Sponsoring Section/Society: North Texas Chapter of the ASA
Session Slot: 2:00- 3:50 Sunday
Estimated Audience Size: 200
AudioVisual Request: xxx
Session Title: Spatial-Temporal Modeling of Environmental Processes
Theme Session: No
Applied Session: No
Session Organizer: Gunst, Richard F. Southern Methodist University
Address: Department of Statistical Science Southern Methodist University Dallas, TX 75275-0332
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 minutes First Speaker - 30 minutes Second Speaker - 30 minutes Third Speaker - 30 minutes Discussant - 0 minutes Floor Discusion - 15 minutes
Session Chair: Gunst, Richard F. Southern Methodist University
Address: Dept. of Statistical Sci. Southern Methodist University Dallas, TX 75275-0332
1. Modeling Contamination Migration with Spatially Correlated Stochastic Differential Equations
Hartfield, Molly, Radian International
Address: Radian International P.O. Box 201088 Austin, TX 78720-1088
Abstract: A class of spatially correlated stochastic differential equation models are applied to the problem of modeling space-time data. In particular, the models are applied to environmental data, where interest is on monitoring contaminant levels in the soil or groundwater, characterizing the rate at which contaminant concentrations are changing in time, or tracking the migration of contaminants across a region. The class of models can be described as continuous-time versions of spatial autoregressive integrated stochastic processes. Model identification techniques borrow from spatial statistical model identification methods including sample semivariogram plots and plots based on generalized increments. Because these spatial statistical techniques were originally developed to accommodate the irregularity that often characterizes spatial data, the model identification methods for the space-time models considered here also do not require that data are collected at evenly spaced time intervals or along a regular spatial grid. An recursive scheme for fully specifying a space-time model and estimating its parameters is applied. Restricted maximum likelihood (REML) methods are used to estimate model parameters and the Kalman filter is demonstrated to be a convenient computational tool for obtaining the REML estimates and providing model diagnostics.
2. Criteria Air Pollutant Levels in Space and Time
Ensor, Katherine Bennett, Rice University
Address: Department of Statistics, MS 138 Rice University Houston, TX 77251-1892
Calizzi, Mary, Rice University
Baggett, Scott, Rice University
Abstract: A state-space formulation of a multivariate spatial-temporal model is developed and applied to air quality data for the Houston area. The goal is to provide an empirical method for predicting the level of ambient pollutants such as ozone, nitric oxides and small particulates for the study area. The major physical components of the system under study, e.g. the pollutant transport due to wind and ozone formulation due to favorable meteorological conditions, are included in the modeling effort.
3. Samping Errors in Some Global Climate Sampling Schemes
Li, Ta-Hsin, University of California at Santa Barbara
Address: Department of Statistics University of California Santa Barbara, CA 93106-3110
Abstract: Spherical harmonics are employed in many general circulation models (GCMs) as part of their numerical scheme. There arises the problem of estimating the coefficients in the spherical harmonic expansion from imperfect observing systems. For climate change assessments, it is important to understand the uncertainty in the estimation of the coefficients that represent the amplitude of spherical waves.
Sampling errors are inevitable when the spherical harmonic coefficients are estimated from observations made by a discrete set of monitoring stations or by asynchronous satellites. The sampling errors not only result from a lack of sufficient density in the monitoring stations and the satellite orbits, but also result, for satellite data, from the time span required for an asynchronous satellite to cover the globe. The sampling errors are menifested as aliasing--the tendency for variations in unresolved scales to contaminate the estimates in resolved scales.
A methodology for systematic analysis of sampling errors is provided. Based on a simple noise-forced energy balance model (EBM), the sampling errors are investigated both analytically and numerically for some sampling schemes. Special attention is paid to the Gauss-Legendre design in which the sampling points are equally spaced along latitude circles but located at the zeros of Legendre polynomial. For the satellte sampling, polar-orbiting satellites are of special interest because of their widespread use in operational monitoring of the climate system. In this study, the Gauss-Legendre design is found to be superior to the latitude-longitude uniform design because it produces smaller errors given the same number of sampling points. For polar-orbiting satellites, the samping errors are found to depend crucially on the time scale of the climate field being sampled--the faster the field changes with time the larger the sampling errors.
List of speakers who are nonmembers: None