Mike Dunbar

Report
Statistical hydro-ecological
models
Mike Dunbar
National Hydroecology Technical Advisor
[email protected]
August 2013
(Statistics for Environmental Evaluation 2004)
Structure
(About Me)
Statistical modelling using monitoring data
Hydroecology: river flows and ecological
response
River ecology and land management stressors
Some history
Mid-1980s
Brookes: quantify massive extent of river channelisation in E & W
More focus on flows downstream of dams
Roll out of national bioassessment methods
1990s
Addressing site-specific low flow problems
Development of River Habitat Survey
Growing interest in river restoration/rehabilitation
Development of LIFE metric (see later)
2000s
European Water Framework Directive
Importance of hydromorphology (made up word) increasingly recognised
DRIED-UP project (basis of this talk)
EU Water Framework Directive
England (2012)
Physical Modification
Phosphate
Abstraction and Flow
Dissolved Oxygen
Sediment
Ammonia
Specific Pollutants
BOD
Pressure on Ground Water
Priority Substances
Alien Species
pH
Nitrate
Temperature
Fish Stocking
Other Pollutants
Still under investigation
0%
10%
20%
30%
40%
50%
60%
Percentage of waterbodies assigned a reason for fauilure attributed to each pressure
Where it all started for me
Extence, Balbi and Chadd (1999)
Dunbar and Clarke, 2002 (2005?)
Centre for Ecology and Hydrology – Mike Dunbar
More context
Desperate need to ‘upscale’ our detailed knowledge
spatially and temporally for it to be useful for river
management
It’s generally well known that
Physical environment affects river and stream biota
Biota have definable niches for physical microhabitat as well as water
quality
Distribution of biota related to catchment characteristics
Multiple pressures are the norm
How to upscale: use national datasets
Macroinvertebrate biological monitoring
River Habitat Survey
Indicator organisms:
Macroinvertebrates
Rhyacophlia
Simulium
Perla
Caenis
Sericostoma
Lymnaea
Fast velocity water, clean gravel /
cobble substrates
Sigara
Gerris
Slow / still water and / or silty substrates
Centre for Ecology and Hydrology – Mike Dunbar
f (flowgroup, abundance)

