Thursday 26 Nov 2015: Statistical Science Seminar: Using physics to enhance predictions in statistical models
Birgir Hrafnkelsson -
In hydrology, hydraulics, meteorology and climatology there are often opportunities to make use of physics to enhance predictions. Most of the processes in these fields obey the laws of physics. Bayesian hierarchical models (BHMs) provide a framework for including these physical laws in a statistical model. However, it is not necessarily straight forward how this inclusion should be conducted. Here, three examples of BHMs that link the underlying physics to the observed data are given. The first example is a BHM for flow in open channels. The hydraulic theory of open channel flow is linked to the observed discharge and water stage through the BHM. Accumulated monthly precipitation is the subject of the second example. To enhance spatial predictions, an output from a regional meteorological model on a fine grid is used to construct spatial covariates for the two latent parameters of the BHM for each month of the year. The regional meteorological model used here is a linear model of orographic precipitation, and it takes into account physical factors such as height above sea level, wind direction, and topological factors that affect the weather. The third example is on spatial prediction of annual maximum 24-h precipitation. To facilitate predictions on a fine grid, the observed annual maximum 24-h precipitation is linked to the annual precipitation extracted from the aforementioned regional meteorological model.