Identifying Model Structure Identifying Model Structure and Scale Dependencies in and Scale Dependencies in

Complex Systems Complex Systems

Donna M. RizzoDonna M. Rizzo

College of College of Engineering & Mathematical SciencesEngineering & Mathematical Sciences

University of Vermont, Burlington, VT University of Vermont, Burlington, VT

Forecast Modeling Forecast Modeling & Heuristic Optimization & Heuristic Optimization

MethodsMethods

“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.”

R. P. Feynmann,The Uncertainty of Science,John Danz Lecture, April 23, 1963

Minimize

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

NN

q F N F f C Ci treatik

w cap MCL

wp

11

( , , )

Multi-objective OptimizationMulti-objective Optimization

10

Performance-Cost “Ratio”

5

Rizzo and Dougherty, Water Resources Research, 30 (2), pp. 483-497, 1994.

Time (years)Time (years)

Mas

s (M

g)

Cos

t ($

10

M)

Mass Remaining and Cost

• 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?

ConclusionsConclusions

There’s no such thing as “correct There’s no such thing as “correct scale”… (it’s problem dependent)scale”… (it’s problem dependent)

Keys: Keys: - recognizing when a change in scale has- recognizing when a change in scale has occurred occurred

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

GeostatsiticsGeostatsitics Variogram – Estimate of Correlation in SpaceVariogram – Estimate of Correlation in Space

Range Range DistanceDistance where samples are where samples are

no longer correlatedno longer correlated

Sill Sill VarianceVariance where samples are where samples are

no longer correlatedno longer correlated

Ordinary KrigingOrdinary Kriging Spatial Estimation at unknown locationsSpatial Estimation at unknown locations

Initial C (ppb), Jan., 1998 Kriged, July, 1999

Bayesian, July, 1999 HGL Model, July, 1999

Combining Geostatistics Combining Geostatistics with Process Modelingwith Process Modeling

Clark, Rizzo, Watzin, and Hession, Clark, Rizzo, Watzin, and Hession, River Research and ApplicationsRiver Research and Applications, , 23, DOI: 10.1002/rra.1085, 2007.23, DOI: 10.1002/rra.1085, 2007.

MB

LR

SB

FR

ABBB

17

19

21

23

25

27

29

0 1 2 3 4 5 6 7

Patchiness Rank

MW

IBI

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

Parameter Estimation Parameter Estimation Application:Application:

Estimation of Berea Sandstone Estimation of Berea Sandstone Geophysical PropertiesGeophysical Properties

Lance BesawLance Besaw

Berea Sandstone DataBerea Sandstone Data

Data collected by New England Research, Inc. (see Boinott, G. N., G. Y. Bussod, Data collected by New England Research, Inc. (see Boinott, G. N., G. Y. Bussod, et alet al., 2004. ., 2004. "Physically Based Upscaling of Heterogeneous Porous Media: An Illustrated Example Using Berea "Physically Based Upscaling of Heterogeneous Porous Media: An Illustrated Example Using Berea Sandstone." Sandstone." The Leading EdgeThe Leading Edge..

Sample DatasetSample Dataset

Exhaustive Dataset: All measurements (3800)Exhaustive Dataset: All measurements (3800) Sample Dataset (limited number of data):Sample Dataset (limited number of data):

Primary data (air permeability) known at screened elevations Primary data (air permeability) known at screened elevations (46 measurements).(46 measurements).

Secondary data (compressional-wave velocity & electrical Secondary data (compressional-wave velocity & electrical resistivity) known along 10 well borings (380 measurements).resistivity) known along 10 well borings (380 measurements).

X Direction (mm)

Z D

irect

ion (

mm

)

Artificial Neural Networks Artificial Neural Networks (ANNs)(ANNs)

Data driven, real-time predictionData driven, real-time prediction Large amounts of multiple data typesLarge amounts of multiple data types Parallel processingParallel processing Non-parametric statistics (few data assumptions)Non-parametric statistics (few data assumptions)

Σ vi wip = sp

V1

V2

.

.

.

VN

Sp

f(Sp)

W1

W2

.

.

.

