Canonical Valuations and the Birational Section Conjecture
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.Climate SPHINX: evaluating the impact of resolution and stochastic physics parameterisations in climate simulations
Geoscientific Model Development European Geosciences Union
Abstract:
Continuous Structural Parameterization: A method for representing different model parameterizations within one structure demonstrated for atmospheric convection
Divergent convective outflow in ICON deep convection-permitting and parameterised deep convection simulations (under review, as of Sept 2023)
Pre-print under review for Weather and Climate Dynamics, Copernicus
Abstract:
Upper-tropospheric deep convective outflows during an event on 10th–11th of June 2019 over Central Europe are analysed from simulation output of the operational numerical weather prediction model ICON. Both, a parameterised and an explicit representation of deep convective systems are studied. Near-linear response of deep convective outflow strength to net latent heating is found for parameterised convection, while coherent patterns in variability are found in convection-permitting simulations at 1 km horizontal grid spacing. Furthermore, three hypotheses on factors that may affect the magnitude of the convective outflow are tested in the convection-permitting configuration: organisation of convection through dimensionality of the systems, organisation of convection through aggregation and convective momentum transport.
Convective organisation and aggregation induce a non-linear increase in the magnitude of deep convective outflows with increasing net latent heating, as shown by the confidence interval of the best fit between power transformed net latent heating and detected magnitude of outflows. However, mixed and weaker than expected signals are found in an attempt to detect the representation of dimensionality of the convection and its consequences for the divergent outflows with an ellipse fitting algorithm that describes the elongation of the intense (convective) precipitation systems. As opposed to expectations, convective momentum transport is identified to slightly increase the magnitude of divergent outflows in this case study.
Convective organisation and aggregation induce a non-linear increase in the magnitude of deep convective outflows with increasing net latent heating, as shown by the confidence interval of the best fit between power transformed net latent heating and detected magnitude of outflows. However, mixed and weaker than expected signals are found in an attempt to detect the representation of dimensionality of the convection and its consequences for the divergent outflows with an ellipse fitting algorithm that describes the elongation of the intense (convective) precipitation systems. As opposed to expectations, convective momentum transport is identified to slightly increase the magnitude of divergent outflows in this case study.