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In this paper, we address the problem of verifying and calibrating ensemble‐based probabilistic volcanic ash forecasts. The ensemble members are constructed from dispersion model simulations with different meteorological fields obtained from an ensemble meteorological forecast model and different values of ash source parameters such as ash column height and vertical mass distribution. The Brier score is employed to verify the probabilistic forecasts relative to binary‐valued ash detection fields and fully quantitative satellite‐retrieved ash mass load fields. A new ensemble forecast calibration methodology, which treats the meteorological and source term variations on equal footing, is also developed. This enables the creation of an ensemble subset yielding higher Brier skill scores than the uncalibrated ensemble during a calibration time window of about 6 hr after the start of an eruption. It is shown that this can be used to improve probabilistic forecasts up to 24 hr after the start of the eruption using the Indonesian 13 February 2014 Kelut and 6 November 2015 Rinjani eruptions as case studies.

Subgrid-scale parameterizations with self-similar scaling laws are developed for large-eddy simulations (LESs) of atmospheric flows. The key new contribution is the development of scaling laws that govern how these parameterizations depend on the LES resolution and flow strength. Both stochastic and deterministic representations of the effects of subgrid-scale eddies on the retained scales are considered. The stochastic subgrid model consists of a backscatter noise term and a drain eddy viscosity, while in the deterministic subgrid model the net effect of these two terms is represented by a net eddy viscosity. In both cases the subgrid transfers are calculated self-consistently from the statistics of higher-resolution-reference direct numerical simulations (DNSs). The dependence of the subgrid parameterizations on the resolution of the LESs is determined for DNSs having resolutions up to triangular 504 wavenumber truncations. The subgrid parameterizations are developed for typical large-scale atmospheric flows and for different strengths and spectra of kinetic energy within a quasigeostrophic spectral model. LESs using the stochastic and deterministic subgrid parameterizations are shown to replicate the kinetic energy spectra of the reference DNS at the scales of the LESs. It is found that the maximum strengths of the drain, net, and backscatter viscosities satisfy scaling laws dependent on the LES truncation wavenumber and that the dependence of these eddy viscosities on total wavenumber can also be written as essentially universal functions that depend on flow strength and resolution. The scaling laws make the subgrid-scale parameterizations more generally applicable in LESs and remove the need to generate them from reference DNSs.

In this paper we demonstrate how parameters describing the geometry of the volcanic ash source for a particular volcanic ash dispersion model (Hybrid Single‐Particle Lagrangian Integrated Trajectory (HYSPLIT)) may be inferred by the use of satellite data and multiple trial simulations. The areas of space likely to be contaminated by ash are identified with the aid of various remote sensing techniques, and polygons are drawn around these areas as they would be in an operational setting. Dispersion model simulations are initialized by either a cylindrical source or a specified ash distribution depending on the context. Parameters of interest such as the base and top height, diameter, and optimal release time of the cylindrical source or the height of the specified ash distribution are inferred by forming a parameter grid and running multiple simulations for each parameter grid point value. Optimal values of the parameter values are identified by calculating spatial correlations between the model simulations and observations. We demonstrate that the methodology can be used to correctly infer various model parameters and improve volcanic ash forecasts in various eruption case studies.

A stochastic subgrid modeling method is used to parameterize horizontal and vertical subgrid-scale transfers in large-eddy simulations (LESs) of baroclinic flows with large-scale jets and energy spectra typical of the atmosphere. The approach represents the subgrid-scale eddies for LES (at resolutions of T63 and T31) by a stochastic model that takes into account the memory effects of turbulent eddies. The statistics of the model are determined from a higher-resolution (T126) direct numerical simulation (DNS). The simulations use a quasigeostrophic two-level model and the subgrid terms are inhomogeneous in the vertical and anisotropic in the horizontal and are represented by 2 3 2 matrices at each wavenumber. The parameterizations have the largest magnitudes at a cusp near the largest total wavenumbers of the truncations. At T63 the offdiagonal elements of the matrices are negligible (corresponding to effectively decoupled levels) and the diagonal elements are almost isotropic. At the lower resolution of T31 the off-diagonal elements are more important and even the diagonal elements are more anisotropic. At both resolutions, and for anisotropic or isotropized subgrid terms, LESs are in excellent agreement with higher-resolution DNS.