Many forecasting centres nowadays create weather forecasts in the form of ensembles, which consist of several simulations of future weather. The heterogeneity of the ensembles is supposed to reflect our uncertainty about the future weather, which has its origin in our uncertainty or ignorance about the current state of the atmosphere and the physical processes involved. In practice, ensemble members are generated through different initial conditions, different model parameters, and stochastic perturbations. Nonetheless, ensembles are not always capable of maintaining all our information and uncertainty faithfully.
The aim of this project is to identify what type of information gets irrevocably lost in the ensemble generation, and what information could still be recovered, even though it might not show up when the ensemble is taken at face value. In particular, this project will focus on the ability to forecast extreme events. Will we become better at forecasting extreme events through stochastic parametrisations, for example, or will we just add spurious variability? Or even if no ensemble member shows an extreme event, are we nonetheless able to estimate the probability of that event?
Data Assimilation (or DA) refers to the following problem: given a dynamical system (e.g. a weather model) and given a series of observations (e.g. wind measurements from the real weather), find a trajectory of the system that matches the observed data. For more information on DA, see the data assimilation web site at UoR A conceptual problem with DA is this: Once the data has been used to estimate the trajectory, one cannot just use the same data again to evaluate that trajectory. A trajectory need not be `good' just because it fits the observations well; the algorithm might just parrot the observations without capturing any genuine features of the underlying dynamics; like students who are given problem sheets with solutions during the module, and then are asked the very same problems again during the exams. Clearly, even if they do well you cannot be sure they've understood anything.
The easiest solution would be to use independent weather observations from the same period and region as the original data. Such data however is hardly ever available. But this problem of incestuous evaluation appears everywhere in statistics, and people have come up with various ways to deal with it (e.g.\ BIC, AIC, Mallows' Cp). A good way to get started with this PhD project would be to check which of these methods could be adapted or modified for data assimilation.
The aim of this project is essentially to get typhoon models on track. The typhoon models looked at in this project are relatively simple models, as used in the insurance sector to predict potential damage in the affected area. The models are essentially computer programmes which, when we let them run, behave a little bit like real typhoons. You can think of this like model railway trains which behave a little bit like real trains.
In this project, you are supposed to devise methods to tell the typhoon model to produce a typhoon which reproduces the observations taken from a specific real typhoon. To stay with the model train example, this is like setting the points and transformers etc so that the train reproduces the time table of a real train. Both with typhoons and train tables, the data is very sparse. You don't know the observed windfield everywhere, but only in a few places, in the same way that you only know the times that the train leaves Reading or arrives in Paddington, and nothing in between. A further complication is that with typhoons (and sadly often with trains, too), the data is inaccurate and fraud with measurement errors.