WN

Y

Single Neuron

Inputs Weights Activation Function

Output

Counterpropagation Counterpropagation AlgorithmAlgorithm

o Supervised neural networkSupervised neural networko Combines Combines

o 1. Kohonen Self-organizing map (unsupervised NN) 1. Kohonen Self-organizing map (unsupervised NN) o 2. Grossberg outstar structure (operates as a 2. Grossberg outstar structure (operates as a

Bayesian classifier)Bayesian classifier)

o Self-organizes in response to examples of Self-organizes in response to examples of some function (training data)some function (training data)o Training phaseTraining phase

o Network learns inherent relationships within dataNetwork learns inherent relationships within data

o Prediction/implementation phasePrediction/implementation phaseo Extracted inherent relationships are utilizedExtracted inherent relationships are utilized

Estimating Air PermeabilityEstimating Air Permeability

. . .

. . .

. . .. . .

. . .

. . .

Hidden Layer (Kohonen) Output Layer

(Grossberg)

Input Layer

x

z

Restivity

P-Velocity

Estimate Air permeability along well

borings

Estimating Air PermeabilityEstimating Air Permeability

. . .

. . .

. . .. . .

. . .

. . .

Hidden Layer (Kohonen) Output Layer

(Grossberg)

Input Layer

x

zEstimate Air permeability everywhere within the

domain

Geostatistics (Cokriging) Estimate FieldGeostatistics (Cokriging) Estimate Field

0 50 100 150 200 250 300 3500

5000

10000

15000Air Permeability Omnidirectional Variogram

Distance (mm)

(p

erm

eabi

lity)

Semi-Variogram Bin Averages95% Confidence Limit

Sandstone Air Permeability

Ordinary Cokriging Permeability Estimates

ANN Estimates of Permeability

0 20 40 60 80 100 120 140 1600

1

2

3

4

5

6

7Sample TW Res Semivariogram

Distance (mm)

Sem

ivar

ianc

e

Model: Exponential

Range: 76

Nugget: 0.4

Sill: 5

Cokriged Estimates of Permeability

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

Department of Civil &

Environmental Engineering

Donna Rizzo Paula Mouser

Department of Geology

Department of Biology

Lori Stevens

Brooke Schwartz

Patrick O’Grady

Greg Druschel

Cassella Waste Services

Schuyler Landfill, N.Y.

Bernie Nadeau

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

contaminated groundwatercontaminated groundwater

Long Term Monitoring Challenges at Long Term Monitoring Challenges at LandfillsLandfills

What do you monitor in landfill leachate? What do you monitor in landfill leachate? What are the monitoring objectives?What are the monitoring objectives? Monitoring for how long and at what Monitoring for how long and at what

frequency?frequency?

MotivationMotivation

Microbial diversity can be leveraged between Microbial diversity can be leveraged between clean and contaminated environments.clean and contaminated environments.

PCA - HydrochemistryPCA - Hydrochemistry

Contaminated Locations Contaminated Locations Separate Across PC1Separate Across PC1

Fringe Locations Not Fringe Locations Not Separated Across PC1-PC3Separated Across PC1-PC3

60% Variance Explained 60% Variance Explained in first 2 PCsin first 2 PCs

PC1 CorrelationsPC1 Correlations TDS, Mg, Cl, Spec Cond, TDS, Mg, Cl, Spec Cond,

Hardness, Alkalinity, COD, Hardness, Alkalinity, COD, TOC, NH3TOC, NH3

PC2 CorrelationsPC2 Correlations Organic-N, PhenolsOrganic-N, Phenols

PCA - All DataPCA - All Data

Clean, Fringe, and Contaminated Clean, Fringe, and Contaminated Locations Separated in PC1-PC2Locations Separated in PC1-PC2

22% Variance Explained22% Variance Explained PC1 CorrelationsPC1 Correlations

TDS, Mg, Spec Cond, Alkalinity, Na, Cl, TDS, Mg, Spec Cond, Alkalinity, Na, Cl, Hardness, COD, TOC, NHHardness, COD, TOC, NH33, Eh, Mn, SO, Eh, Mn, SO44

