2 Laboratory of Soil Science and Geology, Wageningen University; P.O. Box 37, 6700 AA Wageningen, The Netherlands; gerard.heuvelink@wur.nl

Abstract. The accuracy of model output increases with a decreasing support size of the input data, due to the increase of detail. This paper examines whether this is true for various spatial models developed for simulating rockfall. We analyze the effect of the support size on the accuracy of a set of models and their parameters. The validation data were obtained from real-size rockfall experiments in which high-speed video cameras recorded the trajectories and velocities of more than 200 individual falling rocks with diameters between 0.8 and 1.5 meter. These observed data are thoroughly compared with the output of the various models. One of the main findings is that a larger support size can be a more important cause of a larger model error than poor data quality.

Lucie Doudová

MasarykUniversity

Brno

Czech Republic

ldoudova@centrum.cz

Abstract. The data with negative binomial distribution with parameters μ and κ will be considered in the contribution. If κ is known the standard GLM technique can be applied. The situation where κ is unknown and depends on covariates is more complicated. The aim of the study will be oriented to the comparison of populations with negative binomial distribution where both parameters μ and κ depend on covariates. Then the robustness of the comparison will be studied by simulation.

Finally the obtained results will be applied to the environmental study. The populations of roe deer (Capreolus capreolus) from different territories in the Czech Republic will be compared and analysed.

Michael Dowd

Dept. of Mathematics & Statistics

Dalhousie University

Halifax, N.S. Canada, B3H 3J5

Phone: 902-494-1048

Fax:902-494-5130

mdowd@mathstat.dal.ca

Abstract. Statistical approaches to the inverse problem associated with combining time-dependent dynamic models of marine ecosystems with observations are investigated. The goal is to combine prior information, in the form of model dynamics and substantive knowledge about uncertain parameters, with available measurements in order to produce posterior estimates of time-varying ecological state variables, along with their uncertainty. Ecological models of interacting populations are represented as stochastic difference equations. The estimation, or inverse, problem is then treated from the perspective of nonlinear, nonGaussian state space models. Some simple marine ecosystem models and observations are used to illustrate important aspects of the Bayesian approach to this inverse problem.

Keywords: ecosystem, state space models, inverse problems

Charles R. Ehlschlaeger

Department of Geography

Western Illinois University

1 University Circle

Macomb, IL 61455 USA

cre111@wiu.edu

Abstract. Modeling digital elevation model (DEM) uncertainty can be as "simple" as developing a distribution of application results using Monte Carlo simulation (MCS). MCS requires equiprobable realizations of input maps and parameters in order for the distribution of application results to be an accurate reflection of what could be reality. For a DEM, this process involves designing a single model that represents the distribution of elevation errors and a measure of spatial autocorrelation. Commonly, conditional stochastic modeling using mathematic principles from the kriging process is used to develop the DEM uncertainty model.

Two critical questions need to be asked. 1) Whether the kriging process is an appropriate model for developing a distribution of DEM errors. 2) Whether any single DEM uncertainty model can possibly be a representation for any application. This paper explores these questions and proposes a methodology similar to Beven’s Generalized Likelihood Uncertainty Estimation (GLUE) process.

Keywords: DEM, uncertainty modeling, Monte Carlo simulation

D.W. Engel, A.M. Liebetrau, K.D. Jarman, T.A. Ferryman, T.D. Scheibe, and B.T. Didier

Pacific Northwest National Laboratory

P.O. Box 999

Richland, Washington 99352 USA

dave.engel@pnl.gov

Abstract. The reliability of and confidence in predictions from model simulations are crucial because these predictions can significantly affect risk assessment decisions. For instance, the fate of contaminants at the Department of Energy’s Hanford site is a critical problem that impacts long-term waste management strategies. In the uncertainty estimation efforts for the Hanford Site-wide Groundwater Modeling program, computational issues severely constrain both the number of uncertain parameters that can be considered and the degree of realism that can be included in the models. Substantial improvements in the overall efficiency of uncertainty analysis are needed to fully explore and quantify significant sources of uncertainty. We have combined state-of-the-art statistical and mathematical techniques in a unique iterative, limited sampling approach to efficiently quantify both local and global prediction uncertainties due to model input uncertainties (which include uncertainties in physical or fitted parameters, in initial and boundary conditions, and in model parameterizations). The approach is designed for application to a wide diversity of problems across multiple scientific domains. An analysis has been performed on a simplified contaminant fate transport and groundwater flow model to illustrate this approach. The results show that our iterative method for computing uncertainty estimates of specified precision is more efficient (i.e., requires less computing time) than traditional approaches based upon simple random sampling approach and other non-iterative sampling methods.

Keywords: iterative, uncertainty, risk, groundwater

Nina H. Fefferman, Jyotsna S. Jagai, Elena N. Naumova

Tufts University School of Medicine

Family Medicine and Community

Health

Tufts University

136 Harrison Ave. Boston, MA 02140

elena.naumova@tufts.edu

Abstract. In epidemiology, techniques that examine periodicity in times series data can be used to understand weekly, biannual or seasonal patterns of disease. However, a simple understanding of periodicity is not sufficient to examine the possible influence of variation in incubation period, distributed sources of infection, and due to environmental factors, especially if these influences affect the rate of disease on various spatio-temporal scales.

