Erin Peterson Environmental Risk Technologies CSIRO Mathematical & Information Sciences St Lucia,...

Erin Peterson

Environmental Risk Technologies

CSIRO Mathematical & Information Sciences

St Lucia, Queensland

Predicting Water Quality Impaired Stream Segments using

Landscape-scale Data and a Regional Geostatistical Model

The work reported here was developed under STAR Research Assistance Agreement CR-829095 awarded by the U.S.

Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by

EPA. EPA does not endorse any products or commercial services mentioned in this presentation.

Space-Time Aquatic Resources Modeling and Analysis Program

This research is funded by

U.S.EPA凡Science To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095

This research is funded by

U.S.EPAScience To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095

Collaborators

Dr. David M. TheobaldNatural Resource Ecology LabDepartment of Recreation & TourismColorado State University, USA

Dr. N. Scott UrquhartDepartment of StatisticsColorado State University, USA

Dr. Jay M. Ver HoefNational Marine Mammal Laboratory, Seattle, USA

Andrew A. MertonDepartment of StatisticsColorado State University, USA

Introduction~

Background~

Patterns of spatial autocorrelation in stream

water chemistry~

Predicting water quality impaired stream segments using landscape-scale data and a regional geostatistical

model: A case study in Maryland, USA

Overview

Water Quality Monitoring Goals

• Create a regional water quality assessment• Ecosystem Health Monitoring Program

• Identify water quality impaired stream segments

Probability-based Random Survey Designs

Advantages• Statistical inference about population of streams over

large area• Reported in stream kilometers

Disadvantages

• Does not take watershed influence into account• Does not identify spatial location of impaired stream

segments

Purpose

Develop a geostatistical methodology based on coarse-scale GIS data and field surveys that can be used to predict water

quality characteristics about stream segments found throughout a large geographic area (e.g., state)

SCALE: Grain

Substrate

Biotic Condition

OverhangingVegetation

Segment

River Network

Network Connectivity

Tributary Size DifferencesNetwork Geometry

Stream Network

ConnectivityFlow Direction Network Configuration

Drainage DensityConfluence Density

Cross Sectional AreaChannel Slope, Bed MaterialsLarge Woody Debris

Biotic Condition, Substrate Type, Overlapping VegetationDetritus, Macrophytes

Microhabitat

Segment Contributing Area

Riparian Vegetation Type & ConditionFloodplain / Valley Floor Width

Localized DisturbancesLand Use/ Land Cover

Landscape

ClimateAtmospheric depositionGeology

TopographySoil Type

Microhabitat

ShadingDetritus Inputs

Riparian Zone

Nested Watersheds

Land UseTopography

Vegetation TypeBasin Shape/Size

COARSE

FINE

Reach

AquaticTerrestrial

Fit an autocovariance function to data• Describes relationship between observations based on

separation distance

Geostatistical Modeling

Separation Distance

Sem

ivar

ian

ce

Sill

Nugget Range

10000

0

10

Distances and relationships are represented differently depending on the distance measure

Distance Measures & Spatial Relationships

A

B

C

Straight-line Distance (SLD)Geostatistical models typically based on SLD

A

B

C

Symmetric Hydrologic Distance (SHD)Hydrologic connectivity: Fish movement


A

B

C

Asymmetric Hydrologic DistanceLongitudinal transport of material


A

B

C

Challenge: • Spatial autocovariance models developed for SLD may

not be valid for hydrologic distances– Covariance matrix is not positive definite


Asymmetric Autocovariance Models for Stream Networks

• Weighted asymmetric hydrologic distance (WAHD)

• Developed by Jay Ver Hoef

• Moving average models

• Incorporate flow volume, flow direction, and use hydrologic distance

• Positive definite covariance matrices

Flow

Ver Hoef, J.M., Peterson, E.E., and Theobald, D.M., Spatial Statistical Models that Use Flow and Stream Distance, Environmental and Ecological Statistics. In Press.

