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Eutrophication of lakes and the risk of harmful cyanobacterial blooms due is a major challenge for management of aquatic ecosystems, and climate change is expected to reinforce these problems. Modelling of aquatic ecosystems has been widely used to predict effects of altered land use and climate change on water quality, assessed by chemistry and phytoplankton biomass. However, the European Water Framework Directive requires more advanced biological indicators for the assessment of ecological status of water bodies, such as the amount of cyanobacteria. We applied a Bayesian network (BN) modelling approach to link future scenarios of climate change and land-use management to ecological status, incorporating cyanobacteria biomass as one of the indicators. The case study is Lake Vansjø in Norway, which has a history of eutrophication and cyanobacterial blooms. The objective was (i) to assess the combined effect of changes in land use and climate on the ecological status of a lake and (ii) to assess the suitability of the BN modelling approach for this purpose. The BN was able to model effects of climate change and management on ecological status of a lake, by combining scenarios, process-based model output, monitoring data and the national lake assessment system. The results showed that the benefits of better land-use management were partly counteracted by future warming under these scenarios. Most importantly, the BN demonstrated the importance of including more biological indicators in the modelling of lake status: namely, that inclusion of cyanobacteria biomass can lower the ecological status compared to assessment by phytoplankton biomass alone. Thus, the BN approach can be a useful supplement to process-based models for water resource management.
Content may be subject to copyright.
Ecological
Modelling
337
(2016)
330–347
Contents
lists
available
at
ScienceDirect
Ecological
Modelling
j
ourna
l
h
omepa
ge:
www.elsevier.com/locate/ecolmodel
Climate
change,
cyanobacteria
blooms
and
ecological
status
of
lakes:
A
Bayesian
network
approach
S.
Jannicke
Moea,,
Sigrid
Haandea,
Raoul-Marie
Couturea,b
aNorwegian
Institute
for
Water
Research
(NIVA),
Gaustadalléen
21,
0349
Oslo,
Norway
bUniversity
of
Waterloo,
200
University
Ave
W,
Waterloo,
Ontario,
N2L
3G1,
Canada
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
10
July
2015
Received
in
revised
form
21
April
2016
Accepted
7
July
2016
Available
online
1
August
2016
Keywords:
Phytoplankton
Biological
indicators
Eutrophication
Probabilistic
model
Uncertainty
Water
framework
directive
a
b
s
t
r
a
c
t
Eutrophication
of
lakes
and
the
risk
of
harmful
cyanobacterial
blooms
due
is
a
major
challenge
for
man-
agement
of
aquatic
ecosystems,
and
climate
change
is
expected
to
reinforce
these
problems.
Modelling
of
aquatic
ecosystems
has
been
widely
used
to
predict
effects
of
altered
land
use
and
climate
change
on
water
quality,
assessed
by
chemistry
and
phytoplankton
biomass.
However,
the
European
Water
Framework
Directive
requires
more
advanced
biological
indicators
for
the
assessment
of
ecological
status
of
water
bodies,
such
as
the
amount
of
cyanobacteria.
We
applied
a
Bayesian
network
(BN)
modelling
approach
to
link
future
scenarios
of
climate
change
and
land-use
management
to
ecological
status,
incorporating
cyanobacteria
biomass
as
one
of
the
indicators.
The
case
study
is
Lake
Vansjø
in
Norway,
which
has
a
history
of
eutrophication
and
cyanobacterial
blooms.
The
objective
was
(i)
to
assess
the
combined
effect
of
changes
in
land
use
and
climate
on
the
ecological
status
of
a
lake
and
(ii)
to
assess
the
suitability
of
the
BN
modelling
approach
for
this
purpose.
The
BN
was
able
to
model
effects
of
climate
change
and
man-
agement
on
ecological
status
of
a
lake,
by
combining
scenarios,
process-based
model
output,
monitoring
data
and
the
national
lake
assessment
system.
The
results
showed
that
the
benefits
of
better
land-use
management
were
partly
counteracted
by
future
warming
under
these
scenarios.
Most
importantly,
the
BN
demonstrated
the
importance
of
including
more
biological
indicators
in
the
modelling
of
lake
status:
namely,
that
inclusion
of
cyanobacteria
biomass
can
lower
the
ecological
status
compared
to
assessment
by
phytoplankton
biomass
alone.
Thus,
the
BN
approach
can
be
a
useful
supplement
to
process-based
models
for
water
resource
management.1
©
2016
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Eutrophication
of
lakes
due
to
nutrient
run-off
from
the
catchments
is
a
major
challenge
for
environmental
management
world-wide
(Schindler,
2012).
The
consequences
of
eutrophica-
tion
for
aquatic
ecosystem
include
harmful
cyanobacterial
blooms
(reviewed
by
Merel
et
al.,
2013)
and
altered
fish
communities
(Jeppesen
et
al.,
2010).
Climate
change
is
expected
to
reinforce
the
problems
with
eutrophication
due
to
i.a.
higher
water
tem-
perature
and
increased
nutrient
run-off
(Jeppesen
et
al.,
2009).
