Nonhydrostatic Atmospheric Modeling using a<i>z</i>-Coordinate Representation

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Requirements and problems in parallel model development at

Nearly 30 years after introducing the first computer model for weather forecasting, the Deutscher Wetterdienst (DWD) is developing the 4th generation of its numerical weather prediction (NWP) system. It consists of a global grid point model (GME) based on a triangular grid and a non-hydrostatic Lokal Modell (LM). The operational demand for running this new system is immense and can only be met by parallel computers. From the experience gained in developing earlier NWP models, several new problems had to be taken into account during the design phase of the system. Most important were portability (including efficieny of the programs on several computer architectures) and ease of code maintainability. Also the organization and administration of the work done by developers from different teams and institutions is more complex than it used to be. This paper describes the models and gives some performance results. The modular approach used for the design of the LM is explained and the effects on the development are discussed

Forecasts covering one month using a cut-cell model

This paper investigates the impact and potential use of the cut-cell vertical discretisation for forecasts covering five days and climate simulations. A first indication of the usefulness of this new method is obtained by a set of five-day forecasts, covering January 1989 with six forecasts. The model area was chosen to include much of Asia, the Himalayas and Australia. The cut-cell model LMZ (Lokal Modell with z-coordinates) provides a much more accurate representation of mountains on model forecasts than the terrain-following coordinate used for comparison. Therefore we are in particular interested in potential forecast improvements in the target area downwind of the Himalayas, over southeastern China, Korea and Japan. The LMZ has previously been tested extensively for one-day forecasts on a European area. Following indications of a reduced temperature error for the short forecasts, this paper investigates the model error for five days in an area influenced by strong orography. The forecasts indicated a strong impact of the cut-cell discretisation on forecast quality. The cut-cell model is available only for an older (2003) version of the model LM (Lokal Modell). It was compared using a control model differing by the use of the terrain-following coordinate only. The cut-cell model improved the precipitation forecasts of this old control model everywhere by a large margin. An improved, more transferable version of the terrain-following model LM has been developed since then under the name CLM (Climate version of the Lokal Modell). The CLM has been used and tested in all climates, while the LM was used for small areas in higher latitudes. The precipitation forecasts of the cut-cell model were compared also to the CLM. As the cut-cell model LMZ did not incorporate the developments for CLM since 2003, the precipitation forecast of the CLM was not improved in all aspects. However, for the target area downstream of the Himalayas, the cut-cell model considerably improved the prediction of the monthly precipitation forecast even in comparison with the modern CLM version. The cut-cell discretisation seems to improve in particular the localisation of precipitation, while the improvements leading from LM to CLM had a positive effect mainly on amplitude

Spherical Grid Creation and Modeling Using the Galerkin Compiler GC_Sphere

The construction of spherical grids is, to a large extent, a question of organized programming. Such grids come in the form of rhomboidal/triangular grids and hexagonal grids. We are here mainly interested in Local-Galerkin high-order schemes and consider the classical fourth-order o4 method for comparison. High-order Local-Galerkin schemes imply sparse grids in a natural way, with an expected saving of computer runtime. Sparse grids on the sphere are described for rhomboidal and hexagonal cells. They are obtained by not using some of the full grid points. Technical problems and grid organization will be discussed with the purpose of reaching fully realistic applications. We present the description of a programming concept allowing people, using different programming styles at different locations, to work together. The concept of geometric files is introduced. Such geometric files can be offered for downloading and are supposed to allow Local-Galerkin methods to be introduced into an existing model with little effort. When the geometric files are known, the solution on a spherical grid is equivalent to the limited-area Galerkin solutions on the (irregular) plane grids on the patches. The proposed grids can be used with spectral elements (SE) and the Local-Galerkin methods o2o3 and o3o3. The latter offer an increased numerical efficiency which, in a toy model test, resulted in a ten-times-reduced computer run time

Short Review of Current Numerical Developments in Meteorological Modelling

This paper reviews current numerical developments for atmospheric modelling. Numerical atmospheric modelling now looks back to a history of about 70 years after the first successful numerical prediction. Currently, we face new challenges, such as variable and adaptive resolution and ultra-highly resolving global models of 1 km grid length. Large eddy simulation (LES), special applications like the numerical prediction of pollution and atmospheric contaminants belong to the current challenges of numerical developments. While pollution prediction is a standard part of numerical modelling in case of accidents, models currently being developed aim at modelling pollution at all scales from the global to the micro scale. The methods discussed in this paper are spectral elements and other versions of Local-Galerkin (L-Galerkin) methods. Classic numerical methods are also included in the presentation. For example, the rather popular second-order Arakawa C-grid method can be shown to result as a special case of an L-Galerkin method using low-order basis functions. Therefore, developments for Galerkin methods also apply to this classic C-grid method, and this is included in this paper. The new generation of highly parallel computers requires new numerical methods, as some of the classic methods are not well suited for a high degree of parallel computing. It will be shown that some numerical inaccuracies need to be resolved and this indicates a potential for improved results by going to a new generation of numerical methods. The methods considered here are mostly derived from basis functions. Such methods are known under the names of Galerkin, spectral, spectral element, finite element or L-Galerkin methods. Some of these new methods are already used in realistic models. The spectral method, though highly used in the 1990s, is currently replaced by the mentioned local L-Galerkin methods. All methods presented in this review have been tested in idealized numerical situations, the so-called toy models. Waypoints on the way to realistic models and their mathematical problems will be pointed out. Practical problems of informatics will be highlighted. Numerical error traps of some current numerical approaches will be pointed out. These are errors not occurring with highly idealized toy models. Such errors appear when the test situation becomes more realistic. For example, many tests are for regular resolution and results can become worse when the grid becomes irregular. On the sphere no regular grids exist, except for the five derived from Platonic solids. Practical problems beyond mathematics on the way to realistic applications will also be considered. A rather interesting and convenient development is the general availability of computer power. For example, the computational power available on a normal personal computer is comparable to that of a supercomputer in 2005. This means that interesting developments, such as the small sphere atmosphere with a resolution of 1 km and a spherical circumference between 180 and 360 km are available to the normal owner of a personal computer (PC). Besides the mathematical problems of new approaches, we will also consider the informatics challenges of using the new generation of models on mainframe computers and PCs

Challenges and Prospects for Numerical Techniques in Atmospheric Modeling

The authors summarized the presentations and contributions to the Mathematics of the Weather conference 2022. The conference was held from 4.10.22 to 6.10.22 to disucss new numerical algorithms that have been or could be applied in numerical weather prediction, research or model development. This year, the conference had the application of deep learning as a special subject. Each contribution of the conference and their key-thesis are represented in this report

Challenges and Prospects for Numerical Techniques in Atmospheric Modeling

The authors summarized the presentations and contributions to the Mathematics of the Weather conference 2022. The conference was held from 4.10.22 to 6.10.22 to disucss new numerical algorithms that have been or could be applied in numerical weather prediction, research or model development. This year, the conference had the application of deep learning as a special subject. Each contribution of the conference and their key-thesis are represented in this report

Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains

Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs