Kilometer-scale models allow for an explicit simulation of deep convective overturning but many subgrid processes that are crucial for convective initiation are still poorly represented. This leads to biases such as insufficient convection triggering and late peak of summertime convection. A physically based stochastic perturbation scheme (PSP) for subgrid processes has been proposed (Kober and Craig) that targets the coupling between subgrid turbulence and resolved convection. The first part of this study presents four modifications to this PSP scheme for subgrid turbulence: an autoregressive, continuously evolving random field; a limitation of the perturbations to the boundary layer that removes artificial convection at night; a mask that turns off perturbations in precipitating columns to retain coherent structures; and nondivergent wind perturbations that drastically increase the effectiveness of the vertical velocity perturbations. In a revised version, PSP2, the combined modifications retain the physically based coupling to the boundary layer scheme of the original scheme while removing undesirable side effects. This has the potential to improve predictions of convective initiation in kilometer-scale models while minimizing other biases. The second part of the study focuses on perturbations to account for convective initiation by subgrid orography. Here the mechanical lifting effect is modeled by introducing vertical and horizontal wind perturbations of an orographically induced gravity wave. The resulting perturbations lead to enhanced convective initiation over mountainous terrain. However, the total benefit of this scheme is unclear and we do not adopt the scheme in our revised configuration.

Cold-pool-driven convective initiation is investigated in high-resolution, convection-permitting simulations with a focus on the diurnal cycle and organization of convection and the sensitivity to grid size. Simulations of four different days over Germany were performed using the ICON-LEM model with grid sizes from 156 to 625 m. In these simulations, we identify cold pools, cold-pool boundaries and initiated convection. Convection is triggered much more efficiently in the vicinity of cold pools than in other regions and can provide as much as 50% of total convective initiation, in particular in the late afternoon. By comparing different model resolutions, we find that cold pools are more frequent, smaller and less intense in lower-resolution simulations. Furthermore, their gust fronts are weaker and less likely to trigger new convection. To identify how model resolution affects this triggering probability, we use a linear causal graph analysis.In doing so, we postulate a graph structure with potential causal pathways and then apply multi-linear regression accordingly. We find a dominant, systematic effect: reducing grid sizes directly reduces upward mass flux at the gust front, which causes weaker triggering probabilities. These findings are expected to be even more relevant for km-scale, numerical weather prediction models. We thus expect that a better representation of cold-pool-driven convective initiation will improve forecasts of convective precipitation. K E Y W O R D S causal effect estimation, numerical weather prediction, convection organization INTRODUCTIONConvection-permitting models have become increasingly prominent for numerical weather prediction in recent years (Baldauf et al., 2011;Clark et al., 2016). Such models have a grid size of several hectometres to a few kilometres which is sufficient to run without the use of a convection parametrization. Due to the many underlying approximations and systematic biases of convection schemes (e.g., Gentine et al., 2018), being able to simulateThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

A B S T R A C TThe present study investigates non-linear dynamics of atmospheric flow phenomena on different scales as interactions of vortices. Thereby, we apply the idealised, two-dimensional concept of point vortices considering two important issues in atmospheric dynamics. First, we propose this not widely spread concept in meteorology to explain blocked weather situations using a three-point vortex equilibrium. Here, a steady state is given if the zonal mean flow is identical to the opposed translational velocity of the vortex system. We apply this concept exemplarily to two major blocked events establishing a new pattern recognition technique based on the kinematic vorticity number to determine the circulations and positions of the interacting vortices. By using reanalysis data, we demonstrate that the velocity of the tripole in a westward direction is almost equal to the westerly flow explaining the steady state of blocked events. Second, we introduce a novel idea to transfer a stability analysis of a vortex equilibrium to the stability of the polar vortex concerning its interaction with the quasi-biennial oscillation (QBO). Here, the point vortex system is built as a polygon ring of vortices around a central vortex. On this way we confirm observations that perturbations of the polar vortex during the QBO east phase lead to instability, whereas the polar vortex remains stable in QBO west phases. Thus, by applying point vortex theory to challenging problems in atmospheric dynamics we show an alternative, discrete view of synoptic and planetary scale motion.

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We investigate a reduced point vortex model for statistical and dynamical analyses of atmospheric blocking phenomena. Thereby, we consider High-over-low and Omega blocking as relative equilibria of two and three point vortices. Under certain conditions, such point vortex systems move westward opposing the mean westerly flow and hence can become stationary. Based on the kinematic vorticity number, two novel, independent methods, the contour and the trapezoid method, are introduced in order to identify the vortices that form the blocking pattern, their local positions and circulation magnitudes. While the contour method takes into account the observed stationarity of blocking, the trapezoid method minimizes the total circulation of the vortex system following point vortex theory. Using an instantaneous blocking index, a total number of 347 blocking periods were identified in NCEP-NCAR Reanalysis data for the Euro-Atlantic region during the time period 1990-2012. This procedure provides the basis to corroborate the applicability of the point vortex model to atmospheric blocking in a statistical framework. The calculated translation speed of point vortex systems associated with the atmospheric blocking appears to match the zonal mean velocity reasonably well. This model explains the stationary behaviour of blocking patterns. A comparison between the theoretical and a statistical model further reveals that the circulation of the blocking high follows the principles of the point vortex model to a large extent. However, the low-pressure systems behave more variable. Moreover, the stability of point vortex equilibria is analysed regarding the relative distances by considering linear stability analysis and simulations. This reveals that the point vortex blocking model corresponds to an unstable saddle point. Furthermore, we take viscosity and a Brownian motion into account to simulate the influence of the smaller, subgrid-scale disturbances. As a result, a clustering near the equilibrium state emerges indicating the persistence of the atmospheric blocking pattern.

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