Physical Statistical Environmental Modeling

Mark Berliner

Department of Statistics

Ohio State University

1958 Neil Avenue

Columbus, OH 43210-1247 USA

mb@stat.ohio-state.edu

**Abstract**: I discuss the hierarchical Bayesian framework
for analyzing environmental problems. This paradigm provides opportunities for
the combination of physical reasoning and observational data in a coherent
analysis framework, but in a fashion which manages the uncertainties in both
information sources. A key to the hierarchical viewpoint is that separate
statistical models are developed for the process variables studied and the
observations conditional on those variables. Modeling process variables in this
way enables incorporation of scientific models across a spectrum of levels of
intensity ranging from qualitative use of physical reasoning to strong reliance
on numerical models. Selected examples from this spectrum are reviewed.

Wildfire Chances and Probabilistic Risk Assessment

David R. Brillinger

Statistics Department

University of California

Berkeley, CA 94720 USA

brill@stat.berkeley.edu

**Abstract**. Forest fires are an important societal problem
in many countries and regions. They cause extensive damage and substantial
amounts are spent preparing for and fighting them. This talk will apply methods
of probabilistic risk assessment to estimate chances of fires given a variety of
explanatory variables. Updating methods and random effect models will be
considered in particular. The work is collaborative with researchers at the U.S.
Forest Service.

Efficient Posterior Inference and Prediction of Space-Time Processes Using Dynamic Process Convolutions

Catherine A. Calder

Department of Statistics

The Ohio State University

1958 Neil Ave.

Columbus, OH 43210

calder@stat.ohio-state.edu

**Abstract.** Bayesian dynamic process convolution models
provide an appealing approach for modeling both univariate and multivariate
spatial temporal data. Their structure can be exploited to significantly reduce
the dimensionality of a complex spatial temporal process. This results in
efficient Markov chain Monte Carlo (MCMC) algorithms required for full Bayesian
inference. In addition, the dynamic process convolution framework readily
handles both missing data and misaligned multivariate space-time data without
the need for imputation. We review the dynamic process convolution framework and
discuss these and other computational advantages of the approach. We present an
application involving the modeling of air pollutants to demonstrate how this
approach can be used to effectively model a space-time process and provide
predictions along with corresponding uncertainty statements.

The Role of Precaution in Quantitative and Qualitative Analysis of Environmental Decisions

Alison Cullen

University of Washington

Seattle, Washington, USA

alison@u.washington.edu

**Abstract. **Environmental risks are often described
quantitatively, but they are invariably interpreted in light of individual and
social values, and receive attenuation (or not) according to both quantitative
and qualitative factors. Legal, cultural, political, and practical expectations
and constraints also influence individual and social tolerance of risks. The
question remains, in the face of uncertain risks, what is the appropriate
response of government? A range of responses are revealed across political and
geographic boundaries as well as risk contexts, from strict precaution where the
presence of uncertainty is argued to justify action, to an insistence on
evidence of harm before action is taken.

Recent media coverage paints a picture contrasting precautionary European countries with a risk tolerant US, in matters of environmental health. However it is not difficult to identify risk decisions for any given country which fall along the entire precaution spectrum. In this paper we

undertake an international comparison of the driving factors characterizing several risk decisions about environmental health, such as those inherent in food safety, energy generation, waste management and climate policy. The role and limits of quantitative and qualitative analysis in this process are explored and the accompanying level of precaution revealed.

Hierarchical Bayesian spatio-temporal modeling for wind data

Li Chen, Montserrat Fuentes

Department of Statistics

and

Jerry M. Davis

Department of MEAS

North Carolina State University

Raleigh, NC 27695-8203

lchen4@unity.ncsu.edu

**Abstract. **Classical geostatistics and time series methods
are powerful tools for stationary and separable space-time processes. However,
it is well recognized that in real applications spatio-temporal processes are
rarely stationary and separable. In this work, some new approaches to model and
estimate nonstationarity and nonseparability are presented. We present new
classes of nonseparable and nonstationary models for space-time processes. We
also propose a test for separability to better understand the space-time
dependence. We apply the above statistical methods to model spatio-temporal
structures of wind fields and assess the performance of numerical models for
wind prediction. Consequently improved wind field map can be obtained by
combining observed wind data with numerical model output.