In
particular,
altered
conditions
in
lakes
due
to
climate
change
can
favour
cyanobacteria
over
other
phytoplankton
species
(Paerl
and
Huisman,
2008).
Therefore,
climate
change
may
counteract
the
Corresponding
author.
E-mail
address:
jmo@niva.no
(S.J.
Moe).
1Abbreviations:
BN
=
Bayesian
network;
Chl-a
=
chlorophyll
a;
WFD
=
Water
Framework
Directive.
effects
of
mitigation
measures
for
nutrient
enrichment,
and
make
it
more
difficult
to
obtain
management
targets
for
lakes.
Modelling
of
aquatic
ecosystems
has
been
used
widely
to
sup-
port
water
management,
and
to
predict
effects
of
altered
land
use
and/or
climate
(Gal
et
al.,
2014;
Mooij
et
al.,
2010;
Recknagel
et
al.,
2014;
Trolle
et
al.,
2012).
Process-based
models
for
catchments
and
lakes
typically
aim
at
predicting
changes
in
water
chem-
istry
(e.g.
phosphorus,
nitrogen
and
oxygen)
or
physical
conditions
(e.g.
transparency,
thermal
stratification)
(e.g.,
Jackson-Blake
et
al.,
2015).
Many
lake
models
also
predict
chlorophyll
a
(chl-a),
which
is
a
proxy
of
phytoplankton
biomass
(e.g.
Saloranta
and
Andersen,
2007),
and
a
traditional
indicator
of
water
quality.
However,
the
European
legislation
for
water
management
(the
Water
Framework
Directive
WFD
EC,
2000)
requires
use
of
more
advanced
biological
indicators
for
the
assessment
of
ecological
status
of
water
bod-
ies.
The
key
indicators
of
lake
eutrophication
should
represent
not
only
phytoplankton
biomass,
but
also
other
aspects
of
the
plank-
ton
community.
Many
European
countries
have
therefore
included
intensity
of
cyanobacterial
blooms
as
an
indicator
in
their
assess-
ment
systems
(Poikane
et
al.,
2015).
http://dx.doi.org/10.1016/j.ecolmodel.2016.07.004
0304-3800/©
2016
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.
0/).
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
331
The
relationships
between
climatic
variables,
nutrients
and
cyanobacteria
have
been
thoroughly
studied
by
experiments
(e.g.
Davis
et
al.,
2009),
long-term
monitoring
(e.g.
Nõges
et
al.,
2010)
and
analysis
of
time
series
(e.g.
Huber
et
al.,
2012;
Wagner
and
Adrian,
2009)
and
of
multi-lake
data
sets
(Carvalho
et
al.,
2013;
Rigosi
et
al.,
2015).
However,
only
a
few
process-based
lake
mod-
els
have
so
far
incorporated
such
knowledge,
according
to
a
recent
review
(Elliott,
2012).
These
models
are
PROTECH
(Elliott,
2010;
Elliott
and
May,
2008),
PCLake
(Mooij
et
al.,
2007),
DYRESM-
CAEDYM
(Trolle
et
al.,
2011),
CLAMM
(Howard
and
Easthope,
2002),
PROBE
&
BIOLA
(Arheimer
et
al.,
2005)
and
PROTBAS
(Markensten
and
Pierson,
2007).
For
example,
an
application
of
PROTECH
to
Esthwaite
Water
(a
relatively
shallow
English
lake),
predicted
that
under
scenarios
of
increased
water
temperature
and
decreased
flushing
rate,
cyanobacteria
abundance
increased,
comprised
a
higher
proportion
of
the
phytoplankton
and
had
a
longer
duration
(Elliott,
2010).
However,
lake
models
that
comprise
cyanobacteria
have
not
yet
been
used
in
efforts
to
assess
ecological
status
(sensu
WFD),
to
our
knowledge.
In
this
study,
we
apply
a
Bayesian
network
(BN)
modelling
approach
to
link
future
scenarios
of
climate
change
and
land-
use
management
to
ecological
status,
incorporating
cyanobacteria
biomass
as
well
as
other
indicators.
A
BN
provides
a
framework
for
summarising
large
amounts
of
information
(e.g.,
from
process-
based
models)
and
for
integrating
different
types
of
information.
It
also
provides
a
tool
for
displaying
effects
of
different
scenar-
ios,
where
the
change
in
each
component
can
be
easily
visualised.
The
probabilistic
output
can
readily
be
interpreted
as
the
risk
of
failing
a
certain
management
target
and
support
decision
making.
For
these
reasons,
BNs
have
been
increasingly
used
in
environ-
mental
modelling
(reviewed
by
Aguilera
et
al.,
2011),
and
applied
in
the
context
of
e.g.
risk
assessment
(Lecklin
et
al.,
2011;
Moe,
2010),
resource
management
(Barton
et
al.,
2012)
and
ecosystem
services
(Landuyt
et
al.,
2013).
