Modelling hypoxia in the Hamilton Harbour, Ontario, Canada: A Bayesian approach
George Arhonditsis and Dong Kyun Kim
Ecological Modelling Laboratory
Department of Physical & Environmental Sciences University of Toronto
Hamilton Harbour
Phosphorus
Inputs Cause and Effect
Relationships
Frequency of Hypoxia Duration of
Stratification Harmful
Algal Blooms
Carbon Production
Sediment Oxygen Demand Exchanges
with Lake Ontario
Algal
Density Chlorophyll
Violations
Number of Fishkills
Fish Health Water
clarity
Macrophyte abundance
Exchanges with Lake Ontario
Allochthonous Inputs
Water quality standards
Total Phosphorus ≤ 17 (or 20) μg L
-1Chlorophyll a ≤ 5-10 μg L
-1Secchi disk depth ≥ 3 m TP loading ≤ 142 kg day
-1DO ≥ 4 mg L
-1• There is a great deal of modelling work that has been done
toward establishing realistic water quality goals in the Hamilton Harbour and impartially evaluating the likelihood of delisting the system for the BUI "Eutrophication or Undesirable Algae".
• There are watershed, eutrophication, and food web
models in place that aim to shed light on different facets of
the ecosystem functioning.
10-20% violations
Probabilistic projection of system response to nutrient
loading reduction strategies
Chlorophyll a predictive distributions for different levels of Total Phosphorus
Present loading conditions
Nutrient
loading
reduction
Objectives
• How possible is it to meet the DO delisting objective, if the nutrient loading reductions proposed by the
Hamilton Harbour Remedial Action Plan are actually implemented?
• What additional remedial actions are needed to increase the likelihood of meeting the DO target?
•What are the major sources of uncertainty that will
ultimately determine the attainment of the existing
delisting goal?
Spatial Segmentation
Date
Good
Requires Verification Failed
Centre Mid Centre Deep LaSalle STP West
2006 2007 2008 2009 2010 2011 2012 2013
Spatial Segmentation
0%
20%
40%
60%
80%
100%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Frequency
>6 mg/l 3-6 mg/l
<3 mg/l
In modeling context:
( ) ( ) ( )
(
Data)
P
Model P
Model Data
ata P D Model
P =
(
Data Model)
P(
Model)
P
∝
Future
Present Past
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Bayesian Approach
Bayesian DO modelling
Spatially variant intercept Causal factors of hypoxia
• Sediment Oxygen Demand (eutrophication model)
• Hydrodynamic patterns (lake thermal stratification) Conditional autoregressive term to accommodate the
serial correlation of the daily data
Model structural error
Bayesian DO modelling
Conditional autoregressive term to accommodate the serial correlation of the daily data
~ ) ,
|
(δt δ t ω2
P −
) , 2
( δt+1 −δt+2 ω2 N
− + + − +
, 5 5
4
2δt 1 δt 1 δt 2 ω2 N
− − + − + + − + , 6 6
4
4 1 1 2 2
2 δ δ δ ω
δt t t t
N
− − + − + + , 5 5
2
4 1 1 2
2 δ δ ω
δt t t
N
) , 2
(δt−2 − δt−1 ω2 N
for t = 1 for t = 2
for t = 3, …, T-2
for t = T-1 for t = T
Device for evaluating SOD response to external
nutrient loading
Bayesian Kriging
DO prediction
West Centre
LaSalle STP
Woodward
Present Condition
West Centre
LaSalle STP
Woodward
RAP Scenario
DO prediction (Jun. to Sep.)
Present Condition
DO prediction (Jun. to Sep.)
RAP Scenario
DO violations (<4 mg L
-1Jun. to Sep.)
Present Condition
Overall 8%
Overall 26%
Overall 47%
Overall 35%
Violations
DO violations (<4 mg L
-1Jun. to Sep.)
RAP Scenario
Overall 4% Overall 19% Overall 39% Overall 25%
Violations
Advantages of our Bayesian Emulator
• Flexible structure with low computational demands (1/200 of the typical computational time of 3-D hydrodynamic
models);
• Explicit consideration of all the sources of uncertainty (structural, parametric, natural variability);
• Methodological tool that can be augmented by increasing the fidelity of the hydrodynamic component;
•Ability to sequentially update beliefs as new knowledge is available, and the consistency with the scientific process of progressive learning and the policy practice of adaptive management.
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