**Keywords**: stationary, separability, spatio-temporal, hierarchical,
Bayesian

Data Quality and Uncertainty in Fine Particulate Monitoring

Alessandro Fassò and Orietta Nicolis

University of Bergamo - Dept. IGI

Via Marconi 5, 24044 Dalmine BG I, Italy

alessandro.fasso@unibg.it

**Abstract**: In order to assess compliance with air quality
standards, (Italian) regulations prescribe to monitor concentrations of
particulate matters. The accuracy varies with monitor type, temperature and
pollution level often in a complex nonlinear manner. Consequently, comparisons,
threshold exceedances interpretation and compliance assessment are often
difficult.

For these reasons, in this paper we consider dynamical modelling of spatio-temporal and instrumental uncertainty. An application to north Italy air quality network allows to make some empirical conclusions.

**
Spatial-temporal
modeling of the association between speciated fine particles and human health
effects**

M. Fuentes, H. R. Song, S. Ghosh, and D. Holland.

Patterson Hall 210 C

Box 8203 NCSU

Department of Statistics

North Carolina State University

Raleigh, NC 27695

fuentes@stat.ncsu.edu

**
Abstract**.
Particulate matter (PM) has been linked to a range of serious cardiovascular and
respiratory health problems. Some of the recent epidemiologic studies suggest
that exposures to PM may result in tens of thousands of excess deaths per year,
and many more cases of illness among the US population. The main objective of
our research is to quantify uncertainties about the impacts of fine PM exposure
on mortality. We develop a multivariate spatial regression model for better
estimation of the mortality effects from fine PM and its components across the
coterminous US. Our approach adjusts for meteorology and other confounding
influences, such as socioeconomic factors, age, gender and ethnicity,
characterizes different sources of uncertainty of the data, and models the
spatial structure of several components of fine PM. We consider a flexible
Bayesian hierarchical model for a space-time series of (mortality) counts by
constructing a likelihood based version of a generalized Poisson regression
model. The model has the advantage of incorporating both over and under
dispersion in addition to correlations that occur in space and time. We apply
these methods to daily mortality county counts, measurements of total and
several components of fine PM from national monitoring networks in the US, and
the output of deterministic air quality models.

Separable Approximations of Space-Time Covariances

Marc G. Genton

Department of Statistics

Box 8203

North Carolina State University

Raleigh, NC 27695-8203 USA

genton@stat.ncsu.edu

**Abstract.** Statistical modeling of space-time data has
often been based on separable covariance functions, that is covariances that can
be written as a product of a purely spatial covariance and a purely temporal
covariance. The main reason is that the structure of separable covariances
dramatically reduces the number of parameters in the covariance matrix and thus
facilitates computational procedures for large space-time data sets. In this
talk, we discuss separable approximations of space-time covariances. In
particular, we describe the nearest (in the Froebinius norm) Kronecker product
approximation of a space-time covariance matrix. The algorithm is simple to
implement and preserves symmetry and positive definiteness of the solution. The
separable approximation allows for fast kriging of large space-time data sets.
We present several illustrative examples and an application to the Irish wind
speed data.

Modeling Uncertainty about Pollutant Concentration and Human Exposure Using Geostatistics and a Space-time Information System: Application to Arsenic in Groundwater of Southeast Michigan

Pierre Goovaerts

Biomedware, Inc.

516 North State Street

Ann Arbor, MI 48104, USA

goovaerts@biomedware.com

**Abstract**. Assessment of the health risks associated with
exposure to elevated levels of arsenic in drinking water has become the subject
of considerable interest and some controversy in both regulatory and public
health communities. The objective of this research is to explore the factors
that have contributed to the observed geographic co-clustering in bladder cancer
mortality and arsenic concentrations in drinking water in Michigan. The study
requires: 1) the building of a probabilistic space-time model of arsenic
concentrations, accounting for information collected at private residential
wells and the hydrogeochemistry of the area, 2) the estimation of lifetime
arsenic exposure, accounting for the impact of job location and occupational
exposures to arsenic into the daily water ingestion habit.

Because of the small changes in concentration observed in time, the study has focused on the spatial variability of arsenic, which can be considerable over very short distances. Various geostatistical techniques, based either on lognormal or indicator transforms of the data to accommodate the highly skewed distribution, have been compared using a cross validation procedure. The most promising approach involves a soft indicator coding of arsenic measurements, which allows one to account for data below the detection limit and the magnitude of measurement errors. Prior probabilities of exceeding various arsenic thresholds are also derived from secondary information, such as type of bedrock and surficial material, well casing depth, using logistic regression.