G505, B244, B122, G80, B168, G165, G505, B244, B122, G80, B168, G165, A244A244

PC2 CorrelationsPC2 Correlations Fe, NOFe, NO33, pH, pH B121, B160, G424, A118, G510, A144, B121, B160, G424, A118, G510, A144,

B492, G484, B279, B470B492, G484, B279, B470

Delineating contamination at landfill Delineating contamination at landfill sites without prior knowledgesites without prior knowledge

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

MotivationMotivation

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

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

Andrea Pearce

Kohonen self-organizing Kohonen self-organizing mapmap

o Non parametric clustering algorithm - useful when groupings unknowno Unsupervised ANNUnsupervised ANNo Usages: complex non-linear mappings, Usages: complex non-linear mappings,

data compression, clusteringdata compression, clusteringo Disparate data typesDisparate data typeso Used in ecological studies to model Used in ecological studies to model

benthic macro invertebrates in streams benthic macro invertebrates in streams Park et al.Park et al. (2003) and (2003) and GevreyGevrey et al.et al. (2004)(2004)

small medium big 2 legs 4 legs hair hooves mane feathers hunt run fly swimdove 1 0 0 1 0 0 0 0 1 0 0 1 0hen 1 0 0 1 0 0 0 0 1 0 0 0 0

duck 1 0 0 1 0 0 0 0 1 0 0 1 1goose 1 0 0 1 0 0 0 0 1 0 0 1 1

owl 1 0 0 1 0 0 0 0 1 1 0 1 0hawk 1 0 0 1 0 0 0 0 1 1 0 1 0eagle 0 1 0 1 0 0 0 0 1 1 0 1 0

fox 0 1 0 0 1 1 0 0 0 1 0 0 0dog 0 1 0 0 1 1 0 0 0 0 1 0 0wolf 0 1 0 0 1 1 0 0 0 1 1 0 0cat 1 0 0 0 1 1 0 0 0 1 0 0 0

tiger 0 0 1 0 1 1 0 0 0 1 1 0 0lion 0 0 1 0 1 1 0 1 0 1 1 0 0

horse 0 0 1 0 1 1 1 1 0 0 1 0 0zebra 0 0 1 0 1 1 1 1 0 0 1 0 0

cow 0 0 1 0 1 1 1 0 0 0 0 0 0

Kohonen’s Animal Example

Output Space2D Map

6 features per sampling location25 sampling locations

The Self-Organizing Map

W(i,j,1)

W(i,j,2)

W(i,j,3)

W(i,j,4)

W(i,j,5)

Small

Medium

4-legs

2-legs

Big

Hair

W(i,j,6)

The algorithm finds the best matching node on the output map…

Output Space2D Map

6 features per sampling location25 sampling locations

The Self-Organizing Map

W(i,j,1)

W(i,j,2)

W(i,j,3)

W(i,j,4)

W(i,j,5)

W(i,j,6)

…and updates weights in the neighborhood of that node.

Small

Medium

4-legs

Big

Hair

2-legs

Kohonen’s Animal ExampleUnified Distance Matrix (U-Matrix)

Kohonen’s Animal ExampleComponent Planes

Cyanobacteria Blooms Cyanobacteria Blooms and Cyanotoxin and Cyanotoxin

ProductionProduction

www.lcbp.orgA bloom near Venise-en-Quebec in August, 2008.

Credit: Quebec Ministry of Sustainable Development, Environment and Parks.

•We will cluster samples based on cyanobacterial communities using a Self-Organizing Map (SOM)•Then compare the clusters to measured cyanotoxin concentrations

Advances in Watershed Advances in Watershed Management and Fluvial Management and Fluvial Hazard Mitigation Using Hazard Mitigation Using

Artificial NeuralArtificial Neural Networks Networks and Remote Sensingand Remote Sensing

Lance BesawLance Besaw11, Donna M. Rizzo, Donna M. Rizzo11, Michael Kline, Michael Kline33, Kristen , Kristen UnderwoodUnderwood44, Leslie Morrissey, Leslie Morrissey22 and Keith Pelletier and Keith Pelletier22

