Book•
Atmospheric Modeling, Data Assimilation and Predictability
01 Nov 2002-
TL;DR: A comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability.
Abstract: This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers 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 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. 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.
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TL;DR: The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Abstract: The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.
1,695 citations
TL;DR: The Simple Ocean Data Assimilation (SODA) reanalysis of ocean climate variability is described in this article, where a model forecast produced by an ocean general circulation model with an average resolution of 0.25° 0.4° 40 levels is continuously corrected by contemporaneous observations with corrections estimated every 10 days.
Abstract: This paper describes the Simple Ocean Data Assimilation (SODA) reanalysis of ocean climate variability. In the assimilation, a model forecast produced by an ocean general circulation model with an average resolution of 0.25° 0.4° 40 levels is continuously corrected by contemporaneous observations with corrections estimated every 10 days. The basic reanalysis, SODA 1.4.2, spans the 44-yr period from 1958 to 2001, which complements the span of the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA-40). The observation set for this experiment includes the historical archive of hydrographic profiles supplemented by ship intake measurements, moored hydrographic observations, and remotely sensed SST. A parallel run, SODA 1.4.0, is forced with identical surface boundary conditions, but without data assimilation. The new reanalysis represents a significant improvement over a previously published version of the SODA algorithm. In particular, eddy kinetic energy and sea level variability are much larger than in previous versions and are more similar to estimates from independent observations. One issue addressed in this paper is the relative importance of the model forecast versus the observations for the analysis. The results show that at near-annual frequencies the forecast model has a strong influence, whereas at decadal frequencies the observations become increasingly dominant in the analysis. As a consequence, interannual variability in SODA 1.4.2 closely resembles interannual variability in SODA 1.4.0. However, decadal anomalies of the 0–700-m heat content from SODA 1.4.2 more closely resemble heat content anomalies based on observations.
1,614 citations
TL;DR: As a computational problem, global weather prediction is comparable to the simulation of the human brain and of the evolution of the early Universe, and it is performed every day at major operational centres across the world.
Abstract: Advances in numerical weather prediction represent a quiet revolution because they have resulted from a steady accumulation of scientific knowledge and technological advances over many years that, with only a few exceptions, have not been associated with the aura of fundamental physics breakthroughs. Nonetheless, the impact of numerical weather prediction is among the greatest of any area of physical science. As a computational problem, global weather prediction is comparable to the simulation of the human brain and of the evolution of the early Universe, and it is performed every day at major operational centres across the world.
1,475 citations
University of East Anglia1, University of Giessen2, King's College London3, Imperial College London4, University College London5, Met Office6, University of Birmingham7, Deutscher Wetterdienst8, University of Bonn9, Centre national de la recherche scientifique10, RWTH Aachen University11, University of Graz12
TL;DR: In this paper, the authors integrate perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps.
Abstract: Precipitation downscaling improves the coarse resolution and poor representation of precipitation in global climate models and helps end users to assess the likely hydrological impacts of climate change. This paper integrates perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps. End users need a reliable representation of precipitation intensities and temporal and spatial variability, as well as physical consistency, independent of region and season. In addition to presenting dynamical downscaling, we review perfect prognosis statistical downscaling, model output statistics, and weather generators, focusing on recent developments to improve the representation of space-time variability. Furthermore, evaluation techniques to assess downscaling skill are presented. Downscaling adds considerable value to projections from global climate models. Remaining gaps are uncertainties arising from sparse data; representation of extreme summer precipitation, subdaily precipitation, and full precipitation fields on fine scales; capturing changes in small-scale processes and their feedback on large scales; and errors inherited from the driving global climate model.
1,443 citations
References
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TL;DR: The NCEP/NCAR 40-yr reanalysis uses a frozen state-of-the-art global data assimilation system and a database as complete as possible, except that the horizontal resolution is T62 (about 210 km) as discussed by the authors.
Abstract: The NCEP and NCAR are cooperating in a project (denoted “reanalysis”) to produce a 40-year record of global analyses of atmospheric fields in support of the needs of the research and climate monitoring communities. This effort involves the recovery of land surface, ship, rawinsonde, pibal, aircraft, satellite, and other data; quality controlling and assimilating these data with a data assimilation system that is kept unchanged over the reanalysis period 1957–96. This eliminates perceived climate jumps associated with changes in the data assimilation system. The NCEP/NCAR 40-yr reanalysis uses a frozen state-of-the-art global data assimilation system and a database as complete as possible. The data assimilation and the model used are identical to the global system implemented operationally at the NCEP on 11 January 1995, except that the horizontal resolution is T62 (about 210 km). The database has been enhanced with many sources of observations not available in real time for operations, provided b...
28,145 citations
23,905 citations
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
Book•
31 Jul 1988
TL;DR: In this article, the boundary layer is defined as the boundary of a boundary layer, and the spectral gap is used to measure the spectral properties of the boundary layers of a turbulent flow.
