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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 $$$ + l * (Performance & Resource Targets). N. N. p. w. å. å. =. +. +. ). q. F. N. F.
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Donna M. Rizzo
College of
Engineering & Mathematical Sciences
University of Vermont, Burlington, VT
= Real $$$+l * (Performance & Resource Targets)
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“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.”
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treat
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MCL
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R. P. Feynmann,The Uncertainty of Science,
John Danz Lecture, April 23, 1963
Forecast Modeling & Heuristic Optimization MethodsCost ($ 10M)
Mass (Mg)
PerformanceCost “Ratio”
Time (years)
Time (years)
l
=
1
l
=
5
l
=
10
Multiobjective Optimization
Rizzo and Dougherty, Water Resources Research, 30 (2), pp. 483497, 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?
 determining what information (and what scale) data must be collected
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 patchordered rank.
Clark, Rizzo, Watzin, and Hession, River Research and Applications,
23, DOI: 10.1002/rra.1085, 2007.
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.
X Direction (mm)
Sample DatasetV1
V2
.
.
.
VN
W1
W2
.
.
.
WN
f(Sp)
Σ vi wip = sp
Y
Sp
Artificial Neural Networks (ANNs)Inputs
Weights
Activation Function
Output
Output Layer
(Kohonen)
(Grossberg)
Input Layer
x
Estimate Air permeability along well borings
z
. . .
. . .
. . .
. . .
Restivity
. . .
. . .
PVelocity
Estimating Air PermeabilityOutput Layer
(Kohonen)
(Grossberg)
Input Layer
x
Estimate Air permeability everywhere within the domain
z
. . .
. . .
. . .
. . .
. . .
. . .
Estimating Air PermeabilityAir Permeability Omnidirectional Variogram
15000
SemiVariogram 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 FieldBesaw and Rizzo, Water Resources Research, 43, W11409, DOI: 10.1029/2006WR005509, 2007.
Improving site characterization & monitoring environmental change using microbial profiles and geochemistry in landfillleachate contaminated groundwater
Cassella Waste Services
Schuyler Landfill, N.Y.
Department of Civil &
Environmental Engineering
Bernie Nadeau
Donna Rizzo Paula Mouser
Department of Biology
Department of Geology
Greg Druschel
Patrick O’Grady
Lori Stevens
Brooke Schwartz
Mouser, Rizzo, Röling, and van Breukelen, Environmental Science & Technology, 39 (19) pp. 75517559, 2005.
Mouser, Rizzo, Röling, and van Breukelen, Environmental Science & Technology, 39 (19) pp. 75517559, 2005.
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)
2legs
The algorithm finds the best matching node on the output map…
W(i,j,5)
W(i,j,6)
4legs
Hair
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)
2legs
…and updates weights in the neighborhood of that node.
W(i,j,5)
W(i,j,6)
4legs
Hair
Unified Distance Matrix (UMatrix)
Component Planes
www.lcbp.org
A bloom near VeniseenQuebec in August, 2008.
Credit: Quebec Ministry of Sustainable Development, Environment and Parks.
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
(g) Stream Sensitivity SOM
Width/depth ratio
Sinuosity
Slope
…
Channel material
…
…
…
Impervious area
Riparian vegetation
Stream Sensitivity
GeomorphicCondition
Degradation
Aggradation
Widening
…
Planform Change
Hierarchical ANNs for Stream SensitivitySingle/multiple threads
Entrenchment ratio

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 Inputshttp://www.anr.state.vt.us/dec/waterq/rivers.htm
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
Adjust internal weights
Channel Degradation
Channel Aggradation
Channel Widening
Planform Change
Input
Layer
Hidden
Layer
Output
Layer
Input
Pattern
R2 = 0.854
Entrenchment ratio
Inherent Vulnerability
Width/depth ratio
Sinuosity
Slope
…
Channel material
Inherent Vulnerability ANN(Combined Rosgen and Montgomery & Buffington)Inherent Vulnerability
Single/multiple threads
Entrenchment ratio
(g) Stream Sensitivity SOM
Width/depth ratio
Sinuosity
Slope
…
Channel material
…
…
…
Impervious area
Riparian vegetation
GeomorphicCondition
Degradation
Aggradation
Widening
…
Planform Change
Low & Very Low
Moderate
ic
High
High
Nc
High
Very High & Extreme
Very High
Extreme
Selforganizing mapInput nodes
Inputs
Inherent Vulnerability
Geomorphic Condition
 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
Questions