11College of Engineering and Mathematics, University of Vermont, College of Engineering and Mathematics, University of Vermont, Burlington, VTBurlington, VT22 Rubenstein School of Natural Resources,University of Vermont, Burlington, VT33River Management Program, Vermont Agency of Natural Resources, River Management Program, Vermont Agency of Natural Resources, Waterbury, VTWaterbury, VT44South Mountain Research & Consulting, Bristol, VTSouth Mountain Research & Consulting, Bristol, VT

Stressors Leading Stressors Leading toto

Channel InstabilityChannel Instability Increased hydraulic loading Increased hydraulic loading (climatic and % impervious)(climatic and % impervious)

Increased sediment loadsIncreased sediment loads Channelization / Channelization /

StraighteningStraightening Floodplain encroachmentFloodplain encroachment Loss of riparian bufferLoss of riparian buffer Channel ArmoringChannel Armoring Undersized bridges / culverts Undersized bridges / culverts

(constriction)(constriction)• Instability resulting from multiple (natural and human) stressors causes natural and human) stressors causes stream to move out of dynamic stream to move out of dynamic equilibrium. equilibrium.

•The State of Vermont wants to make The State of Vermont wants to make reasonable predictions of instability.reasonable predictions of instability.

Vermont Agency of Natural ResourcesVermont Agency of Natural ResourcesRiver Management ProgramRiver Management Program

Channel and watershed Channel and watershed managementmanagement Channel dynamic equilibriumChannel dynamic equilibrium Avoid infrastructure disastersAvoid infrastructure disasters

State wide data State wide data collectioncollection

Expert assessmentsExpert assessments Fluvial erosion hazard mappingFluvial erosion hazard mapping Stakeholder Planning ToolStakeholder Planning Tool

Data driven, translate to multiple geographic locationsData driven, translate to multiple geographic locations GIS-based for visualization, quantification, communication, prioritizationGIS-based for visualization, quantification, communication, prioritization Incorporate process-based classification of river networksIncorporate process-based classification of river networks Real-time, multiple-objective management decisionsReal-time, multiple-objective management decisions

http://www.anr.state.vt.us/dec/waterq/rivers.htmhttp://www.anr.state.vt.us/dec/waterq/rivers.htm

State Wide Stream AssessmentsState Wide Stream Assessments

o Phase 1 – watershed and Phase 1 – watershed and channel corridor featureschannel corridor featureso Land cover/useLand cover/useo SinuositySinuosityo Channel slopeChannel slopeo Geologic soils, etcGeologic soils, etc

o Phase 2 - Field assessmentPhase 2 - Field assessmento Incision ratioIncision ratioo Access to flood plainAccess to flood plaino Grain size distribution, etcGrain size distribution, etco Rapid geomorphic Rapid geomorphic

assessment (RGA)assessment (RGA)

Stream SensitivityStream Sensitivity Likelihood of stream adjustment in response Likelihood of stream adjustment in response

to watershed or local stressors to watershed or local stressors fluvial fluvial erosion hazard ratings, water quality, erosion hazard ratings, water quality, habitat indiceshabitat indices

Based on…Based on… Inherent vulnerability – hydraulic geometry and Inherent vulnerability – hydraulic geometry and

sediment regimesediment regime Geomorphic condition– degree of departure from Geomorphic condition– degree of departure from

dynamic equilibrium (or reference condition)dynamic equilibrium (or reference condition) Based on research findings from Based on research findings from LaneLane

(1955), (1955), SchummSchumm (1977), Knighton (1988), (1977), Knighton (1988), RosgenRosgen (1996), Simon and Thorne (1996), (1996), Simon and Thorne (1996), Montgomery and BuffingtonMontgomery and Buffington (1997), (1997), MacBroom (1998) and others. MacBroom (1998) and others.

