Oliver Fuhrer

A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models

Most numerical weather prediction models rely on a terrain-following coordinate framework. The computational mesh is thus characterized by inhomogeneities with scales determined by the underlying topography. Such inhomogeneities may affect the truncation error of numerical schemes. In this study, a new class of terrainfollowing coordinate systems for use in atmospheric prediction models is proposed. Unlike conventional systems, the new smooth level vertical (SLEVE) coordinate yields smooth coordinates at mid- and upper levels. The basic concept of the new coordinate is to employ a scale-dependent vertical decay of underlying terrain features. The decay rate is selected such that small-scale topographic variations decay much faster with height than their large-scale counterparts. This generalization implies a nonlocal coordinate transformation. The new coordinate is tested and compared against standard sigma and hybrid coordinate systems using an idealized advection test. It is demonstrated that the presence of coordinate transformations induces substantial truncation errors. These are critical for grid inhomogeneities with wavelengths smaller than approximately eight grid increments, and may overpower the regular-grid truncation error of the underlying finite-difference approximation. These results are confirmed by a theoretical analysis of the truncation error. In addition, the new coordinate is tested in idealized and real-case numerical experiments using a nonhydrostatic model. The simulations using the new coordinate yield a substantial reduction of small-scale noise in dynamical and thermodynamical model fields.

Embedded Cellular Convection in Moist Flow past Topography

Abstract Marginally unstable air masses impinging upon a mountain ridge may lead to the development of a nominally stratiform orographic cloud with shallow embedded convection. Rainfall amounts and distribution are then strongly influenced by the convective dynamics. In this study, the transition from purely stratiform orographic precipitation to flow regimes with embedded convection is systematically investigated. To this end, idealized cloud-resolving numerical simulations of moist flow past a two-dimensional mountain ridge are performed in a three-dimensional domain. A series of simulations with increasing upstream potential instability shows that the convective dynamics may significantly increase precipitation amounts, intensity, and efficiency, to an extent that cannot be replicated by two-dimensional simulations. Under conditions of uniform upstream flow, the embedded convection is of the cellular type. It is demonstrated that simple stability measures of the upstream profile are poor predictors for...

Long-Term Simulations of Thermally Driven Flows and Orographic Convection at Convection-Parameterizing and Cloud-Resolving Resolutions

AbstractThe purpose of this paper is to validate the representation of topographic flows and moist convection over the European Alps in a convection-parameterizing simulation (CPM; Δx = 6.6 km) and two cloud-resolving simulations (CRM; Δx = 1.1 and 2.2 km). All simulations and further sensitivity experiments are validated against a large set of observations for an 18-day fair-weather summer period. The episode considered is characterized by pronounced plain–valley pressure gradients, strong daytime upvalley flows, and weak nighttime down-valley flows. In addition, convective precipitation is recorded during the late afternoon and is preceded by a phase of shallow convection. The observed transition from shallow to deep convection occurs within a 3-h period. The results indicate good agreement between both CRMs and the observed diurnal evolution in terms of near-surface winds, cloud formation, and precipitation. The differences between the two CRMs are surprisingly small. In contrast, the CPM produces too-...

A Generalization of the SLEVE Vertical Coordinate

Abstract Most atmospheric models use terrain-following coordinates, and it is well known that the associated deformation of the computational mesh leads to numerical inaccuracies. In a previous study, the authors proposed a new terrain-following coordinate formulation [the smooth level vertical (SLEVE) coordinate], which yields smooth vertical coordinate levels at mid and upper levels and thereby considerably reduces numerical errors in the simulation of flow past complex topography. In the current paper, a generalization of the SLEVE coordinate is presented by using a modified vertical decay of the topographic signature with height. The new formulation enables an almost uniform thickness of the lowermost computational layers, while preserving the fast transition to smooth levels in the mid and upper atmosphere. This allows for a more consistent and more stable coupling with planetary boundary layer schemes, while retaining the advantages over classic sigma coordinates at upper levels. The generalized SLE...

Using Compiler Directives to Port Large Scientific Applications to GPUs: An Example from Atmospheric Science

For many scientific applications, Graphics Processing Units (GPUs) can be an interesting alternative to conventional CPUs as they can deliver higher memory bandwidth and computing power. While it is conceivable to re-write the most execution time intensive parts using a low-level API for accelerator programming, it may not be feasible to do it for the entire application. But, having only selected parts of the application running on the GPU requires repetitively transferring data between the GPU and the host CPU, which may lead to a serious performance penalty. In this paper we assess the potential of compiler directives, based on the OpenACC standard, for porting large parts of code and thus achieving a full GPU implementation. As an illustrative and relevant example, we consider the climate and numerical weather prediction code COSMO (Consortium for Small Scale Modeling) and focus on the physical parametrizations, a part of the code which describes all physical processes not accounted for by the fundamental equations of atmospheric motion. We show, by porting three of the dominant parametrization schemes, the radiation, microphysics and turbulence parametrizations, that compiler directives are an efficient tool both in terms of final execution time as well as implementation effort. Compiler directives enable to port large sections of the existing code with minor modifications while still allowing for further optimizations for the most performance critical parts. With the example of the radiation parametrization, which contains the solution of a block tri-diagonal linear system, the required code modifications and key optimizations are discussed in detail. Performance tests for the three physical parametrizations show a speedup of between 3× and 7× for execution time obtained on a GPU and on a multi-core CPU of an equivalent generation.