Patterns of Spatial Autocorrelation in Stream Water Chemistry

Evaluate 8 chemical response variables1. pH measured in the lab (PHLAB)2. Conductivity (COND) measured in the lab μmho/cm3. Dissolved oxygen (DO) mg/l4. Dissolved organic carbon (DOC) mg/l5. Nitrate-nitrogen (NO3) mg/l6. Sulfate (SO4) mg/l7. Acid neutralizing capacity (ANC) μeq/l8. Temperature (TEMP) °C

Determine which distance measure is most appropriate• SLD• SHD• WAHD• More than one?

Find the range of spatial autocorrelation

Objectives

Dataset

Maryland Biological Stream Survey (MBSS) Data

• Maryland Department of Natural Resources– Maryland, USA – 1995, 1996, 1997

• Stratified probability-based random survey design

• 881 sites in 17 interbasins

Baltimore

Annapolis

Washington D.C.Chesapeake Bay

Maryland, USA

Study Area

Spatial Distribution of MBSS Data

N

GIS ToolsAutomated tools needed to extract data about hydrologic relationships

between survey sites did not exist!

Wrote Visual Basic for Applications (VBA) programs to:

1. Calculate watershed covariates for each stream segment• Functional Linkage of Watersheds and Streams (FLoWS)

2. Calculate separation distances between sites• SLD, SHD, Asymmetric hydrologic distance (AHD)

3. Calculate the spatial weights for the WAHD4. Convert GIS data to a format compatible with statistics software

FLoWS tools will be available on the STARMAP website:http://nrel.colostate.edu/projects/starmap

1 2

3

1 2

3

SLD

1 2

3

SHD AHD

http://nrel.colostate.edu/projects/starmap

Spatial Weights for WAHD

Proportional influence (PI): influence of each neighboring survey site on a downstream survey site• Weighted by catchment area: Surrogate for flow volume

1. Calculate the PI of each upstream segment on segment directly downstream

2. Calculate the PI of one survey site on another site• Flow-connected sites• Multiply the segment PIs

BA

C

Watershed Segment B

Watershed Segment A

Segment PI of A

Watershed Area A

Watershed Area B=


A

BC

DE

F

G

H

survey sitesstream segment





A

BC

DE

F

G

H

Site PI = B * D * F * G




Data for Geostatistical Modeling

1. Distance matrices• SLD, SHD, AHD

2. Spatial weights matrix• Contains flow dependent weights

for WAHD

3. Watershed covariates • Lumped watershed covariates

– Mean elevation, % Urban

4. Observations• MBSS survey sites

Validation Set• Unique for each chemical response variable

Initial Covariate Selection• 5 covariates

Model Development• Restricted model space to all possible linear models• 4 model sets:

Response Significant CovariatesANC (μeq/l) PASTUR, LOWURB, WOODYWET, YR96, YR97COND (μmho/cm) HIGHURB, LOWURB, COALMINE, YR96, NORTHINGDOC (mg/l) WOODYWET, CONIFER, MIXEDFOR, LOWURB, NORTHINGDO (mg/l) DECIDFOR, HIGHURB, WOODYWET, YR96, YR97NO3 (mg/l) PASTUR, PROBCROP, ROWCROP, LOWURB, WATERpH Lab PROBCROP, DECIDFOR, WOODYWET, ACREAGE, CONIFERSO4 (mg/l) LOWURB, COALMINE, NORTHING, ER67, ER69TEMP (°C) PROBCROP, LOWURB, WATER, YR96, YR97

Geostatistical Modeling Methods

Geostatistical model parameter estimation• Maximize the profile log-likelihood function


Log-likelihood function of the parameters ( ) given the observed data Z is:2, ,

)()'(2

1log

2

1)2log(

2);,,( 1

222

XZXZ

nZ

Maximizing the log-likelihood with respect to B and sigma2 yields:

2log

2

1)ˆlog(

2)2log(

2),ˆ,ˆ;( 22 nnnZprofile

ZXXX 111 ')'(ˆ 1

2ˆ ˆ( ) ' ( )

ˆZ X Z X

n

and

Both maximum likelihood estimators can be written as functions of alone

Derive the profile log-likelihood function by substituting the MLEs ( ) back into the log-likelihood function

2ˆ ˆ,

Covariance matrix for SLD and SHD models• Fit exponential autocorrelation function