In order to examine the feasibility of using wavelets to assess dependencies over different spatio-temporal scales in a time series of disease incidence, we abstracted 10 years of daily records of ambient temperature and precipitation in addition to daily disease incidence data for Massachusetts for five enterically transmitted diseases.

We eliminated periodic fluctuation in both seasonal and weekly case reporting using various techniques (Fourier transformation, "loess" smoothing, and ARIMA) on each time series of disease data. Different methods were employed in order to examine the possible effect of removed periodicities on the variance of the data. We then performed a wavelet decomposition to examine the residuals from these analyses on a variety of temporal scales and examined the resulting correlations to the environmental data.

Keywords: wavelet decomposition, variance heterogeneity, biosurveillance, outbreak modeling

Mark Finco

Remote Sensing Band

Forest Inventory and Analysis

USDA Forest Service

Salt Lake City, UT

mfinco@fs.fed.us

Abstract: USFS Forest Inventory and Analysis (FIA) data have historically been used to produce estimates of forest population totals over large geographic areas. Recent emphasis has been placed on delivering this traditional forest resource information to a larger and more diverse audience by producing regional maps of forest characteristics. Maps provide a more flexible, easily understood, and visually accessible product that enhances the general utility of the information traditionally provided in tables and graphs. Over the last year, the FIA Remote Sensing Band and the USFS Remote Sensing Applications Center (RSAC) have collaboratively developed a strategy for producing national forest characteristics geospatial datasets. The first of these national maps is of forest biomass across the contiguous United States, Alaska and Puerto Rico.

In this paper we investigate and discuss the limitations and appropriate application of these maps. In this age of Geographic Information Systems (GIS), there is a great temptation to misuse moderate resolution datasets by calculating and comparing summaries for relatively small areas. Standard remote sensing methodologies for calculating map accuracy based on a confusion matrix are inadequate to providing the map user concrete guidance on how the map should be used. Here we present alternatives to the confusion matrix for assessing map accuracy and discuss appropriate applications of the FIA national biomass map.

Tressa L. Fowler*, Jamie T. Braid, and Anne Holmes

Research Applications Program

National Center for Atmospheric Research

P.O. Box 3000

Boulder, CO 80307-3000

tressa@ucar.edu

Abstract. Ceiling and visibility forecasts are issued for use in flight planning, particularly for general aviation. METAR station information is used for verification of these forecasts. Unfortunately, stations are sparse in many areas and quite dense in others. Additionally, the quality and type of information available from METAR stations may differ considerably depending on whether the station is automated or manual, the location, the type of instrumentation, the level of training and expertise of a manual observer, etc. Thus, in order to reduce the effect of these differences on verification, it is desirable to identify a consistent subset of METAR stations to be used for verification.

A comparison of stations with their neighbors can aid in the identification process. All METAR stations in the CONUS are matched with their neighbors within 20 and 40 kilometer radii. The agreement of ceiling and visibility observations between the stations is assessed. Disagreement may be due to erroneous observations or environmental conditions that differ considerably over the distance between stations. Preliminary findings of the neighbor comparison indicate that observations between neighboring stations tend to correspond for a high percentage of the non-events. However, during ceiling and visibility events, measurements at neighboring stations correspond less often.

David Gadish

California State University Los Angeles

5151 State University Drive

Los Angeles, CA, 90032

dgadish@calstatela.edu

Abstract - Effective use of data stored in spatial databases requires methods for evaluation and enhancement of the quality of the data. Spatial data quality can be evaluated using a measure of internal validity, or consistency, of a data set. Capturing spatial data consistency is possible with a multi-step approach.

A distance measure is used to detect implicit spatial relations between neighboring objects. The next step involves identifying the types of relations between these neighboring objects using topology based constraints.

The semantic information of objects, together with topological relations are combined to discover patterns, or rules, in the data. These rules are based on the analysis of the relations between each object and each of its neighbors, as well as between each object and all of its neighbors.

Patterns of spatial relations, represented as rules are validated using available metadata, as well as trend analysis and Monte Carlo simulation techniques. These can now be used as the basis for automated detection of inconsistencies among spatial objects, where possible inconsistencies are detected when one or more rules are violated. Detected inconsistencies can then be adjusted, thus increasing the quality of spatial data sets.

Key Words - Consistency, Patterns, Spatial Relations

Marco Giannitrapani, Ron Smith, Marian Scott, and Adrian Bowman

Department of Statistics
Mathematics Building
University Gardens
University of Glasgow
G12 8QW Glasgow, Scotland, United Kingdom
marco@stats.gla.ac.uk

Abstract. From the 1970’s, a co-ordinated international programme monitoring acidifying air pollution was initiated in direct response to observed acidification. At the same time, several international protocols on the reduction of acidifying and eutrophying emissions (SO₂, SO₄ etc) were also agreed.