STELLA: a domain-specific tool for structured grid methods in weather and climate models

Many high-performance computing applications solving partial differential equations (PDEs) can be attributed to the class of kernels using stencils on structured grids. Due to the disparity between floating point operation throughput and main memory bandwidth these codes typically achieve only a low fraction of peak performance. Unfortunately, stencil computation optimization techniques are often hardware dependent and lead to a significant increase in code complexity. We present a domain-specific tool, STELLA, which eases the burden of the application developer by separating the architecture dependent implementation strategy from the user-code and is targeted at multi- and manycore processors. On the example of a numerical weather prediction and regional climate model (COSMO) we demonstrate the usefulness of STELLA for a real-world production code. The dynamical core based on STELLA achieves a speedup factor of 1.8x (CPU) and 5.8x (GPU) with respect to the legacy code while reducing the complexity of the user code.

Investigating Exchange Processes over Complex Topography: The Innsbruck Box (i-Box)

AbstractThe flow and turbulence structure in the atmospheric boundary layer over complex mountainous terrain determines Earth–atmosphere interaction, that is, the exchange of energy, mass, and momentum between the surface over such terrain and the free atmosphere. Numerical models for weather and climate, even when operated at high or very high grid resolution, are known to be deficient, leading to inaccurate local forecasts (weather) or scenarios (climate). The nature and reasons for these deficiencies, however, are difficult to assess because systematic and long-term combined observational/modeling studies in mountainous terrain are missing. The Innsbruck Box (i-Box) project aims at filling in this gap through a network of long-term turbulence sites in truly complex terrain, complemented by similarly continuous (surface based) remote sensing and numerical modeling at high to highest [i.e., large-eddy simulation (LES)] resolution. This contribution details the i-Box approach, the experimental design, and...

Dynamics of Orographically Triggered Banded Convection in Sheared Moist Orographic Flows

Abstract Shallow orographic convection embedded in an unstable cap cloud can organize into convective bands. Previous research has highlighted the important role of small-amplitude topographic variations in triggering and organizing banded convection. Here, the underlying dynamical mechanisms are systematically investigated by conducting three-dimensional simulations of moist flows past a two-dimensional mountain ridge using a cloud-resolving numerical model. Most simulations address a sheared environment to account for the observed wind profiles. Results confirm that small-amplitude topographic variations can enhance the development of embedded convection and anchor quasi-stationary convective bands to a fixed location in space. The resulting precipitation patterns exhibit tremendous spatial variability, since regions receiving heavy rainfall can be only kilometers away from regions receiving little or no rain. In addition, the presence of banded convection has important repercussions on the area-mean pr...

Application centric energy-efficiency study of distributed multi-core and hybrid CPU-GPU systems

We study the energy used by a production-level regional climate and weather simulation code on a distributed memory system with hybrid CPU-GPU nodes. The code is optimised for both processor architectures, for which we investigate both time and energy to solution. Operational constraints for time to solution can be met with both processor types, although on different numbers of nodes. Energy to solution is a factor 3 lower with GPUs, but strong scaling can be pushed to larger node counts with CPUs to minimize time to solution. Our data shows that an affine relationship exists between energy and node hours consumed by the simulation. We use this property to devise a simple and practical methodology for optimising for energy efficiency that can be applied to other applications, which we demonstrate with the HPCG benchmark. We conclude with a discussion about the relationship to the commonly-used GF/Watt metric.

Designing Bit-Reproducible Portable High-Performance Applications

Bit-reproducibility has many advantages in the context of high-performance computing. Besides simplifying and making more accurate the process of debugging and testing the code, it can allow the deployment of applications on heterogeneous systems, maintaining the consistency of the computations. In this work we analyze the basic operations performed by scientific applications and identify the possible sources of non-reproducibility. In particular, we consider the tasks of evaluating transcendental functions and performing reductions using non-associative operators. We present a set of techniques to achieve reproducibility and we propose improvements over existing algorithms to perform reproducible computations in a portable way, at the same time obtaining good performance and accuracy. By applying these techniques to more complex tasks we show that bit-reproducibility can be achieved on a broad range of scientific applications.