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Extreme Events in Climate Models and Spatial Scaling

Project Abstract

Research in climate and weather extremes is fundamentally motivated by their impacts on society, which are considerable. Consequently, the research of valid mathematical models based on extreme value theory is a key element in our understanding of climate and weather extremes. We propose different potential ways of modelling extreme events and spatial scaling.



The evaluation of the impacts of extreme events in regional and global data either from numerical models, proxies or observations is a crucial area of research in atmospheric sciences and is fundamentally linked to our understanding of past and future climates (Palmer et al. 2002, Zwiers et al. 1998). Determining how extremes for point measurements at small scales (for example rain gauges) relate to corresponding extremes for grid cell averages captured by climate models is the fundamental question of our research. It is not only a necessary step in any uncertainty and spatial study of extremes, but it also underlines the pivotal role of extreme value theory.

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The figure to the left shows mean changes in the annual number of frost days, computed as the difference between the current (1961--1990) mean climate and the future (2080--2099) mean climate, as simulated by the PCM. North America shows negative changes everywhere (less frost days to be expected in the future everywhere), but different regions show different magnitude of changes. The larger changes extend from the North West inland, and the gradient becomes less steep we move eastward. Areas of the Pacific Northwest and Alaska see up to 50 to 70 frost days less per year (red colors). Changes in the Eastern part of the continent are around 20 frost days less per year (green colors). This spatial pattern of change is similar to what is currently observed in the late 20th century trends.

Recent advances in the statistical modelling of spatio-temporal datasets provide a unique opportunity for studying the scaling of extremes (Katz et al. 2002, Coles 2001). Our focus is currently on the following three tasks: (a) collecting different sets of extremes, from daily precipitation observations to extremes (but averaged) outputs from climate models, (b) identifying inadequacies in existing scaling theory, and (c) developing innovative mathematical methods to incorporate scaling behaviours into classical extreme value models.

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The figure to the left shows future changes in mean sea-level pressure over North America. Red colors indicate positive anomalies (ridges), green to blue colors indicate negative anomalies (troughs). These changes can be linked to changes in the large scale flows: The anomalous ridge of high pressure (dark red area over the Northwest) brings warmer air from the ocean to northwestern U.S. causing relatively less frost days compared to the northeastern U.S. where an anomalous trough (blue area dipping south from the arctic regions) brings colder air from the north.

Because of inherent non-stationarity and significant non-linearities in the climate system, the spatio-temporal integration of scale changes in extreme value models makes the search for flexible and efficient statistical models a difficult mathematical challenge. Consequently, one of the first steps in this analysis is to determine how the three parameters of extreme value models vary with scale-changes, especially with grid cell averages captured by climate models. Our strategy is to first assume a Gaussian random field with a given covariance structure. We will then investigate analytically and with simulations how an extreme value at a specific location relates to the extreme values of the aerial average and how the spatial structure of extremes changes under scaling. Because atmospheric variables are strongly interconnected, a bivariate study with the inclusion of predictors will present an interesting second step, scientifically and statistically.

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(Click on image to enlarge)
The figure to the left compares trends in the number of frost days for current climate, as observed (on the left column) and as simulated by the NCAR Parallel Climate Model (PCM) ensemble.


Meehl GA, Tebaldi C, Nychka D, Changes in frost days in simulations of 21st century climate. Climate Dynamics, (in press).

Naveau P., and Schneider U.: Threshold selection for modeling exceedances over high thresholds. (Manuscript in preparation).


Project PI, Leads, and Staff

  • Doug Nychka, PI, Project Lead
    Geophysical Statistics Project, NCAR
  • Gerald Meehl, Project Lead
    Climate & Global Dynamics Division, NCAR
  • Richard Smith, Project Lead
    University of North Carolina
  • Richard Katz
    Environmental & Societal Impacts Group, NCAR
  • Linda Mearns
    Environmental & Societal Impacts Group, NCAR
  • Philippe Naveau
    University of Colorado, Boulder
  • Uli Schneider
    Geophysical Statistics Project, NCAR
  • Claudia Tebaldi
    Environmental & Societal Impacts Group, NCAR

For more information about this project, please contact Doug Nychka at:, Gerald Meehl at:, or Richard Smith at: rls@email.unc.ed

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