Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Case study of the use of remotely sensed data for modeling flood inundation on the river Severn, UK.

A methodology for using remotely sensed data to both generate and evaluate a hydraulic model of floodplain inundation is presented for a rural case study in the United Kingdom: Upton-upon-Severn. Remotely sensed data have been processed and assembled to provide an excellent test data set for both model construction and validation. In order to assess the usefulness of the data and the issues encountered in their use, two models for floodplain inundation were constructed: one based on an industry standard one-dimensional approach and the other based on a simple two-dimensional approach. The results and their implications for the future use of remotely sensed data for predicting flood inundation are discussed. Key conclusions for the use of remotely sensed data are that care must be taken to integrate different data sources for both model construction and validation and that improvements in ground height data shift the focus in terms of model uncertainties to other sources such as boundary conditions. The differences between the two models are found to be of minor significance.