Data Fusion: A decision analysis tool that quantifies geological and parametric uncertainty Page: 4 of 8
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modeling, decision makers have a quantitative basis
for action so the following benefits can be realized:
" Enables remedial simulation to optimize
cleanup. Remediation solutions can be
exercised in the computer to match
quantified safety margins.
" Enables real-time monitoring during
remediation. Contaminant plumes can be
continuously monitored while they are being
cleaned up.
" Provides quantitative basis for cost
reduction/avoidance.
" Establishes data worth, before expending
funds for field data acquisition, to determine
if reduction in uncertainty pays for the cost
of acquisition.
" Derives the most out of existing data sets to
avoid cost of unnecessary acquisition.
Data Fusion and modeling have a solid
foundation in the hydrogeological community. Freeze
et.al. published a framework for hydrogeological
decision analysis in references 1 to 4. A pragmatic
engineering approach to decision making is described
that balances benefits, costs, and uncertainties. We
have adopted the decision analysis viewpoint and
approach in our Data Fusion as shown in Figure 1.1.
Engineers face uncertainty in parameters (such as
hydraulic conductivity) and in the geometry of the
problem through the geology. Data Fusion quantifies
geological and parametric uncertainty. As shown in
Figure 1.1, hydrogeological simulation is performed
(e.g., to see plume movement) using geological and
parametric inputs. Fusion propagates geological and
parametric uncertainties through the simulation so the
confidence in plume movement is quantified.
Engineering reliability uncertainties in the engineered
components of remediation also enter into decisions,
but the hydrogeological uncertainties usually
dominate.Ged.ow Paramuric
*mu n - . Rdiblity
nedde
Figure 1.1 Data Fusion Role in Decision Analysis
2. THEORY
A Data Fusion perspective is presented,
beginning with the hydrogeological foundation. Data
assimilation is described as a starting point for fusion.
Then the following fusion methods are described:
Markov Random Field (MRF) model, Square Root
Information Smoother (SRIS), and Generalized
Expectation Maximization (GEM) method.
The methodology of references 1 to 4 views
hydrogeology as a predictive science that must
incorporate the fundamental heterogeneity of the
subsurface. Consequently, hydraulic conductivity is
treated as an autocorrelated spatial stochastic process
so the variability and spatial continuity of the
conductivity is modeled.
Bayesian estimation is performed, but Freeze
et al. point out that a limitation of the Bayesian
approach is the application of inverse modeling. Data
assimilation methods incorporate inverse modeling in
a fundamental way, but they are too numerically
demanding for practical applications (see Ref. 5).
Consequently, it is not practical to combine all the
important data sets to reduce and quantify the
uncertainty in the subsurface. Data Fusion resolves
this limitation by building on data assimilation to
produce a full inverse modeling approach that is
numerically practical.
Data assimilation methods are well
established in numerical weather prediction, have
moved into physical oceanography and are being
established in hydrogeology (see Refs. 5 to 8). The
methods take many forms from adjoint to variational
to Kalman filtering.
Our Data Fusion approach provides Bayesian
inverse modeling as shown in Figure 2.1. It begins
with prior knowledge about the state variables to be -
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Porter, D.W. Data Fusion: A decision analysis tool that quantifies geological and parametric uncertainty, report, April 1, 1996; United States. (https://digital.library.unt.edu/ark:/67531/metadc675478/m1/4/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.