https://faculty.nps.edu/fxgirald/Homepage/Publications_files/Kelly_Giraldo_JCP_2012_published.pdf

Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode

We present semi-implicit (implicit-explicit) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of the compressible NSE and describe in detail how to formulate the semi-implicit time-integration method for these equations. Finally, we compare all five equations and compare the semi-implicit formulations of these equations both using the Schur and No Schur forms against an explicit Runge-Kutta method. Our simulations show that, if efficiency is the main criterion, it matters which form of the governing equations you choose. Furthermore, the semi-implicit formulations are faster than the explicit Runge-Kutta method for all the tests studied, especially if the Schur form is used. While we have used the spectral element method for discretizing the spatial operators, the semi-implicit formulations that we derive are directly applicable to all other numerical methods. We show results for our five semi-implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling, including inertia-gravity waves, density current (i.e., Kelvin-Helmholtz instabilities), and mountain test cases; the latter test case requires the implementation of nonreflecting boundary conditions. Therefore, we show results for all five semi-implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling: no-flux (reflecting) and nonreflecting boundary conditions (NRBCs). It is shown that the NRBCs exert a strong impact on the accuracy and efficiency of the models.

/pdf/semi-implicit-formulations-of-the-navier-stokes-equations-4sjfeuhe2t.pdf

Semi-Implicit Formulations of the Navier-Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling

¶Currently available computer power allows to run operational numerical weather prediction models at resolutions higher than 10 km. The aim of such high resolution modeling is the prediction of local weather, including orographically induced winds and local precipitation patterns. In this range the hydrostatic approximation is no longer valid and nonhydrostatic models have to be used instead. For several decades these models have been developed for research purposes only, but operational application is now reality. In this paper, the numerical methods used in current nonhydrostatic forecast models will be reviewed and some promising techniques in this field will be discussed. Special attention is given to aspects such as the choice of the vertical coordinate, the efficiency of algebraic solvers for semi-implicit time discretizations, and accurate and non-oscillatory advection schemes.

/pdf/review-of-numerical-methods-for-nonhydrostatic-weather-4zwoyorktp.pdf

Review of numerical methods for nonhydrostatic weather prediction models

Adaptive Discontinuous Evolution Galerkin Method for Dry Atmospheric Flow

. The formation and persistence of low-lying mixed-phase clouds (MPCs) in the Arctic depends on a multitude of processes, such as surface conditions, the environmental state, air mass advection, and the ambient aerosol concentration.
In this study, we focus on the relative importance of different instantaneous aerosol perturbations (cloud condensation nuclei and ice-nucleating particles; CCN and INPs, respectively) on MPC properties in the European Arctic. To address this topic, we performed high-resolution large-eddy simulation (LES) experiments using the Consortium for Small-scale Modeling (COSMO) model and designed a case study for the Aerosol-Cloud Coupling and Climate Interactions in the Arctic (ACCACIA) campaign in March 2013. Motivated by ongoing sea ice retreat, we performed all sensitivity studies over open ocean and sea ice to investigate the effect of changing surface conditions.
We find that surface conditions highly impact cloud dynamics, consistent with the ACCACIA observations: over sea ice, a rather homogeneous, optically thin, mixed-phase stratus cloud forms. In contrast, the MPC over the open ocean has a stratocumulus-like cloud structure. With cumuli feeding moisture into the stratus layer, the cloud over the open ocean features a higher liquid (LWP) and ice water path (IWP) and has a lifted cloud base and cloud top compared to the cloud over sea ice.
Furthermore, we analyzed the aerosol impact on the sea ice and open ocean cloud regime. Perturbation aerosol concentrations relevant for CCN activation were increased to a range between 100 and 1000  cm−3 and ice-nucleating particle perturbations were increased by 100 % and 300 % compared to the background concentration (at every grid point and at all levels). The perturbations are prognostic to allow for fully interactive aerosol–cloud interactions.
Perturbations in the INP concentration increase IWP and decrease LWP consistently in both regimes. The cloud microphysical response to potential CCN perturbations occurs faster in the stratocumulus regime over the ocean, where the increased moisture flux favors rapid cloud droplet formation and growth, leading to an increase in LWP following the aerosol injection. In addition, IWP increases through new ice crystal formation by increased immersion freezing, cloud top rise, and subsequent growth by deposition. Over sea ice, the maximum response in LWP and IWP is delayed and weakened compared to the response over the open ocean surface. Additionally, we find the long-term response to aerosol perturbations to be highly dependent on the cloud regime. Over the open ocean, LWP perturbations are efficiently buffered after 18 h simulation time. Increased ice and precipitation formation relax the LWP back to its unperturbed range. On the contrary, over sea ice the cloud evolution remains substantially perturbed with CCN perturbations ranging from 200 to 1000 CCN  cm−3 .

/pdf/response-of-arctic-mixed-phase-clouds-to-aerosol-4f19ks1dyd.pdf

Response of Arctic mixed-phase clouds to aerosol perturbations under different surface forcings

Nearly 30 years after introducing the first computer model for weather forecasting, the {\sl 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 {\sl 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.

/pdf/requirements-and-problems-in-parallel-model-development-at-4usjmlw8fv.pdf

G "unther Doms

Papers

Requirements and problems in parallel model development at DWD