This work presents an evaluation of the observed spatial and temporal trends in SO₂ in Europe for the last quarter of the twentieth century, on the basis of data from EMEP (Co-operative Programme for Monitoring and Evaluation of the long Range Transmission of Air Pollutants in Europe). The policy question of interest is whether the protocols have resulted in a real improvement in environmental quality and a real change in the acidifying environment

In the first part of the work, we report on non-parametric modelling of the temporal trends, accounting for the effect of meteorological covariates using generalised additive models (GAMs). The need of circular smoothers for some covariates (specifically wind direction and weeks of the year), and the correlation of the data, led us to develop and fit a generalised version of a Local Linear Regression smoother. The model fitting used a reformulated version of the back-fitting algorithm that provides the projection matrix at convergence, which is used for model testing purposes. A generalised version of a bivariate Local Linear Regression smoother has also been fitted and tested against the additive model, in order to test for changes in seasonality.

The second part of the work has considered the spatial patterns in the SO₂ field and their temporal evolution. A regression surface has been fit to each month, the spatial correlation modelled and a time series analysis of the spatial parameters carried out.

At each time point, different spatial surfaces (i.e. linear models, nonparametric smoothers, etc…) have been fitted and variograms have been fitted to the residuals. Kriging analysis have produced estimates of the spatial distributions.

We report on our findings.

Eric Gilleland

National Center for Atmospheric Research

Research Applications Program

Boulder, CO 80307-3000

ericg@ucar.edu

Abstract. Methods are given and explored for thinning METAR stations in order to make more meaningful verification analyses of cloud ceiling and visibility forecasts. Verification of these forecasts is performed based on data from surface METAR stations, which for some areas are densely located and others only sparsely located. Forecasts, which are made over an entire grid, may be penalized multiple times for an incorrect forecast if there are many METAR stations situated closely together. A coverage design technique in conjunction with a probability of detection analysis is employed to find an "optimal" network design to be used to better score forecasts over densely located regions. Preliminary results for a network of 48 monitors in the San Francisco bay area suggest that the removal of some stations would provide a more accurate verification of forecasts.

Amy Grady

National Institute of Statistical Science

agrady@niss.org

Richard L. Smith

Department of Statistic

University of North Carolina at Chapel Hill

rls@email.unc.edu

Abstract. In the past decade, marked emphasis in climate change research has been placed on extremes and their environmental impacts. In particular, precipitation has and continues to be looked at not only because current research indicates positive trends but also the direct impacts precipitation extremes can have – e.g. floods, landslides, and infrastructural damage. Focusing on the continental U.S., the general consensus within the climate change community indicates significant positive trends in both the average rainfall and its extremes across most of the U.S. In fact, work of Karl et al of the National Climatological Data Center suggest that the trends in the extremes are driving the trends in the total rainfall. To date, most of the analytical work on this data has been more empirical – first aggregating the data across large regions into summary statistics and then performing trend analyses on these aggregated statistics. As increased emphasis is placed on impact analysis and validation within general circulation models with respect to extremes, the need for more sophisticated statistics has also increased. Here, we analyze the individual precipitation series from 5873 stations across the continental U.S. from the Historical Climatological Network using a threshold model from extreme value theory. To combine the stations, we utilize a spatial integration model which not only takes into account a spatial covariance that models the dependence between the stations’ parameters but also measurement error.

Keywords: U.S. Precipitation, Extreme Value Theory, Threshold Models, Spatial Integration Models

Brian Gray¹, Roger Haro², Jim Rogala¹ and Jennifer Sauer¹

¹Upper Midwest Environmental Sciences Center

U.S. Geological Survey, La Crosse, WI USA

brgray@usgs.gov

²River Studies Center

University of Wisconsin, La Crosse

La Crosse, WI USA

Abstract. Zero-inflated count distributional assumptions have become increasingly popular for modelling counts with "excess zeroes." This modelling approach assumes that structural zeroes complement zeroes arising from count distributional assumptions. For this reason, zero inflated approaches have been helpful for modelling ostensible count data with zeroes deriving from observer error or from sampling under circumstances unsuitable for generating counts. The benefits and potential drawbacks associated with zero-inflated count models are discussed with reference to zero-inflated negative binomial (Poisson-gamma mixture) models of mayfly abundance data. For these data, a count model was substantially improved by the addition of a postulated zero process (χ2 LRT statistic = 78.0, df = 3). The model assumed mean counts varied across a range of habitat conditions while the zero process varied by “suitable,” “intermediate” and “unsuitable" habitat categories. The odds of a zero process was estimated as 0.00, 0.25 and 3.90, respectively. Negative binomial dispersion parameter estimates decreased following inclusion of the zero process component, and notably for heterogeneous, high-energy habitats. This example demonstrates that zero-inflated models may usefully augment count models in circumstances where count processes appear unlikely.

Keywords: negative binomial distribution, LTRMP, zero inflated count models

S. Grunwald, B.E. Weinrich, K.R. Reddy, and J. P. Prenger

Soil and Water Science Department

University of Florida

2169 McCarty Hall

PO Box 110290

Gainesville, FL 32611, USA

SGrunwald@mail.ifas.ufl.edu

Abstract. The eutrophication of subtropical wetland ecosystems results in changes of biogeochemical patterns, pedo- and biodiversity, and ecological function. We investigated an impacted subtropical wetland, which is undergoing natural succession. We collected 20 biogeochemical soil properties at 267 sites to characterize the current ecological status. This exhaustive dataset served as a reference. Our goal was to identify properties which accounted for much of the spatial and the parameter variability. We used Conditional Sequential Gaussian Simulation (CSGS) to generate realizations of biogeochemical properties to characterize spatial patterns and to assess explicitly the uncertainty of predictions. We used Principal Component (PC) Analysis to transform a number of possibly correlated variables into a smaller number of uncorrelated variables reducing character space. CSGS was used to generate realizations of PCs. Each biogeochemical property was mapped into a PC indicating its significance to explain variability in the dataset. We randomly reduced the number of observations before generating realizations and tested the accuracy with a validation dataset. Results for P indicated that a sample density of > 2.52 sites/100 ha was the minimum to reproduce the spatial patterns and variability across the site.

