Reinhard Furrer

Challenges in Combining Projections from Multiple Climate Models

Recent coordinated efforts, in which numerous general circulation climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multimodel ensembles sample initial conditions, parameters, and structural uncertainties in the model design, and they have prompted a variety of approaches to quantifying uncertainty in future climate change. International climate change assessments also rely heavily on these models. These assessments often provide equal-weighted averages as best-guess results, assuming that individual model biases will at least partly cancel and that a model average prediction is more likely to be correct than a prediction from a single model based on the result that a multimodel average of present-day climate generally outperforms any individual model. This study outlines the motivation for using multimodel ensembles and discusses various challenges in interpreting them. Among these challenges are that the number of models in these ensembles is usually small, their distribution in the model or parameter space is unclear, and that extreme behavior is often not sampled. Model skill in simulating present-day climate conditions is shown to relate only weakly to the magnitude of predicted change. It is thus unclear by how much the confidence in future projections should increase based on improvements in simulating present-day conditions, a reduction of intermodel spread, or a larger number of models. Averaging model output may further lead to a loss of signal— for example, for precipitation change where the predicted changes are spatially heterogeneous, such that the true expected change is very likely to be larger than suggested by a model average. Last, there is little agreement on metrics to separate ‘‘good’’ and ‘‘bad’’ models, and there is concern that model development, evaluation, and posterior weighting or ranking are all using the same datasets. While the multimodel average appears to still be useful in some situations, these results show that more quantitative methods to evaluate model performance are critical to maximize the value of climate change projections from global models.

Covariance Tapering for Interpolation of Large Spatial Datasets

Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.

Multivariate Bayesian analysis of atmosphere-ocean general circulation models

Numerical experiments based on atmosphere–ocean general circulation models (AOGCMs) are one of the primary tools in deriving projections for future climate change. Although each AOGCM has the same underlying partial differential equations modeling large scale effects, they have different small scale parameterizations and different discretizations to solve the equations, resulting in different climate projections. This motivates climate projections synthesized from results of several AOGCMs’ output. We combine present day observations, present day and future climate projections in a single highdimensional hierarchical Bayes model. The challenging aspect is the modeling of the spatial processes on the sphere, the number of parameters and the amount of data involved. We pursue a Bayesian hierarchical model that separates the spatial response into a large scale climate change signal and an isotropic process representing small scale variability among AOGCMs. Samples from the posterior distributions are obtained with computer-intensive MCMC simulations. The novelty of our approach is that we use gridded, high resolution data covering the entire sphere within a spatial hierarchical framework. The primary data source is provided by the Coupled Model Intercomparison Project (CMIP) and consists of 9 AOGCMs on a 2.8 by 2.8 degree grid under several different emission scenarios. In this article we consider mean seasonal surface temperature and precipitation as climate variables. Extensions to our model are also discussed.

Aerosol indirect effect studies at Southern Great Plains during the May 2003 Intensive Operations Period

During May 2003 the Department of Energys Atmospheric Radiation Measurement Program conducted an Intensive Operations Period (IOP) to measure the radiative effects of aerosol and clouds. A suite of both in situ and remote sensing measurements were available to measure aerosol and cloud parameters. This paper has three main goals: First, it focuses on comparison between in situ retrievals of the radiatively important drop effective radius r e and various satellite, airborne, and surface remote sensing retrievals of the same parameter. On 17 May 2003, there was a fortuitous, near-simultaneous sampling of a stratus cloud by five different methods. The retrievals of r e agree with one another to within ∼20%, which is approximately the error estimate for most methods. Second, a methodology for deriving a best estimate of r e from these different instruments, with their different physical properties and sampling volumes, is proposed and applied to the 17 May event. Third, the paper examines the response of r e to changes in aerosol on 3 days during the experiment and examines the consistency of remote sensing and in situ measurements of the effect of aerosol on r e . It is shown that in spite of the generally good agreement in derived r e , the magnitude of the response of r e to changes in aerosol is quite sensitive to the method of retrieving r e and to the aerosol proxy for cloud condensation nuclei. Nonphysical responses are sometimes noted, and it is suggested that further work needs to be done to refine these techniques.

Spatial relationship between climatologies and changes in global vegetation activity

Vegetation forms a main component of the terrestrial biosphere and plays a crucial role in land-cover and climate-related studies. Activity of vegetation systems is commonly quantified using remotely sensed vegetation indices (VI). Extensive reports on temporal trends over the past decades in time series of such indices can be found in literature. However, little remains known about the processes underlying these changes at large spatial scales. In this study, we aimed at quantifying the spatial relationship between changes in potential climatic growth constraints (i.e. temperature, precipitation and incident solar radiation) and changes in vegetation activity (1982-2008). We demonstrate an additive spatial model with 0.5° resolution, consisting of a regression component representing climate-associated effects and a spatially correlated field representing the combined influence of other factors, including land-use change. Little over 50% of the spatial variance could be attributed to changes in climatologies; conspicuously, many greening trends and browning hotspots in Argentina and Australia. The nonassociated model component may contain large-scale human interventions, feedback mechanisms or natural effects, which were not captured by the climatologies. Browning hotspots in this component were especially found in subequatorial Africa. On the scale of land-cover types, strongest relationships between climatologies and vegetation activity were found in forests, including indications for browning under warming conditions (analogous to the divergence issue discussed in dendroclimatology).

