Book contents
- Frontmatter
- Contents
- Preface
- 1 Overview
- 2 Governing equations for mesoscale motions
- 3 Basic wave dynamics
- 4 Mesoscale wave generation and maintenance
- 5 Orographically forced flows
- 6 Thermally forced flows
- 7 Mesoscale instabilities
- 8 Isolated convective storms
- 9 Mesoscale convective systems
- 10 Dynamics of fronts and jet streaks
- 11 Dynamics of orographic precipitation
- 12 Basic numerical methods
- 13 Numerical modeling of geophysical fluid systems
- 14 Parameterizations of physical processes
- Appendices
- Index
- References
13 - Numerical modeling of geophysical fluid systems
Published online by Cambridge University Press: 15 December 2009
Book contents
- Frontmatter
- Contents
- Preface
- 1 Overview
- 2 Governing equations for mesoscale motions
- 3 Basic wave dynamics
- 4 Mesoscale wave generation and maintenance
- 5 Orographically forced flows
- 6 Thermally forced flows
- 7 Mesoscale instabilities
- 8 Isolated convective storms
- 9 Mesoscale convective systems
- 10 Dynamics of fronts and jet streaks
- 11 Dynamics of orographic precipitation
- 12 Basic numerical methods
- 13 Numerical modeling of geophysical fluid systems
- 14 Parameterizations of physical processes
- Appendices
- Index
- References
Summary
In Chapter 12, we discussed various numerical approximations of the advection equation. However, to simulate a geophysical fluid system, such as the atmosphere and ocean, within a finite region, we need to choose the domain size, grid size, time interval, total integration time, and consider other factors, such as the initial condition and boundary conditions. In addition, when we deal with a real fluid system, the governing equations are much more complicated than the one-dimensional, linear advection equation, as considered in Chapter 12. For example, we have to integrate three-dimensional nonlinear governing equations with several dependent variables, instead of a one-dimensional advection equation with only one variable. When a nonlinear equation is being approximated by numerical methods, one may face new problems, such as nonlinear computational instability and nonlinear aliasing. Special numerical techniques are required to avoid these types of problems. Once optimal approximate forms of the equations are selected, it is still necessary to define the domain and grid structure over which the partial differential equations will be approximated. In this chapter, we will also briefly describe on how to build a basic numerical model based on a set of partial differential equations governing a shallow water system, and a hydrostatic or nonhydrostatic continuously stratified fluid system.
Grid systems and vertical coordinates
The first step in developing a mesoscale numerical model is to determine the appropriate domain size, grid intervals, time interval, and total integration time of the model.
- Type
- Chapter
- Information
- Mesoscale Dynamics , pp. 518 - 562Publisher: Cambridge University PressPrint publication year: 2007
References
, , , 2006. Ensemble-based simultaneous state and parameter estimation with MM5. Geophys. Res. Lett., 33, L12801, doi:10.1029/2006GL026186, 2006.CrossRefGoogle Scholar
, 2001. An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–903.2.0.CO;2>CrossRefGoogle Scholar
and , 1978. Development of hydrostatic models suitable for air pollution and other mesometeorological studies. Mon. Wea. Rev., 106, 1045–78.2.0.CO;2>CrossRefGoogle Scholar
and , 1977. Computational design of the basic dynamical processes of the UCLA general circulation model. In Methods in Computational Physics, 17, Academic Press, 174–265.Google Scholar