n


LIFE
n
Where n = number of different taxa in sample
Groups based on a huge literature survey (which I didn’t do)
Group
Abundance in sample
A
1-9
B
10-99
C
100-999
D
1000+
I
Rapid
9
10
11
12
II
Moderate/fast
8
9
10
11
III
Slow/sluggish
7
7
7
7
IV
Flowing/standing
6
5
4
3
V
Standing
5
4
3
2
VI
Drought resistant
4
3
2
1
Standard sampling method
Assess habitat
3 minute kick/sweep sample
1 minute hand search
Sample processing
DRIED-UP
Distinguishing the Relative Importance of
Environmental Data Underpinning flow
Pressure assessment
Four R&D phases so far (DU1-4)
Mainly funded by Environment Agency, some
contribution from NERC/CEH and EU
Two papers (DU1&2), ~Three reports
Currently undergoing testing in the EA
Centre for Ecology and Hydrology – Mike Dunbar
Flow
Life Score
8.0
1.00
7.5
0.10
7.0
0.01
6.5
0.00
6.0
86
88
90
92
94
Year
96
98
00
LIFE Score
Discharge (m³/s)
10.00
Sp
Au
++++ ++++
++++
+
+
++
++++
+ +
+ +++ +
+
++++
++
+++++
+++ ++
78117
+
++
++ +
75896
+
64268
53858
+
69367
67808
+ +
+++
+
++++++
+++
+ ++++
+++
+ + ++
++ +
+++
++
69055
+++ +++
+++ +
68570
89481
+
++++ ++
+ +
9
8
7
6
++
+++++ +
+
++
67456
+ ++
++ +
++
53857
+
++++
+++ +
++
79079
+ ++ + +
+
+++++
+ ++++
++
++
++++
+++++ +
+
+
+
+
++++++
66546
66050
78718
+
+
+++
++ ++
53811
78698
65984
65889
+
+ +++
+
+++
+++
+
+
+ +
++ ++
++
+++ +
+++
++
+++
+
-2 0 2
53810
+
++++++
++++
78517
+
+++ ++
++
+ +
53782
78377
+ +
+++
+++++
++
+++
+ +++++
+++++
++
++
65509
++++ + +
+ +
++++++++ +++
++
++
+
+++ ++++
+
-2 0 2
53729
78217
65477
53618
+++
++++++ ++
+ ++++++++++ + +
52058
+++
++
+++++
+
++++ +++
+++++++ +
++
+
++
+
++
+++
64287
63497
64100
+++
+ +++
++++
++ + +
+ ++
+++
+++++
+
+
53617
+ +++
+++
++
++++ + +
+ ++
53552
+ ++
++ +
+++ +
++++
++++++++
+
+ +
+ + +++++
++
53277
+++ +
+ +++++ ++
+
+
+
+ +
++++ +
51788
+ + ++
+++ +
+ +++
+
++
+++
53217
53160
++
+++
+++
++++
+++++ +
+
++ +
+
52957
+
+ + + ++++
+++++ +
52646
+++++ +
+ +++++ +
52408
52238
+ +++
++
+ ++ +++
++
+
++
+++++++
+
++
++
++++
+++ +
+ ++
++
+
+
+
54221
+
+++++ +++++
+ ++++
53212
+ ++++++
+ +++ ++
+
52221
+
++ +
++++++++++
++ + ++++++++
+
+++++++ +
53819
+
52133
9
8
7
6
+
++
+++ ++
+++ +
++++ ++
++++++
+
+++++
++++
+
+
+
+++
++
+++ +
+
51902
+
+++
+
+ +++ ++
++ +
+
51847
51649
++ +
+
+++ +
+
49754
+
+
+++
+ + +++
+
+
+
+++ +
51136
++
+++++++
++
++++
+ ++++ + +
+
+++
+++
+
++++ +
++++++++
+
+ +++
+ +++++
++
+++
49498
++++ +
++
++ +++
+ ++
++
+
51097
++++++
+
++ +++
+ ++ ++
++
+++++
++++++++
+
++++++++++
++++
+
48389
48105
+ ++ +
++++ ++
++
+
45201
50995
+ ++ +
+ +
++
+ +++
+ +
45200
+ +
++++++ + ++
+
++ +
10709
+
+ ++
++
++++++ +
+ +
++
50953
50844
50584
++ ++ +
+++
+++++++++
++++++
+ ++
+ + +++++
++ +
+
+ +
+
++
+++ +++
+ + ++
50251
47157
50059
47041
49824
+
++ + +
++
+
++++
+
+
+
+++++ +
++++
++++
++++++++
+++
44546
+ ++++
++++ ++
++
+++
+ ++ + +
++++
+ ++++++++++
+
+
++++ ++
+
++
+++ +
++ +
44436
++ +
+++++
+++++
++
+
++
+++ ++
++ ++
+
+ + + +++++
++++
++
46953
++++ +
+++ + +
10866
45247
++
+ +++
++++
+
+
10790
++++
++++++
++ ++++++++
45202
47712
47862
++
+
+ +++
++++
++
++ +
+ +++
+
+
+ +++
+
+ +++ +
++ ++
++
10775
++
+++++ ++++
++ +
++++
++ ++ ++
+++
+ ++++
+
+++ ++
10753
+
++++++
+
++
+ ++++ +
++ +
45199
+ ++
+++
+
+
+++
+++
+ +
+
++
+ ++
+ +++
+++
10708
+
+
++
+ +
++++++++
+ +
+
++
+ ++
+ ++
45137
+
+
+
+++
+
45136
++
+
+++++
+ +
++++
++
+++
++ +++
++++
10080
+ +++++
+++++++
509
+
++
+++++++++
+
+++
291
+
+
1587
+
+ + ++
+ +
+
47497
47379
+
+ + +++
+ +
+++
45135
++
+++++ +
+ +
++ ++
45133
47257
++
+
+ +
+
+
++++ +
++
+ ++++
++
+ ++
+
+
+
++ ++
+
9
8
7
6
++ ++++++++
++
++++++
+ +++++
+++ +
47672
50454
+
+
++ ++
+
+ ++
+++++
+ +++++++++
+
+ +
+ ++++ +
+ ++ +++
++
+
9
8
7
6
9
8
7
6
+
44803
9
8
7
6
50378
+
215
LIFE_F
9
8
7
6
+ ++
++++
++
+
+
50349
-2 0 2
+
+
++++ +
+ ++ +
+
+ +++++
++
+++++
+++
+ +++
+ ++
+ ++++
+++ +
+ ++
+++
+++
+ ++
++
+
+
-2 0 2
-2 0 2
-2 0 2
-2 0 2
Q10z
-2 0 2
-2 0 2
-2 0 2
9
8
7
6
-1
0
1
2
8.0
6.0
7.0
LIFE
7.5
7.0
6.5
LIFE
8.0
6.5 7.0 7.5 8.0 8.5
LIFE
-2
-2
0
1
2
-2
Normalised Flow
-1
0
1
2
Normalised Flow
0
1
2
-2
0
1
-2
Normalised Flow
6.5
LIFE
7.5
LIFE
-1
0
1
Normalised Flow
2
-2
-1
0
1
Normalised Flow
-1
0
1
2
Normalised Flow
7.6
LIFE
7.2
6.8
-2
6.5 7.0 7.5 8.0
2
8.5
Normalised Flow
-1
2
6.5 7.0 7.5 8.0
-1
LIFE
7.5
-2
6.5 7.0
LIFE
7.5
6.5
LIFE
8.0
Normalised Flow
-1
-2
-1
0
1
2
Normalised Flow
Original data
Analysis
Data
Using subset of Environment Agency historical
macroinvertebrate monitoring data
• Extensively screened for water quality impacts
Model historical daily flows where gauges not available
Physical habitat quantified by a River Habitat Survey
Biotic index LIFE, in the manner of other biotic indices
Relate preceding flows to the LIFE score for each
sample
Explanatory variables
Flow magnitudes,
statistics of flows
preceding sample
http://www.ceh.ac.uk/data/nrfa/
River Habitat Survey
