Research products are usually refereed papers and conference presentations. For some projects, the research may be of interest to a general audience, in which case we release an additional research product on the web; we call these Web-Projects.

  • The Web-Project Global CO2 Flux shows global estimation of CO2 sources and sinks (flux) and their associated uncertainties, obtained from atmospheric CO2 concentration data and sophisticated Bayesian statistical models. 
  • The Web-Project Warming shows North American temperature change projected in the next 50 years.
  • The Web-Project Ice Streams shows the results of Bayesian hierarchical modelling of ice streams' stress fields and velocity fields.
  • The Web-Project ENSO (El Nino Southern Oscillation) shows long-lead forecasting of sea surface temperature in the tropical Pacific Ocean.
  • The Web-Projects TCO (Total Column Ozone) and CO2 (Carbon Dioxide) show daily maps, respectively, of TCO and CO2 values, where each map comes with a second map that visualises its uncertainty.
  • The Web-Project STB (Sources to Biomarkers) seeks to characterise multi-pollutant human exposures by linking sources to biomarkers using a hierarchical Bayesian statistical model.

Global CO2 Flux: Bayesian statistical inversion using the WOMBAT framework

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This Web-Project by Noel Cressie, Josh Jacobson, and Michael Bertolacci, features WOMBAT (the WOllongong Methodology for Bayesian Assimilation of Trace-gases), a framework for estimating fluxes on a global scale. Carbon dioxide (CO2) is one of several greenhouse gases, so-called because they trap heat in Earth’s lower atmosphere. Locations across Earth’s surface where CO2 is added to or removed from the atmosphere are known as sources and sinks – the rate at which this happens is known as flux. The aim of flux inversion is to characterise the pattern and scale of sources and sinks in both space and time. The nature of COsources and sinks can be very different from one location and time point to the next. For example, temperate forests occupy large parts of the terrestrial biosphere and transition from sinks to sources during the year, while volcanoes are local sources with sporadic and unpredictable outgassing of CO2. Human activity has also caused changes to the natural processes that cause these sources and sinks. As a tool to improve our understanding of the scale, variability, and patterns of the sources and sinks of the leading greenhouse gas CO2, WOMBAT produces flux estimates accompanied by uncertainty bounds on the estimates. The framework is designed to help scientists and policy-makers take uncertainty in COflux estimates into account and thus better respond to climate change.

Warming: Temperature change projected for North America

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This Web-Project represents an accounting of temperature change that is projected for North America in 2041-2070. The preponderance of our results throughout all regions of North America is one of warming, usually more than 2°C (3.6°F). Climate models have become the primary tools for scientists to project future climate change and to understand its potential impact. General Circulation Models (GCMs) usually oversimplify the regional climate processes and geophysical features, such as topography and land cover. Since local/regional climate effects are more relevant to natural-resource management and environmental-policy decisions, Regional Climate Models (RCMs) have been developed to produce high-resolution outputs on scales of 20 to 50 km. RCMs can simulate 3-hourly "weather" over long time periods and generate a vast array of outputs, from which long-run averages are commonly used as a summary of how a climate model approximates the Earth's climate. With anthropogenic forcings incorporated, they provide a means to assess natural and anthropogenic influences on climate variability.

In this Web-Project, we consider a subset of the climate-model experiment associated with the North American Regional Climate Change Assessment Program (NARCCAP). Regional Climate Models (RCMs) are run into the future for small, 50 km x 50 km regions in North America, from which we obtain 50-year temperature-change projections for all regions and all four seasons. The statistical framework to analyse the approximately 100,000 data is based on a Bayesian hierarchical spatial analysis of variance (ANOVA) model that incorporates dimension reduction.

Ice Streams: Understanding the behaviour of ice streams

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The mass balance and equilibrium state of the polar ice sheets are complex functions of external climate forcings and internal dynamical processes. To understand the behaviour of vast ice sheets and to assess future behaviour, we seek to understand the dominant forces controlling ice flow and how these forces have responded and will respond to changes in climate and external forcings. We study ice-stream dynamics via a fully Bayesian statistical analysis that incorporates physical models that are not perfectly known, and using data that are both incomplete and noisy. The physical-statistical models we propose account for these uncertainties in a coherent, hierarchical manner. Use of Bayes' Theorem allows us to make inference on all unknowns given the data. The result of that inference is a (posterior) distribution of possible values that can be summarised in a number of possible ways. For example, the posterior mean of the stress field gives average behaviour at any location in the field, and the posterior standard deviation associated with a posterior mean value shows how variable the possible values are. There are no direct measurements on stress; we infer it from basal-elevation data, surface-elevation data, and velocity data. Forward-smoothing methods can be used, but their disadvantage is that they lack a coherent accounting of uncertainties. This Ice Streams website analyses data from the Northeast Ice Stream in Greenland and indicates how scientific conclusions may be drawn from Bayesian analyses. It also includes a Tutorial on Bayesian Statistics for Geophysicists.