A spatial analysis of multivariate output from regional climate models

Climate models have become an important tool in the study of climate and climate change, and ensemble experiments consisting of multiple climate-model runs are used in studying and quantifying the uncertainty in climate-model output. However, there are often only a limited number of model runs available for a particular experiment, and one of the statistical challenges is to characterize the distribution of the model output. To that end, we have developed a multivariate hierarchical approach, at the heart of which is a new representation of a multivariate Markov random field. This approach allows for flexible modeling of the multivariate spatial dependencies, including the cross-dependencies between variables. We demonstrate this statistical model on an ensemble arising from a regional-climate-model experiment over the western United States, and we focus on the projected change in seasonal temperature and precipitation over the next 50 years.

Organic pollutants in compost and digestate.

In Europe, 9.3 x 10(6) t(dry weight (dw)) of compost and digestate are produced per year. Most of this is applied to agricultural land, which can lead to considerable inputs of organic pollutants, such as polychlorinated biphenyls (PCB) and polycyclic aromatic hydrocarbons (PAH) to soil. This paper presents an inventory of the pollutant situation in source-separated composts, digestates and presswater in Switzerland by a detailed analysis of over 70 samples. PCB concentrations ( summation PCB 28, 52, 101, 118, 138, 153, 180) were significantly higher in urban (median: 30 microg kg(-1)dw, n = 52) than in rural samples (median: 14 microg kg(-1)dw, n = 16). Together with low concentrations in general, this points to aerial deposition on compost input material as the major contamination pathway. Enantiomeric fractions of atropisometric PCB were close to racemic. Median PAH concentration was 3010 microg kg(-1)dw( summation 15PAH, n = 69), and one quarter of the samples exhibited concentrations above the relevant Swiss guide value for compost (4000 microg kg(-1)dw). The levels were influenced by the treatment process (digestate > compost), the season of input material collection (spring-summer > winter > autumn), the particle size (coarse-grained > fine-grained), and maturity (mature > less mature). The main source of PAH in compost was pyrogenic, probably influenced mainly by liquid fossil fuel combustion and some asphalt abrasion, as suggested by multiple linear regression. This study, together with a companion paper reporting on other organic contaminates including emerging compound classes, provides a starting point for a better risk-benefit estimation of the application of compost and digestate to agricultural soil in Switzerland.

Anisotropy in the Spatial Distribution of Roller-Measured Soil Stiffness

The geostatistical analysis of roller-measured soil properties (from continuous compaction control and intelligent compaction) is required for advanced quality control/quality assurance of earthwork and asphalt compaction. This paper explores the existence of anisotropy in the spatial distribution of roller-measured soil stiffness and the effect of anisotropy on kriging. Field testing was conducted to collect roller measurement value (MV) data over typical roadway embankment evaluation areas and on a large square area to enable a robust investigation of anisotropy. The semivariogram analysis of the field data clearly indicates that range anisotropy exists. The spatial distributions of roller MV data are different in the longitudinal x -direction than in the transverse y -direction. Magnitudes of range anisotropy ( x-range/y-range ) varied from 2.4 to over 5. The observed range anisotropy is not due to the roller measurement system; rather, it is likely due to the directional nature of earthwork constructi...

Spatial model fitting for large datasets with applications to climate and microarray problems

Many problems in the environmental and biological sciences involve the analysis of large quantities of data. Further, the data in these problems are often subject to various types of structure and, in particular, spatial dependence. Traditional model fitting often fails due to the size of the datasets since it is difficult to not only specify but also to compute with the full covariance matrix describing the spatial dependence. We propose a very general type of mixed model that has a random spatial component. Recognizing that spatial covariance matrices often exhibit a large number of zero or near-zero entries, covariance tapering is used to force near-zero entries to zero. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches. Results will be demonstrated with two datasets. The first consists of regional climate model output that is based on an experiment with two regional and two driver models arranged in a two-by-two layout. The second is microarray data used to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.

Scale space multiresolution analysis of random signals

A method to capture the scale-dependent features in a random signal is proposed with the main focus on images and spatial fields defined on a regular grid. A technique based on scale space smoothing is used. However, while the usual scale space analysis approach is to suppress detail by increasing smoothing progressively, the proposed method instead considers differences of smooths at neighboring scales. A random signal can then be represented as a sum of such differences, a kind of a multiresolution analysis, each difference representing details relevant at a particular scale or resolution. Bayesian analysis is used to infer which details are credible and which are just artifacts of random variation. The applicability of the method is demonstrated using noisy digital images as well as global temperature change fields produced by numerical climate prediction models.