Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

Submission to Energy and Climate Change Committee inquiry: Leaving the EU - implications for UK climate policy

The UK has consistently played a leading role in supporting and delivering strong EU climate change action, including the creation of EU CCS development policy and supporting policies. • CCS deployment across multiple sectors is critical to meeting UK, EU and international objectives to mitigate climate change. The UK has a European-scale strategic asset in geological CO2 storage and subsurface industry expertise. • The EU Emissions Trading System (EU-ETS) is a key policy for supporting CCS deployment. The UK has been instrumental in guiding its improvement and creating direct funding for CCS from New Entrants' Reserve scheme revenues and the forthcoming Innovation Fund. The UK's exit from the EU-ETS would be hugely disrupting and would result in the loss of access to these substantial funds. We strongly advocate that the UK remains within the EU-ETS and retains eligibility for the Innovation Fund. • EU climate legislation largely complements and supports the UK's domestic climate legislation. Continued collaboration and coordination on climate policy is necessary and will bring substantial mutual benefit. Misalignment of UK and EU climate mitigation objectives would damage low-carbon developer and investor confidence, and the UK Government should be mindful to avoid any uncertainty with respect to UK legislation, which has been framed with reference to EU legislation.The UK has consistently played a leading role in supporting and delivering strong EU climate change action, including the creation of EU CCS development policy and supporting policies. • CCS deployment across multiple sectors is critical to meeting UK, EU and international objectives to mitigate climate change. The UK has a European-scale strategic asset in geological CO2 storage and subsurface industry expertise. • The EU Emissions Trading System (EU-ETS) is a key policy for supporting CCS deployment. The UK has been instrumental in guiding its improvement and creating direct funding for CCS from New Entrants' Reserve scheme revenues and the forthcoming Innovation Fund. The UK's exit from the EU-ETS would be hugely disrupting and would result in the loss of access to these substantial funds. We strongly advocate that the UK remains within the EU-ETS and retains eligibility for the Innovation Fund. • EU climate legislation largely complements and supports the UK's domestic climate legislation. Continued collaboration and coordination on climate policy is necessary and will bring substantial mutual benefit. Misalignment of UK and EU climate mitigation objectives would damage low-carbon developer and investor confidence, and the UK Government should be mindful to avoid any uncertainty with respect to UK legislation, which has been framed with reference to EU legislation

House of Commons Energy and Climate Change Committee Fifth Carbon Budget Enquiry

More than a decade of UK state R&D investment, totalling in excess of £250 million, has shown CCS to be effective, achievable and strategically beneficial to UK objectives. The cancellation in November 2015 of the UK Government's £1 billion CCS capital allocation is an unforeseen and fundamental change to UK energy and climate policy, carried out without consultation. UK Committee on Climate Change (CCC) advice was framed in expectation of UK CCS commercialisation programme delivery leading to routine delivery of the technology on electricity generation and some process industries towards 2030s. Removal of the CCS contribution towards the Fifth Carbon Budget and beyond severely limits flexibility in the delivery of other low-carbon generation, especially new nuclear where forecast delivery is increasingly in doubt - the CCC and the Department of Energy and Climate Change (DECC) should consider the impact of scenarios with no CCS and delayed nuclear capacity.More than a decade of UK state R&D investment, totalling in excess of £250 million, has shown CCS to be effective, achievable and strategically beneficial to UK objectives. The cancellation in November 2015 of the UK Government's £1 billion CCS capital allocation is an unforeseen and fundamental change to UK energy and climate policy, carried out without consultation. UK Committee on Climate Change (CCC) advice was framed in expectation of UK CCS commercialisation programme delivery leading to routine delivery of the technology on electricity generation and some process industries towards 2030s. Removal of the CCS contribution towards the Fifth Carbon Budget and beyond severely limits flexibility in the delivery of other low-carbon generation, especially new nuclear where forecast delivery is increasingly in doubt - the CCC and the Department of Energy and Climate Change (DECC) should consider the impact of scenarios with no CCS and delayed nuclear capacity