Habitat Modification
Habitat Quality
3
8
7.9
2.5
7.8
Flow (m³/s)
7.6
1.5
7.5
7.4
1
7.3
7.2
0.5
7.1
0
01/01/95
7
01/01/96
01/01/97
01/01/98
01/01/99
01/01/00
01/01/01
01/01/02
01/01/03
01/01/04
LIFE score
7.7
2
Examples of sites
Multilevel statistical models
Also called mixed-effects, or hierarchical
Extension of linear regression to hierarchically
structured data
Very common in social sciences, educational,
medical statistics
Not very common in environmental sciences
Multilevel / hierarchical approach
Terminology: i sample (level 1), nested within j site (level 2)
Problems with alternative approaches
Site-by-site
You need a surprisingly large amount of biological data to model
the LIFE-flow relationship for a site
Particularly if you are interested in response to different flow
variables
So site-specific flow-biology relationships can be highly uncertain
(and misleading)
If multiple flow variables are “tested”, this uncertainty
is even greater than you think
Ignore group structure
Weak, unrealistic models
Unsuitable for prediction
Can’t handle multi-level predictors
Common patterns
BOTH high (Q10) and low (Q95) flow
magnitudes influence LIFE score
Autumn samples more sensitive to high flow
magnitude
Extent of Resectioning decreases LIFE score
Extent of Resectioning increases response of
LIFE to low flow magnitude
Year trend: upwards, varies by site
DRIED-UP 1: 2005
7.5
5.5
6.5
LIFE score (species)
7.5
6.5
5.5
LIFE score (species)
8.5
b
8.5
a
-2
-1
0
1
2
Flow (Q95) z-scores
3
-2
-1
0
1
2
Flow (Q95) z-scores
Data from 11 sites in E.Midlands
3
DRIED-UP 3: 2010
Influence of HMSRS on response (upland sites)
7.0
8.0
100%
7.5
33%
66%
7.0
LIFE score (family)
7.5
0%
0%
33%
66%
6.0
6.0
6.5
6.5
LIFE score (family)
8.0
8.5
8.5
Influence of HMSRS on response (lowland sites)
-2
-1
0
1
2
Normalised antecdent low flows (Q95)
100%
-2
-1
0
1
2
Normalised antecdent low flows (Q95)
8.5
Modelled response of each individual site
7.5
7.0
6.5
6.0
LIFE score (family)
8.0
Modelled mean response of LIFE score to
Q95z for upland and lowland sites as
mediated by HMSRS, and response of each
individual site. Percentages are of the
maximum HMSRS score observed in the
dataset. NB
model fitted excluding
normalised Q10 term.
-2
-1
0
1
Normalised antecdent low flows (Q95)
2
Borrowing strength
In DRIED-UP, each site in the model
“borrows strength” from the dataset as a
whole
Or.. The DU dataset makes site-specific
relationships more robust
This is very handy for prediction
Prediction
In ecology at least, too much focus on model
selection as the end point
Actually we should take more time making
predictions...
Plug in flow (norm seasonal Q95 and Q10) +
habitat
1. No new biol data
2. New biol data (borrowing strength)
Example later..
Conclusions
Modelling approach accounts for the spatial-temporal
structure in the data
Common effect of both high and low flows for both upland
and lowland sites
Physical habitat can influence both overall LIFE and its
response to flow
Consistent signature from resectioning across upland and lowland
Effect of high flows greater on autumn samples (ie summer
flows)
There are implications for water resource management,
river rehabilitation, climate change mitigation
More information?
Taking the modelling forward
DRUWID – DRIED-UP with Incremental Drought
Chilterns NW of London
Major aquifer: large number of water supply
boreholes
Abstraction impacts on river flows
New housing development
“Chalk Streams”: high conservation value and
public interest
Strong climatic control, overlaid with
anthropogenic influence
E.g. River Misbourne
Photo: Misbourne River Action
DRUWID concept
6 years in the making...
How to capture more of the complexity of the
flow regime?
How to describe impact of drought
Solutions
Mixed effects approach
More flow variables AND
Flow-flow interactions
Multi-model inference
Rank alternate competing hypotheses
Often no single model “best”
Stepwise etc approaches all flawed
Totally avoids issues of “significance”, in-out
Information Theoretic approach
Further details:
Burnham and Anderson (2002): model selection and multi-model
inference...
Anderson (2010): model-based inference in the life sciences...
Hydrological complexity: existing
approaches:
DRUWID application to Chilterns
42 sites in 9 catchments
Still using gauged flows, but also indicator as
to whether site was dry the summer before
sampling
Chose lags up to 2 years as reasonable
compromise
Separate models for spring and autumn
Reasonable compromise- this formula:
yijk = β0 + v1jk x1ik + β2x2ik + u3jk x3ik + u4jk x4ik + u2jk β8 x8i + w1k +
β5 + β6 + β7 +
β9x9j + β10x10j + β10x10j + β11x11j + β12x12j +
β 13 x1ik x2ik + β 14 x1ik x3ik + β 15 x2ik x3ik + β 16 x3ik x4ik +eijk
v1jk = β1 + β17 x9j + β18 x10j + β19 x11j + β20 x12j +u1jk
w1k ~ N(0, 2)
u ~ MVN(0, Ω)
  12  12 2  132  14 2 
 2
2
2
2




