Practical rare event sampling for extreme mesoscale weather

Abstract

Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new rare event sampling algorithm called Quantile Diffusion Monte Carlo (Quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of Quantile DMC compared to other sampling methods and discuss practical aspects of implementing Quantile DMC. To test the feasibility of Quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate Quantile DMC's potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for Quantile DMC to attain greater efficiency in future applications.

Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration

“…The statistical efficiency is expected to increase linearly with m for m sufficiently large (but still much smaller than N FCI ). 24 Similar faster-than-m pre-asymptotic scaling has been observed in other methods that use sequential Monte Carlo sampling on a classical problem, 50 suggesting that it is not (solely) a manifestation of the fermion sign problem in this case. Before considering the effect of matrix compression on the statistical error, we comment briefly on the benefits of using stochastic, rather than deterministic, vector compression.…”

Applications of large deviation theory in geophysical fluid dynamics and climate science

“…This procedure helps to avoid that for large values of k the trajectory with the largest weight in the ensemble dominates all the others in the cloning rate, thus reducing the degree of degeneracy of the trajectories in the resampled ensemble. Applying this method [212,272] were able to obtain a large number of trajectories of extremely intense tropical cyclones in simulations featuring boundary conditions corresponding to two historical tropical cyclones (Fig. 8), thus showing the potential of this approach even with some of the most challenging applications in climate modelling.…”

“…In recent years there has been several attempts to apply these methods for geophysical applications. They have been applied to Lorenz models [275], partial differential equations [226], turbulence problems [77,113,160,164,165], geophysical fluid dynamics [28], heatwaves in general circulation models [217][218][219] and data-based stochastic weather generators [281], and tropical cyclones in regional climate models [212,272]. Here we give an overview of methods and their applications that have been used to study problems directly related to the dynamics of planetary atmospheres and making use of concepts from LDT.…”

“…A similar method has been used by [212,272] to study the intensification of tropical cyclones in the high resolution, non-hydrostatic regional climate model WRF. In this case the score function has been taken as the surface pressure anomaly at the centre of the cyclone.…”

“…In this case the score function has been taken as the surface pressure anomaly at the centre of the cyclone. Additionally, the trajectory selection and cloning procedure has been modified by mapping at each resampling step the distribution of the weights on a Gaussian distribution on an equal-quantile basis [272]. This procedure helps to avoid that for large values of k the trajectory with the largest weight in the ensemble dominates all the others in the cloning rate, thus reducing the degree of degeneracy of the trajectories in the resampled ensemble.…”