Abstract: 1 Mean Boundary Layer Characteristics.- 1.1 A boundary-layer definition.- 1.2 Wind and flow.- 1.3 Turbulent transport.- 1.4 Taylor's hypothesis.- 1.5 Virtual potential temperature.- 1.6 Boundaiy layer depth and structure.- 1.7 Micrometeorology.- 1.8 Significance of the boundary layer.- 1.9 General references.- 1.10 References for this chapter.- 1.11 Exercises.- 2 Some Mathematical and Conceptual Tools: Part 1. Statistics.- 2.1 The significance of turbulence and its spectrum.- 2.2 The spectral gap.- 2.3 Mean and turbulent parts.- 2.4 Some basic statistical methods.- 2.5 Turbulence kinetic energy.- 2.6 Kinematic flux.- 2.7 Eddy flux.- 2.8 Summation notation.- 2.9 Stress.- 2.10 Friction velocity.- 2.11 References.- 2.12 Exercises.- 3 Application of the Governing Equations to Turbulent Flow.- 3.1 Methodology.- 3.2 Basic governing equations.- 3.3 Simplifications, approximations, and scaling arguments.- 3.4 Equations for mean variables in a turbulent flow.- 3.5 Summary of equations, with simplifications.- 3.6 Case studies.- 3.7 References.- 3.8 Exercises.- 4 Prognostic Equations for Turbulent Fluxes and Variances.- 4.1 Prognostic equations for the turbulent departures.- 4.2 Free convection scaling variables.- 4.3 Prognostic equations for variances.- 4.4 Prognostic equations for turbulent fluxes.- 4.5 References.- 4.6 Exercises.- 5 Turbulence Kinetic Energy, Stability, and Scaling.- 5.1 The TKE budget derivation.- 5.2 Contributions to the TKE budget.- 5.3 TKE budget contributions as a function of eddy size.- 5.4 Mean kinetic energy and its interaction with turbulence.- 5.5 Stability concepts.- 5.6 The Richardson number.- 5.7 The Obukhov length.- 5.8 Dimensionless gradients.- 5.9 Miscellaneous scaling parameters.- 5.10 Combined stability tables.- 5.11 References.- 5.12 Exercises.- 6 Turbulence Closure Techniques.- 6.1 The closure problem.- 6.2 Parameterization rules.- 6.3 Local closure - zero and half order.- 6.4 Local closure - first order.- 6.5 Local closure - one-and-a-half order.- 6.6 Local closure - second order.- 6.7 Local closure - third order.- 6.8 Nonlocal closure - transilient turbulence theory.- 6.9 Nonlocal closure - spectral diffusivity theory.- 6.10 References.- 6.11 Exercises.- 7 Boundary Conditions and External Forcings.- 7.1 Effective surface turbulent flux.- 7.2 Heat budget at the surface.- 7.3 Radiation budget.- 7.4 Fluxes at interfaces.- 7.5 Partitioning of flux into sensible and latent portions.- 7.6 Flux to and from the ground.- 7.7 References.- 7.8 Exercises.- 8 Some Mathematical and Conceptual Tools: Part 2. Time Series.- 8.1 Time and space series.- 8.2 Autocorrelation.- 8.3 Structure function.- 8.4 Discrete Fourier transform.- 8.5 Fast Fourier Transform.- 8.6 Energy spectrum.- 8.7 Spectral characteristics.- 8.8 Spectra of two variables.- 8.9 Periodogram.- 8.10 Nonlocal spectra.- 8.11 Spectral decomposition of the TKE equation.- 8.12 References.- 8.13 Exercises.- 9 Similarity Theory.- 9.1 An overview.- 9.2 Buckingham Pi dimensional analysis methods.- 9.3 Scaling variables.- 9.4 Stable boundary layer similarity relationship lists.- 9.5 Neutral boundary layer similarity relationship lists.- 9.6 Convective boundary layer similarity relationship lists.- 9.7 The log wind profile.- 9.8 Rossby-number similarity and profile matching.- 9.9 Spectral similarity.- 9.10 Similarity scaling domains.- 9.11 References.- 9.12 Exercises.- 10 Measurement and Simulation Techniques.- 10.1 Sensor and measurement categories.- 10.2 Sensor lists.- 10.3 Active remote sensor observations of morphology.- 10.4 Instrument platforms.- 10.5 Field experiments.- 10.6 Simulation methods.- 10.7 Analysis methods.- 10.8 References.- 10.9 Exercises.- 11 Convective Mixed Layer.- 11.1 The unstable surface layer.- 11.2 The mixed layer.- 11.3 Entrainment zone.- 11.4 Entrainment velocity and its parameterization.- 11.5 Subsidence and advection.- 11.6 References.- 11.7 Exercises.- 12 Stable Boundary Layer.- 12.1 Mean Characteristics.- 12.2 Processes.- 12.3 Evolution.- 12.4 Other Depth Models.- 12.5 Low-level (nocturnal) jet.- 12.6 Buoyancy (gravity) waves.- 12.7 Terrain slope and drainage winds.- 12.8 References.- 12.9 Exercises.- 13 Boundary Layer Clouds.- 13.1 Thermodynamics.- 13.2 Radiation.- 13.3 Cloud entrainment mechanisms.- 13.4 Fair-weather cumulus.- 13.5 Stratocumulus.- 13.6 Fog.- 13.7 References.- 13.8 Exercises.- 14 Geographic Effects.- 14.1 Geographically generated local winds.- 14.2 Geographically modified flow.- 14.3 Urban heat island.- 14.4 References.- 14.5 Exercises.- Appendices.- A. Scaling variables and dimensionless groups.- B. Notation.- C. Useful constants parameters and conversion factors.- D. Derivation of virtual potential temperature.- Errata section.
9,111 citations
Book•
01 Jan 1996
TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.
Abstract: Preface. Basic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.- Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flow.- Efficiency and Accuracy Improvement. Special Topics.- Appendeces.
7,066 citations