1 1 21 2

1 if 0( ; , )

(1 )exp( / ) if 0

hC h

h h

where C1 is the covariance based on the distance between two sites, h, given the autocorrelation parameter estimates: nugget ( ), sill ( ), and range ( ).0 1 2


1 0

1

0 locations are not flow connected,

( , | ) (0) if location 1 = location 2,

( ) otherwise.D

i j

j B j

C s s C

w C h

Covariance matrix for WAHD model• Fit exponential autocorrelation function (C1)• Hadamard (element-wise) product of C1 & square root of spatial

weights matrix forced into symmetry ( )Dj B jw


Model selection between model types• 100 Predictions: Universal kriging algorithm • Mean square prediction error (MSPE)• Cannot use AICC to compare models based on different distance

measures

Model comparison: r2 for observed vs. predicted values

Model selection within model set• GLM: Akaike Information Corrected Criterion (AICC)• Geostatistical models: Spatial AICC (Hoeting et al., in press)

2

12),,;(2 2

kpn

kpnZAICC profile

where n is the number of observations, p-1 is the number of covariates, and k is the number of autocorrelation parameters.

http://www.stat.colostate.edu/~jah/papers/spavarsel.pdf

Results

Summary statistics for distance measures• Spatial neighborhood differs• Affects number of neighboring sites• Affects median, mean, and maximum separation distance

* Asymmetric hydrologic distance is not weighted here

Summary statistics for distance measures in kilometers using DO (n=826).

Distance Measure N Pairs Min Median Mean Max

Straight Line Distance 340725 0.05 101.02 118.16 385.53

Symmetric Hydrologic Distance 62625 0.05 156.29 187.10 611.74

Pure Asymmetric * Hydrologic Distance 1117 0.05 4.49 5.83 27.44

SLD

SHD

WAHD

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

ANC COND DOC DO NO3 PHLAB SO4 TEMP

Ran

ge

(km

)

180.79 301.76

Range of spatial autocorrelation differs:• Shortest for SLD• TEMP = shortest range values• DO = largest range values

Results

Mean Range ValuesSLD = 28.2 kmSHD = 88.03 kmWAHD = 57.8 km

ANC

0.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

GLM SL SH WAH

COND

0.00

5000.00

10000.00

15000.00

20000.00

25000.00

30000.00

35000.00

40000.00

GLM SL SH WAH

DOC

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

GLM SL SH WAH

DO

0.00

0.50

1.00

1.50

2.00

2.50

GLM SL SH WAH

NO3

0.00

0.20

0.40

0.60

0.80

1.00

1.20

GLM SL SH WAH

SO4

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

GLM SL SH WAH

TEMP

6.50

7.00

7.50

8.00

8.50

9.00

GLM SL SH WAH

PHLAB

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

GLM SL SH WAH

MS

PE

GLM

SLD

SHD

WAHD

Distance Measures: • GLM always has less predictive ability• More than one distance measure usually performed well

• SLD, SHD, WAHD: PHLAB & DOC• SLD and SHD : ANC, DO, NO3• WAHD & SHD: COND, TEMP

• SLD distance: SO4

Results

Strong: ANC, COND, DOC, NO3, PHLAB Weak: DO, TEMP, SO4

GLM

SLD

SHD

WAHD

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

ANC COND DOC DO NO3 PHLAB SO4 TEMP

R2r2

Results

r2 Predictive ability of models:

Discussion

• Site’s relative influence on other sites• Dictates form and size of spatial neighborhood

Important because…• Impacts accuracy of the geostatistical model predictions

Distance measure influences how spatial relationships are represented in a stream network

SHD WAHDSLD

SLD

SHD

• Geostatistical models describe more variability than GLM

Patterns of spatial autocorrelation found at relatively coarse scale

• > 1 distance measure performed well• SLD never substantially inferior• Do not represent movement through network

Different range of spatial autocorrelation?• Larger SHD and WAHD range values • Separation distance larger when restricted to

network

SLD, SHD, and WAHD represent spatial autocorrelation in continuous coarse-scale variables

Discussion

Probability-based random survey design (-) affected WAHD• Maximize spatial independence of sites