Carbon Capture and Storage (CCS) in the European Union Energy Union's Governance

Carbon Capture and Storage (CCS) in the European Union Energy Union's Governance Submission to the House of Lords EU Energy and Environment Sub-Committee inquiry: EU Energy GovernanceCarbon Capture and Storage (CCS) in the European Union Energy Union's Governance Submission to the House of Lords EU Energy and Environment Sub-Committee inquiry: EU Energy Governanc

Carbon Capture and Storage in Scotland and the European Union

Carbon capture and storage (CCS) is critical to decarbonising power sector and industrial emissions, and achieving climate mitigation targets. With world-leading decarbonisation targets, a large and mature hydrocarbon sector, existing pipeline infrastructure and extensive opportunities for geological CO2 storage under the North Sea, Scotland is uniquely placed to both deliver and benefit from CCS. The technology has the potential to enable major emissions reductions towards the Scottish Government's 2050 target - it can directly address over 50% of current total emissions from Scotland's energy sector and industry. Geological CO2 storage offshore Scotland represents a resource of European significance, which could securely contain many decades' worth of power and industrial emissions from across the European Union.Carbon capture and storage (CCS) is critical to decarbonising power sector and industrial emissions, and achieving climate mitigation targets. With world-leading decarbonisation targets, a large and mature hydrocarbon sector, existing pipeline infrastructure and extensive opportunities for geological CO2 storage under the North Sea, Scotland is uniquely placed to both deliver and benefit from CCS. The technology has the potential to enable major emissions reductions towards the Scottish Government's 2050 target - it can directly address over 50% of current total emissions from Scotland's energy sector and industry. Geological CO2 storage offshore Scotland represents a resource of European significance, which could securely contain many decades' worth of power and industrial emissions from across the European Union

Scottish Energy Strategy - Consultation Response: SCCS response to the Scottish Government consultation on the draft Scottish Energy Strategy

Scotland has achieved great progress in decarbonising its energy system since 1990, largely by means of closure of historic industries and installation of renewable electricity generation. To decarbonise further requires more than just more renewable energy; a low-carbon approach for all energy is needed, not just for electricity. Deployment of CCS is essential to achieving deep decarbonisation of the Scottish economy. CCS is a suite of technologies for directly and substantially reducing carbon dioxide (CO2) emissions resulting from the use of carbon-containing fuels, including biomass and fossil hydrocarbons. Scotland is uniquely placed to develop, demonstrate and deploy CCS through its combination of excellent resources and applicable industries and skills. SCCS welcomes the Scottish Government's increased recognition of the importance of CCS and their corresponding support for its development and deployment.Scotland has achieved great progress in decarbonising its energy system since 1990, largely by means of closure of historic industries and installation of renewable electricity generation. To decarbonise further requires more than just more renewable energy; a low-carbon approach for all energy is needed, not just for electricity. Deployment of CCS is essential to achieving deep decarbonisation of the Scottish economy. CCS is a suite of technologies for directly and substantially reducing carbon dioxide (CO2) emissions resulting from the use of carbon-containing fuels, including biomass and fossil hydrocarbons. Scotland is uniquely placed to develop, demonstrate and deploy CCS through its combination of excellent resources and applicable industries and skills. SCCS welcomes the Scottish Government's increased recognition of the importance of CCS and their corresponding support for its development and deployment

Briefing: Carbon capture and storage in Scotland

With world-leading decarbonisation targets, a large and mature hydrocarbon sector, existing pipeline infrastructure and extensive opportunities for geological CO2 storage under the North Sea, Scotland is uniquely placed to deliver and benefit from carbon capture and storage (CCS). CCS has the potential to enable major Scottish emissions reductions towards the 2050 target - it can directly address over 50% of current total emissions from energy and industry.With world-leading decarbonisation targets, a large and mature hydrocarbon sector, existing pipeline infrastructure and extensive opportunities for geological CO2 storage under the North Sea, Scotland is uniquely placed to deliver and benefit from carbon capture and storage (CCS). CCS has the potential to enable major Scottish emissions reductions towards the 2050 target - it can directly address over 50% of current total emissions from energy and industry