There
are
many
examples
of
BN
mod-
els
addressing
water
resource
management
(Barton
et
al.,
2005;
Borsuk
et
al.,
2004;
Castelletti
and
Soncini-Sessa,
2007;
Keshtkar
et
al.,
2013;
Martín
de
Santa
Olalla
et
al.,
2007;
Molina
et
al.,
2010;
Ticehurst
et
al.,
2007;
Varis
and
Kuikka,
1999).
Here,
we
focus
on
the
assessment
of
ecological
status
classes
of
water
bodies
sensu
WFD
(High,
Good,
Moderate,
Poor
and
Bad).
The
BN
methodology
typi-
cally
predicts
the
probability
of
different
states,
and
can
therefore
be
particularly
suitable
for
this
purpose
(Lehikoinen
et
al.,
2014).
As
a
case
study
for
this
BN
model
we
have
selected
Lake
Vansjø
in
South-East
Norway.
This
lake
has
a
history
of
high
levels
of
phosphorus
and
phytoplankton
biomass,
and
has
experienced
sev-
eral
cyanobacterial
blooms
(Haande
et
al.,
2011).
The
lake
has
been
monitored
since
1980,
and
has
been
subject
to
modelling
by
process-based
models
(Couture
et
al.,
2014;
Saloranta
and
Andersen,
2007)
as
well
as
Bayesian
networks
(Barton
et
al.,
2014
(basin
Vanemfjorden);
Barton
et
al.,
2008
(basin
Storefjorden)).
However,
this
is
the
first
effort
to
incorporate
cyanobacteria
in
a
model
for
Lake
Vansjø,
and
to
link
the
model
to
climate
change
scenarios.
The
objective
of
the
study
is
(i)
to
assess
the
combined
effect
of
changes
in
land
use
and
climate
on
the
ecological
status
of
a
lake,
considering
both
physico-chemical
indicators
and
phy-
toplankton,
including
cyanobacterial
blooms,
and
(ii)
to
assess
the
suitability
of
the
BN
modelling
approach
for
this
purpose.
2.
Material
and
methods
2.1.
Study
site
The
Vansjø-Hobøl
catchment
(area
690
km2),
also
referred
to
as
the
Morsa
catchment,
is
located
in
south-eastern
Norway.
The
Hobøl
River
drains
a
sub-catchment
of
ca.
440
km2into
Lake
Vansjø,
which
is
the
catchment’s
main
lake.
Lake
Vansjø
has
a
surface
area
of
36
km2and
consists
of
several
sub-basins,
the
two
largest
being
the
deeper,
siliceous
basin
Storefjorden
(eastern
basin)
and
the
shallower,
calcareous
basin
Vanemfjorden
(western
basin).
In
addition,
there
are
six
smaller
sub-basins
which
together
represent
less
than
15%
of
the
lake
surface
area.
The
Storefjorden
basin
water
flows
into
the
Vanemfjorden
basin
through
a
shallow
channel.
In
this
study
we
have
used
data
from
the
most
impacted
basin,
Vanem-
fjorden
(national
water
body
code
003-291-L,
59.443N,
10.755E).
This
basin
is
shallow
(mean
depth
is
3.8
m
and
maximum
depth
is
19.0
m)
and
the
water
column
does
not
stratify
stably.
The
sur-
face
area
is
12
km2,
the
residence
time
is
0.21
year
and
the
water
body
is
humic.
The
phytoplankton
growth
in
this
system
is
proba-
bly
limited
by
light,
because
of
the
high
humic
content
in
the
lake
and
hence
low
transparency
in
the
water
column
(Skarbøvik
et
al.,
2014).
The
current
physico-chemical
and
ecological
status
of
Vanem-
fjorden
are
moderate
(Haande
et
al.,
2011),
hence
it
fails
the
WFD’s
requirement
of
good
ecological
status
(EC,
2000).
However,
the
WFD
also
requires
that
the
current
status
of
a
water
body
should
not
be
worsened.
We
are
therefore
also
interested
in
the
risk
of
deterioration
from
moderate
to
poor
status
of
Vanemfjorden.
2.2.
Data
and
other
information
2.2.1.
Scenarios
The
future
scenarios
apply
for
the
period
2030–2052
(i.e.,
40
years
after
the
reference
period
1990–2012)
and
are
described
in
detail
by
Couture
et
al.
(2014).
In
this
study
we
have
used
the
outcome
of
a
climate
scenario,
“Had”:
The
global
climate
model
HADCM3
combined
with
the
regional
climate
model
(RCM)
HADRM3.
This
scenario
predicts
changes
in
both
yearly
mean
air
temperature
(+1.6 C)
and
yearly
precipitation
(+78.8
mm).
Daily
resolution
scenario
data
for
surface
air
temperature
and
pre-
cipitation
were
derived
from
a
sub-set
of
the
RCM
simulations
and
implemented
by
scaling
the
observed
weather
(1990–2012).
The
observed
temperatures
were
changed
to
reflect
the
increase
in
both
median
and
variance
predicted
by
the
climate
models.
