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Identifying Model Structure and Scale Dependencies in Complex Systems

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Title: Identifying Model Structure and Scale Dependencies in Complex Systems


1
Identifying Model Structure and Scale
Dependencies in Complex Systems
  • Donna M. Rizzo
  • College of
  • Engineering Mathematical Sciences
  • University of Vermont, Burlington, VT

2
Forecast Modeling Heuristic Optimization
Methods
3
Multi-objective Optimization
Rizzo and Dougherty, Water Resources Research, 30
(2), pp. 483-497, 1994.

Which scheme is optimal ?
- How long do we really have to operate? - How
long do we really have to monitor? - How much
residual risk are we willing to accept? - Will a
new technology or public policy shift become
available?
4
Conclusions
  • Theres no such thing as correct scale (its
    problem dependent)
  • Keys - recognizing when a change in scale has
    occurred
  • - determining what information (and what
    scale) data must be collected

5
Geostatsitics
  • Variogram Estimate of Correlation in Space
  • Range
  • Distance where samples are no longer correlated
  • Sill
  • Variance where samples are no longer correlated
  • Ordinary Kriging
  • Spatial Estimation at unknown locations

6
Combining Geostatistics with Process Modeling
7
  • Clark, Rizzo, Watzin, and Hession, River Research
    and Applications,
  • 23, DOI 10.1002/rra.1085, 2007.

8
Parameter Estimation Application
Estimation of Berea Sandstone Geophysical
Properties Lance Besaw
9
Berea Sandstone Data
Data collected by New England Research, Inc. (see
Boinott, G. N., G. Y. Bussod, et al., 2004.
"Physically Based Upscaling of Heterogeneous
Porous Media An Illustrated Example Using Berea
Sandstone." The Leading Edge.
10
Sample Dataset
  • Exhaustive Dataset All measurements (3800)
  • Sample Dataset (limited number of data)
  • Primary data (air permeability) known at screened
    elevations (46 measurements).
  • Secondary data (compressional-wave velocity
    electrical resistivity) known along 10 well
    borings (380 measurements).

11
Artificial Neural Networks (ANNs)
  • Data driven, real-time prediction
  • Large amounts of multiple data types
  • Parallel processing
  • Non-parametric statistics (few data assumptions)

Inputs
Weights
Activation Function
Output
12
Counterpropagation Algorithm
  • Supervised neural network
  • Combines
  • 1. Kohonen Self-organizing map (unsupervised NN)
  • 2. Grossberg outstar structure (operates as a
    Bayesian classifier)
  • Self-organizes in response to examples of some
    function (training data)
  • Training phase
  • Network learns inherent relationships within data
  • Prediction/implementation phase
  • Extracted inherent relationships are utilized

13
Estimating Air Permeability
14
Estimating Air Permeability
15
Geostatistics (Cokriging) Estimate Field
Besaw and Rizzo, Water Resources Research, 43,
W11409, DOI 10.1029/2006WR005509, 2007.
16
Improving site characterization monitoring
environmental change using microbial profiles and
geochemistry in landfill-leachate contaminated
groundwater
17
Long Term Monitoring Challenges at Landfills
  • What do you monitor in landfill leachate?
  • What are the monitoring objectives?
  • Monitoring for how long and at what frequency?

18
Motivation
Microbial diversity can be leveraged between
clean and contaminated environments.
19
PCA - Hydrochemistry
  • Contaminated Locations Separate Across PC1
  • Fringe Locations Not Separated Across PC1-PC3
  • 60 Variance Explained in first 2 PCs
  • PC1 Correlations
  • TDS, Mg, Cl, Spec Cond, Hardness, Alkalinity,
    COD, TOC, NH3
  • PC2 Correlations
  • Organic-N, Phenols

20
PCA - All Data
  • Clean, Fringe, and Contaminated Locations
    Separated in PC1-PC2
  • 22 Variance Explained
  • PC1 Correlations
  • TDS, Mg, Spec Cond, Alkalinity, Na, Cl, Hardness,
    COD, TOC, NH3, Eh, Mn, SO4
  • G505, B244, B122, G80, B168, G165, A244
  • PC2 Correlations
  • Fe, NO3, pH
  • B121, B160, G424, A118, G510, A144, B492, G484,
    B279, B470

21
Delineating contamination at landfill sites
without prior knowledge
Mouser, Rizzo, Röling, and van Breukelen,
Environmental Science Technology, 39 (19) pp.
7551-7559, 2005.
22
Motivation
Mouser, Rizzo, Röling, and van Breukelen,
Environmental Science Technology, 39 (19) pp.
7551-7559, 2005.
23
A Modified Self-Organizing Map for Spatial
Clustering
Andrea Pearce
24
Kohonen self-organizing map
  • Non parametric clustering algorithm - useful when
    groupings unknown
  • Unsupervised ANN
  • Usages complex non-linear mappings, data
    compression, clustering
  • Disparate data types
  • Used in ecological studies to model benthic macro
    invertebrates in streams Park et al. (2003) and
    Gevrey et al. (2004)