Computation of human exposure is achieved by modeling each study subject as a spatio-temporally referenced object that moves through space and time. Monte-Carlo simulation is used to propagate the uncertainty about arsenic concentration through the exposure model, leading to an individual model of uncertainty for arsenic exposure

Assessing Progress Towards Environmental Objectives

Anders Grimvall

Department of Mathematics

Linköpings universitet

58183 Linköping, Sweden

angri@mai.liu.se

**Abstract.** International and national bodies have
established a large number of environmental objectives and interim targets.
Furthermore, considerable efforts have been made to assess progress towards the
established goals. In this paper, we review: (i) the reliability and validity of
proposed indicators of progress, and (ii) the appropriateness of the currently
used statistical procedures. In particular, we discuss and illustrate how
currently used tools can be modified to facilitate the communication between
scientists and decision-makers. Taking selected water and air quality objectives
as a starting point, we show how the combined use of statistical tools and
physics-based models can facilitate the interpretation of observed changes in
the state of the environment. Also, we show how data reduction involving
monotonic constraints can be employed to meteorologically normalize time series
of environmental quality data and thereby clarify the presence of monotonic
temporal and spatio-temporal trends.

Setting Environmental Standards: Some Case Studies and a Research Plan

Peter Guttorp

University of Washington

peter@stat.washington.edu

**Abstract**. The setting of environmental standards by
government agencies, such as the US Environmental Protection Agency, are
frequently done without taking into account measurement error as well as the
statistical quality of the decision rule given. I will outline a statistical
approach to the setting of standards, present some examples of such standards
(and how they could/should be revised), and finally describe a research plan for
how a scientist would go about protecting the health of the people from
environmental insults.

Why aren’t we making better use of uncertainty information in decision–making?

Kim Lowell

Centre de recherche en géomatique

Pavillon Casault, Université Laval

Québec, Québec G1K 7P4 CANADA

(418) 656-2131 ext. 7998

Fax : (418) 656-7411

Kim.Lowell@scg.ulaval.ca

**Abstract.** All decisions
involve an assessment of potential risk relative to potential reward. In cases
where the potential reward is clearly much greater than the potential risk or
vice-versa, the course of action to pursue in any decision is very clear.
However, if the potential reward and the potential risk are approximately the
same, a better assessment of the two should be conducted. In fact, the two
should be an integral part of the decision-making and not merely an
afterthought.

Since the advent of statistical models, model users have been aware of potential errors in model estimates because of sampling issues associated with data. As the field of spatial uncertainty has developed over the last decade, users of spatial databases are similarly aware of potential errors due to cartographic methods and procedures. However, little work has been conducted to use such information as input into the decision-making process.

This paper will present 1)a discussion of the consequences of not considering model and data uncertainty in the decision-making process, 2)a conceptual model for doing this, and 3)a discussion of when it might not be necessary to do so. These topics will be addressed for spatial as well as aspatial models.

Estimating and modeling space-time variograms

Donald E. Myers

University of Arizona

myers@math.arizona.edu

**Abstract**. As with a spatial variogram or spatial
covariance, a principal purpose of estimating and modeling a space-time
variogram is to quantify the spatial temporal dependence reflected in a data
set. The resulting model might then be used for spatial interpolation and/or
temporal prediction which might take several forms, e.g. kriging and Radial
Basis functions. There are significant problems to overcome in both the
estimation and the modeling stages for space-time problems unlike the purely
spatial application where estimation is the more difficult step. The key point
is that a spatial-temporal variogram as a function must be conditionally
negative definite (not just semi-definite) which can be a difficult condition to
verify in specific cases. In the purely spatial context one relies on a known
list of isotropic valid models, e.g., the Matern class as well as the
exponential and gaussian models, as well as on positive linear combinations of
known valid models. Bochner’s Theorem (or the extension given for generalized
covariances by Matheron) characterizes non-negative definite functions but does
not easily distinguish the strictly positive definite functions.