Our results are valuable to document the current ecological spatial patterns in this wetland and the constraints to characterize spatial and parameter variability.

Keywords: stochastic simulation, spatial variability, parameter variability, biogeochemical properties, wetlands

N. Hamm*, J. W. Hall* and M. G. Anderson**

*Department of Civil Engineering

**School of Geographical Sciences

University of Bristolr

Queen's Building

University Walk

Bristol BS8 1TR

United Kingdom

n.hamm@bristol.ac.uk

Abstract. This research investigated the sensitivity–analysis and uncertainty–analysis of a combined (slope) hydrological and stability model (CHASM) (Wilkinson et al., 2002). CHASM has been developed at the University of Bristol over the past two decades and its fast execution time make it appropriate for the implementation of large numbers of simulations. We implemented the variance–based sensitivity analysis approach (Chan et al., 2000) which allowed analysis of first and higher order effects attributed to the model parameters and input data. This was then extended to investigate the significance of spatial structure in the parameter uncertainty (Hall et al., in review). Some general sensitivity analysis had been conducted on CHASM in the past (Anderson & Kemp, 1992), however, this type of formal sensitivity analysis is novel in its application to geotechnical models of this type. It was found to be valuable for gaining a detailed understanding of the statistical importance of the model parameters, leading to an enhanced understanding of the physical processes. This is a necessary precursor for investigating the uncertainty imposed on the model output as attributed to climate change scenarios (which leads to uncertainty in the input data). Finally, the fast execution time means that this simulation based analysis can be used to investigate the viability of less computationally expensive (but more approximate) methods for sensitivity and uncertainty analysis.

Keywords: CHASM (combined hydrological and stability model); Variance–based sensitivity analysis; Uncertainty analysis; Geotechnical models

N. Hamm, P. M. Atkinson and E. J. Milton

School of Geography

University of Southampton

Southampton SO17 1BJ

United Kingdom

n.hamm@soton.ac.uk

Abstract. The empirical line method (ELM) is a used widely for the atmospheric correction of remotely sensed imagery. The ELM is based on a linear regression model, where at–surface reflectance (measured in the field) is the dependent variable and at–sensor radiance (from the remotely sensed imagery) is the predictor variable. Hence it is necessary to pair the field measurements with the spatially coincident remotely sensed measurements. The ELM has also been extended to ensure that the field and remotely sensed data are defined on the same support by using block kriging and block conditional–simulation to aggregate the field measurements to pixel sized supports (Hamm et al., 2002). Implementations generally assume (implicitly) that the location of the field measurements and the geometric correction of the imagery are perfect. This research relaxes that assumption and has sought to quantify the uncertainty in implementation of the ELM that is attributed to uncertainty in the location of the field measurements. This can be constrained by sample size and pixel size (which also affect prediction accuracy). Hence, if the remote sensing practitioner requires a specific prediction accuracy this allows us to specify both the number of field measurements he or she needs to collect and the accuracy with which they need to record location. The approach of Hamm et al. (in press) has been considerably refined in two ways. First, we have adopted a model–based rather than simulation–based approach to investigating positional uncertainty. Second, we have gone beyond demonstrating the problem to quantifying it and providing advice for reducing its impact. This has also provided further methodological benefits by demonstrating the impact of positional uncertainty on geostatistical estimation and prediction.

John Haslett

Dept of Statistics

Trinity College

Dublin Ireland

John.Haslett@tcd.ie

M. Whiley, S. Bhattacharya, J.R.M Allen, B. Huntley, and F. Mitchell

Abstract. We consider the problem of reconstructing pre-historic climates using fossil data extracted from lake sediment cores. A hierarchical Bayesian modelling approach is presented and its use demonstrated in a relatively small but statistically challenging exercise, the reconstruction of pre-historic climate at Glendalough in Ireland using fossil pollen data. This computationally intensive method extends current approaches by (a) explicitly modelling uncertainty at all stages and (b) reconstructing entire climate histories.

The statistical issues raised relate to the use of compositional data (pollen) with covariates (climate) which are available at many modern sites but are missing for the fossil data. The compositional data arise as mixtures and the missing covariates have a temporal structure.

Novel aspects of the method include non-parametric modelling of two dimensional response surfaces, the exploitation of parallel processing and the use of a random walk with long tailed increments.

We present some details of the study, contrasting its reconstructions with those generated by a method in use in the palaeoclimatology literature. We suggest that the method provides a basis for resolving important challenging issues in palaeoclimate research but draw attention to several challenging statistical issues.