Precipitation
was
scaled
using
a
ratio
of
change
approach,
mul-
tiplying
observation
by
the
ratio
of
observed
(1990–2012)
over
predicted
(2030–2052)
precipitation.
Climate
conditions
during
the
reference
period
are
referred
to
as
climate
“Ref”.
The
man-
agement
scenarios
are
referred
to
as
Ref”
=
reference
(historical
data),
“Best”
=
best
case
(water-quality
focus),
“Worst”
=
“worst
case”
(economic
focus).
The
“Best”
scenario
is
defined
by
four
cri-
teria:
(1)
a
10%
reduction
in
agricultural
land,
which
is
converted
to
forest,
(2)
a
25%
decrease
in
vegetable
production,
which
is
con-
verted
to
grass
production,
(3)
a
25%
decrease
in
P-based
fertilizer
application,
and
(4)
a
90%
improvement
in
the
P-removing
perfor-
mance
of
WWTPs.
Conversely,
the
“Worst”
scenario
is
defined
by
(1)
a
10%
reduction
of
forest
cover,
which
is
converted
to
agricul-
tural
lands,
(2)
a
shift
of
25%
of
the
grass
production
to
vegetable
production,
(3)
an
increase
of
P-based
fertilizer
application
by
25%,
and
(4)
a
25%
increase
in
the
P
load
of
effluents
from
scattered
dwellings
and
WWTPs
throughout
the
catchment.
More
details
on
the
application
of
these
and
other
scenarios
to
the
catchment
and
lake
process-based
models
are
given
by
Couture
et
al.
(2014).
2.2.2.
Process-based
model
output
All
aspects
of
catchment
and
lake
process-based
modelling
are
described
by
Couture
et
al.
(2014).
In
brief,
the
effects
of
the
climate
and
management
scenarios
on
the
river
hydrology
and
chemistry
were
modelled
by
the
catchment
models
PERSiST
(Futter
et
al.,
2013)
and
INCA-P
(Wade
et
al.,
2002),
respectively.
PERSiST
simulated
daily
runoff
in
the
river
system
using
inputs
of
catch-
ment
characteristics
and
daily
temperature
and
precipitation
time
332
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
Table
1
Overview
of
nodes
in
the
Bayesian
network
model.
Modules
are
defined
in
Fig.
2.
Module
Node
name
Unit
No.
of
values
Node
states
1
2
3
4
5
6
1
Management
Ref
Worst
Best
1
Climate
Ref
Had
1
Year
1990–1995
1996–2001
2002–2007
2008–2012
1
Month
May
Jun
Jul
Aug
Sep
Oct
1
Season
May–Jun
Jul–Aug
Sep–Oct
2
Irradiance
mol/m2s
251,280a0–100
100–150
150–200
200–300
2
Secchi
(pred.)
m
251,280
0–2
2–2.6
2.6–5
2
Total
P
(pred.)
g/L
251,280
0–20
20–25
25–30
30–39
39–50
50–80
2
Chl-a
(pred.)
g/L
251,280
0–5
5–10.5
10.5–15
15–20
20–25
25–60
2
Temp.
(pred.) C 251,280
0–10 10–15 15–19 19–30
3
Secchi
(obs.) m
191
0–2
2–2.6
2.6–5
3
Total
P
(obs.)
g/L
250
0–20
20–39
39–80
3
Chl-a
(obs.)
g/L
250
0–10.5
10.5–20
20–60
3
Temp.
(obs.) C
195
0–19
19–30
3
Cyano
g/L
103
0–1000
1000–2000
2000–6000
3
CyanoMax
g/L
103b0–1000
1000–2000
2000–6000
4
Status
Secchi
HG
M
PB
4
Status
Total
P
HG
M
PB
4
Status
Chl-a HG
M
PB
4
Status
Cyano
HG
M
PB
4
Status
Phys-chem.
HG
M
PB
4
Status
Phytoplankton
HG
M
PB
4
Status
of
lake
HG
M
PB
aThe
number
of
values
in
Module
2
is
generated
by
simulation
of
weekly
values
during
May-Oct
for
23
years
with
60
different
parameter
sets
for
6
scenarios.
bCyanoMax
has
only
9
unique
values
(one
for
each
year
of
observation).
series.
INCA-P
produced
daily
predictions
of
discharge
and
material
transport
in
the
river
(concentration
of
suspended
solids,
soluble
reactive
P
and
total
P
(TP)),
which
were
then
passed
to
the
lake
model.
The
successive
effects
of
the
scenarios
on
the
physical
con-
ditions
and
the
concentration
of
different
P
fractions
in
the
lake
were
modelled
by
the
process-based
model
MyLake
(Saloranta
and
Andersen,
2007).
In
MyLake,
phytoplankton
has
a
constant
C:P
ratio
of
106:1
and
an
organic-P:Chl-a
ratio
of
1:1,
such
that
particu-
late
organic
P
is
a
proxy
for
Chl-a
(Saloranta
and
Andersen,
2007).