Geometric anisotropies can be incorporated via an affine transformation and space-time might be viewed as simply a higher dimensional space but possibly with an anisotropy in the model. This approach implies that there is an appropriate and natural choice of a norm (or metric) on space-time analogous to the usual Euclidean norm for space. The most obvious way to construct a model for space-time is to "separate" the dependence on space and on time. This is not new and in fact a similar problem can occur in spatial application, i.e., a zonal anisotropy. Early attempts used either the sum of two covariances or the sum of two variograms, in either case one component being defined on space and the other on time. It is easily shown that this leads to semi-definite models and hence if used in kriging equations, the result may be a non-invertible coefficient matrix. It is also easy to see that the product of two variograms (even on the same domain) can violate the growth condition. However it is well known that the product of two strictly positive definite functions is again strictly positive definite. In fact a gaussian covaiance model might be viewed as product (of several gaussian models each defined on a lower dimensional space). Likewise one form of the exponential covariance, often used in hydrology applications, is also a product. When converted to variogram form, there is not only a product (with a negative sign) but also a sum. It turns out that the variogram form is more convenient in the estimation stage.

The simple product covariance is somewhat too limiting however, each component effectively must have the same "sill". An obvious extension is the product-sum model which when converted to variogram form is the same as for the product (but with different coefficients), This can be further generalized to an integrated product sum model.

In the estimation stage there are two separate problems, one
is to determine the appropriate model type and the other is to estimate the
model parameters. In a typical spatial application the list of possible models
is usually kept small and hence the primary emphasis is on estimating the model
parameters. In the spatial temporal context the list of possible models is
likely to be much greater and model type selection more difficult. De Ioca,
Myers and Posa have shown that the use of marginal variograms is one way to
attack this problem and have given an example of extending to the integrated
product sum model as well as to the multivariate case using a Linear Coregion__aliz__ation
Model.

The Assessment of the Biodiversity of Nature Reserves: Problems and

Opportunities

Michael W. Palmer

Botany Department

Oklahoma State University

104 LSE

Stillwater OK 74078 USA

carex@okstate.edu

**Abstract.** The science of ecology has moved away from the
belief that natural systems are generally in a state of equilibrium, maintained
by biotic interactions. The lack of a modern synthesis hampers our ability to
articulate and implement conservation goals. However, given the loss of
biodiversity worldwide, we are forced to make decisions based on an incomplete
paradigm. Fortunately, some ecological principles seem to be relatively robust:
communities are open, dynamic systems governed by spatial and temporal
heterogeneity in the environment. The determinants of biodiversity are highly
scale-dependent. Methods for assessing biodiversity are most limited when they
rely on strict targets, and strongest when they appreciate the dynamic nature of
natural communities. While cooperation and communication amongst
conservation-related agencies are likely to be fruitful, it is likely that
having independent agencies, each with their own targets and priorities, is a
net benefit to biodiversity.

Wildfire Threats Count Analysis by Longitudinal Models

J. A. Quintanilha; L. L. Ho

Escola Politecnica – Universidade de São Paulo

Av. Prof. Almeida Prado trav2, n.83

São Paulo SP Brazil

05508-900

jaquinta@usp.br

**Abstract.** The current operational fire monitoring program
conducted by IBAMA (Brazil) has collected data of wildfire threats counts and
other explanatory of Amazon region. The aim of this paper is to present the
results of statistical analysis of this dataset from 1999 to 2002. From original
data, new variables were created. The sample unit was the municipality. The
density of wildfire threats count (the ratio between the wildfire threats counts
and the municipality area) was selected as a dependent variable. A longitudinal
linear model was used and it identified as relevant explanatory variables:
administrative limits, municipalities area, year, rain conditions, legal
conditions of the areas, percentage of : deforestation, illegal human
occupation, population growth index and agricultural area, as also it pointed
out different structures of variance in the dependent variable for different
type of the legal conditions of the areas. From residual analysis, most of
standardized residuals (near 90%) are in the interval (-3, +3). However, some
neighborhood municipalities must be considered differently since wildfire
threats counts are not associated to any of explanatory variables used in this
analysis.

Spatial Scale and Its Effects on Comparisons of Airborne and Ground-based Gamma-ray Spectrometry for Mapping Environmental Radioactivity.

E.M. Scott^{1},
D.C.W. Sanderson^{2}, A.J. Cresswell^{2}, J.J. Lang^{2}

1 Dept of Statistics, University of Glasgow, Glasgow G12 8QW, UK