ENSO: Sea-surface temperature and the El Nino Southern Oscillation

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Tropical Pacific sea surface temperatures (SST) and the accompanying El Nino Southern Oscillation (ENSO) phenomenon are recognised as significant components of climate behaviour. The atmospheric and oceanic processes involved display highly complicated variability over both space and time. Researchers have applied both physically derived modelling and statistical approaches to develop long-lead predictions of tropical Pacific SSTs. The comparative successes of these two approaches are the subject of substantial inquiry and some controversy. A procedure for long-lead forecasting of Pacific SST fields, that expresses qualitative aspects of scientific paradigms for SST dynamics in a statistical manner, is presented. The investigators (Berliner, Wikle, and Cressie) would like to acknowledge the help of National Center for Atmospheric Research (NCAR) scientists in developing this procedure. Through its combining of substantial physical understanding and statistical modelling and learning, the procedure acquires considerable predictive skill. Specifically, a Markov model, applied to a low-order (EOF-based) dynamical system of tropical Pacific SSTs, with a stochastic regime transition is considered. The approach accounts explicitly for uncertainty in the formulation of the model, which leads to realistic error bounds on forecasts. The methodology that makes this possible is Bayesian hierarchical dynamic (HiDyn) modelling.

TCO: Ozone mapping

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The Antarctic ozone-hole event has become a symbol of global ozone depletion since its discovery in 1985. However, Total Ozone Mapping Spectrometer (TOMS) ozone datasets are not complete because of restrictions in sunlight availability, the coverage of satellite orbits, and other engineering problems. In order to address this deficiency in spatial coverage, Johannesson and Cressie (2004) proposed the Multi-resolution Spatial Model (MRSM), which is an effective statistical method for estimation of spatial processes based on the change-of-resolution Kalman filter (Chou et al. 1994; Huang et al. 2002) and variance-covariance likelihood inference.

During the 1990s, the patterns in the ozone hole during the Antarctic winter were similar from year to year. In September 2002, the ozone hole split, unlike in any previous years where data were available. Researchers have proposed several theories to explain the 2002 ozone-hole splitting based on a diverse collection of ozone datasets. TOMS is one of the most important resources of total column ozone (TCO) data.

This TCO website shows completed TCO estimates based on the TOMS data and the MRSM, along with a measure of each value's uncertainty. The website also contains brief background descriptions of the MRSM, the atmospheric ozone distribution, and the 2002 ozone-hole splitting event.

CO2: Global mapping of CO2

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There is increasing concern about climate change; monitoring CO2 (a leading greenhouse gas) has become a crucial scientific endeavour. Global monitoring relies in large part on satellite instruments. For example, NASA's Orbiting Carbon Observatory-2 (OCO-2) instrument to determine CO2 sources and sinks was launched in July 2014; and the Atmospheric InfraRed Sounder (AIRS) on NASA's Aqua satellite is capable of measuring radiances from which derivation of mid-tropospheric CO2 concentrations can be obtained. Daily retrievals of CO2 are sparse and incomplete with respect to the globe as a whole. Hence, statistical methods are needed that are able to exploit spatial and temporal dependencies in the data to produce complete global maps of CO2, together with the associated uncertainty estimates. Such methods need to be flexible to accommodate differing spatial variability of CO2 around the globe. In addition, they need to allow for computationally feasible statistical inference for very-large-to-massive datasets. In this Web-Project, we describe the Spatial Random Effects (SRE) model and a related optimal spatial prediction method called Fixed Rank Kriging (FRK). We discuss parameter estimation and spatio-temporal extensions. The website gives an analysis of spatial data derived from a CO2 transport model, and it shows results of a spatio-temporal analysis of mid-tropospheric CO2 from the AIRS instrument; data and associated Matlab code are provided. It also includes a Tutorial on Fixed Rank Kriging (FRK) of CO2 data.

STB: Sources to biomarkers

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An important problem in human-exposure assessment is to characterise links from sources to biomarkers (STB). In this Web-Project, we use a multi-scale (areal, residential, and personal) Bayesian hierarchical model (BHM), which describes how multi-media pathways contribute to direct routes of exposure (inhalation, ingestion, dermal). The statistical-modelling framework coherently manages and accounts for variability and uncertainty and has explicit stages for sources, areal environmental levels, indoor (residential) environmental levels, personal exposures, and biomarkers. The primary data sources are the National Human Exposure Assessment Survey (NHEXAS) Phase I data from EPA Region 5 (the six Midwest states of Illinois, Indiana, Michigan, Minnesota, Ohio, and Wisconsin) and Arizona, supplemented by census data, ambient-air monitoring data, and emissions data. NHEXAS data provide information to different stages of the model that address areal and indoor environmental conditions, personal exposures, and biomarkers. These stages combine this information in a manner akin to structural-equation modelling to discern pathways and routes of exposure. The results include characterisations of the distribution of biomarkers across the population as a whole and within sub-populations, as well as the relative contribution to biomarkers from various pathways and routes of exposure.