Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

Long-term effect of volcanic forcing on ocean heat content

Explosive volcanic eruptions cause episodic negative radiative forcing of the climate system. Using coupled atmosphere-ocean general circulation models (AOGCMs) subjected to historical forcing since the late nineteenth century, previous authors have shown that each large volcanic eruption is associated with a sudden drop in ocean heat content and sea-level from which the subsequent recovery is slow. Here we show that this effect may be an artefact of experimental design, caused by the AOGCMs not having been spun up to a steady state with volcanic forcing before the historical integrations begin. Because volcanic forcing has a long-term negative average, a cooling tendency is thus imposed on the ocean in the historical simulation. We recommend that an extra experiment be carried out in parallel to the historical simulation, with constant time-mean historical volcanic forcing, in order to correct for this effect and avoid misinterpretation of ocean heat content changes

Vertical heat transports in the ocean and their effect on time-dependent climate change

In response to increasing atmospheric con- centrations of greenhouse gases, the rate of time- dependent climate change is determined jointly by the strength of climate feedbacks and the e�ciency of pro- cesses which remove heat from the surface into the deep ocean. This work examines the vertical heat transport processes in the ocean of the HADCM2 atmosphere± ocean general circulation model (AOGCM) in experi- ments with CO2 held constant (control) and increasing at 1% per year (anomaly). The control experiment shows that global average heat exchanges between the upper and lower ocean are dominated by the Southern Ocean, where heat is pumped downwards by the wind- driven circulation and di�uses upwards along sloping isopycnals. This is the reverse of the low-latitude balance used in upwelling±di�usion ocean models, the global average upward di�usive transport being against the temperature gradient. In the anomaly experiment, weakened convection at high latitudes leads to reduced diffusive and convective heat loss from the deep ocean, and hence to net heat uptake, since the advective heat input is less a�ected. Reduction of deep water produc- tion at high latitudes results in reduced upwelling of cold water at low latitudes, giving a further contribution to net heat uptake. On the global average, high-latitude processes thus have a controlling in¯uence. The impor- tant role of di�usion highlights the need to ensure that the schemes employed in AOGCMs give an accurate representation of the relevant sub-grid-scale processes.

Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Simulations of the London urban heat island

We present simulations of London's meteorology using the Met Office Unified Model with a new, sophisticated surface energy-balance scheme to represent the urban surfaces, called MORUSES. Simulations are performed with the urban surfaces represented and with the urban surfaces replaced with grass in order to calculate the urban increment on the local meteorology. The local urban effects were moderated to some extent by the passage of an onshore flow that propagated up the Thames estuary and across the city, cooling London slightly in the afternoon. Validations of screen-level temperature show encouraging agreement to within 1–2 K, when the urban increment is up to 5 K. The model results are then used to examine factors shaping the spatial and temporal structure of London's atmospheric boundary layer. The simulations reconcile the differences in the temporal evolution of the urban heat island (UHI) shown in various studies and demonstrate that the variation of UHI with time depends strongly on the urban fetch. The UHI at a location downwind of the city centre shows a decrease in UHI during the night, while the UHI at the city centre stays constant. Finally, the UHI at a location upwind of the city centre increases continuously. The magnitude of the UHI by the time of the evening transition increases with urban fetch. The urban increments are largest at night, when the boundary layer is shallow. The boundary layer experiences continued warming after sunset, as the heat from the urban fabric is released, and a weakly convective boundary layer develops across the city. The urban land-use fraction is the dominant control on the spatial structure in the sensible heat flux and the resulting urban increment, although even the weak advection present in this case study is sufficient to advect the peak temperature increments downwind of the most built-up areas. Copyright © 2011 Royal Meteorological Society and British Crown Copyright, the Met Office

Prediction of the thermal performance of horizontal-coupled ground source heat exchangers

The thermal performance of a horizontal-coupled ground-source heat pump system has been assessed both experimentally and numerically in a UK climate. A numerical simulation of thermal behaviour of the horizontal-coupled heat exchanger for combinations of different ambient air temperatures, wind speeds, refrigerant temperature and soil thermal properties was studied using a validated 2D transient model. The specific heat extraction by the heat exchanger increased with ambient temperature and soil thermal conductivity, however it decreased with increasing refrigerant temperature. The effect of wind speed was negligible.

Assimilation impacts on Arctic Ocean circulation, heat and freshwater

We investigate the Arctic basin circulation, freshwater content (FWC) and heat budget by using a high-resolution global coupled ice–ocean model implemented with a state-of-the-art data assimilation scheme. We demonstrate that, despite a very sparse dataset, by assimilating hydrographic data in and near the Arctic basin, the initial warm bias and drift in the control run is successfully corrected, reproducing a much more realistic vertical and horizontal structure to the cyclonic boundary current carrying the Atlantic Water (AW) along the Siberian shelves in the reanalysis run. The Beaufort Gyre structure and FWC and variability are also more accurately reproduced. Small but important changes in the strait exchange flows are found which lead to more balanced budgets in the reanalysis run. Assimilation fluxes dominate the basin budgets over the first 10 years (P1: 1987–1996) of the reanalysis for both heat and FWC, after which the drifting Arctic upper water properties have been restored to realistic values. For the later period (P2: 1997–2004), the Arctic heat budget is almost balanced without assimilation contributions, while the freshwater budget shows reduced assimilation contributions compensating largely for surface salinity damping, which was extremely strong in this run. A downward trend in freshwater export at the Canadian Straits and Fram Strait is found in period P2, associated with Beaufort Gyre recharge. A detailed comparison with observations and previous model studies at the individual Arctic straits is also included.