25
Kohonens Animal Example
26
The Self-Organizing Map
6 features per sampling location 25 sampling
locations
Output Space 2D Map
Small
W(i,j,1)
W(i,j,2)
Medium
W(i,j,3)
Big
W(i,j,4)
2-legs
The algorithm finds the best matching node on the
output map
W(i,j,5)
W(i,j,6)
4-legs
Hair
27
The Self-Organizing Map
6 features per sampling location 25 sampling
locations
Output Space 2D Map
Small
W(i,j,1)
W(i,j,2)
Medium
W(i,j,3)
Big
W(i,j,4)
2-legs
and updates weights in the neighborhood of that
node.
W(i,j,5)
W(i,j,6)
4-legs
Hair
28
Kohonens Animal Example Unified Distance Matrix
(U-Matrix)
29
Kohonens Animal Example Component Planes
30
Cyanobacteria Blooms and Cyanotoxin Production
  • We will cluster samples based on cyanobacterial
    communities using a Self-Organizing Map (SOM)
  • Then compare the clusters to measured cyanotoxin
    concentrations

www.lcbp.org A bloom near Venise-en-Quebec in
August, 2008. Credit Quebec Ministry of
Sustainable Development, Environment and Parks.
31
Advances in Watershed Management and Fluvial
Hazard Mitigation Using Artificial Neural
Networks and Remote Sensing
  • Lance Besaw1, Donna M. Rizzo1, Michael Kline3,
    Kristen Underwood4, Leslie Morrissey2 and Keith
    Pelletier2

1College of Engineering and Mathematics,
University of Vermont, Burlington, VT 2
Rubenstein School of Natural Resources,University
of Vermont, Burlington, VT 3River Management
Program, Vermont Agency of Natural Resources,
Waterbury, VT 4South Mountain Research
Consulting, Bristol, VT
32
Stressors Leading to Channel Instability
  • Increased hydraulic loading (climatic and
    impervious)
  • Increased sediment loads
  • Channelization / Straightening
  • Floodplain encroachment
  • Loss of riparian buffer
  • Channel Armoring
  • Undersized bridges / culverts (constriction)
  • Instability resulting from multiple (natural and
    human) stressors causes stream to move out of
    dynamic equilibrium.
  • The State of Vermont wants to make reasonable
    predictions of instability.

33
Vermont Agency of Natural Resources River
Management Program
  • Channel and watershed management
  • Channel dynamic equilibrium
  • Avoid infrastructure disasters
  • State wide data collection
  • Expert assessments
  • Fluvial erosion hazard mapping
  • Stakeholder Planning Tool
  • Data driven, translate to multiple geographic
    locations
  • GIS-based for visualization, quantification,
    communication, prioritization
  • Incorporate process-based classification of river
    networks
  • Real-time, multiple-objective management
    decisions
  • http//www.anr.state.vt.us/dec/waterq/rivers.htm

34
State Wide Stream Assessments
  • Phase 1 watershed and channel corridor features
  • Land cover/use
  • Sinuosity
  • Channel slope
  • Geologic soils, etc
  • Phase 2 - Field assessment
  • Incision ratio
  • Access to flood plain
  • Grain size distribution, etc
  • Rapid geomorphic assessment (RGA)

35
Stream Sensitivity
  • Likelihood of stream adjustment in response to
    watershed or local stressors ? fluvial erosion
    hazard ratings, water quality, habitat indices
  • Based on
  • Inherent vulnerability hydraulic geometry and
    sediment regime
  • Geomorphic condition degree of departure from
    dynamic equilibrium (or reference condition)
  • Based on research findings from Lane (1955),
    Schumm (1977), Knighton (1988), Rosgen (1996),
    Simon and Thorne (1996), Montgomery and
    Buffington (1997), MacBroom (1998) and others.

