) Ecological Informatics. Springer, Cham. https://doi.org/10.1007/978-3-319-59928-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-59928-1_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59926-7
Online ISBN: 978-3-319-59928-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)