The
MyLake
model
was
automatically
calibrated
against
monitor-
ing
data
from
the
years
2005–2012,
using
a
probabilistic
Bayesian
inference
calibration
scheme.
In
this
scheme
each
parameter
was
given
a
prior
and
a
posterior
distribution,
within
the
framework
of
a
self-adaptive
differential
evolution
learning
scheme
(DREAM),
implemented
in
Matlab
(Starrfelt
and
Kaste,
2014).
The
MCMC
algo-
rithm
was
run
along
eight
chains
until
convergence,
monitored
visually,
was
obtained.
Four
hundred
iterations
were
saved
and
used
to
determine
posterior
parameter
distribution.
An
envelope
of
60
parameter
sets
of
equal
likelihood
was
sampled
to
gener-
ate
a
set
of
60
model
realisations
with
daily
resolution
for
23
years
(1990–2012).
The
variability
among
these
sets
(median
and
interquartile
space)
was
discussed
by
Couture
et
al.
(2014).
For
the
BN
model,
all
60
realisations
of
the
process-based
models
are
used
as
input
and
considered
a
source
of
uncertainty.
Specifically,
the
following
outcome
of
the
lake
model
was
used
as
nodes
in
the
BN
model
(see
Table
1):
surface
water
temperature
(hence-
forth
referred
to
as
“temperature”),
Secchi
depth,
total
P
(TP)
and
Chl-a.
Secchi
depth
(SD)
was
calculated
using
the
light
extinc-
tion
coefficient
()
calculated
by
MyLake
and
the
relationship
=
1.7/SD
(French
et
al.,
1982).
Temperature
and
concentrations
were
averaged
for
depths
0–4
m
(to
match
the
monitoring
data).
In
addition
we
included
surface
irradiance
at
noon
(an
input
variable
for
MyLake),
to
represent
seasonal
change
in
addition
to
tempera-
ture.
For
each
variable,
values
for
one
day
per
week
were
selected
(to
match
the
sampling
frequency
of
the
monitoring
data).
2.2.3.
Lake
monitoring
data
The
main
data
source
for
this
study
was
the
data
series
from
Lake
Vansjø,
the
basin
Vanemfjorden
(see
Table
1
and
Fig.
1).
All
data
were
downloaded
from
NIVA’s
monitoring
database
(http://
www.aquamonitor.no).
The
following
data
were
included
in
this
study:
water
temperature
(years
1993–1996,
2005–2012),
Sec-
chi
depth
(2000–2001,
2005–2012),
total
P
(1990–2012),
Chl-a
(1990–2012)
and
biomass
of
cyanobacteria
(2004–2012).
Inte-
grated
water
samples
from
0
to
4
m
were
collected
for
the
chemical
and
biological
analyses.
Only
data
from
the
months
of
May
to
October
were
included
(following
the
national
classification
sys-
tem;
section
2.2.4).
From
2005
all
variables
were
measured
weekly,
except
for
cyanobacteria,
which
were
measured
bi-weekly.
In
addition,
the
larger
dataset
EUREGI
was
used
for
evaluation
of
the
model
(as
described
in
section
3.3).
The
EUREGI
lake
dataset
results
from
the
regional
eutrophication
survey
in
Norway
in
1988
(Oredalen
and
Faafeng,
2002).
The
dataset
includes
quantitative
analyses
from
more
than
400
lakes,
sampled
minimum
4
times.
The
locations
are
selected
in
order
to
cover
the
broadest
possible
gradient
of
human
influence.
Parameters
that
typically
represent
eutrophication
(TP
and
Chl-a)
range
over
two
orders
of
magnitude
in
this
dataset.
Eutrophic
lakes
are
overrepresented
regarding
the
proportion
of
area
covered
by
these
lakes;
nevertheless,
the
dataset
contains
more
oligotrophic
than
eutrophic
lakes.
Almost
75%
of
the
lakes
are
clear-water
lakes,
of
which
the
majority
is
calcium-poor
lakes.
The
remaining
25%
are
humic
lakes;
this
group
has
equal
proportions
of
calcium-poor
and
calcium-rich
lakes.
In
total
599
samples
from
EUREGI
were
used
in
this
study;
samples
that
com-
prised
values
for
water
temperature,
Chl-a
and
cyanobacteria.
2.2.4.
National
classification
system
for
lakes
The
status
assessment
in
this
study
is
based
on
the
main
eutrophication
indicators
and
their
combination
rules
in
the
Norwegian
lake
classification
system,2with
status
class
bound-
aries
defined
for
the
lake
type
L-N8
(lowland,
large,
shallow,
siliceous/moderate
alkalinity,
humic).
Three
of
the
indicators
in
the
classification
system
were
obtained
from
MyLake
model
predictions,
and
included
in
this
study:
seasonal
averages
of
2http://www.vannportalen.no/Revidert
klassifiseringsveileder140123
VZIS-.
pdf.file.
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
333
Fig.
1.