Keywords: Compositional data, Gaussian processes, long tailed increments,Markov chain Monte Carlo

G.B.M. Heuvelink1), J.M. Schoorl, B. Minasny, A. Veldkamp and D. Pennock

1)ALTERRA and Department of Soil Science and Geology, Wageningen University and Research Centre, P.O. Box 47, 6700 AA

Wageningen, The Netherlands

gerard.heuvelink@wur.nl

Abstract. Soil redistribution is the net result of erosion and sedimentation. Knowledge of how soil is redistributed in space and time is of great importance for land managers, be it from an agricultural, land planning or land protection perspective. Assessment of soil redistribution in a given landscape over a given period of time may be done using process-based and empirical approaches. Process-based approaches rely on knowledge of how various environmental processes acting in the landscape cause soil to move from one place to another. Empirical approaches rely on observations of soil redistribution, which are interpolated in space and time using (geo)statistical methods. In this paper we use space-time Kalman filtering to combine the two basic approaches. At each time step, the Kalman filter first predicts soil redistribution using process knowledge as contained in the state equation. Next, these predictions are conditioned to the observations. The case study that is used to illustrate the methodology concerns a six hectare part of the Hepburn research site, located on the hummocky till plains of Saskatchewan, Canada. Tillage erosion causes soil to move downward along the steepest gradient, whereby the amount of soil loss per year is assumed linearly related to slope angle. Observations of soil redistribution are derived using Cesium 137 as a tracer.

Keywords: geostatistics, space-time interpolation, tillage erosion, data assimilation

Ivana Horova, Zdenek Pospisil, and Jiri Zelinka

Department of Applied Mathematics

Masaryk University in Brno

60200 Brno

Czech Republic

horova@math.muni.cz

Abstract. The puropse of this contribution is to present both nonparametric and deterministic modelling of survival data.We consider the model of random censorship where the data are censored from the right.This type of censorship is often met in many applications,especially in clinical research and in life testing of complex technical systems.First,the hazard function for given breast carcinoma data set is estimated by a kernel method. On the other hand,the data on events observed over time can be described by a deterministic dynamical model depending on the parameters.The obtained kernel estimate of the hazard function now serves as a basis for the identification of parameters in the deterministic model.Further,these parameters make possible to find the solution of this dynamical model.This procedure offers a suitable tool for analyzing in hazard rates.

Keywords: Hazard function,kernel,dynamical model

Zuzana Hrdličková

Department of Applied Mathematics, Masaryk University Brno,

Janáčkovo nám. 2a, 662 95 Brno

Czech Republic

zuzka@math.muni.cz

Abstract. The approximation of the power of the test used in generalized linear models for comparing the population means (ANOVA type models) and based on scale deviance statistics will be derived in the contribution. The algorithm for calculation of the asymptotic power of the above mentioned test will be described and this algorithm will be computer implemented in MATLAB. The asymptotic power will be compared with the simulated power of the test for small sample sizes (for some variables with exact distribution such as Poisson or Gamma for example). Finally obtained results will be applied to environmetrical data for finding the suitable experimental design.

Keywords: power function, exponential class of distributions, generalized linear model, ANOVA type model

Model Testing for Spatial Strong-mixing Data

Rosaria Ignaccolo* e Nunziata Ribecco**

*Dipartimento di Staistica e Matmatica Applicata

University degli Studi di Torino, Italy

ignaccolo@econ.unito.it

** Dipartimento di Scienze Statistiche

University degli Studi di Bari, Italy

ribecco@dss.uniba.it

Abstract. In analysing the distribution of a variable in a space, each value is subject not only to the source of the phenomenon but also to its localisation. In this paper, we fit the model of the distribution, taking explicitly into account the spatial autocorrelation among the observed data. To this end we first suppose that the observations are generated by a strong-mixing random field. Then, after estimating the density of the considered variable, we construct a test statistics in order to verify the goodness of fit of the observed spatial data.. The proposed class of tests is a generalization of the classical chi-square-test and of the Neyman smooth test. The asymptotic behaviour of the test is analysed and some indications about its implementation are provided.

Keywords: goodness of fit; correlated data; spatial process; mixing random field.

J.S. Iiames¹*, R. Congalton², D. Pilant³, and T. Lewis³

¹Environmental Protection Agency

Research Triangle Park, NC USA

iiames.john@epa.gov

²University of New Hampshire

Durham, NH

³Environmental Protection Agency

Research Triangle Park, NC USA

Abstract. The ability to effectively use remotely sensed data for environmental spatial analysis is dependent on understanding the underlying procedures and associated variances attributed to the data processing and image analysis technique. Equally important, also, is understanding the error associated with the given reference data used to assess the accuracy of the image product. This paper details measurement variance accumulated in the development of a leaf area index (LAI) reference map used to assess the accuracy of the Moderate Resolution Imaging Spectroradiometer (MODIS) MOD15A LAI 1000-m product in the southeastern United States.