, 1972. Frequency filter for time integration. Mon. Wea. Rev., 100, 487–90.2.3.CO;2>CrossRefGoogle Scholar
, , , , , , , , , , and , 2000. A dynamically adapting weather and dispersion model: The operational multiscale environment model with grid adaptivity (OMEGA). Mon. Wea. Rev., 128, 2044–76.2.0.CO;2>CrossRefGoogle Scholar
, 1964. A technique for maximizing details in numerical weather map analysis. J. Appl. Meteor., 3, 396–409.2.0.CO;2>CrossRefGoogle Scholar
, , , , , , , , , and , 2004. An hourly assimilation–forecast cycle: the RUC. Mon. Wea. Rev., 132, 495–518.2.0.CO;2>CrossRefGoogle Scholar
, 1983. A non-reflective upper boundary condition for limited-height hydrostatic models. Mon. Wea. Rev., 111, 420–9.2.0.CO;2>CrossRefGoogle Scholar
, 1983. Limitations of some common lateral boundary conditions used in regional NWP models. Mon. Wea. Rev., 111, 1002–12.2.0.CO;2>CrossRefGoogle Scholar
and , 1992. Application of continuous dynamic grid adaptation techniques to meteorological modeling. Part I: Basic formulation and accuracy. Mon. Wea. Rev., 120, 1675–1706.2.0.CO;2>CrossRefGoogle Scholar
, 1984. A kinematic analysis of frontogenesis associated with a nondivergent vortex. J. Atmos. Sci., 41, 1242–8.2.0.CO;2>CrossRefGoogle Scholar
, 1998. Numerical Methods for Wave Equations in Geophysical Fluid Mechanics. Springer-Verlag.Google Scholar
, 1997. Predicting the uncertainty of numerical weather forecast: a review. Meteor. Z., 6, 147–83.Google Scholar
, 2003. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–67.CrossRefGoogle Scholar
, 1988. Complex quality control of meteorological observations. Mon. Wea. Rev., 116, 1137–56.2.0.CO;2>CrossRefGoogle Scholar
, 1961. A statistical theory of meteorological measurements and predictions. J. Meteor., 18, 192–8.2.0.CO;2>CrossRefGoogle Scholar
and , 1980. Numerical Prediction and Dynamic Meteorology. 2nd edn., John Wiley & Sons.Google Scholar
Hamill, T. M., 2006. Ensemble-based atmospheric data assimilation. In Predictability of Weather and Climate, (ed.), Cambridge University Press, 124–156.CrossRefGoogle Scholar
and , 1976. The initialization of numerical models by a dynamical initialization technique. Mon. Wea. Rev., 104, 1551–6.2.0.CO;2>CrossRefGoogle Scholar
, , , , , , and , 2005. Atmospheric data assimilation with an ensemble Kalman filter: results with real observations. Mon. Wea. Rev., 133, 604–20.CrossRefGoogle Scholar
, , , and , 2006. 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of Fort Worth tornadic thunderstorms. Part II: Impact of radial velocity analysis via 3DVAR. Mon. Wea. Rev., 134, 699–721.CrossRefGoogle Scholar
, 2000. A forward-in-time anelastic nonhydrostatic model in a terrain-following coordinate. Mon. Wea. Rev., 128, 2108–34.2.0.CO;2>CrossRefGoogle Scholar
1999. A generalization of using an adjoint model in intermittent data assimilation systems. Mon. Wea. Rev., 127, 766–87.2.0.CO;2>CrossRefGoogle Scholar
and , 1961. New results in linear filtering and prediction theory. Trans. ASME. J. Basic Eng., 83D, 95–108.CrossRefGoogle Scholar
, 2003. Atmospheric Modeling, Data Assimilation and Prediction. Cambridge University Press.Google Scholar
and , 1983. An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev., 111, 430–44.2.0.CO;2>CrossRefGoogle Scholar
and , 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci., 35, 78–107.2.0.CO;2>CrossRefGoogle Scholar
and , 1978. The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–96.2.0.CO;2>CrossRefGoogle Scholar
, , and , 2006. Multi-resolution ensemble forecasts of an observed tornadic thunderstorm system, Part I: Comparison of coarse and fine-grid experiments. Mon. Wea. Rev., 134, 807–33.CrossRefGoogle Scholar
