Modeling Weather Extremes

Figure 1. 20-year return levels calculated at individual grid points for CAPE (J/kg) x Sear (m/s) as estimated using a fitted Generalized Extreme-Value (GEV) distribution. Data are estimates of CAPE and Shear based on global model reanalysis data; CAPE is the convective available potential energy and Shear is the magnitude of the vector difference between the surface and 6-km estimates wind.  The grid resolution is approximately 1.875 degrees longitude by 1.915 degrees latitude, yielding 17,856 grid points, on a 192 x 94 grid.  Temporally, values are available every 6 hours over 42 years (1958 through 1999).  In fitting the GEV distributions, only the annual maxima are used so that 42 values were fit at each of the nearly 18,000 grid points.

In the third and fourth Assessment Reports of the Intergovernmental Panel on Climate Change, discussions of severe thunderstorms were limited to comments regarding the difficulty of using storm report databases to determine if changes have taken place historically.  Because convective storms occur on very fine scales, it is not possible to directly resolve such phenomena from coarse-scale global datasets.  However, large-scale indicators can be employed to study trends in environments that are conducive to such severe weather. Current work in this area by M. Pocernich (RAL), E. Gilleland (RAL), H. Brooks (NSSL), and B. Brown (RAL) has focused on identification of useful measures of large-scale environments that are relevant for severe thunderstorm formation based on NCAR global model reanalysis data. These data have been used to investigate trends in the large scale environmental characteristics, as well as spatial and extreme value distribution attributes. This work has led to identification of several statistical challenges as well as new areas for research. Statistical challenges include methods for modeling extreme values in a spatial context; addressing the issue of multiple comparisons inherent in working with gridded data; and making inferences about changes in distribution parameters.

Accomplishments in FY06

A global reanalysis dataset was created using the NCAR model reanalysis dataset, which included two important severe storm indicators: convective available potential energy (CAPE) and Shear.  Analyses of CAPE, Shear, and functions of these variables, such as CAPE x Shear, were applied to smaller regions where trustworthy severe storm reports could be used to investigate the relationships between the coarse-grid, large-scale indicators and these fine scale events. After verifying these relationships, it was found that concurrently high values of these variables are reasonable indicators of the potential for severe storms.  The variable CAPE x Shear was identified as being a good indicator that also simplifies the problem both meteorologically and statistically.  Counts of high values of CAPE x Shear were analyzed at each global grid location, and temporal trends were analyzed over the 42-yr historical record.  A false discovery rate (FDR) procedure was employed to account for the effects of multiple hypothesis testing and to make the analysis spatially robust.  Two manuscripts based on these analyses are in preparation, and results have been presented at several national and international conferences.

This work was sponsored by the National Science Foundation through the Weather and Climate Assessment Program at ISSE.

Plans for FY07

A logical extension of the current research is the development and application of approaches to investigate trends in indices of convective activity in future climate scenarios. In particular, the techniques developed using the reanalysis data will be applied to global climate model (GCM) output to study how the frequency and intensity of environments conducive to severe weather activity change under a future climate scenario. The aim of this work is to determine the current distributions of environments conducive to severe weather, and study how these environments are changing.  Relevant to this issue is the question of how long we would need to wait to identify significant trends (i.e., how much data do we need in order to have statistical power when testing for significant trends?). Initial steps include determining whether the climate models produce the correct spatial patterns found in the reanalysis data, and in particular, if they correctly place the extrema both spatially and temporally.  Once this is verified, then it will be possible to address what the differences are between current and future climates.  Apart from the FDR procedure, which is robust to spatial dependence, the analyses used so far do not account for spatial structure in the data.  Spatial extreme value statistics, a fertile area for new statistical applications and research, will be investigated as a way to incorporate spatial structure into the analyses. Finally, we will begin to investigate approaches for making inferences about changes in the extreme value distribution parameters.