Hierarchical ANNs for Stream Hierarchical ANNs for Stream SensitivitySensitivity

Entrenchment ratioWidth/depth ratio

SinuositySlope

Channel material………

Impervious areaRiparian vegetation

…

Inherent VulnerabilitySingle/multiple threads

(g) Stream Sensitivity SOM

Geomorphic Condition

…

Degradation

Aggradation

Widening

Planform Change

34

21 4

3

412243

32

22

23

3

N

EW

S

1 0 1 2 Miles

Reach-based Subwatersheds

ANN Assigned Vulnerability1234567

Middlebury River and Major Tributaries

Shading indicates ANN-assignedVulnerability Ranking from 1 to 7

Numbers Indicate ANN-assigned Geomorphic ConditionRanking from 1 to 4

LEGEND

Stream Sensitivity

Remote Sensing – Sensitivity Remote Sensing – Sensitivity AnalysisAnalysis

o Light Detection and Light Detection and Ranging (LIDAR)Ranging (LIDAR)o Aid land use/land cover Aid land use/land cover

classificationsclassificationso More accurately computeMore accurately compute

o Valley widthValley widtho Channel/valley slopeChannel/valley slope

o Definiens eCognition – Definiens eCognition – object based classifierobject based classifiero Classify SinuosityClassify Sinuosityo Incorporate LIDAR for land Incorporate LIDAR for land

use/land cover classificationuse/land cover classification

Geomorphic ConditionGeomorphic ConditionDegradation / IncisionDegradation / Incision

AggradationAggradation

Over-WideningOver-Widening

Planform ChangePlanform Change

Geomorphic Condition ANN Geomorphic Condition ANN InputsInputs

Rapid Geomorphic Assessment:Rapid Geomorphic Assessment:

ranks dominant process of adjustment ranks dominant process of adjustment (degradation, aggradation, widening, and (degradation, aggradation, widening, and planform change) and stage of channel evolutionplanform change) and stage of channel evolution

http://www.anr.state.vt.us/dec/waterq/rivers.htm

Reach-level Condition

Input Code

RGA score quartile (VTDEC, 2002)

Poor 1 1 to 5 Fair 2 6 to 10

Good 3 11 to 15 Optimal 4 16 to 20

Input

Pattern

Channel Degradation

Channel Aggradation

Channel Widening

Planform Change

Scores

InputLayer

OutputLayer

HiddenLayer

OutputPattern

0.4

0.1

0.3

0.2

yGeomorphic

Condition

TargetPattern

0

1

0

0

15

12

9

14

Predicting Geomorphic ConditionPredicting Geomorphic Condition

Adjust internal weights

OutputPattern

0

1

0

0

y

Geomorphic Condition ANN: Example

Burlington

Lewis Creek

Middlebury River

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

Geomorphic Condition ANN Geomorphic Condition ANN ResultsResults

RR22 = 0.854 = 0.854

Geomorphic Condition of Middlebury River

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Stream Reaches

Cla

ssif

icat

ion

Average Expert Opinion ANN Trained on LC

Inherent Vulnerability ANNInherent Vulnerability ANN(Combined Rosgen and Montgomery & (Combined Rosgen and Montgomery &

Buffington)Buffington)

o Trained to be Trained to be Quality AssuranceQuality Assurance look-up table look-up tableo Predict stream inherent vulnerability on 789 VT Predict stream inherent vulnerability on 789 VT

reachesreacheso Prediction AccuracyPrediction Accuracy

o 80% classification agreement with recorded field data 80% classification agreement with recorded field data o 12% due to imprecise parameter boundaries (overlap)12% due to imprecise parameter boundaries (overlap)o 8% due to data transfer mistakes (or additional expert 8% due to data transfer mistakes (or additional expert

knowledge)knowledge)

Single/multiple channel(s)Entrenchment ratio

Width/depth ratioSinuosity

SlopeChannel material

…

Inherent Vulnerability

Stream Interpretation Quality Stream Interpretation Quality AssuranceAssurance

(g) Stream Sensitivity SOM

Geomorphic Condition

…

Entrenchment ratioWidth/depth ratio

SinuositySlope

Channel material

………

Impervious areaRiparian vegetation

…

Inherent VulnerabilitySingle/multiple threads

Degradation

Aggradation

Widening

Planform Change

Hierarchical ANNs for Stream SensitivityHierarchical ANNs for Stream Sensitivity

ANN Predictions

Experts

  ExtremeVery High High Moderate Low

Very Low

Extreme 9 44 13 0 0 0

Very High 2 284 44 1 0 0

High 1 37 231 20 0 0

Moderate 0 4 27 58 0 0

Low 1 0 3 1 0 0

Very Low 0 1 0 0 2 6

o Predicting Stream Sensitivity (789 reaches)Predicting Stream Sensitivity (789 reaches)o 75% classification agreement75% classification agreemento 22% differ by 1 class22% differ by 1 classo 3% differ by >1 class3% differ by >1 class

