Spatio-temporal stochastic models
Professor Ulla Holst, Department of Mathematical Statistics, Lund University, is leading a STINT Institutional Grant for long-term cooperation with Professor Peter Guttorp, University of Washington, Seattle, and the National Center for Atmospheric Research, NCAR, in Boulder, Colorado since the beginning of 2006. The theme is spatio-temporal stochastic models and their use in climatology, meteorology, ocean engineering and safety. The total sum allocated for a four-year period is 2 million SEK.
Spatio-temporal stochastic modeling means to find means to describe and analyze the variability of large systems, covering large geographical areas with many different time scales.
A typical example is weather, which exhibits regional dependence by the scale of low pressures and local structure, depending on topography, as well as temporal structure coming from the weather dynamics and from the flow of the seasons.
Even if weather is entirely governed by physical laws, one needs statistical methods to describe its long term behavior. In the cooperation, researchers from the three groups work on methods to analyze such random systems, when their basic properties change with time, like in case of a climate change. Thanks to the institutional grant we have been able to organize a series of exchanges of researchers and teachers, organize courses at the PhD level, and to organize workshops and special sessions at international conferences.
Some of the themes on spatio-temporal stochastic models are oriented towards applications, as ”Climate and environment” and ”Marine safety”, other themes cover basic research on stochastic models and methods to understand and draw conclusions from observed spatial and temporal data. Two examples show the exchange between the different themes.
In Climate and environment research observational facts are combined with theoretical models of how different environmental systems interact. These models are never so detailed that they can explain the variation that is present in data. On the other hand, observed data are always inexact, and give only uncertain information about the model. We contribute with spatio-temporal stochastic models and use regional and temporal dependence to improve on the conclusions drawn from the observations. Monte Carlo simulations of regional climate models show both the systematic effects of certain climate gases in terms of for example average temperature, and also the type and range of the temperature variation and on how extreme dry or wet periods one can expect in different scenarios. Another example is how satellite estimation of change in vegetation index can be improved by taking account of the spatial dependence. We learn from the probabilistic weather forecasts that are being developed in Seattle and at NCAR.
Marine safety is built on ship building knowledge and ship management, but also on a large amount of historical data that show what a ship can expect to meet on a route, for example across the North Atlantic A phenomenon like the 100 year wave is expressed by means of probability and statistics. Therefore, climate change gives rise to a question on how such probabilities might change. It is partly a spatio-temporal statistical problem to translate wave observations made by satellites and stationary observations from an offshore platform, to changed marine rules and routines.
Department of Mathematical Statistics
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