Observed
(open
black
circles)
and
predicted
(red
curves)
values
of
(a)
temper-
ature,
(b)
Secchi
depth,
(c)
total
P,
(d)
chl-a
and
(e)
cyanobacteria.
Predicted
values
are
median
values
(with
25
and
75
percentiles)
of
60
runs
of
the
process
model
MyLake
with
different
parameter
combinations
(see
section
2.1.1).
(Predicted
values
for
cyanobacteria
are
not
available
from
this
model).
Blue
triangles
represent
sea-
sonal
mean
values
for
Secchi
depth,
total
P
and
chl-a,
and
seasonal
maximum
value
for
cyanobacteria
(corresponding
to
the
node
CyanoMax).
Horizontal
lines
indicate
the
boundaries
between
ecological
status
classes:
High-Good
(H-G),
Moderate
(M)
and
Poor-Bad
(P-B).
Secchi
depth,
TP
and
Chl-a.
According
to
the
classification
system,
physico-chemical
indicators
(here:
Secchi
depth
and
TP)
should
be
combined
by
averaging.
Phytoplankton
status
should
in
prin-
ciple
be
assessed
by
four
indicators:
Chl-a,
total
phytoplankton
biomass,
PTI
(a
measure
of
sensitive
vs.
tolerant
taxa;
(Ptacnik
et
al.,
2009))
and
the
yearly
maximum
of
cyanobacterial
biomass.
All
four
indices
can
be
calculated
from
the
monitoring
data,
but
they
are
all
correlated,
and
only
one
can
be
predicted
by
MyLake
(Chl-a).
We
therefore
chose
to
include
only
one
additional
phytoplankton
index
in
the
BN,
namely
the
yearly
maximum
of
cyanobacteria
(termed
“CyanoMax”).
Combined
phytoplankton
status
should
be
obtained
as
follows:
if
CyanoMax
have
worse
status
than
chl-a,
then
the
two
indicators
should
be
averaged;
if
CyanoMax
has
equal
or
better
sta-
tus
than
chl-a,
then
CyanoMax
should
be
ignored.
Thus,
including
cyanobacteria
can
only
result
in
worse
or
equal
status
of
phyto-
plankton
compared
to
the
status
determined
by
chl-a
alone.
Finally,
while
the
overall
ecological
status
of
the
lake
is
determined
pri-
marily
by
biology
(here:
phytoplankton),
it
can
be
compromised
by
physico-chemical
elements.
If
the
status
set
by
biology
is
High
or
Good,
and
the
physico-
chemical
status
is
worse
than
the
biological
status,
then
the
overall
ecological
status
should
be
reduced
by
one
class
(i.e.,
from
High
to
Good
or
from
Good
to
Moderate).
(More
details
are
given
in
Appendix
A).
The
full
classification
system
comprises
several
more
indicators
including
both
physico-chemical
quality
elements
(e.g.
Total
N)
and
biological
quality
elements
(BQEs;
macrophytes,
ben-
thic
invertebrates
and
fish).
In
this
study,
however,
we
included
only
the
indicators
that
could
be
predicted
by
MyLake
or
that
could
be
linked
to
MyLake
predictions
with
high
confidence
(i.e.,
cyanobacteria).
2.3.
Bayesian
network
modelling
For
constructing
the
BN
model,
we
followed
recent
guidelines
for
use
of
BN
in
ecological
modelling
(Marcot
et
al.,
2006;
Pollino
and
Henderson,
2010):
(1)
Defining
the
objective
of
the
model
and
its
final
node
(here:
ecological
status
of
the
lake);
(2)
generating
a
conceptual
model
(nodes
and
arrows)
based
on
knowledge
from
the
literature
and
on
expert
knowledge;
(3)
establishing
the
model
states
and
quantifying
the
relationships.
The
BN
model
was
devel-
oped
and
run
in
the
software
Hugin
Expert,
version
8
(http://www.
hugin.com).
2.3.1.
Model
structure
In
a
BN
model,
each
node
(variable)
is
typically
defined
by
a
discrete
probability
distribution
across
a
number
of
alternative
states
(i.e.,
intervals
or
categories).
This
structure
enables
differ-
ent
types
of
information
to
be
linked
by
conditional
probability
tables
(CPT)
(see
Table
2
and
section
3.1).
Although
continuous
variables
may
also
be
included
in
a
BN
with
certain
restrictions,
this
type
of
nodes
are
not
considered
here.
All
nodes
with
outgoing
arrows
are
termed
“parent
nodes”,
while
all
nodes
with
incoming
arrows
are
termed
“child
nodes”.
In
a
CPT,
the
probabilistic
depen-
dencies
between
a
child
node
and
its
parents
are
defined.
When
the
model
is
run,
probability
distribution
of
the
child
node
is
updated
accordingly,
given
the
states
of
the
parent
nodes,
following
the
Bayes’
theorem
for
conditional
probability
calculation
(Koski
and
Noble,
2009).
The
probability
distributions
in
the
CPTs
can
repre-
sent
the
natural
variability
in
the
system
as
well
as
any
other
type
of
uncertainty
concerning
the
relationship
between
the
variables.
