mars wp7 bn_vansjo_jmo_20151113

Bayesian network modelling in MARS:

Example from Lake Vansjø

Task 7.3: Combining abiotic and biotic models for river basin management planning

Jannicke Moe, Raoul Couture (NIVA)

MARS WP7 meeting 13.11.2015, Berlin

13.11.2015Jannicke Moe 1

Background: text from DoW (Task 7.3)• Analysing options for empirical and probabilistic

linking of "abiotic" and "biotic" models, including the experiences in WP4

• The individual models will be connected to the MARS conceptual framework

• Several case studies from WP4 will be used to validate the improved models• Regge and Dinkel, Elbe, Otra, Vansjø-Hobøl,

Kokemäenjoki, Odense, Sorraia


What is a Bayesian network (BN)?


Symptom 1Symptom 2Symptom 3

Disease 1Disease 2

• A Bayesian network = probability network = belief network = influence diagram= probabilistic directed acyclic graphical model

• = a probabilistic model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG).

• For example, a BN could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the BN can be used to compute the probabilities of the presence of various diseases.

(Source: Wikipedia)

Example: BN for cyanobacterial bloom hazard in lakes


Rigosi et al. 2015. Ecol. Appl. 25:186

Based on data from 20 lakes

Key properties of a BN model• Probabilistic

• all variables and relationships are probability distributions

• can represent uncertainty

• Integrates information• observed data, model output,

knowledge, assumptions...

• Causal relationships• "Acyclic": No feedback loops

• Not dynamic• applies for a given time interval


A BN for multiple stressors in lake Vansjø

Moe, Haande & Couture. Ecological Modelling (in review)


• Aim: predict effects of scenarios on ecological status• 4 modules: different sources of information

What are inside the nodes?- discrete probability distributions


Abiotic and biotic indicators:•Intervals (concentrations)

Ecological status:•Categories (ranked)

States

Probabilities

What are inside the arrows? - conditional probability tables (CPT)


CPT for Cyano•Based on 90 observations

CPT for Status Phytoplankton•Based on knowledge (combination rules)

States

Probabilities

The MARS conceptual model


The MARS conceptual model: example


Mapping the BN for Vansjø to the MARS conceptual model (DPSIR)


DRIVER

DRIVER

PRESSURE (nutrient

loads etc.)

PRESSURE

STATE: ABIOTIC INDICATORS

STATE: BIOTIC INDICATORS

STATE:

BIOTIC IND.

RESPONSE

STATE:WFD STATUS

• What about IMPACT - functions and services?

Other BNs for Vansjø include IMPACT


Barton et al. 2016. Eutropia – integrated valuation of lake eutrophication abatement decisions using a Bayesian belief network. In: Z.Neal (ed.). Handbook of Applied Systems Science. Routledge.

• IMPACT nodes can be linked to STATE nodes• Suitability for fishing • Suitability for bathing

IMPACT

IMPACTSTATES

Structure of BN model: nodes with discrete states


Module 3:states = 2-3 intervals

Module 4:states = 3 categories: - High/Good- Moderate- Poor/Bad

Module 1:states = scenarios

Module 2:states = 3-6 intervals

States

Probabilities

Module 1: Scenarios (from REFRESH)• Case study: Lake Vansjø, basin

Vanemfjorden• Catchment dominated by forest

and agriculture• Moderate ecological status

• Climate scenarios:• Reference• «Hadley»: higher temp,

more precipitation• Management scenarios:

• Reference• Best (water quality focus): more

TP• Worst (economy focus):

less TP


Haande, Lyche Solheim, Moe & Brænden 2011. NIVA report

Module 2: Output from process-based models


• Process-based models: • Persist (hydrology)• INCA-P (catchment) • MyLake (lake) input to BN

• 60 realisations of the model (parameter combinations) give rise to probability distributions in the BN model


Module 3: Monitoring data - cyanobacteria

• Multiple regressions:Identify significant predictor variables structure of nodes and arrows in BN model

• Regression tree analysis:Identify breakpoints in predictor variables discretisation (setting intervals) of nodes in BN

Empirical relationships between abiotic and biotic variables quantified by data analysis (WP4)


Module 4: Ecological status• Status for different quality elements are combined in

CPTs according to the national classification system

• E.g. status of phytoplankton:• If status of cyanobacteria < chl-a,

the combined status is averaged• If status of cyanobacteria > chl-a,

cyanobacteria are not considered

Running the BN model• General: Use new "evidence" to update prior

probabilities • Using Bayes' rule• Calculate posterior probability distributions

for all child nodes

• Here: "Evidence" comes from scenarios via process-based model simulations • 3 x management scenarios• 2 x climate scenarios

• A BN model can also be run "backwards"!


