Final Report: Local Inferences from Aquatic Studies

EPA Grant Number: R829095C002
Subproject: this is subproject number 002 , established and managed by the Center Director under grant R829095
(EPA does not fund or establish subprojects; EPA awards and manages the overall grant for this center).

Center: Space-Time Aquatic Resources Modeling and Analysis Program (STARMAP)
Center Director: Urquhart, N. Scott
Title: Local Inferences from Aquatic Studies
Investigators: Breidt, F. Jay , Davis, Richard A. , Hoeting, Jennifer A. , Opsomer, Jean
Institution: Colorado State University , Iowa State University
EPA Project Officer: Hiscock, Michael
Project Period: October 1, 2001 through September 30, 2006
RFA: Research Program on Statistical Survey Design and Analysis for Aquatic Resources (2001) RFA Text |  Recipients Lists
Research Category: Aquatic Ecosystems , Ecological Indicators/Assessment/Restoration , Water and Watersheds , Water , Ecosystems

Objective:

The objective is to develop hierarchical spatio-temporal models for local inferences about aquatic resources.

Summary/Accomplishments (Outputs/Outcomes):

This project had an overall goal of developing hierarchical spatio-temporal models for local inferences about aquatic resources. The project was conducted jointly with a Designs and Models for Aquatic Resource Surveys (DAMARS) project on development of nonparametric model-assisted estimators for data obtained in probability surveys of aquatic resources. Accomplishments include:

  • Extension of nonparametric model-assisted and model-based estimators for standard survey problems and for small area estimation problems;
  • Adaptation of deconvolution methods for spatial distribution function estimation;
  • Development of new state-space models and estimation methods for stream networks; and
  • Development of a novel algorithm (spatial least absolute shrinkage and selection operator [Lasso]) for selection of covariates and neighborhoods from geographic information systems (GIS) data in spatial regression problems.

The extensions of the nonparametric model-assisted methodology allow for a variety of complex designs and for incorporation of the major smoothing techniques in use today (including spline-based regression, additive models, and semi-parametric models). The methods were applied to the general problems of estimation of population means, totals, and distribution functions. In many surveys, estimators are desired for small domains within the overall population. Because a survey often is not designed to provide reliable estimators for such small domains, the estimation requires the assumption of a model for the population. Investigators in this Project adapted the nonparametric methodology used in the model-assisted context to this situation and showed how this approach generalizes existing small area estimation methods.

In addition to studying estimation of the distribution function in the design-based setting using nonparametric model-assisted estimators, we also considered deconvolution, which is the estimation of the cumulative distribution function (cdf) of a variable given noisy measurements of that variable and distributional information about the measurement noise. We treated this problem as one of constrained Bayes estimation, which we extended to hierarchical Bayesian spatial models and studied under aggregation of small areas.

Because of the natural flow of water in a stream network, characteristics of a downstream reach may depend on characteristics of upstream reaches. The flow of water from reach to reach provides a natural time-like ordering throughout the stream network. Investigators in this Project developed a state-space model to describe the spatial dependence in this tree-like structure with ordering based on flow. The model formulation is flexible, allowing for a variety of spatial and temporal covariance structures in the state and measurement equations. They also derived a variation of the Kalman filter and smoother to allow recursive estimation of unobserved states and prediction of missing observations on the network, as well as computation of the Gaussian likelihood. The state-space formulation is extensible to non-linear and non-Gaussian processes. The Project investigators also developed several models of within-stream dependence, including network analogues of autoregressive-moving average models and of structural models, and fitted those models to real and simulated data.

GIS tools organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. Project investigators formalized this problem and proposed the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. They incorporated spatial smoothness in selected coefficients through use of a priori spatial covariance structure, leading to a modification of the Lasso procedure. The Least Angle Regression (LARS) algorithm, which can be used in a fast implementation of Lasso, was also modified to yield a fast implementation of spatial Lasso. The spatial Lasso performed well in numerical examples, including an application to prediction of soil moisture. The work reported in this paragraph was done in cooperation with investigators working under Project 3 (R829095C003).

A number of graduate students were involved in this research, including Ji-Yeon Kim and Curtis Miller (Iowa State University); and Alicia Johnson, Siobhan Everson-Stewart, Mark Delorey, and Bill Coar (Colorado State University). Work also involved a postdoctoral fellow, Giovanna Ranalli (Colorado State University), plus two junior researchers (Hsin-Cheng Huang, Academica Sincia and Nan-Jung Hsu, National Tsing-Hua University).

The results of this Project were communicated to diverse audiences, ranging from state-level aquatic scientists to international investigators. Those communications, organized by type of communication, are listed in the Final Report for R829095, which is the overall Center report for the the Space-Time Aquatic Resources Modeling and Analysis Program (STARMAP) grant.

Significance of Accomplishments

This Project has developed statistical analysis tools of relevance to aquatic scientists concerned with surveys and spatial-temporal modeling. The client community for the results of this research program consisted of aquatic monitoring scientists in state, tribal, federal, and more local agencies charged with monitoring aquatic resources in compliance with the Clean Water Act. Such aquatic scientists will be assisted by affiliated statisticians and landscape ecologists.

Stakeholders and Users of Results

There are many potential users of the methods developed by STARMAP and DAMARS under this joint Project. The two Programs have organized and presented a number of conferences or parts of conferences directed specifically at potential users. Program personnel also have participated in a number of conferences at the invitation of potential users. Some of the conferences are explained in more detail under Project 4 (R829095C004), Outreach and Extension.

How Products Will Further Science/Management of Resources

The statistical analysis tools (products) developed and disseminated by this Project provide aquatic scientists and affiliated statisticians with expanded and more defensible ways to draw inferences to local concerns from wide-area surveys than were available prior to this Project. These tools extend previously available spatial-temporal methods to accommodate the branching nature of streams and rivers.

Listing of Specific Communications Related to Local Estimation

The complete list of outputs from STARMAP, including those originating from Project 2, is available on the Web at http://www.stat.colostate.edu/starmap Exit .

Journal Articles:

No journal articles submitted with this report: View all 83 publications for this subproject

Supplemental Keywords:

kernel regression, thin plate splines,, RFA, Scientific Discipline, Ecosystem Protection/Environmental Exposure & Risk, Aquatic Ecosystems & Estuarine Research, Aquatic Ecosystem, Environmental Monitoring, EMAP, ecosystem monitoring, statistical survey design, spatial and temporal modeling, aquatic ecosystems, water quality, Environmental Monitoring and Assessment Program, modeling ecosystems, STARMAP

Relevant Websites:

http://www.stat.colostate.edu/starmap Exit

Progress and Final Reports:

Original Abstract
  • 2002
  • 2003 Progress Report
  • 2004 Progress Report
  • 2005 Progress Report

  • Main Center Abstract and Reports:

    R829095    Space-Time Aquatic Resources Modeling and Analysis Program (STARMAP)

    Subprojects under this Center: (EPA does not fund or establish subprojects; EPA awards and manages the overall grant for this center).
    R829095C001 Combining Environmental Data Sets
    R829095C002 Local Inferences from Aquatic Studies
    R829095C003 Development and Evaluation of Aquatic Indicators
    R829095C004 Extension of Expertise on Design and Analysis to States and Tribes
    R829095C005 Integration and Coordination for STARMAP