In
our
model
the
main
sources
of
variability
are
(1)
the
tempo-
ral
variation
in
the
predicted
and
observed
time
series
(within
the
specified
time
intervals)
and
(2)
uncertainty
in
the
predictions
of
the
process-based
models
that
are
included
in
the
BN.
The
com-
plexity
of
a
BN
grows
exponentially
with
the
number
of
nodes
and
arrows;
therefore
it
is
often
desirable
to
limit
the
number
of
nodes
(Varis
and
Kuikka,
1999).
The
computing
capacity
of
computers
have
increased
to
the
extent
that
even
relatively
complex
and
big
networks
can
be
built
and
run
(Lehikoinen
et
al.,
2013),
but
more
complex
BNs
nevertheless
require
more
data
or
other
information
than
simpler
ones.
In
this
study,
we
aimed
at
including
only
the
nodes
that
were
necessary
to
(i)
run
the
model
according
to
selected
scenarios,
(ii)
represent
particular
processes
that
were
important
334
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
Table
2
Examples
of
conditional
probability
tables
(CPT)
for
each
module
of
the
BN
model.
Each
column
contains
the
probability
distribution
of
a
child
node
for
a
given
combination
of
states
of
the
parent
nodes.
The
bottom
row
(“Experience”)
contains
the
total
count
of
observations
for
each
combination
of
parent
nodes.
(a)
CPT
(the
first
8
columns)
for
Chl-a
(predicted)
conditional
on
management,
years,
irradiance
and
water
temperature.
The
full
table
contains
3
(management
scenarios)
x
4
(year
intervals)
x
4
(irradiance
intervals)
x
4
(temperature
intervals)
=
192
columns.
Management
Reference
Years
1990–1995
Irradiance
0–100
100–150
Temp.
(pred.)
0–10
10–15
15–19
19–25
0–10
10–15
15–19
19–25
Chl-a
(pred.)
0–5
0.013
0.012
0
0
0.124
0.067
0.004
0
5–10.5 0.104
0.106
0.117
0.117
0.588
0.180
0.065
0.092
10.5–15 0.066
0.020
0.017
0.017
0.148
0.223
0.082
0.042
15–20
0.297
0.085
0.000
0.000
0.036
0.026
0.033
0.000
20–25
0.313
0.264
0.104
0.104
0.050
0.168
0.018
0.000
25–60
0.206
0.512
0.763
0.763
0.055
0.337
0.798
0.867
Experience
3015
2445
540
0a420
1200
1980
480
(b)
CPT
for
Cyanobacteria
conditional
on
Chl-a
(observed)
and
water
temperature
(observed).
Chl-a
(obs.) 0–10.5 10.5–20
20–60
Temp.
(obs)
0–19
19–25
0–19
19–25
0–19
19–25
Cyano
0–1000
1
1
1
0.923
0.333
0.323
1000–2000
0
0
0
0.077
0.333
0.290
2000–6000
0
0
0
0
0.333
0.387
Experience
20
1
22
13
3
31
(c)
CPT
for
CyanoMax
conditional
on
Cyanobacteria
and
Season.
Cyano
0–1000
1000–2000
2000–6000
Season
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
CyanoMax
0–1000 0.618
0.724
0.667
0
0
0
0
0
0
1000–2000
0.088
0.138
0.111
0.167
0.167
0
0
0
0
2000–6000
0.294
0.138
0.222
0.833
0.833
1
1
1
1
Experience
34
29
27
6
6
2
1
12
2
(d)
CPT
for
Status
of
lake
conditional
on
status
of
phytoplankton
(PP)
and
status
of
physico-chemical
(PC)
variables.
HG
=
High-Good,
M
=
Moderate,
PB
=
Poor-Bad.
Status
PP
HG
M
PB
Status
PC
HG
M
PB
HG
M
PB
HG
M
PB
Status
Lake
HG
1
0
0
0
0
0
0
0
0
M
0
1
1
1
1
0
0
0
0
PB
0
0
0
0
0
1
1
1
1
aAssumed
probability
distributions
inserted
where
no
observations
were
available.
for
the
cyanobacteria
and
other
phytoplankton
and
(iii)
assess
the
effects
of
the
scenarios
on
the
status
indicators.
A
BN
is
usually
not
a
dynamic
model,
meaning
that
it
does
not
have
a
time
dimension.
Instead,
the
predictions
of
a
BN
can
represent
the
probability
of
realising
different
outcomes
during
a
specified
period.
The
BN
in
our
study
represents
the
whole
period
for
which
the
MyLake
model
was
run
(1990–2012).
However,
there
has
been
substantial
changes
in
the
concentrations
of
TP
and
chl-a
during
this
period
(Fig.
1c
and
d),
which
could
be
useful
to
account
for
in
the
BN.
