Identifying Model Structure and Scale Dependencies in Complex Systems

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Identifying Model Structure and Scale Dependencies in Complex Systems . Donna M. Rizzo College of Engineering &amp; Mathematical Sciences University of Vermont, Burlington, VT . Minimize = Real \$\$\$ + l * (Performance &amp; Resource Targets). N. N. p. w. å. å. =. +. +. ). q. F. N. F.

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Identifying Model Structure and Scale Dependencies in Complex Systems

Donna M. Rizzo

College of

Engineering & Mathematical Sciences

University of Vermont, Burlington, VT

Minimize

= Real \$\$\$+l * (Performance & Resource Targets)

N

N

p

w

å

å

=

+

+

)

q

F

N

F

f

(

l

C

,

C

,

W,T

“The extrapolations are the only things that have any real value. … Knowledge is of no real value if all you can tell me is what happened yesterday….you must be willing to stick your neck out.”

i

treat

w

cap

MCL

=

=

1

1

k

i

R. P. Feynmann,The Uncertainty of Science,

John Danz Lecture, April 23, 1963

Forecast Modeling & Heuristic Optimization Methods

Mass Remaining and Cost

Cost (\$ 10M)

Mass (Mg)

Performance-Cost “Ratio”

Time (years)

Time (years)

l

=

1

l

=

5

l

=

10

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?

Conclusions

• There’s no such thing as “correct scale”… (it’s problem dependent)
• Keys: - recognizing when a change in scale has occurred

- determining what information (and what scale) data must be collected

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

Initial C (ppb), Jan., 1998

Kriged, July, 1999

HGL Model, July, 1999

Bayesian, July, 1999

Combining Geostatistics with Process Modeling

Figure 5. General positive relationship between MWIBI (Mixed Water Index of Biotic Integrity) and patch-ordered rank.

Clark, Rizzo, Watzin, and Hession, River Research and Applications,

23, DOI: 10.1002/rra.1085, 2007.

Parameter Estimation Application:

Estimation of Berea Sandstone Geophysical Properties

Lance Besaw

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.

Z Direction (mm)

X Direction (mm)

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).

Single Neuron

V1

V2

.

.

.

VN

W1

W2

.

.

.

WN

f(Sp)

Σ vi wip = sp

Y

Sp

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

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

Hidden Layer

Output Layer

(Kohonen)

(Grossberg)

Input Layer

x

Estimate Air permeability along well borings

z

. . .

. . .

. . .

. . .

Restivity

. . .

. . .

P-Velocity

Estimating Air Permeability

Hidden Layer

Output Layer

(Kohonen)

(Grossberg)

Input Layer

x

Estimate Air permeability everywhere within the domain

z

. . .

. . .

. . .

. . .

. . .

. . .

Estimating Air Permeability

Sandstone Air Permeability

Air Permeability Omnidirectional Variogram

15000

Semi-Variogram Bin Averages

95% Confidence Limit

10000

(permeability)

5000

g

0

0

50

100

150

200

250

300

350

Cokriged Estimates of Permeability

Distance (mm)

Ordinary Cokriging Permeability Estimates

ANN Estimates of Permeability

Geostatistics (Cokriging) Estimate Field

Besaw and Rizzo, Water Resources Research, 43, W11409, DOI: 10.1029/2006WR005509, 2007.

Improving site characterization & monitoring environmental change using microbial profiles and geochemistry in landfill-leachate contaminated groundwater

Cassella Waste Services

Schuyler Landfill, N.Y.

Department of Civil &

Environmental Engineering

Donna Rizzo Paula Mouser

Department of Biology

Department of Geology

Greg Druschel

Lori Stevens

Brooke Schwartz

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?
Motivation

Microbial diversity can be leveraged between

clean and contaminated environments.

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
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

Mouser, Rizzo, Röling, and van Breukelen, Environmental Science & Technology, 39 (19) pp. 7551-7559, 2005.

Motivation

Mouser, Rizzo, Röling, and van Breukelen, Environmental Science & Technology, 39 (19) pp. 7551-7559, 2005.

### A Modified Self-Organizing Map for Spatial Clustering

Andrea Pearce

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 Gevreyet al.(2004)

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

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

Kohonen’s Animal Example

Unified Distance Matrix (U-Matrix)

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.

### Advances in Watershed Management and Fluvial Hazard Mitigation Using Artificial NeuralNetworks 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

2Rubenstein 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

• 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.
Vermont Agency of Natural ResourcesRiver 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
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
• Grain size distribution, etc
• Rapid geomorphic assessment (RGA)
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.

Inherent Vulnerability

(g) Stream Sensitivity SOM

Width/depth ratio

Sinuosity

Slope

Channel material

Impervious area

Riparian vegetation

Stream Sensitivity

GeomorphicCondition

Widening

Planform Change

Hierarchical ANNs for Stream Sensitivity

Entrenchment ratio

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
Geomorphic Condition

Over-Widening

Planform Change

Reach

-

level

Input

RGA score quartile

Condition

Code

(VTDEC, 2002)

Poor

1

1 to 5

Fair

2

6 to 10

Good

3

11 to 15

Optimal

4

16 to 20

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

y

y

Geomorphic Condition

0.4

0.1

0.3

0.2

0

1

0

0

0

1

0

0

15

12

9

14

Output

Pattern

Output

Pattern

Target

Pattern

Predicting Geomorphic Condition

Scores

Channel Widening

Planform Change

Input

Layer

Hidden

Layer

Output

Layer

Input

Pattern

Geomorphic Condition ANN: Example

Burlington

Lewis Creek

Middlebury River

Single/multiple channel(s)

Entrenchment ratio

Inherent Vulnerability

Width/depth ratio

Sinuosity

Slope

Channel material

• 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)
Hierarchical ANNs for Stream Sensitivity

Inherent Vulnerability

Entrenchment ratio

(g) Stream Sensitivity SOM

Width/depth ratio

Sinuosity

Slope

Channel material

Impervious area

Riparian vegetation

GeomorphicCondition

Widening

Planform Change

Hierarchical ANNs for Stream Sensitivity
• Predicting Stream Sensitivity (789 reaches)
• 75% classification agreement
• 22% differ by 1 class
• 3% differ by >1 class

Kohonen hidden nodes

Low & Very Low

Moderate

ic

High

High

Nc

High

Very High & Extreme

Very High

Extreme

Self-organizing map

Input nodes

Inputs

Inherent Vulnerability

Geomorphic Condition

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

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

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.