Hierarchical ANNs for Stream Hierarchical ANNs for Stream SensitivitySensitivity

Self-organizing mapSelf-organizing map

Inherent Vulnerability

Geomorphic Condition

Input nodes

Inputs

Nc

ic

Kohonen hidden nodes

Low & Very Low

Moderate

HighHigh

Very High

High

Very High &

Extreme

Extreme

ConclusionsConclusions

ANNs are data-driven (flexible and simple to ANNs are data-driven (flexible and simple to modify enabling a truly adaptive management modify enabling a truly adaptive management approach)approach)

Can be modified to recognize when a change in Can be modified to recognize when a change in scale has occurredscale has occurred

Process of trainingProcess of training

- elicits significance of governing factors in - elicits significance of governing factors in determination of sensitivitydetermination of sensitivity

- helps document similarities/differences- helps document similarities/differences among experts (and weighting of parameters among experts (and weighting of parameters

for classifying vulnerability, condition, andfor classifying vulnerability, condition, and overall sensitivity overall sensitivity

o VT Agency of Natural Resources, River Management ProgramVT Agency of Natural Resources, River Management Programo USGSUSGSo NSF EPSCoR Graduate Research AssistantshipNSF EPSCoR Graduate Research Assistantship o Evan Fitzgerald; School of Natural Resources, University of Evan Fitzgerald; School of Natural Resources, University of

Vermont, Burlington, VTVermont, Burlington, VTo Jeff Doris; Sanborn, Head and Associates, Randolph, VTJeff Doris; Sanborn, Head and Associates, Randolph, VT

AcknowledgementsAcknowledgements

QuestionsQuestions

ReferencesReferenceso Gevrey, M., Rimet, F., Park, Y. S., Giraudel, J.-L., Ector, L., and Lek, S. Gevrey, M., Rimet, F., Park, Y. S., Giraudel, J.-L., Ector, L., and Lek, S.

(2004). "Water quality assessment using diatom assemblages and (2004). "Water quality assessment using diatom assemblages and advanced modelling techniques." advanced modelling techniques." Freshwater BiologyFreshwater Biology, 49, 208-220., 49, 208-220.

o Kohonen, T. (1989). Self-Organization and Associative Memory, Kohonen, T. (1989). Self-Organization and Associative Memory, Springer Verlag, New York.Springer Verlag, New York.

o Lane, E.W. (1955) “The importance of fluvial morphology in hydraulic Lane, E.W. (1955) “The importance of fluvial morphology in hydraulic engineering.” engineering.” Proceedings of the Ammerican Society of Civil Proceedings of the Ammerican Society of Civil Engineers, Journal of the Hydraulics Division,Engineers, Journal of the Hydraulics Division, (81), paper no. 745. (81), paper no. 745.

o Montgomery, D. R. and Buffington, J. M. (1997) “Channel-reach Montgomery, D. R. and Buffington, J. M. (1997) “Channel-reach morphology in mountain drainage basins.” morphology in mountain drainage basins.” Geological Society of Geological Society of America Bulletin, America Bulletin, 109(5), 596-611.109(5), 596-611.

o Park, Y.-S., Cereghino, R., Compin, A., and Lek, S. (2003). Park, Y.-S., Cereghino, R., Compin, A., and Lek, S. (2003). "Applications of artificial neural networks for patterning and "Applications of artificial neural networks for patterning and predicting aquatic insect species richness in running waters." predicting aquatic insect species richness in running waters." Ecological Modelling,Ecological Modelling, 160, 265-280. 160, 265-280.

o Rosgen, D. L. (1996) Rosgen, D. L. (1996) Applied Fluvial MorphologyApplied Fluvial Morphology, Wildland Hydrology, , Wildland Hydrology, Pasoda Springs, CO.Pasoda Springs, CO.

o Schumm, S. A. (1977) Schumm, S. A. (1977) The Fluvial SystemThe Fluvial System, John Wiley and Sons, New , John Wiley and Sons, New York, NY.York, NY.