Kristian Strommen

Abstract:

There is growing evidence that the atmospheric dynamics of the Euro-Atlantic sector during winter is driven in part by the presence of quasi-persistent regimes. However, general circulation models typically struggle to simulate these, with e.g. an overly weakly persistent blocking regime. Previous studies have showed that increased horizontal resolution can improve the regime structure of a model, but have so far only considered a single model with only one ensemble member at each resolution, leaving open the possibility that this may be either coincidental or model-dependent. We show that the improvement in regime structure due to increased resolution is robust across multiple models with multiple ensemble members. However, while the high resolution models have notably more tightly clustered data, other aspects of the regimes may not necessarily improve, and are also subject to a large amount of sampling variability that typically requires at least three ensemble members to surmount.

Abstract:

Studies conducted by the UK Met Office reported significant skill in predicting the winter North Atlantic Oscillation (NAO) index with their seasonal prediction system. At the same time, a very low signal‐to‐noise ratio was observed, as measured using the “ratio of predictable components” (RPC) metric. We analyse both the skill and signal‐to‐noise ratio using a new statistical toy model, which assumes NAO predictability is driven by regime dynamics. It is shown that if the system is approximately bimodal in nature, with the model consistently underestimating the level of regime persistence each season, then both the high skill and high RPC value of the Met Office hindcasts can easily be reproduced. Underestimation of regime persistence could be attributable to any number of sources of model error, including imperfect regime structure or errors in the propagation of teleconnections. In particular, a high RPC value for a seasonal mean prediction may be expected even if the model's internal level of noise is realistic.

Abstract:

We develop a notion of a `canonical $\mathcal{C}$-henselian valuation' for a class $\mathcal{C}$ of field extensions, generalizing the construction of the canonical henselian valuation of a field. We use this to show that the $p$-adic valuation on a finite extension $F$ of $\mathbb{Q}_p$ can be recovered entirely (or up to some indeterminacy of the residue field) from various small quotients of $G_F$, the absolute Galois group of $F$. In particular, it can be recovered fully from the maximal solvable quotient. We use this to prove several versions of the birational section conjecture for varieties over $p$-adic fields.