Predictability of weather and climate

Abstract:

Observations are increasingly used to constrain multi-model projections for future climate assessments. This study assesses the performance of five constraining methods, which have previously been applied to attempt to improve regional climate projections from CMIP5-era models. We employ an out-of-sample testing approach to assess the efficacy of these constraining methods when applied to “pseudo-observational” datasets to constrain future changes in the European climate. These pseudo-observations are taken from CMIP6 simulations, for which future changes were withheld and used for verification. The constrained projections are more accurate and broadly more reliable for regional temperature projections compared to the unconstrained projections, especially in the summer season, which was not clear prior to this study. However, the constraining methods do not improve regional precipitation projections. We also analysed the performance of multi-method projections by combining the constrained projections, which are found to be competitive with the best-performing individual methods and demonstrate improvements in reliability for some temperature projections. The performance of the multi-method projection highlights the potential of combining constraints for the development of constraining methods.

Abstract:

Let (Formula presented.) be a field with (Formula presented.), where (Formula presented.) denotes the maximal pro-2 quotient of the absolute Galois group of a field (Formula presented.). We prove that then (Formula presented.) admits a (non-trivial) valuation (Formula presented.) which is 2-henselian and has residue field (Formula presented.). Furthermore, (Formula presented.) is a minimal positive element in the value group (Formula presented.) and (Formula presented.). This forms the first positive result on a more general conjecture about recovering (Formula presented.) -adic valuations from pro- (Formula presented.) Galois groups which we formulate precisely. As an application, we show how this result can be used to easily obtain number-theoretic information, by giving an independent proof of a strong version of the birational section conjecture for smooth, complete curves (Formula presented.) over (Formula presented.), as well as an analogue for varieties.