2
23
24 
   12 2
2
2
  13  23  3  34 2 
 2

2
2
2 




24
34
4 
 14
eijk ~ N(0, σ2 )
20 fixed parameters (intercept and 19 slopes) plus 6
variances and 6 covariances
And catchment ID only varies overall LIFE, not any of the
flow response slopes
Chilterns DRUWID: Summary of variables
Interactions are v.v. important
Further illustration of one flow:flow
interaction
Prediction
DRUWID is work in progress
Was funded by CEH, but development used
EA Chilterns data
Methodology can be applied elsewhere
Relatively quick to set up, just need the data..
DRUWID shows that
Can expand number of antecedent flow
descriptors without model selection / overfitting problems
Can use interaction effects neatly
Chilterns DRUWID shows that
See lag effects in ecological response to past
flow conditions, over at least two years
Sequencing is important
Drying pattern matters
Resectioning important again... Also livestock
poaching
Habitat still matters...
Photo: Misbourne River Action
DRIED-UP and DRUWID summary
Both totally reliant on multilevel / mixed effects approach
DRIED-UP = a “national” model
derive robust site-specific relationships where relatively short series of
monitoring data are available
WFD, RSA, drought, ?licensing?
influential in building our understanding that ecological response is a
consequence of interacting multiple stressors
DRUWID extends the DRIED-UP concept to consider
impacts of drought
DRUWID is a framework rather than a specific model
It’s more complex so works best using relatively compact regional datasets
Stats learnings
Power of mixed-effects / multilevel approach
Need good understanding of multiple linear
regression
No single go-to book
Look outside environmental sciences: social,
medical
End of Part 1!

similar documents