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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Atmospheric Modeling, Data Assimilation and Predictability

Description of the NCAR Community Atmosphere Model (CAM 3.0)

The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112070000691

A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

An efficient time-dependent equation for predicting ground surface temperature devised by Bhumralkar (1975) and Blackadar (1976) is tested against a 12-layer soil model and compared with five other approximate methods in current use. It is found to be generally superior if diurnal forcing is present and very much superior to the use of the insulated surface assumption. An analogous method of predicting ground surface moisture content is presented which allows the surface to become moist quickly during rainfall or to become drier than the bulk soil while evaporation occurs. These improved methods are not of much relevance unless the main influences of a vegetation layer are included. An efficient one-layer foliage parameterization is therefore developed that extends continuously from the case of no shielding of the ground by vegetation to complete shielding. It includes influences of both ground and foliage albedos and emissivities, net leaf area index, stomatal resistance, retained water on the foliage, and several other considerations. When it is tested against data for wheat measured by Penman and Long (1960), it appears quite adequate despite the many simplifying assumptions. The parameterization predicts that errors of up to a factor of 2 in evapotranspiration can be incurred by ignoring the presence of a vegetation layer.

Efficient prediction of ground surface temperature and moisture, with inclusion of a layer of vegetation

(2005). Atmospheric Modeling, Data Assimilation, and Predictability. Technometrics: Vol. 47, No. 4, pp. 521-521.

Atmospheric Modeling, Data Assimilation, and Predictability

For numerical weather prediction with primitive equations (the Eulerian hydrodynamic equations modified by the assumption of hydrostatic equilibrium), various coordinate systems are used to represent the vertical structure of the atmosphere. In this paper, we review the essential features of prediction equations, satisfying the conservation of mass and total energy, in various vertical coordinate systems. We formulate the equations of horizontal motion, hydrostatic balance, mass continuity, and thermodynamics using a generalized vertical coordinate in which any variable that gives a single-valued monotonic relationship with a geometric height can be used as a vertical coordinate. Conditions to conserve total energy in a generalized vertical coordinate are investigated. Various prediction schemes using pressure, height, and potential temperature as a vertical coordinate are derived from the set of basic equations in the generalized coordinate system. These three coordinate systems are unique in th...

Various Vertical Coordinate Systems Used for Numerical Weather Prediction

The shallow water theory is applied to the study of one dimensional fluid flows over an isolated ridge. The work was motivated by the desire to investigate the phenomenon called the chinook which occurs on the eastern side of the Rockies and is characterized by extremely strong winds which blow from the mountains. The motion that arises from an initially uniform flow involves the formation of hydraulic jumps both on the windward and leeward sides of a ridge. Special emphasis is put on determining analytically the asymptotic structure of such flows with jumps by solving the appropriate "steady" state equations. The presence of the hydraulic jumps and a rarefaction wave was revealed by preliminary numerical solutions of the time dependent problems. These numerical results demonstrate the evolution in time of the various features of the flow found in the asymptotic solutions.

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Nonlinear shallow fluid flow over an isolated ridge

An attempt is made to investigate theoretically the controlling influence of compensating downward motions on the development of cumulus clouds and the size of the cloudless areas associated with them. The model consists of two circular concentric air columns, the inside column corresponding to the updraft (cloud) region and the outside concentric annular column to the downward motion region. The combined cell is surrounded by the atmospheric at rest. The governing equations of both the updraft and the compensating downward motion are derived from the conservation equations of momentum, heat, moisture and mass. The differential equations are solved numerically to compute the vertical velocity, temperature, specific humidity and liquid water content in and out of the cloud as functions of height and time. Two experiments were performed with and without the effect of compensating downward motion. The main conclusions are the following: Without the effect of the compensating motion, the structure of...

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A Theoretical Study of the Compensating Downward Motions Associated with Cumulus Clouds

Spherical harmonics have been used to analyze global meteorological data, and because they are the solutions of a linearized nondivergent vorticity equation, it is appropriate to use them as orthogonal basis functions for analysis and prediction. However, for ultralong waves—geostrophic motions of the second type—horizontal divergence plays as essential a role as the vertical component of vorticity. Hence, it will be advantageous to use the solutions of linearized primitive equations over a sphere as basis functions. This will also permit identification of the characteristics of wave motions for the initialization of primitive equation models. Such solutions have been investigated in the past in conjunction with atmospheric tidal theories and the basic mathematical tools already available piecewise in the literature. This paper reviews the mathematical development behind the construction of the eigensolutions (referred to as normal modes) of linearized primitive equations over a sphere. The basic...

Normal Modes of Ultralong Waves in the Atmosphere

To represent atmospheric data spectrally in three indices (zonal wavenumber, and meridional and vertical modal indices), we propose to use three-dimensional normal mode functions (NMF's) to express the wind and mass fields simultaneously. The NMF's are constructed from the eigensolutions of a global primitive equation model and they are orthogonal functions. The vertical parts are obtained from the solutions of the vertical structure equation with the equivalent height as the eigenvalue. The vertical modal index is associated with a different value of the equivalent height. The horizontal parts of NMF's are Hough harmonics with zonal wavenumber and meridional modal index as two-dimensional scalings. The expansion of global data in terms of NMF's permits the partition of energy into two distinct kinds of motions-gravity-inertia modes and rotational modes of Rossby/Haurwitz type. Both kinds of motion are also partitioned into different vertical modes. Results of the spectral distribution of atmosph...

Akira Kasahara

Papers

Various Vertical Coordinate Systems Used for Numerical Weather Prediction

Nonlinear shallow fluid flow over an isolated ridge

A Theoretical Study of the Compensating Downward Motions Associated with Cumulus Clouds

Normal Modes of Ultralong Waves in the Atmosphere

Spectral representation of three-dimensional global data by expansion in normal mode functions