MODIS LAI was compared with reference data derived from Landsat Enhanced Thematic Mapper (ETM+) during the 2002 field season in the Albemarle-Pamlico Basin in Virginia and North Carolina. Ground-based optical LAI estimates were correlated with various ETM+ derived vegetation indices (VI’s) at a 30-m resolution pixel. These 30-m pixels were scaled up to the 1000-m MODIS LAI pixel resolution and averaged to give one LAI value. A detailed listing of error propagation for this reference data set includes uncertainty associated with: (1) two integrated optical LAI field estimating techniques (Tracing Radiation and Architecture of Canopies, TRAC instrument, and hemispherical photography), (2) choice of site-specific VI’s, and (3) image-to-image registration.

Keywords: MODIS, LAI, error propagation, accuracy

Geoffrey M. Jacquez

BioMedware, Inc.

516 North State Street

Ann Arbor, MI 48104

Jacquez@BioMedware.com

Abstract: Real-world systems are dynamic, complex and geographic, yet many modeling tools for analyzing complex systems are not spatial, and GIS do to adequately represent time. This presentation describes two new approaches: Space-Time Information Systems (STIS), and Model Transition Sensitivity Analysis (MTSA).

Current GIS are based on spatial data models (the "what, when" diad) that inadequately characterize the "what, where, when" triad" needed for effective representation of complex systems. Purely spatial GIS cannot deal readily with space-time georeferencing nor space-time queries, and instead are best suited to "snapshots" of static systems. These deficiencies prompted many geographers to call for a "higher-dimensional GIS" (a STIS) to better represent space-time dynamics. When formulating models of complex systems, critical choices are made regarding model type and complexity. Model type is the mathematical approach employed, for example, a deterministic model versus a stochastic model. Model complexity is determined by the amount of abstraction and simplification employed during model construction. A growing body of work demonstrates that choice of model type and complexity has substantial impacts on simulation results and on model-based decisions. This presentation describes STIS and MTSA approaches that allow researchers to transit seamlessly from a deterministic model, to its stochastic counterpart, and on to its individual event history representation.

Keywords: Complex systems; space-time information systems; Model Transition Sensitivity Analysis

Olaf Jensen¹, Mary Christman², Glenn Moglen³, and Thomas Miller¹

¹Center for Environmental Science

Chesapeake Biological Laboratory

University of Maryland, MD 20688 USA

jensen@cbl.umces.edu

²Dept. Animal and Avian Sciences

University of Maryland

College Park, MD 20742 USA

³Department of Civil and Environmental Engineering

University of Maryland

College Park, MD 20742 USA

Abstract. Effective management of marine resources requires that we develop accurate, unbiased estimates of the abundance of those resources. Traditionally, abundances have been estimated from design-based survey methods. More recently, model-based geostatistical approaches have gained favor. Typically, a Euclidean distance metric is used for variogram calculation and kriging. While such a metric makes sense within convex polygons, it has the potential to introduce error in highly invaginated regions such as estuaries. A natural alternative is the use of "through the water distance" (TTWD). We used TTWD-based kriging to estimate the abundance of blue crab (Callinectes sapidus) within the Chesapeake Bay from 11 years of survey data. To do so, we developed efficient and adaptable algorithms in a GIS to calculate TTWD. The algorithms are based on a rasterized water body and a cost-distance function that estimates the shortest path through the water between two points. TTWD-based variogram and kriging routines were developed and used to predict the distribution and abundance of crabs throughout the Chesapeake Bay. Here we compare three different methods: the traditional survey method, kriging using Euclidean distance, and kriging using TTWD. Cross-validation confirmed that the TTWD metric resulted in consistently more accurate predictions than the Euclidean metric. Consistent reductions in the range and sill parameters of the variogram were observed as well.

Keywords: estuary, distance metric, Geographic Information System, geostatistics, variogram

Kazutomo Kawamura

The National Defense Academy (NDA)

Dept of Mathematics, Hashirimizu 1-10-20

Yokosuka, 239-8686 Japan

kawamura@nda.ac.jp

Abstract. For given lattice space as in figure 1, we consider a path by movement of point P from initial point A to opposite corner point B. The movement consists of two single (1-step )movements, one is to east E and the other is to south S at each step.

We consider cost or risk function on the space having two types of particular distributions. One of the distributions is uniform and the other is exponential. The reason of the selection of the particular distributions comes from the idea of modification about the cost or the risk in natural environment. We specially select them to evaluate the risk in jungle exploration and the cost or the risk in a flight of aircraft in the sky.

We can evaluate a path by calculating the sum of costs we have to pay on it. The aim of this work is to find affordable optimal procedure, which yields a optimal path with lower evaluation.

We have developed PC software of simulation with Yoshihiro Honda and have practiced it. The simulation is based on deriving cost matrices N=1000 times to pursue the optimality. And have derived k-steps optimal (k=0, 1. 2, … ) path and its total cost corresponding those paths on each simulated cost matrix. Simply talking, we have derived N=1000 times data of total costs corresponding k-steps optimal (k=0, 1. 2, … ) paths on a simulated matrix.

As a conclusion, we can express followings. By statistical investigation, we have confirmed that our procedure with 1-step optimality has incredible good property. The other property is expressed that the relation of distribution from total cost are almost same regardless which distribution of the cost has applied.

Keywords: Mathematical Programming, Dynamic Programming, Random Cost Function, Step-wise Optimality, Risk Control.

