Time-dependent boundaries in numerical models

This dissertation describes the development of a new numerical framework enabling the study of principal atmospheric mechanisms as well as aspects of numerical realisability that are neither easily deduced from highly optimised operational numerical weather prediction models nor idealised laboratory studies. The theoretical development and efficient numerical implementation of a generalised time-dependent coordinate transformation is demonstrated, creating a unified numerical framework for investigating the influence of upper and lower boundary conditions on atmospheric and oceanic flows. In technical terms, the dissertation also enhances the adaptivity of numerical models to boundary forcings determined by data. The theoretical development is illustrated with numerical simulations of idealised flows. An example of a practical application is given which incorporates a long-wave-approximation for a finite-amplitude free-surface upper boundary, directly relevant to ocean models. Finally, the utility of the generalised vertical coordinate in simulating stratified flows with intricate geometric, time-dependent boundary forcings is demonstrated in the direct numerical simulation of the laboratory analogue of the quasi-biennial oscillation (QBO), the dominant variability in the equatorial stratosphere. While the laboratory experiment exhibits the principal mechanism of the QBO, and despite numerous studies of the stratospheric phenomenon, a complete understanding of the QBO eludes the efforts. On the basis of the numerical results presented in this thesis, the original explanation of the laboratory experiment is revised. The findings stress the utility of this numerical framework and further elevate the importance of the laboratory setup for its fundamental similarity to the atmosphere. A detailed study of parametric and numerical sensitivities of the oscillation is presented and implications on the successful simulation and on the existing theory of equatorial oscillations are discussed

A finite-volume module for simulating global all-scale atmospheric flows

The paper documents the development of a global nonhydrostatic finite-volume module designed to enhance an established spectral-transform based numerical weather prediction (NWP) model. The module adheres to NWP standards, with formulation of the governing equations based on the classical meteorological latitude-longitude spherical framework. In the horizontal, a bespoke unstructured mesh with finite-volumes built about the reduced Gaussian grid of the existing NWP model circumvents the notorious stiffness in the polar regions of the spherical framework. All dependent variables are co-located, accommodating both spectral-transform and grid-point solutions at the same physical locations. In the vertical, a uniform finite-difference discretisation facilitates the solution of intricate elliptic problems in thin spherical shells, while the pliancy of the physical vertical coordinate is delegated to generalised continuous transformations between computational and physical space. The newly developed module assumes the compressible Euler equations as default, but includes reduced soundproof PDEs as an option. Furthermore, it employs semi-implicit forward-in-time integrators of the governing PDE systems, akin to but more general than those used in the NWP model. The module shares the equal regions parallelisation scheme with the NWP model, with multiple layers of parallelism hybridising MPI tasks and OpenMP threads. The efficacy of the developed nonhydrostatic module is illustrated with benchmarks of idealised global weather

Uncertainty in the Representation of Orography in Weather and Climate Models and Implications for Parameterized Drag

The representation of orographic drag remains a major source of uncertainty for numerical weather prediction (NWP) and climate models. Its accuracy depends on contributions from both the model grid‐scale orography (GSO) and the subgrid‐scale orography (SSO). Different models use different source orography datasets and different methodologies to derive these orography fields. This study presents the first comparison of orography fields across several operational global NWP models. It also investigates the sensitivity of an orographic drag parameterisation to the inter‐model spread in SSO fields and the resulting implications for representing the northern hemisphere winter circulation in a NWP model. The inter‐model spread in both the GSO and the SSO fields is found to be considerable. This is due to differences in the underlying source dataset employed and in the manner in which this dataset is processed (in particular how it is smoothed and interpolated) to generate the model fields. The sensitivity of parameterised orographic drag to the inter‐model variability in SSO fields is shown to be considerable and dominated by the influence of two SSO fields: the standard deviation and the mean gradient of the SSO. NWP model sensitivity experiments demonstrate that the inter‐model spread in these fields is of first‐order importance to the inter‐model spread in parameterised surface stress, and to current known systematic model biases. The revealed importance of the SSO fields supports careful reconsideration of how these fields are generated, guiding future development of orographic drag parameterisations and re‐evaluation of the resolved impacts of orography on the flow

