Modelling the hydraulics of the Carlisle 2005 flood event

The performance of a 2D numerical model of flood hydraulics is tested for a major event in Carlisle, UK, in 2005. This event is associated with a unique data set, with GPS surveyed wrack lines and flood extent surveyed 3 weeks after the flood. The Simple Finite Volume (SFV) model is used to solve the 2D Saint-Venant equations over an unstructured mesh of 30000 elements representing channel and floodplain, and allowing detailed hydraulics of flow around bridge piers and other influential features to be represented. The SFV model is also used to corroborate flows recorded for the event at two gauging stations. Calibration of Manning's n is performed with a two stage strategy, with channel values determined by calibration of the gauging station models, and floodplain values determined by optimising the fit between model results and observed water levels and flood extent for the 2005 event. RMS error for the calibrated model compared with surveyed water levels is ~±0.4m, the same order of magnitude as the estimated error in the survey data. The study demonstrates the ability of unstructured mesh hydraulic models to represent important hydraulic processes across a range of scales, with potential applications to flood risk management.

Modelling climate change: the role of unresolved processes

Our understanding of the climate system has been revolutionized recently, by the development of sophisticated computer models. The predictions of such models are used to formulate international protocols, intended to mitigate the severity of global warming and its impacts. Yet, these models are not perfect representations of reality, because they remove from explicit consideration many physical processes which are known to be key aspects of the climate system, but which are too small or fast to be modelled. The purpose of this paper is to give a personal perspective of the current state of knowledge regarding the problem of unresolved scales in climate models. A recent novel solution to the problem is discussed, in which it is proposed, somewhat counter-intuitively, that the performance of models may be improved by adding random noise to represent the unresolved processes.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Predicting mesh density for adaptive modelling of the global atmosphere

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1–20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.