36
Hierarchical ANNs for Stream Sensitivity
Single/multiple threads
Entrenchment ratio
37
Remote Sensing Sensitivity Analysis
  • Light Detection and Ranging (LIDAR)
  • Aid land use/land cover classifications
  • More accurately compute
  • Valley width
  • Channel/valley slope
  • Definiens eCognition object based classifier
  • Classify Sinuosity
  • Incorporate LIDAR for land use/land cover
    classification

38
Geomorphic Condition
Over-Widening
Degradation / Incision
Planform Change
Aggradation
39
Geomorphic Condition ANN Inputs
  • Rapid Geomorphic Assessment ranks dominant
    process of adjustment (degradation, aggradation,
    widening, and planform change) and stage of
    channel evolution

http//www.anr.state.vt.us/dec/waterq/rivers.htm
40
Predicting Geomorphic Condition
Scores
Adjust internal weights
Channel Degradation Channel Aggradation Cha
nnel Widening Planform Change
Input Layer
Output Layer
Hidden Layer
Input Pattern
41
Geomorphic Condition ANN Example
Watershed Lewis Creek Middlebury River
Data Use in the ANNs Training Data Set Interpolation Data Set
Land Area 210 km2 163 km2
Land Use Distribution Forest / Wetland 70 Agricultural 24 Developed 6 Forest / Wetland 87 Agricultural 12 Developed 1
Elevation Range Highest Point 239 m Lowest Point 116 m Highest Point 640 m Lowest Point 105 m
No. of Stream Reaches 20 19
Burlington
Lewis Creek
Middlebury River
42
Geomorphic Condition ANN Results
  • R2 0.854

43
Inherent Vulnerability ANN (Combined Rosgen and
Montgomery Buffington)
  • Trained to be Quality Assurance look-up table
  • Predict stream inherent vulnerability on 789 VT
    reaches
  • Prediction Accuracy
  • 80 classification agreement with recorded field
    data
  • 12 due to imprecise parameter boundaries
    (overlap)
  • 8 due to data transfer mistakes (or additional
    expert knowledge)

44
Stream Interpretation Quality Assurance
45
Hierarchical ANNs for Stream Sensitivity
Inherent Vulnerability
Single/multiple threads
Entrenchment ratio
(g) Stream Sensitivity SOM
Width/depth ratio
Sinuosity
Slope

Channel material



Impervious area
Riparian vegetation
Geomorphic Condition
Degradation
Aggradation
Widening

Planform Change
46
Hierarchical ANNs for Stream Sensitivity
ANN Predictions ANN Predictions ANN Predictions ANN Predictions ANN Predictions ANN Predictions
Experts   Extreme Very High High Moderate Low Very Low
Experts Extreme 9 44 13 0 0 0
Experts Very High 2 284 44 1 0 0
Experts High 1 37 231 20 0 0
Experts Moderate 0 4 27 58 0 0
Experts Low 1 0 3 1 0 0
Experts Very Low 0 1 0 0 2 6
  • Predicting Stream Sensitivity (789 reaches)
  • 75 classification agreement
  • 22 differ by 1 class
  • 3 differ by gt1 class

47
Self-organizing map
Input nodes
Inputs
Inherent Vulnerability
Geomorphic Condition
48
Conclusions
  • ANNs are data-driven (flexible and simple to
    modify enabling a truly adaptive management
    approach)
  • Can be modified to recognize when a change in
    scale has occurred
  • Process of training
  • - elicits significance of governing factors in
  • determination of sensitivity - helps
    document similarities/differences among experts
    (and weighting of parameters
  • for classifying vulnerability, condition,
    and overall sensitivity

49
Acknowledgements
  • VT Agency of Natural Resources, River Management
    Program
  • USGS
  • NSF EPSCoR Graduate Research Assistantship
  • Evan Fitzgerald School of Natural Resources,
    University of Vermont, Burlington, VT
  • Jeff Doris Sanborn, Head and Associates,
    Randolph, VT

Questions
50
References
  • Gevrey, M., Rimet, F., Park, Y. S., Giraudel,
    J.-L., Ector, L., and Lek, S. (2004). "Water
    quality assessment using diatom assemblages and
    advanced modelling techniques." Freshwater
    Biology, 49, 208-220.
  • Kohonen, T. (1989). Self-Organization and
    Associative Memory, Springer Verlag, New York.
  • Lane, E.W. (1955) The importance of fluvial
    morphology in hydraulic engineering. Proceedings
    of the Ammerican Society of Civil Engineers,
    Journal of the Hydraulics Division, (81), paper
    no. 745.
  • Montgomery, D. R. and Buffington, J. M. (1997)
    Channel-reach morphology in mountain drainage
    basins. Geological Society of America Bulletin,
    109(5), 596-611.
  • Park, Y.-S., Cereghino, R., Compin, A., and Lek,
    S. (2003). "Applications of artificial neural
    networks for patterning and predicting aquatic
    insect species richness in running waters."
    Ecological Modelling, 160, 265-280.
  • Rosgen, D. L. (1996) Applied Fluvial Morphology,
    Wildland Hydrology, Pasoda Springs, CO.
  • Schumm, S. A. (1977) The Fluvial System, John
    Wiley and Sons, New York, NY.
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