the numerics of physical parametrization in the ecmwf model

The numerical aspects of physical parametrization are discussed mainly in the context of the ECMWF Integrated Forecasting System. Two time integration techniques are discussed. With parallel splitting the tendencies of all the parametrized processes are computed independently of each other. With sequential splitting, tendencies of the explicit processes are computed first and are used as input to the subsequent implicit fast process. It is argued that sequential splitting is better than parallel splitting for problems with multiple time scales, because a balance between processes is obtained during the time integration. It is shown that sequential splitting applied to boundary layer diffusion in the ECMWF model leads to much smaller time truncation errors than does parallel splitting. The so called Semi-Lagrangian Averaging of Physical Parametrizations (SLAVEPP), as implemented in the ECMWF model, is explained. The scheme reduces time truncation errors compared to standard first order methods, although a few implementation questions remain. In the scheme fast and slow processes are handled differently and it remains a research topic to find the optimal way of handling convection and clouds. Process specific numerical issues are discussed in the context of the ECMWF parametrization package. Examples are the non-linear stability problems in the vertical diffusion scheme, the stability related mass flux limit in the convection scheme and the fast processes in the cloud microphysics. Vertical resolution in the land surface scheme is inspired by the requirement to represent diurnal to annual time scales. Finally, a new coupling strategy between atmospheric models and land surface schemes is discussed. It allows for fully implicit coupling also for tiled land surface schemes

The ESCAPE project : Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations require algorithms that minimise the energy footprint along with the time required to produce a solution, maintain the physically required level of accuracy, are numerically stable, and are resilient in case of hardware failure. The European Centre for Medium-Range Weather Forecasts (ECMWF) led the ESCAPE (Energy-efficient Scalable Algorithms for Weather Prediction at Exascale) project, funded by Horizon 2020 (H2020) under the FET-HPC (Future and Emerging Technologies in High Performance Computing) initiative. The goal of ESCAPE was to develop a sustainable strategy to evolve weather and climate prediction models to next-generation computing technologies. The project partners incorporate the expertise of leading European regional forecasting consortia, university research, experienced high-performance computing centres, and hardware vendors. This paper presents an overview of the ESCAPE strategy: (i) identify domain-specific key algorithmic motifs in weather prediction and climate models (which we term Weather & Climate Dwarfs), (ii) categorise them in terms of computational and communication patterns while (iii) adapting them to different hardware architectures with alternative programming models, (iv) analyse the challenges in optimising, and (v) find alternative algorithms for the same scheme. The participating weather prediction models are the following: IFS (Integrated Forecasting System); ALARO, a combination of AROME (Application de la Recherche a l'Operationnel a Meso-Echelle) and ALADIN (Aire Limitee Adaptation Dynamique Developpement International); and COSMO-EULAG, a combination of COSMO (Consortium for Small-scale Modeling) and EULAG (Eulerian and semi-Lagrangian fluid solver). For many of the weather and climate dwarfs ESCAPE provides prototype implementations on different hardware architectures (mainly Intel Skylake CPUs, NVIDIA GPUs, Intel Xeon Phi, Optalysys optical processor) with different programming models. The spectral transform dwarf represents a detailed example of the co-design cycle of an ESCAPE dwarf. The dwarf concept has proven to be extremely useful for the rapid prototyping of alternative algorithms and their interaction with hardware; e.g. the use of a domain-specific language (DSL). Manual adaptations have led to substantial accelerations of key algorithms in numerical weather prediction (NWP) but are not a general recipe for the performance portability of complex NWP models. Existing DSLs are found to require further evolution but are promising tools for achieving the latter. Measurements of energy and time to solution suggest that a future focus needs to be on exploiting the simultaneous use of all available resources in hybrid CPU-GPU arrangements

A stratospheric prognostic ozone for seamless Earth system models: performance, impacts and future