Scenario: reference


Probability of Poor-Bad status equal for Cyanobacteria and Chl-a (~45%)

Scenario: best management, future climate


Probability of Poor-Bad status higher for Cyano (40%) than for Chl-a (36%)

Results - all scenarios


0

20

40

60

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100

Ref Had Ref Had Ref HadClimate scenario

Worst Ref BestManagement scenario

Secchi depth

Pro

babi

lity

(%)

(a)

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80

100



Total P(b)

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Phys.-chem.(c)

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Chla

Pro

babi

lity

(%)

(d)

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100



Cyanobacteria(e)

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100



Phytoplankton(f)

Poor-BadModerateHigh-Good

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100



Lake

Pro

babi

lity

(%)

(g)

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60

80

100



Secchi depth

Pro

babi

lity

(%)

(a)

0

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80

100



Total P(b)

0

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100



Phys.-chem.(c)

0

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Chla

Pro

babi

lity

(%)

(d)

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100



Cyanobacteria(e)

0

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100



Phytoplankton(f)


0

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Lake

Pro

babi

lity

(%)

(g)

-

• Cyanobacteria has similar response to scenarios as chl-a• Including cyanobacteria reduces the probability of good

ecological status for phytoplankton

0

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100



Secchi depth

Pro

babi

lity

(%)

(a)

0

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60

80

100



Total P(b)

0

20

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60

80

100



Phys.-chem.(c)

0

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80

100



Chla

Pro

babi

lity

(%)

(d)

0

20

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60

80

100



Cyanobacteria(e)

0

20

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60

80

100



Phytoplankton(f)


0

20

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60

80

100



Lake

Pro

babi

lity

(%)

(g)

0

20

40

60

80

100



Secchi depth

Pro

babi

lity

(%)

(a)

0

20

40

60

80

100



Total P(b)

0

20

40

60

80

100



Phys.-chem.(c)

0

20

40

60

80

100



Chla

Pro

babi

lity

(%)

(d)

0

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40

60

80

100



Cyanobacteria(e)

0

20

40

60

80

100



Phytoplankton(f)


0

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80

100



Lake

Pro

babi

lity

(%)

(g)

How can BN models be developed for other MARS catchments?


How can BN models be developed for other MARS catchments?• Develop conceptual model [done!]

• Variables and causal relationships• Define and discretize variables [partly done]

• Define the states (intervals or categories)• Assign prior probability distribution

• Quantify relationships between variables [hard]• Fill in conditional probability tables• Based on data analysis (WP4), literature, knowledge, ...

• Run the model, e.g. different scenarios [easy]• Model validation, model revision etc. [hard]

• (example: Death et al. 2015. Freshw. Biol. )


Use of BNs for MARS catchments: challenges• BN modelling differs from "traditional" modelling

• No temporal dimension• Probability distributions instead of single values• Conditional probability tables (CPTs) instead of equations

• Filling in CPTs require much information• Number of columns = product of no. of states

of all parent nodes• E.g.: 2 parent nodes with 4 states each

4x4=16 probability distributions • New method and software

• Requires training and effort by partners• Hugin (license); Netica (free)


General challenges with BNs• Discretisation of variables - losing much detail• Complex networks need much data for

"parametrisation" (filling in CPTs)• Uncertainty/variability grows with length of the

network


Can BN still be a useful tool for MARS?Yes, •as a bridge between conceptual models and process-based models

• aggregating outcome of process-based models• linking abiotic and biotic components• including biotic components where data are sparse but

knowledge is available•for quickly running scenarios

• forwards and backwards•for incorporating and visualising uncertainty•for communication with stakeholders


mars wp7 bn_vansjo_jmo_20151113

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