Daniel Cooley

Return Periods and Return Levels Under Climate Change

We investigate the notions of return period and return level for a nonstationary climate. We discuss two general methods for communicating risk. The first eschews the term return period and instead communicates yearly risk in terms of a probability of exceedance. The second extends the notion of return period to the non-stationary setting. We examine two different definitions of return period under non-stationarity. The first, which appears in Olsen et al. (Risk Anal 18:497–510, 1998), defines the m-year return level as the level for which the expected waiting time until the exceedance is m years. The second, which appears in Parey et al. (Clim chang 81(3):331–352, 2007) and Parey et al. (Environmetrics 21:698–718, 2010), defines the m-year return level as the level for which the expected number of events in an m year period is one. We illustrate the various risk communications with an application to annual peak flow measurements for the Red River of the North.

Evaluating atmospheric CO2 inversions at multiple scales over a highly inventoried agricultural landscape.

An intensive regional research campaign was conducted by the North American Carbon Program (NACP) in 2007 to study the carbon cycle of the highly productive agricultural regions of the Midwestern United States. Forty-five different associated projects were conducted across five US agencies over the course of nearly a decade involving hundreds of researchers. One of the primary objectives of the intensive campaign was to investigate the ability of atmospheric inversion techniques to use highly calibrated CO2 mixing ratio data to estimate CO2 flux over the major croplands of the United States by comparing the results to an inventory of CO2 fluxes. Statistics from densely monitored crop production, consisting primarily of corn and soybeans, provided the backbone of a well studied bottom-up inventory flux estimate that was used to evaluate the atmospheric inversion results. Estimates were compared to the inventory from three different inversion systems, representing spatial scales varying from high resolution mesoscale (PSU), to continental (CSU) and global (CarbonTracker), coupled to different transport models and optimization techniques. The inversion-based mean CO2 -C sink estimates were generally slightly larger, 8-20% for PSU, 10-20% for CSU, and 21% for CarbonTracker, but statistically indistinguishable, from the inventory estimate of 135 TgC. While the comparisons show that the MCI region-wide C sink is robust across inversion system and spatial scale, only the continental and mesoscale inversions were able to reproduce the spatial patterns within the region. In general, the results demonstrate that inversions can recover CO2 fluxes at sub-regional scales with a relatively high density of CO2 observations and adequate information on atmospheric transport in the region.

DOWNSCALING EXTREMES: A COMPARISON OF EXTREME VALUE DISTRIBUTIONS IN POINT-SOURCE AND GRIDDED PRECIPITATION DATA

There is substantial empirical and climatological evidence that precipitation extremes have become more extreme during the twentieth century, and that this trend is likely to continue as global warming becomes more intense. However, understanding these issues is limited by a fundamental issue of spatial scaling: most evidence of past trends comes from rain gauge data, whereas trends into the future are produced by climate models, which rely on gridded aggregates. To study this further, we fit the Generalized Extreme Value (GEV) distribution to the right tail of the distribution of both rain gauge and gridded events. The results of this modeling exercise confirm that return values computed from rain gauge data are typically higher than those computed from gridded data; however, the size of the difference is somewhat surprising, with the rain gauge data exhibiting return values sometimes two or three times that of the gridded data. The main contribution of this paper is the development of a family of regression relationships between the two sets of return values that also take spatial variations into account. Based on these results, we now believe it is possible to project future changes in precipitation extremes at the point-location level based on results from climate models.

The pairwise beta distribution: A flexible parametric multivariate model for extremes

We present a new parametric model for the angular measure of a multivariate extreme value distribution. Unlike many parametric models that are limited to the bivariate case, the flexible model can describe the extremes of random vectors of dimension greater than two. The novel construction method relies on a geometric interpretation of the requirements of a valid angular measure. An advantage of this model is that its parameters directly affect the level of dependence between each pair of components of the random vector, and as such the parameters of the model are more interpretable than those of earlier parametric models for multivariate extremes. The model is applied to air quality data and simulated spatial data.

Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures

The Brown-Resnick max-stable process has proven to be well-suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is intractable and inference must be based on a composite likelihood, thereby preventing the use of classical Bayesian techniques. In this paper we exploit a case in which the full likelihood of a Brown-Resnick process can be calculated, using componentwise maxima and their partitions in terms of individual events, and we propose two new approaches to inference. The first estimates the partitions using declustering, while the second uses random partitions in a Markov chain Monte Carlo algorithm. We use these approaches to construct a Bayesian hierarchical model for extreme low temperatures in northern Fennoscandia.

Extreme value analysis for evaluating ozone control strategies

Tropospheric ozone is one of six criteria pollutants regulated by the US EPA, and has been linked to respiratory and cardiovascular endpoints and adverse effects on vegetation and ecosystems. Regional photochemical models have been developed to study the impacts of emission reductions on ozone levels. The standard approach is to run the deterministic model under new emission levels and attribute the change in ozone concentration to the emission control strategy. However, running the deterministic model requires substantial computing time, and this approach does not provide a measure of uncertainty for the change in ozone levels. Recently, a reduced form model (RFM) has been proposed to approximate the complex model as a simple function of a few relevant inputs. In this paper, we develop a new statistical approach to make full use of the RFM to study the effects of various control strategies on the probability and magnitude of extreme ozone events. We fuse the model output with monitoring data to calibrate the RFM by modeling the conditional distribution of monitoring data given the RFM using a combination of flexible semiparametric quantile regression for the center of the distribution where data are abundant and a parametric extreme value distribution for the tail where data are sparse. Selected parameters in the conditional distribution are allowed to vary by the RFM value and the spatial location. Also, due to the simplicity of the RFM, we are able to embed the RFM in our Bayesian hierarchical framework to obtain a full posterior for the model input parameters, and propagate this uncertainty to the estimation of the effects of the control strategies. We use the new framework to evaluate three potential control strategies, and find that reducing mobile-source emissions has a larger impact than reducing point-source emissions or a combination of several emission sources.

Approximating the conditional density given large observed values via a multivariate extremes framework, with application to environmental data

Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which approximates the conditional distribution of an unobserved component of a random vector given large observed values. Specifically, for

A comparison of U.S. precipitation extremes under RCP8.5 and RCP4.5 with an application of pattern scaling

\mathbf{Z}=(Z_1,...,Z_d)^T

A constrained least-squares approach to combine bottom-up and top-down CO2 flux estimates

and

A Response to Bradwell's Commentary on Recent Statistical Studies in Lichenometry

\mathbf{Z}_{-d}=(Z_1,...,Z_{d-1})^T