If geo-sequestration of CO 2 is to be employed as a key emissions reduction method in the global effort to mitigate against climate change, simple yet robust screening of the risks of disposal in brine aquifers will be needed. There has been significant development of simple analytical and semi-analytical techniques to support screening analysis and performance assessment for potential carbon sequestration sites. These techniques have generally been used to estimate the size of CO 2 plumes for the purpose of leakage rate estimation. A common assumption is that both the fluids and the geological formation are incompressible. Consequently, calculation of pressure distribution requires the specification of an arbitrary radius of influence. In this article, a new similarity solution is derived using the method of matched asymptotic expansions. A large time approximation of this solution is then extended to account for inertial effects using the Forchheimer equation. By allowing for slight compressibility in the fluids and formation, the solutions improve on previous work by not requiring the specification of an arbitrary radius of influence. The validity of both solutions is explored by comparison with equivalent finite difference solutions, revealing that the new method can provide robust and mathematically rigorous solutions for screening level analysis, where numerical simulations may not be justified or cost effective.

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Climate change is impacting coral reefs now. Recent pan-tropical bleaching events driven by unprecedented global heat waves have shifted the playing field for coral reef management and policy. While best-practice conventional management remains essential, it may no longer be enough to sustain coral reefs under continued climate change. Nor will climate change mitigation be sufficient on its own. Committed warming and projected reef decline means solutions must involve a portfolio of mitigation, best-practice conventional management and coordinated restoration and adaptation measures involving new and perhaps radical interventions, including local and regional cooling and shading, assisted coral evolution, assisted gene flow, and measures to support and enhance coral recruitment. We propose that proactive research and development to expand the reef management toolbox fast but safely, combined with expedient trialling of promising interventions is now urgently needed, whatever emissions trajectory the world follows. We discuss the challenges and opportunities of embracing new interventions in a race against time, including their risks and uncertainties. Ultimately, solutions to the climate challenge for coral reefs will require consideration of what society wants, what can be achieved technically and economically, and what opportunities we have for action in a rapidly closing window. Finding solutions that work for coral reefs and people will require exceptional levels of coordination of science, management and policy, and open engagement with society. It will also require compromise, because reefs will change under climate change despite our best interventions. We argue that being clear about society's priorities, and understanding both the opportunities and risks that come with an expanded toolset, can help us make the most of a challenging situation. We offer a conceptual model to help reef managers frame decision problems and objectives, and to guide effective strategy choices in the face of complexity and uncertainty.