We have implemented a new stratospheric ozone model in the European Centre for Medium-Range Weather Forecasts (ECMWF) system and tested its performance for different timescales to assess the impact of stratospheric ozone on meteorological fields. We have used the new ozone model to provide prognostic ozone in medium-range and long-range (seasonal) experiments, showing the feasibility of this ozone scheme for a seamless numerical weather prediction (NWP) modelling approach. We find that the stratospheric ozone distribution provided by the new scheme in ECMWF forecast experiments is in very good agreement with observations, even for unusual meteorological conditions such as Arctic stratospheric sudden warmings (SSWs) and Antarctic polar vortex events like the vortex split of year 2002. To assess the impact it has on meteorological variables, we have performed experiments in which the prognostic ozone is interactive with radiation. The new scheme provides a realistic ozone field able to improve the description of the stratosphere in the ECMWF system, as we find clear reductions of biases in the stratospheric forecast temperature. The seasonality of the Southern Hemisphere polar vortex is also significantly improved when using the new ozone model. In medium-range simulations we also find improvements in high-latitude tropospheric winds during the SSW event considered in this study. In long-range simulations, the use of the new ozone model leads to an increase in the correlation of the winter North Atlantic Oscillation (NAO) index with respect to ERA-Interim and an increase in the signal-to-noise ratio over the North Atlantic sector. In our study we show that by improving the description of the stratospheric ozone in the ECMWF system, the stratosphere–troposphere coupling improves. This highlights the potential benefits of this new ozone model to exploit stratospheric sources of predictability and improve weather predictions over Europe on a range of timescales

The Aqua-Planet Experiment (APE): CONTROL SST Simulation

Climate simulations by 16 atmospheric general circulation models (AGCMs) are compared on an aqua-planet, a water-covered Earth with prescribed sea surface temperature varying only in latitude. The idealised configuration is designed to expose differences in the circulation simulated by different models. Basic features of the aqua-planet climate are characterised by comparison with Earth. The models display a wide range of behaviour. The balanced component of the tropospheric mean flow, and mid-latitude eddy covariances subject to budget constraints, vary relatively little among the models. In contrast, differences in damping in the dynamical core strongly influence transient eddy amplitudes. Historical uncertainty in modelled lower stratospheric temperatures persists in APE.Aspects of the circulation generated more directly by interactions between the resolved fluid dynamics and parameterized moist processes vary greatly. The tropical Hadley circulation forms either a single or double inter-tropical convergence zone (ITCZ) at the equator, with large variations in mean precipitation. The equatorial wave spectrum shows a wide range of precipitation intensity and propagation characteristics. Kelvin mode-like eastward propagation with remarkably constant phase speed dominates in most models. Westward propagation, less dispersive than the equatorial Rossby modes, dominates in a few models or occurs within an eastward propagating envelope in others. The mean structure of the ITCZ is related to precipitation variability, consistent with previous studies.The aqua-planet global energy balance is unknown but the models produce a surprisingly large range of top of atmosphere global net flux, dominated by differences in shortwave reflection by clouds. A number of newly developed models, not optimised for Earth climate, contribute to this. Possible reasons for differences in the optimised models are discussed.The aqua-planet configuration is intended as one component of an experimental hierarchy used to evaluate AGCMs. This comparison does suggest that the range of model behaviour could be better understood and reduced in conjunction with Earth climate simulations. Controlled experimentation is required to explore individual model behavior and investigate convergence of the aqua-planet climate with increasing resolution

DYAMOND: the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains

A review of the experimental protocol and motivation for DYAMOND, the first intercomparison project of global storm-resolving models, is presented. Nine models submitted simulation output for a 40-day (1 August–10 September 2016) intercomparison period. Eight of these employed a tiling of the sphere that was uniformly less than 5 km. By resolving the transient dynamics of convective storms in the tropics, global storm-resolving models remove the need to parameterize tropical deep convection, providing a fundamentally more sound representation of the climate system and a more natural link to commensurately high-resolution data from satellite-borne sensors. The models and some basic characteristics of their output are described in more detail, as is the availability and planned use of this output for future scientific study. Tropically and zonally averaged energy budgets, precipitable water distributions, and precipitation from the model ensemble are evaluated, as is their representation of tropical cyclones and the predictability of column water vapor, the latter being important for tropical weather