Functional Data Analysis in Groundwater Modeling
Creators: name: Mendes, Bruno
name: Draper, David
name: Mendes, Bruno
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: In groundwater contamination studies, uncertainties are a constant
presence. We have in previous work classified the different sources of
uncertainty one can encounter in such studies 
[www.ams.ucsc.edu/~draper/writings.html items 43 and 55], and we have 
proposed a framework to tackle them involving four hierarchical layers
of uncertainty:
* Scenario (there may be uncertainty about relevant inputs to the 
physical process under study),
* Structure (conditional on scenario, the precise mathematical form of 
the best model to capture all relevant physical processes (advection,
diffusion, ...) may not be known,
* Parametric (conditional on scenario and structure, the model will
typically have one or more unknown physical constants that need to be
estimated from data), and
* Predictive (conditional on scenario, structure, and parameters, the
model predictions may still not agree perfectly with the observed data).

We have been developing work on all of these types of uncertainty and 
the present study focuses on scenario uncertainty. The set of scenarios 
we used was developed by Prado, Eguilior and Saltelli [Level E/G 
test-case specifications (GESAMAC project). CIEMAT, Madrid, 1998]; it 
consists of different sets of hydrogeological assumptions about what 
can go wrong if a deep underground storage chamber for nuclear waste 
material is breached:* Reference (Ref) Scenario (from the PSACOIN 
Level E Intercomparison (NEA PSAG User's Group 1989)); Fast Path (FP) 
Scenario (a fast pathway to the geosphere), Additional Geosphere (AG) 
Scenario (an additional geosphere layer), Glacial Advance (GA) Scenario
(related to the AG scenario but arising from an advancing rather than 
retreating glacier), Human Disposal Errors (HDE) Scenario (corresponding
to deficiencies in the construction of the repository and/or in waste 
disposal operationsleading to premature failing of the near-field 
barriers) and Environmentally Induced Changes (EIC) Scenario (arising 
from human activities or geological events that indirectly are 
responsible for the modification of the disposal system conditions).

Statistical models are often applied to sets of data with a single 
outcome variable and we have indeed performed such studies in this same 
context before [www.ams.ucsc.edu/~draper/writings.html items 43 and 55],
where we studied the values of maximum radiologic dose. In fact the 
deterministic model that we used in this study produces more informative
output than that: among other things, it produces a collection of values
for contaminant concentration for different time points, and this for a 
fixed point in space, which we take to be one at the biosphere. This 
collection of data points can be seen to approximate a continuous 
function of dose versus time. In this paper we describe statistical 
methods that are useful when the outcome of interest is an entire 
function rather than just a single numerical summary of the function.

Functional Principal Component Analysis is performed on the curves in
order to find the curve's main modes of variability, also ANOVA-like
calculations are made where we identify the effects of alternative
scenarios for the physical state of the groundwater system. We performed
functional linear regression of the program's input parameters on the
whole dose curve. It is shown that the application of these innovative
techniques yields new important insights on the uncertainties we should
expect from computer simulations in this field; we noted that scenario
effects can account for as much as a 40-fold increase in the uncertainty
of predicted doses. We also find indications that one should expect 
higher uncertainties in the portions of the curve that come before its 
maximum, than after it.