Konstantin Krivoruchko¹ and Jorge Mateu²

¹Environmental Systems Research Institute

380 New York Street

Redlands, CA 92373-8100, USA

kkrivoruchko@esri.com

²Department of Mathematics

Campus Riu Sec

University Jaume I , E-12071

Castellon, Spain

mateu@mat.uji.es

Abstract. Modern technology, including remote sensing, digital aerial photographs and spectrometer imaging, is used nowadays to develop inventories, posing new statistical problems. The objective of modern forestry includes a multitask problem field, for which forest ecology, landscape ecology and related statistical methods become increasingly important. Forestry uses numerous methods for statistical analysis. A considerable part of them belong to spatial statistics that includes point process statistics as a particular interesting area. Typically point process analysis and modeling in forestry comes down to such details as locations of single trees and tree characteristics such as diameter at breast height, stem increment during a given time span, species code or degree of damage by environmental factors.

In the context of spatial (marked) point patterns we have point locations in form of coordinates (Cartesian, UTM, etc) and marks associated to each location. It is still laborious to obtain such data sets by classical measurements methods. New technological developments are changing the situation drastically. For example, distance measurements can be done using laser techniques and the satellite-based global positioning system (GPS). And individual trees can be observed through image analysis with reasonable precision, with the exception of trees that are very close together or of small trees growing within the canopy of bigger trees. A compromise are indirect observations, such as aerial images combined with ground-based measurement. In any case, even in the most perfect situation, there exists a locational error concerning the precision of the coordinates of each point location.

In this paper we focus on the analysis, determination and specification of locational error in point patterns. We evaluate the importance of locational error when affecting to the interaction structure of the spatial pattern and define practical measures to control the amount of locational error. We analyze several real data sets in environmental applications.

Keywords: Environmental processes, Locational errors, Spatial accuracy, Spatial point patterns, Uncertainty.

Barry Kronenfeld

Department of Geography

University at Buffalo, The State University of New York

105 Wilkeson Quad, Buffalo, NY 14150

bjk3@buffalo.edu

Abstract. The increasing use of continuous classification methods to generalize environmental data has led to a persistent question of how to determine class membership values, as well as how to interpret these values once they have been determined. This paper integrates the above two problems as complementary aspects of the same data reduction process. Within this process, it is shown that a fuzzy classification technique based on Principal Components Analysis will minimize the amount of information lost through classification. The PCA-based fuzzy classification technique is analogous to linear spectral unmixing models in remote sensing, and differs from algorithms such as fuzzy k-Means in that primary attention is focused on preserving an accurate representation of the underlying attribute data, rather than maximizing the internal consistency of each class. This focus suggests that PCA-based fuzzy classification may be particularly appropriate for data modeling applications. The technique is demonstrated and compared to fuzzy k-Means by using forest inventory data from the U.S. Forest Service’s Forest Inventory & Analysis (FIA) program to produce fuzzy ecological regions of the eastern United States.

Data reduction, fuzzy classification, principal components analysis, FIA, ecoregions

Kristopher Kuzera

Clark University

IDCE

950 Main Street

Worcester, MA 01610-1477

kkuzera@clarku.edu

R. Gil Pontius, Jr.

rpontius@clarku.edu

Abstract. The cross-tabulation matrix is the basis for several popular statistics when comparing two maps of a common categorical variable. It is straight forward to compute the matrix when the pixels are hard classified. It is more challenging to compute the matrix when the pixels are soft classified, which is necessary to compare maps at multiple resolutions. This paper contrasts two methods to compute the matrix for soft classified pixels. The first method is based on conventional set theory, hence on a multiplication rule. The second method is based on a hybrid conventional-fuzzy set theory, hence a composite minimum-multiplication rule. For each method, we analyze several popular summary statistics: overall proportion correct, user’s accuracy, producer’s accuracy, conditional Kappa by row, conditional Kappa by column, tau, the Nishii-Tanaka coefficient, and the standard Kappa index of agreement along with its variants Kno & Klocation. We examine the behavior of each statistic at multiple resolutions to see which statistics give which information at which scales. We illustrate the methods by comparing maps of land cover in and near Worcester Massachusetts from 1971 and 1999.

Keywords: coefficient, matrix, resolution, scale, soft classification.

Guillaume Larocque

Natural Resource Sciences Department

Macdonald Campus of McGill University

21,111 Lakeshore

Ste-Anne-de-Bellevue

Québec, Canada H9X 3V9

guillaume.larocque@mail.mcgill.ca

Pierre Dutilleul

Department of Plant Science

Macdonald Campus of McGill University

Bernard Pelletier

Natural Resource Sciences Department and Department of Plant Science

Macdonald Campus of McGill University

James W. Fyles

Natural Resource Sciences Department

Macdonald Campus of McGill University

Abstract. Regionalized multivariate analysis (RMA) and factorial kriging analysis are multivariate geostatistical methods developed in the last two decades to unveil scales of variation in spatial datasets and to assess relationships among regionalized variables at specific scales. Although they have been widely used in the environmental and earth sciences, there has been no adequate assessment of the uncertainty associated with the estimation of parameters of interest in those methods. In this paper, we identify the sources of uncertainty in RMA and develop a theoretical framework to quantify the bias and the variance of estimators of common parameters such as sills, correlation coefficients and R-squares. Our framework is based on the generalized least-squares fit of the linear model of coregionalization. Through Monte Carlo simulations, we demonstrate the effectiveness of our procedure and show that large sample sizes are often needed to obtain accurate and precise estimates in RMA. An example with ecological data illustrates that an assessment of uncertainty is essential to avoid erroneous conclusions about the phenomenon studied.