• Does not represent spatial relationships in networks

• Validation sites randomly selected

0 2

244

149133

109

66

38 32

12 7

3519 15 13 6 1 0

0

275

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Fre

quen

cy

Number of Neighboring Sites

244 sites did not have neighbors Sample Size = 881Number of sites with ≤1 neighbor: 393Mean number of neighbors per site: 2.81

Discussion

0

45004500

0

Diff

ere

nce

(O

– E

)


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1715 16

WAHD GLM

Not when neighbors had:• Similar watershed conditions• Significantly different chemical response values

WAHD models explained more variability as neighboring sites increased

GLM predictions improved as number of neighbors increased

• Clusters of sites in space have similar watershed conditions– Statistical regression pulled towards the cluster

• GLM contained hidden spatial information– Explained additional variability in data with > neighbors

Discussion

0

45004500

0


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1715 16

WAHD GLM

Diff

ere

nce

(O

– E

)

Predictive Ability of Geostatistical Models

r2

PH

Coarse

Fine

Sca

le o

f in

flue

ntia

l e

colo

gic

al p

roce

sse

s ANC

NO3

COND

DOC

SO4

DO

0 0.5 1.0

TEMP

Conclusions

1) Spatial autocorrelation exists in stream chemistry data at a relatively coarse scale

2) Geostatistical models improve the accuracy of water chemistry predictions

3) Patterns of spatial autocorrelation differ between chemical response variables• Ecological processes acting at different spatial scales

4) SLD is the most suitable distance measure at regional scale at this time• Unsuitable survey designs• SHD: GIS processing time is prohibitive

Conclusions

5) Results are scale specific• Spatial patterns change with survey scale• Other patterns may emerge at shorter separation distances

6) Further research is needed at finer scales• Watershed or small stream network

7) New survey designs for stream networks• Capture both coarse and fine scale variation• Ensure that hydrologic neighborhoods are represented

Predicting Water Quality Impaired Stream Segments using

Landscape-scale Data and a Regional Geostatistical Model: A Case Study In

Maryland

Objective

Demonstrate how a geostatistical methodology can be used to compliment regional water quality monitoring efforts

1) Predict regional water quality conditions

2) Identify the spatial location of potentially impaired stream segments

N

1996 MBSS DOC Data

0 20

Kilometers

n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8

Potential covariates

Covariate DescriptionSpatial Resolution

AREA Catchment area (ha) 30 meterURBAN % Urban 30 meterBARREN % Barren 30 meterWATER % Open Water 30 meterCONIFER % Conifer or evergreen forest type 30 meterDECIDFOR % Deciduous forest type 30 meterMIXEDFOR % Mixed forest type 30 meterEMERGWET % Emergent Herbacious Wetlands 30 meterWOODYWET % Woody or shrubby wetlands 30 meterCOALMINE % Coalmine 30 meterEASTING Easting - Albers Equal Area Conic 1 footNORTHING Northing - Albers Equal Area Conic 1 footER63-ER69 Omernik's Level III Ecoregion 1:7,500,000MEANELEV Mean elevation in the watershed 30 meterSLOPE Mean slope in the watershed 30 meterARGPERC % Argillaceous rock type in watershed 1:250,000CARPERC % Carbonic rock type in watershed 1:250,000FELPERC % Felsic rock type in watershed 1:250,000MAFPERC % Mafic rock type in watershed 1:250,000SILPERC % Siliceous rock type in watershed 1:250,000

MEANKMean soil erodability factor in watershed (adjusted for rock fragments) 1 kilometer

MAXTEMP Mean annual maximum temperature (°C) 4 kilometerMINTEMP Mean minimum temperature for January - April (°C) 4 kilometerPRECIP Mean precipitation for January - April (mm) 4 kilometerANPRECIP Mean annual precipitation 4 kilometer

Methods

Potential covariates after initial model selection (10)

