Long-term global scenarios have underpinned research and assessment of global environmental change for four decades. Over the past ten years, the climate change research community has developed a scenario framework combining alternative futures of climate and society to facilitate integrated research and consistent assessment to inform policy. Here we assess how well this framework is working and what challenges it faces. We synthesize insights from scenario-based literature, community discussions and recent experience in assessments, concluding that the framework has been widely adopted across research communities and is largely meeting immediate needs. However, some mixed successes and a changing policy and research landscape present key challenges, and we recommend several new directions for the development and use of this framework.

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The purpose of this note is to prove a conjecture of Huah Chu [1] on modular rational invariants of finite orthogonal groups. In an appendix we briefly describe how similar results can be proved for unitary groups. Recently, in [2], S. D. Cohen established a special case of Huah Chu's conjecture, and here we adopt Cohen's notation. Thus q is an odd prime power, n is a positive integer, V = F£ is an ndimensional vector space over ¥ g = GF{q) and Q n (x lt ...,x n ) is a non-degenerate quadratic form on V. Without loss of generality we may assume that n Qn( X l> • • •' X n) = iLjA-K X k>where the A fc eF ff are non-zero. Here we writeand for i; ^ 1, In the notation of [2] we have Q n (i) = £,/2 for i ^ 1 and Q n (0) = £ 0 . As in [2], we write