CRESP III RNL 03: Quantifying and Reducing Uncertainties in

Characterization, Flow-Transport Analysis and Monitoring of

Subsurface Remediation and Waste Storage Sites

CRESP III Management Board MeetingFebruary 27, 2012

PI: Shlomo P. Neuman

Dept of Hydrology and Water Resources, University of Arizona, Tucson

Project Objectives

Develop/demonstrate tools that would provide quantitative information to decision makers about uncertainties associated with

characterization, flow-transport analysis and monitoring of subsurface remediation and waste storage sites

potential of additional characterization and monitoring data to help reduce these uncertainties and risks associated with particular decisions

Relevance and Impact to DOE

Accounting for scale phenomena and the worth of data within the framework of a comprehensive risk and uncertainty assessment methodology, such as we propose, would greatly enhance confidence in DOE decisions concerning subsurface remediation and waste storage sites

Recent Accomplishments

• Pumping test inference of deep vadose zone properties

• Multimodel Bayesian method to assess the worth

of data

• Characterizing the scaling properties of hydrologic quantities varying randomly in space – time

Pumping Test Inference of Deep Vadose Zone Properties

The Problem: There presently is no good way to assess

large (field) scale vadose zone hydraulic properties at depth

Infiltration experiments and laboratory samples limited mostly to shallow depths

The Solution: Infer such properties by pumping water from saturated zone beneath deep vadose zoneWork Products: 1 doctoral dissertation, 2 papers in archival journal, 1 paper in WM2011

Pumping Test Inference of Deep Vadose Zone Properties

Borden Test Layout:

Pumping Test Inference of Deep Vadose Zone Properties

Borden Best-Fit Solution:

Pumping Test Inference of Deep Vadose Zone Properties

Borden Best-Fit Parameter Estimates:

Pumping Test Inference of Deep Vadose Zone Properties

Borden Vadose Zone Characteristic Estimates:

Multimodel Bayesian Method to Assess the Worth of Data

The Problem: Traditional worth of data analyses do not

consider conceptual & parameter uncertainties Bias and underestimation of uncertainty

The Solution: Multimodel Bayesian approach in cost-risk- benefit frameworkWork Products: 1 doctoral dissertation, 2 papers in archival journals (1 invited in special issue on risk and uncertainty assessment), 1 paper in WM2011, 1 invited paper in International Groundwater Conference proceedings

Multimodel Bayesian Method to Assess the Worth of Data

Apache Leap Research Site (ALRS) example:

-25

-20

-15

-10

-5

0

Z( m)

-100

1020

3040

-100

1020

30

W2aV2

X2Y2

Z2

Y3 Unsaturated fractured tuff

1-m-scale packer tests

Conducted with air

Matrix virtually saturated

Tests see mainly fractures

184 log10 k data

k in m2

Multimodel Bayesian Method to Assess the Worth of Data

ALRS cross validation exercise:

-25

-20

-15

-10

-5

0

Z( m)

-100

1020

3040

-100

1020

30

W2aV2

X2Y2

Z2

Y3

Cross Validation Cases

CV I: D = W2a, Y3, Z2

C1 = X2

C2 = Y2

CV II: D = W2a, X2, Y2

C1 = V2

C2 = Z2

D = given data; C = new

Given funds to drill / test

only one hole in each CV,

should it be C1 or C2?

Multimodel Bayesian Method to Assess the Worth of Data

ALRS alternative model fits:

Multimodel (variogram)

geostatistical analysis:

• Power (Pow0)

• Exponential (Exp0)

• Spherical (Sph0)

Fits based on

(a)– (b) D

(c) – (d) D + C’1

(e) – (f) D + C’2

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Separation distance (m)

Var

iogr

am

(a)

Sample variogram

Exp0

Sph0

Pow 0

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Separation distance (m)

Var

iogr

am

(c)

Sample variogram

Exp0

Sph0

Pow 0

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Separation distance (m)

Var

iogr

am

(e)

Sample variogram

Exp0

Sph0

Pow 0

0 5 10 15 20 250

0.2

0.4

0.6

0.8

Separation distance (m)

Var

iogr

am

(b)

Sample variogram

Exp0

Sph0

Pow 0

0 5 10 15 20 250

0.2

0.4

0.6

0.8

Separation distance (m)

Var

iogr

am

(d)

Sample variogram

Exp0

Sph0

Pow 0

0 5 10 15 20 250

0.2

0.4

0.6

0.8

Separation distance (m)

Var

iogr

am

(f)

Sample variogram

Exp0

Sph0

Pow 0

CV IICV I

Multimodel Bayesian Method to Assess the Worth of Data

ALRS prior & preposterior uncertainty measures:

Multimodel Bayesian Method to Assess the Worth of Data

ALRS posterior & preposterior uncertainty reduction measures:

Though preposterior and posterior measures

differ, both select borehole X2 in CV I and V2

in CV II

Scaling Properties of Space – Time Variables

The Problem: Earth and environmental variables span

multiple space – time scales Their multiscale statistics remain poorly

understoodThe Solution:

New model that unifies seemingly disparate fractal / multifractal Gaussian / non-Gaussian power-law / breakdown scaling behaviors

New statistical inference method based on it Application to synthetic / field / lab data

Work Products: Multiple papers in varied archival journals; invited / keynote talks at AGU / PEDOFRACT

Scaling Properties of Space – Time Variables

AGU Invited Talk: Are log permeabilities Gaussian? Their increments may tell.

The Problem: Log permeabilities appear to be Gaussian or

nearly so (say beta) Their increments are often heavy tailed Can these be reconciled?

The Solution: Demonstrate consistency with our scaling

model Apply model to ALRS log permeability data

Scaling Properties of Space – Time Variables

ALRS log k data are close to Gaussian

Their increments show heavy tails

Scaling Properties of Space – Time Variables

Can fit Levy distributions to increments

Levy index increases with separation

scale (lag) s toward Gaussian value of 2

Consistent with

our model and

Hurst scaling

exponent H = 0.33

Scaling Properties of Space – Time Variables

Model generated signal:

Scaling Properties of Space – Time Variables

Model generated signal:

Scaling Properties of Space – Time Variables

ALRS log k signal (highly irregular, not

unlike synthetic signal):

Scaling Properties of Space – Time Variables

We conclude:

ALRS log k is Levy with index slightly

smaller than Gaussian value of 2

Statistics of earth and environmental

variables should be inferred jointly from

data and their increments in a mutually

consistent manner

Scaling Properties of Space – Time Variables

Additional key findings:

Multifractal scaling, exhibited by many earth

and environmental variables, is fully reproduced

by our (truncated monofractal) signals; as such

it is likely an artifact of sampling

Our model reproduces observed power-law

breakdown at small / large lags

Our model is the first to explain the widely

observed phenomenon of Extended Self

Similarity (ESS)

Current / Future Efforts(with Co-PI Prof. Marcel Schaap)

• Explore extreme value statistics of measured and

synthetic signals that scale in the above manner

• Develop a data base of pedologic and hydraulic properties of samples from the Hanford 200 Area vadose zone

• Use neural network, statistical and inverse methods to estimate vadose zone hydraulic properties at Hanford 200 Area and at Maricopa, AZ.

Comment by PNNL Colleague• There was some effort to develop a database of

physical and hydraulic properties and to port these to the HEIS database. That work was supported by one of the site contractors, CHPRC.

• Unfortunately the project was discontinued in Jan 2011, after CHPRC over-ran their budget on a large-scale pump-and-treat system on site, and no data were actually put into HEIS. There has been no mention of restarting that effort.

• Unless DOE/CHPRC/other decides to fund that effort again, it will not happen.