Numerical Weather Prediction and Data Assimilation Petros Katsafados, Elias Mavromatidis and Christos Spyrou Wiley, 2020, x+208 pages, $165, hardcover ISBN: 978‐1‐786‐30141‐3 (original) (raw)
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Purdue Atmospheric Models and Applications
This article summarizes our research related to geofluid dynamics and numerical modeling. In order to have a better understanding of the motion in the atmosphere, we have been working on various forms of the Navier–Stokes equations, including the linearized and nonlinear systems as well as turbulence parametrization, cumulus parametrization, cloud physics, soil–snow parametrization, atmospheric chemistry, etc. We have also been working on numerical methods in order to solve the equations more accurately. The results show that many weather systems in the initial/growing stage can be qualitatively described by the linearized equations; on the other hand, many developed weather phenomena can be quantitatively reproduced by the nonlinear Purdue Regional Climate Model, when the observational data or reanalysis is used as the initial and lateral boundary conditions. The model can also reveal the detailed structure and physics involved, which sometimes can be misinterpreted by meteorologists according to the incomplete observations. However, it is also noted that systematic biases/errors can exist in the simulations and become difficult to correct. Those errors can be caused by the errors in the initial and boundary conditions, model physics and parametrizations, or inadequate equations or poor numerical methods. When the regional model is coupled with a GCM, it is required that both models should be accurate so as to produce meaningful results. In addition to the Purdue Regional Climate Model, we have presented the results obtained from the nonhydrostatic models, the one-dimensional cloud model, the turbulence-pollution model, the characteristic system of the shallow water equations, etc. Although the numerical model is the most important tool for studying weather and climate, more research should be done on data assimilation , the physics, the numerical method and the mathematic formulation in order to improve the accuracy of the models and have a better understanding of the weather and climate.
Mathematics in atmospheric sciences: An overview
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2009
Several sectors of human activities rely on weather forecasts to plan in preparation of high impact weather events like snow storms, hurricanes or heat waves. Climate studies are needed to make decisions about the long-term development in agriculture, transport and land development. Observing and modeling the evolution of the atmosphere is needed to provide key reliable information for both weather prediction and climate scenarios. This paper gives an overview of the scientific research underlying the development and validation of numerical models of the atmosphere and the monitoring of the quality of the observations collected from several types of instruments. A particular emphasis will be given to data assimilation which establishes the bridge between numerical models and observations. The mathematical problems arising in atmospheric research are diverse as the problem is one of stochastic prediction for which errors in both the model and the observations need to be considered and estimated. Atmospheric predictability is concerned with the chaotic nature of the nonlinear equations that govern the atmosphere. Ensemble prediction is one area that has expanded significantly in the last decade. The interest stems from the necessity to evaluate more than just a forecast: it aims at giving an estimate of its accuracy as well. This brings up more questions than answers.
2016
Atmospheric motions are generally characterized by a wide range of multiple length and time scales, and a numerical method must use a fine grid to resolve such a wide range of scales. Further, a very fine grid requires an extremely small time step in order to keep explicit time integration schemes stable. Therefore, high resolution meteorological simulations are very expensive. A novel multiscale modelling approach is, therefore, presented for simulating atmospheric flows. In this approach, a prognostic variable representing a highly intermittent multiscale feature is decomposed into a significant and a nonsignificant part using wavelets, where the significant part is represented by a small fraction of the wavelet modes. The proposed multiscale methodology has been verified for simulating three cases: Smolarkiewicz's deformational flow model; warm thermals in a dry atmosphere; and the dynamics of a vortex pair with ambient stable stratification. Comparisons with benchmark simulations and with a reference model are evidence for the convergence and stability of the proposed model. The comparison with the reference model has revealed that about 93% of the grid points are not necessary to resolve the significant motion in a warm thermal simulation, saving about 96% of the CPU time. Moreover, the CPU time varies linearly with the number of significant wavelet modes, showing that the present fully implicit adaptive model is asymptotically optimal for this simulation. These primary results point toward the benefit of constructing multiscale atmospheric models using the adaptive wavelet methodology.
Atmospheric Modeling, Data Assimilation, and Predictability
Technometrics, 2005
This page intentionally left blank Atmospheric modeling, data assimilation and predictability This comprehensive text and reference work on numerical weather prediction covers for the first time, not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important new science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. This includes discussions of ensemble forecasting, El Niño events, and how various methods contribute to improved weather and climate prediction. In each of these areas the emphasis is on clear and intuitive explanations of all the fundamental concepts, followed by a complete and sound development of the theory and applications. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book which can also form the basis of one or more graduate-level courses. It will appeal to professionals modeling the atmosphere, weather and climate, and to researchers working on chaos, dynamical systems, ensemble forecasting and problems of predictability.
Toward a Fully Lagrangian Atmospheric Modeling System
Monthly Weather Review, 2008
An improved treatment of advection is essential for atmospheric transport and chemistry models. Eulerian treatments are generally plagued with instabilities, unrealistic negative constituent values, diffusion, and dispersion errors. A higher-order Eulerian model improves one error at significant cost but magnifies another error. The cost of semi-Lagrangian models is too high for many applications. Furthermore, traditional trajectory “Lagrangian” models do not solve both the dynamical and tracer equations simultaneously in the Lagrangian frame. A fully Lagrangian numerical model is, therefore, presented for calculating atmospheric flows. The model employs a Lagrangian mesh of particles to approximate the nonlinear advection processes for all dependent variables simultaneously. Verification results for simulating sea-breeze circulations in a dry atmosphere are presented. Comparison with Defant’s analytical solution for the sea-breeze system enabled quantitative assessment of the model...
A Spectral Element Eulerian-Lagrangian Atmospheric Model (SEELAM)
2008
: A new dynamical core for numerical weather prediction (NWP) based on the spectral element Eulerian-Lagrangian (SEEL) method is presented. This paper represents a departure from previously published work on solving the atmospheric equations in that the horizontal operators are all written, discretized, and solved in 3D Cartesian space. The advantages of this new methodology are: the pole singularity which plagues all gridpoint methods disappears, the horizontal operators can be approximated by local high-order elements, the Eulerian-Lagrangian formulation permits extremely large time-steps, and the fully-implicit Eulerian-Lagrangian formulation only requires the inversion of a 2D Helmholtz operator. In order to validate the SEELAM model, results for four test cases are shown. These are: the Rossby-Haurwitz waves number 1 and 4, and the Jablonowski-Williamson balanced initial state and baroclinic instability tests. Comparisons with four well-established operational models show that ...