Covariate DescriptionSpatial Resolution

AREA Catchment area (ha) 30 meterURBAN % Urban 30 meterBARREN % Barren 30 meterWATER % Open Water 30 meterCONIFER % Conifer or evergreen forest type 30 meterDECIDFOR % Deciduous forest type 30 meterMIXEDFOR % Mixed forest type 30 meterEMERGWET % Emergent Herbacious Wetlands 30 meterWOODYWET % Woody or shrubby wetlands 30 meterCOALMINE % Coalmine 30 meterEASTING Easting - Albers Equal Area Conic 1 footNORTHING Northing - Albers Equal Area Conic 1 footER63-ER69 Omernik's Level III Ecoregion 1:7,500,000MEANELEV Mean elevation in the watershed 30 meterSLOPE Mean slope in the watershed 30 meterARGPERC % Argillaceous rock type in watershed 1:250,000CARPERC % Carbonic rock type in watershed 1:250,000FELPERC % Felsic rock type in watershed 1:250,000MAFPERC % Mafic rock type in watershed 1:250,000SILPERC % Siliceous rock type in watershed 1:250,000

MEANKMean soil erodability factor in watershed (adjusted for rock fragments) 1 kilometer

MAXTEMP Mean annual maximum temperature (°C) 4 kilometerMINTEMP Mean minimum temperature for January - April (°C) 4 kilometerPRECIP Mean precipitation for January - April (mm) 4 kilometerANPRECIP Mean annual precipitation 4 kilometer

Methods

Fit geostatistical models• Two distance measures: SLD and

WAHD

Restricted model space to all possible linear models

• 1024 models per set • 9 model sets

Parameter Estimation• Maximized profile log-likelihood

function

Methods

Autocorrelation Function SLD WAHD

Exponential

Spherical

Mariah

Hole Effect

Linear with Sill

Rational Quadratic

Methods

• Spatial AICC (Hoeting et al., in press)

Model selection within distance measure & autocorrelation function

Model selection between distance measure & autocorrelation function• Cross-validation method using Universal kriging algorithm

– 312 predictions• MSPE

Model comparison: r2 for the observed vs. predicted values

Results

SLD models performed better than WAHD

Exception: Spherical model

Best models:• SLD Exponential, Mariah,

and Rational Quadratic models

r2 for SLD model predictions• Almost identical• Further analysis restricted

to SLD Mariah model

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6

SLD

WAHD

Exp

on

enti

al

Sp

her

ical

Mar

iah

Ho

le E

ffec

t

Lin

ear

wit

h S

ill

Rat

ion

al

Qu

adra

tic

Autocorrelation Function

MS

PE

ExponentialRational

Quadratic MariahExponential 1 0.997 0.990Rational Quadratic 1 0.993Mariah 1

Results

Covariates for SLD Mariah model:WATER, EMERGWET, WOODYWET, FELPERC, & MINTEMP

Positive relationship with DOC:• WATER, EMERGWET, WOODYWET, MINTEMP

Negative relationship with DOC• FELPERC

Nugget Sill Range Intercept WATER EMERGWET WOODYWET FELPERC MINTEMP

0.15 0.28 7.02 0.28 0.05 0.04 0.02 -0.0005 0.07

Cross-validation interval: 95% of regression coefficients produced by leave-one-out cross validation procedure

Narrow intervals• Few extreme regression coefficient values

– Not produced by common sites– Covariate values for the site are represented in observed data– Not clustered in space

Cross-validation intervals for Mariah model regression coefficients

Statistic WATER (%) EMERGWET (%) WOODYWET (%) FELPERC (%) MINT (°C)Minimum 0.0469 0.0306 0.0156 -0.0006 0.0616Maximum 0.0537 0.0425 0.0187 -0.0004 0.071Mean 0.0501 0.0344 0.0176 -0.0005 0.0655Standard Dev 0.0007 0.0009 0.0002 0.00005 0.000795% Lower Limit 0.0485 0.0322 0.017 -0.0006 0.064395% Upper Limit 0.0522 0.0366 0.0179 -0.0005 0.0669

Model coefficients represent change in log10 DOC per unit of X

R2 = 0.7221

0

18

0 5 10 15Observed DOC mg/l

Pre

dic

ted

DO

C m

g/l r2 = 0.7221R2 = 0.7221

0

18

0 5 10 15Observed DOC mg/l

Pre

dic

ted

DO

C m

g/l r2 = 0.7221

r2 Observed vs. Predicted Values

n = 312 sitesr2 = 0.72

1 influential siter2 without site = 0.66

Squared Prediction Error (SPE)

