A comparison study of extreme precipitation from six different regional climate models via spatial hierarchical modeling

Erin M. Schliep 0 1 Daniel Cooley 0 1 Stephan R. Sain 0 1 Jennifer A. Hoeting 0 1 0 S. R. Sain Geophysical Statistics Project, National Center for Atmospheric Research , Boulder, CO, USA 1 OURANOS / UQAM UC San Diego / Scripps Hadley Centre Iowa State University UC Santa Cruz Pacific Northwest Nat'l Lab We analyze output from six regional climate models (RCMs) via a spatial Bayesian hierarchical model. The primary advantage of this approach is that the statistical model naturally borrows strength across locations via a spatial model on the parameters of the generalized extreme value distribution. This is especially important in this application as the RCM output we analyze have extensive spatial coverage, but have a relatively short temporal record for characterizing extreme behavior. The hierarchical model we employ is also designed to be computationally efficient as we analyze RCM output for nearly 12000 locations. The aim of this analysis is to compare the extreme precipitation as generated by these RCMs. Our results show that, although the RCMs produce similar spatial patterns for the 100-year return level, their characterizations of extreme precipitation are quite different. Additionally, we examine the spatial behavior of the extreme value index and find differing spatial patterns for the point estimates for the RCMs. However, these differences may not be significant given the uncertainty associated with estimating this parameter. 1 Introduction The motivation for this work comes from concern about impacts of climate change. The summary for policymakers of the Intergovernmental Panel on Climate Changes (IPCC) 2007: Synthesis Report (IPCC 2007a) begins with the statement: Warming of the climate system is unequivocal, as is now evident from observations of increases in global average air and ocean temperatures, widespread melting of snow and ice and rising global average sea level. As attention turns toward assessing potential impacts of climate change and toward possible approaches for climate change mitigation, many new questions arise. Policymakers will need to not only have scientists best estimates of the effects of climate change, but also accurate quantifications of the uncertainty of these estimates as they weigh the costs of mitigating climate change or the costs of addressing the impacts of a changed climate. In terms of impacts, it is often rare but extreme weather events that are the most costly in economic or human terms. There is currently much interest in assessing possible changes in weather extremes due to climate change, and a recent summary of the state of the science and findings for the United States can be found in CCSP (2008). Because it is impossible to observe weather under a changed climate until the climate change actually occurs, much of our knowledge about the impacts of climate change come from climate model simulations. In this work, we compare the maximum precipitation data generated by a number of climate models to begin to understand and quantify how extreme precipitation may differ between the climate models. Extreme value analyses can be challenging due to the lack of informative data. Even when given a long time series of data, because extreme events are rare, there still can remain considerable uncertainty in the parameter estimates that describe the tail behavior of the modeled distribution. When given data from multiple locations, one may wish to sensibly trade space for time to better estimate the parameters at all locations. There have been several approaches of varying complexity that have attempted to borrow strength across location. The methodology described in this paper is motivated by the data sets which we analyze. We investigate extreme precipitation from six regional climate model (RCM) simulations. The RCM output are spatially rich in that we have daily precipitation amounts at every location in our study domain. At the same time, the RCM output are temporally poor as we have only 20 year simulations, and this is a relatively short period to determine extreme value behavior. Additionally, the data analysis is computationally challenging as we have nearly 12000 locations that we need to model simultaneously. To understand the nature of extreme precipitation as produced by these RCMs, we construct a Bayesian hierarchical model which sensibly borrows strength across location and is computationally feasible. This is done by constructing a multivariate spatial model on the parameters of the extreme value distribution. 1.1 Climate models and the NARCCAP project Climate models are deterministic models that produce simulated weather. These models are able to capture the known physics of the Earths climate system by producing a discretized solution to the differential equations that describe the fluid dynamics of the Earths atmosphere and oceans. The weather from these models is simulated at discrete time intervals on a given spatial grid. Climate models are usually extremely computationally intensive, expensive to run, and run on supercomputers. For an overview of climate models and and their evaluation see IPCC (2007b, ch. 8). The power of climate models is that they allow scientists to not only simulate weather under current atmospheric and ocean conditions, but also under possible altered conditions due to natural and/or anthropogenic causes. The output of a climate model run are a vast collection of simulated weather data. The model records numerous variables (e.g., temperature, precipitation, humidity, barometric pressure to name just a few) at all grid locations and at every time interval. As is common practice in the climate literature, we will refer to the weather data produced by the climate model as model output. There are different types of climate models that are used for different purposes. An atmosphere-ocean general circulation model (AOGCM) is used to model synoptic (large-scale) phenomena. These models are run on a spatial domain that spans the globe and thus are often referred to as global climate models or GCMs. GCMs have grid scales on the order of 100s of kilometers. Therefore, GCMs are able to capture climate phenomena on the continental or sub-continental scale; however their spatial resolution leaves them unable to model climate patterns or changes at a more local level. GCMs differ from weather forecast models. The purpose of a GCM is not to mimic weather at a specific time. That is, the GCM-simulated weather corresponding to a particular day most likely will not resemble the actual observed weather for that day. However, the weather produced by a GCM simulation will span decades of (simulated) time. The climatological characteristics of this simulated weather should capture that of actual weather which would occur given the general atmospheric conditions that characterize the GCM run. While the understanding of synoptic climate phenomena is an important facet of climate change resea (...truncated)