Likun Zhang
Lawrence Berkeley National Laboratory
4:30 PM
127 Hayes-Healy
Colloquium Tea 4:00 - 4:30 PM in 101A Crowley Hall
Modeling extremal dependence in trend analysis of in situ measurements of daily precipitation extremes
The detection of changes over time in the distribution of precipitation extremes is significantly complicated by noise at the spatial scale of daily weather systems. This so-called "storm dependence" is non-negligible for extreme precipitation and makes detecting changes over time very difficult. To appropriately separate spatial signals from spatial noise due to storm dependence, we first utilize a well-developed Gaussian scale mixture model that directly incorporates extremal dependence. Our method uses a data-driven approach to determine the dependence strength of the observed proces (either asymptotic independence or dependence) and is generalized to analyze changes over time and increase the scalability of computations. We apply the model to daily measurements of precipitation over the central United States and compare our results with single-station and conditional independence methods. Our main finding is that properly accounting for storm dependence leads to increased detection of statistically significant trends in the climatology of extreme daily precipitation. Next, in order to extend our analysis to much larger spatial domains, we propose a mixture component model that achieves flexible dependence properties and allows truly high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction via adding non-stationarity to the Gaussian process while allowing the radial variable to vary smoothly across space. As the level of extremeness increases, this single model exhibits both long-range asymptotic independence and short-range weakening dependence strength that leads to either asymptotic dependence or independence. To make inference on the model parameters, we construct global Bayesian hierarchical models and run adaptive Metropolis algorithms concurrently via parallelization. For future work to allow efficient computation, we plan to explore local likelihood and dimension reduction approaches.
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