Model Fit

• SLD models more accurate than WAHD models

• Landscape-scale covariates were not restricted to watershed boundaries

– Geology type– Temperature– Wetlands & water

Discussion

Regression Coefficients

Narrow cross-validation intervals • Spatial location of the sites not as important as watershed

characteristics

Extreme regression coefficient values• Not produced by common sites• Not clustered in space

Local-scale factor may have affected stream DOC • Point source of organic waste

Discussion

North and east of Chesapeake Bay - large SPE values• Naturally acidic blackwater streams with elevated DOC

• Not well represented in observed dataset – 2 blackwater sites

• Geostatistical model unable to account for natural variability– Large square prediction errors

– Large prediction variances

Spatial Patterns in Model Fit

SPE values

West of Chesapeake Bay - low SPE values• Due to statistical and spatial distribution of observed data

– Regression equation fit to the mean in the data – Most observed sites = low DOC values

• Less variation in western and central Maryland – Neighboring sites tend to be similar

• Separation distances shorter in the west – Short separation distances = stronger covariances

Spatial Patterns in Model Fit

SPE values

What caused abrupt differences?• Point sources of organic pollution

– Not represented in the model

• Non-point sources of pollution– Lumped watershed attributes are non-spatial – Differences due to spatial location of landuse are not

represented– Challenging to represent ecological processes using coarse-

scale lumped attributes– i.e. Flow path of water

Model Performance

Unable to account for abrupt differences in DOC values between neighboring sites with similar watershed conditions

Generate Model Predictions

Prediction sites• Study area

– 1st, 2nd, and 3rd order non-tidal streams– 3083 segments = 5973 stream km

• ID downstream node of each segment– Create prediction site

• More than one site at each confluence

Generate predictions and prediction variances• SLD Mariah model• Universal kriging algorithm• Assigned predictions and prediction variances back to

stream segments in GIS

DOC Predictions (mg/l)

Weak Model Fit

Strong Model Fit

Water Quality Attainment by Stream Kilometers

Threshold values for DOC• Set by Maryland Department of Natural Resources• High DOC values may indicate biological or ecological stress

Theshold DOC (mg/l)Stream

Kilometers PercentLow < 5.0 5387.67 90.2Medium 5.0 - 8.0 400.19 6.7High > 8.0 185.16 3.1

Implications for Water Quality Monitoring

• Can be used to provide an estimate of regional stream DOC values• Cannot identify point sources of organic pollution

1) One geostatistical model can be used to predict DOC in stream segments throughout a large area

2) Tradeoff between cost-efficiency and model accuracyWestern Maryland

• Can be described using a single geostatistical model

Eastern and northeastern Maryland • Accept poor model fit• Collect additional survey data• Develop a separate geostatistical model for eastern Maryland

Implications for Water Quality Monitoring

3) Apply this methodology to other regulated indices

• e.g. conductivity and pH• Categorize predictions into potentially impaired or unimpaired status• Report on attainment in stream miles/kilometers

Conclusions

1) Geostatistical models generated more accurate DOC predictions than previous non-spatial models based on coarse-scale landscape data

2) SLD is more appropriate than WAHD for regional geostatistical modeling of DOC at this time• Probability-based random survey designs• Maryland, USA

3) Adds value to existing water quality monitoring efforts• Used to evaluate/report regional water quality conditions• Additional field sampling is not necessary• Generate inferences about regional stream condition • ID spatial location of potentially impaired stream segments

4) Model predictions and prediction variances• Additional field efforts concentrated in

– Areas with large amounts of uncertainty – Areas with a greater potential for water quality

impairment

5) Model results displayed visually• Communicate results to a variety of audiences

Conclusions

Questions?

Erin Peterson Environmental Risk Technologies CSIRO Mathematical & Information Sciences St Lucia,...

Documents

Transcript of Erin Peterson Environmental Risk Technologies CSIRO Mathematical & Information Sciences St Lucia,...