Keywords: uncertainty, coregionalization, multivariate geostatistics, scale, ecology.

Ulrich Leopold (1), Gerard B.M. Heuvelink (2), Aaldrik Tiktak (3)

Institute for Biodiversity and Ecosystem Dynamics

Universiteit van Amsterdam

Amsterdam, The Netherlands

uleopold@science.uva.nl.

Department of Soil Science and Geology

Wageningen University

Wageningen, The Netherlands

Department of Soil and Groundwater

National Institute for Public Health and Environment

Bilthoven, The Netherlands

Abstract. Agricultural activities in the Netherlands cause high nitrogen and phosphorus emissions from soil to ground- and surface water. To study and predict ground- and surface water pollution under different agricultural scenarios, a model chain (STONE) has been developed. STONE has three main components. These are the emission model CLEAN, the atmospheric transport and deposition model OPS and the soil model ANIMO. There are also links to additional models, such as to the hydrological model SWAP and the crop growth model QUADMOD. The models incorporated in STONE operate at different spatial scales (i.e., supports), mainly because each of them describes different processes and uses different input data. Aggregation and disaggregation procedures have been developed to adapt the input supports to the model support and to bring the STONE output to a desired block support of 500 × 500 m. STONE predictions are then made on a regular grid covering relevant parts of the Netherlands. Apart from support problems, another problem is that input and model uncertainties are introduced and propagated to the STONE output. The goal of this study is to quantify the uncertainty in STONE output and to determine the main causes of uncertainty. The uncertainty analysis is based on a Monte Carlo simulation approach and is complicated by the fact that it must take spatial correlation, cross-correlation and differences in spatio-temporal support into account.

Claudia Libiseller

Dept. of Mathematics

Division of Statistics

Linköping University, SE-58183

Linköping, Sweden

cllib@mai.liu.se

Abstract. To correctly assess trends in water quality data it is necessary to take into account influencing variables, such as discharge or water temperature. We distinguish two basic methods: (i) one-step procedures, like the Partial Mann-Kendall (PMK) test or multiple regression, and (ii) two-step procedures, which include a normalisation step followed by a trend test on the residuals. Which procedure is most appropriate depends strongly on the relationship between the response variable under consideration and the influencing variables. For example, PMK tests can be superior if there are long and varying time lags in the water quality response. Two step procedures are particularly useful, when the shape of the temporal trend is of great interest. They can, however, be misleading if one of the influencing variables itself exhibits a trend or long-term tendency. In this paper we will present pros and cons of some trend testing techniques using Swedish water quality data for illustrations.

Greg Liknes and Mark Nelson

USDA Forest Service

1992 Folwell Avenue

St. Paul, MN 55108 USA

gliknes@fs.fed.us

Abstract. The Forest Inventory and Analysis (FIA) program of the USDA Forest Service collects forest attribute data on permanent plots arranged on a hexagonal grid across all 50 states and Puerto Rico. Due to budget constraints and the natural variability among plots, sample sizes sufficient to satisfy national FIA precision standards are seldom achieved for most inventory variables unless the estimation process is enhanced with ancillary data. When used as the basis for creating strata with stratified estimation, classified satellite imagery has been demonstrated to be an effective source of such ancillary data. In particular, the National Land Cover Dataset (NLCD), a national landcover classification based on satellite imagery, has been used to produce substantial increases in the precision of statewide forest inventory estimates.

Because inventories are conducted on an annual basis, it is desirable to create strata using a product that is updated more frequently than the NLCD. In particular, data from the MODIS sensor are available every 1-2 days, although at a much coarser spatial resolution than the Landsat data used in the creation of the NLCD (250m or 500m vs 30m). In this study, the effectiveness of strata created by classifying MODIS satellite imagery in increasing precision of FIA estimates is compared to that of strata created from the NLCD.

Keywords: Stratified estimation, MODIS, spatial resolution

Linda Lilburne and Heather North

Landcare Research

P.O. Box 69

Lincoln, Canterbury, New Zealand

lilburnel@landcareresearch.co.nz

Abstract. Probability of groundwater contamination due to leaching of nitrate from agricultural sources can be modelled at a regional scale. This requires spatial information on soil properties, climate, land use, standard management practices, and aquifer vulnerability. One of the key management pressures in Canterbury, New Zealand is the practice of leaving land fallow during the winter months, because any nitrate that is present is likely to be leached since there is no plant uptake. Remote sensing imagery has been successfully used to identify land that is bare for significant periods in the winter and early spring. This was achieved by use of simple rules on a temporal sequence of three Landsat 7 images.

This paper analyses the sources of error in mapping fallow ground using remote sensing image sequences. Potential sources of error include suitability of the logical model, timing of image acquisition, scale mismatch, incorrect reference data, geometric errors between images, and radiometric variation both within and between images (month to month and year to year). In particular we investigate our ability to correctly classify land into bare, sparsel