We
therefore
included
a
node
“Year”
that
divided
the
23-year
time
span
into
4
periods
of
5–6
years;
this
way
the
effects
of
the
different
scenarios
on
water
quality
(i.e.,
the
CPTs)
could
be
estimated
separately
for
these
periods,
and
the
BN
could
be
run
for
selected
periods.
(The
default
setting
of
the
Year
node
was
a
uni-
form
probability
distribution,
corresponding
to
running
the
BN
for
the
whole
23-year
period).
Moreover,
a
node
“Month”
was
included
to
account
for
seasonal
changes
in
the
water
quality.
The
BN
model
developed
in
this
study
(Fig.
2)
comprises
four
modules,
corresponding
to
the
four
sources
of
information
described
above.
Module
1
contains
all
the
parent
nodes,
representing
the
cli-
mate
and
management
scenarios,
as
well
as
the
nodes
representing
specific
periods
(years
and
month).
Module
2
links
these
scenarios
to
the
output
from
the
process-
based
models,
i.e.
the
predicted
effects
on
physico-chemistry
in
the
lake.
Module
3
links
these
model
predictions
to
the
observed
time
series
for
a
set
of
physical,
chemical
and
biological
variables,
and
furthermore
provides
a
link
from
two
of
these
variables
(chl-a
and
water
temperature)
to
the
observed
cyanobacterial
biomass.
In
addition,
the
yearly
maximum
of
cyanobacteria
(“CyanoMax”)
is
set
equal
to
the
highest
observed
cyanobacteria
biomass
across
all
samples
in
a
given
year.
Thus,
each
observation
of
Cyano
is
asso-
ciated
with
a
CyanoMax
from
the
same
year,
but
possibly
from
a
different
month.
Module
4
links
each
of
the
physico-chemical
and
biological
indi-
cators
to
the
lake
classification
system.
This
enables
prediction
of
the
probability
of
different
status
classes
for
each
indicator
as
well
as
for
the
overall
ecological
status
of
the
lake.
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
335
Fig.
2.
Structure
of
the
Bayesian
Network
(BN)
model
for
ecological
status
of
Lake
Vansjø,
basin
Vanemfjorden.
The
model
consists
of
four
modules:
(1)
Climate
and
management
scenarios
(2),
output
from
the
process-based
lake
model
MyLake;
(3)
monitoring
data
from
Lake
Vansjø
(1990–2012);
(4)
the
national
classification
system
for
ecological
status
of
lakes.
The
prior
probability
distribution
for
each
node
is
displayed
both
as
horizontal
bars
and
by
percentages
(the
first
column
in
each
node),
across
the
states
(the
second
column).
The
set
of
arrows
pointing
to
one
node
represents
the
conditional
probability
table
for
this
node.
Status
classes:
HG
=
High-Good
(required
by
the
WFD),
M
=
moderate,
PB
=
Poor-Bad.
The
causal
links
between
the
nodes
(i.e.,
the
arrows
and
their
directions)
can
be
determined
in
different
ways.
For
nodes
that
are
based
on
data,
it
is
possible
to
let
the
software
estimate
suggest
a
set
of
arrows
and
their
directions
given
specific
criteria.
Neverthe-
less,
we
chose
to
develop
the
structure
based
on
knowledge
and
theory
about
causal
relationships
among
the
nodes.
For
the
nodes
in
Module
2,
regression
tree
analyses
were
performed
to
explore
which
parent
nodes
had
significant
effect
on
the
child
nodes.
The
analyses
were
performed
with
the
packages
rpart
(Therneau
et
al.,
2015)
and
party
(Hothorn
et
al.,
2006)
in
the
software
R
(R
Core
Team,
2015).
All
indicator
nodes
varied
with
year
and
with
month.
The
node
Management
had
significant
effects
on
all
indicator
nodes
predicted
by
MyLake
(Secchi,
TP
and
Chl-a).
Water
temperature
affected
Chl-a,
but
not
Total
P.
The
node
Irradiance
was
included
as
a
parent
for
Chl-a,
because
of
the
particular
importance
for
phytoplankton
growth.
The
purpose
was
to
distinguish
between
effects
of
Irradiance
and
Temperature;
both
variables
varied
dur-
ing
the
year,
but
only
Temperature
was
affected
by
Climate.
TP
and
Chl-a
were
strongly
correlated,
as
is
commonly
observed
in
lakes
(Phillips
et
al.,
2008),
and
therefore
both
variables
could
have
been
a
Fig.
3.
Regression
tree
for
effects
of
temperature
on
the
variable
CyanoMax
(seasonal
maximum
of
cyanobacteria
biomass).
The
numbers
on
the
branches
(18.85
and
20.2)
show
the
significant
breakpoints
along
temperature
gradient.
The
bar
plots
in
each
resulting
node
show
the
probability
distribution
of
CyanoMax
across
the
three
status
classes:
1:
High-Good
(<10.5
g/L),
2:
Moderate
(10.5–20
g/L),
Poor-Bad
(20
g/L).
n
=
number
of
observations
in
each
node.
336
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
suitable
parent
node
for
Cyanobacteria.
We
chose
Chl-a
as