, , , , , , , , , , , and , 2001. Real-time multianalysis-multimodel superensemble forecasts of precipitation using TRMM and SSM/I products. Mon. Wea. Rev., 129, 2861–83.2.0.CO;2>CrossRefGoogle Scholar
and , 1996. Flow regimes and transient dynamics of two-dimensional stratified flow over an isolated mountain ridge. J. Atmos. Sci., 53, 139–58.2.0.CO;2>CrossRefGoogle Scholar
, 1953. Some aspects of stratified fluids. I. A theoretical investigation. Tellus, 5, 42–58.CrossRefGoogle Scholar
1969. The predictability of a flow which possesses many scales of motion. Tellus, 21, 289–307.CrossRefGoogle Scholar
, 1996. Predictability – A problem partly solved. Seminar on Predictability, 1995 ECMWF Seminar Proceedings, ECMWF. Volume I, 1–19.Google Scholar
and , 1978. A test of an upstream spline interpolation technique for the advective terms in a numerical model. Mon. Wea. Rev., 106, 818–30.2.0.CO;2>CrossRefGoogle Scholar
and , 2006. Initial condition sensitivity analysis of a mesoscale forecast using very-large ensembles. Mon. Wea. Rev., 134, 192–207.CrossRefGoogle Scholar
, , , , and , 1988. The step-mountain coordinate: model description and performance for cases of Alpine lee cyclogenesis and for a case of an Appalachian redevelopment. Mon. Wea. Rev., 116, 1493–518.2.0.CO;2>CrossRefGoogle Scholar
and , 1968. A method of initialization for dynamical weather forecasting. Tellus, 20, 115–128.CrossRefGoogle Scholar
, , , and , 1996. The ECMWF ensemble prediction system. Methodology and validation. Quart. J. Roy. Meteor. Soc., 122, 73–120.CrossRefGoogle Scholar
and , 1962. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173–9.2.0.CO;2>CrossRefGoogle Scholar
and , 1978. Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. Int'l J. Numer. Methods Fluids, 21, 183–204.Google Scholar
, 1976. A simple boundary condition for unbounded hyperbolic flows. J. Compu. Phys., 21, 251–269.CrossRefGoogle Scholar
and , 1976. A time-dependent lateral boundary scheme for limited-area primitive equation models. Mon. Wea. Rev., 104, 744–55.2.0.CO;2>CrossRefGoogle Scholar
, 1957. A coordinate system having some special advantages for numerical forecasting. J. Meteor., 14, 184–5.2.0.CO;2>CrossRefGoogle Scholar
, , , , , , , , , , , and , 1998: Changes to the NCEP operational “early” Eta analysis/forecast system. NWS Tech. Proc. Bull., Ser. No. 447, NWS, NOAA. (http://www.nws.noaa.gov/om/tpb/447.htm)
, 1962. Finite amplitude free convection as an initial value problem – I, J. Atmos. Sci., 19, 329–41.2.0.CO;2>CrossRefGoogle Scholar
, 1970. Some basic formulations in numerical variational analysis. Mon. Wea. Rev., 98, 875–83.2.3.CO;2>CrossRefGoogle Scholar
Schoenstadt, A. L., 1978. A transfer function analysis of numerical schemes used to simulate geostrophic adjustment. NPS Report. NPS-53-79-001.
Shaw, B. L., S. Albers, D. Birkenheuer, J. Brown, J. McGinley, P. Schultz, J. Smart, and E. Szoke, 2004. Application of the Local Analysis and Prediction System (LAPS) diabatic initialization of mesoscale numerical weather prediction models for the IHOP-2002 field experiment. Preprints, 20th Conference on Weather Analysis and Forecasting and 16th Conference on Numerical Weather Prediction, Amer. Meteor. Soc., Seattle, WA.
, 1989. Truncation error estimates for refinement criteria in nested adaptive models. Mon. Wea. Rev., 117, 872–86.2.0.CO;2>CrossRefGoogle Scholar
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Giu, D. M. Barker, W. Wang and J. G. Powers, 2005. A Description of the Advanced Research WRF Version 2. NCAR Technical Note, NCAR/TN-468 + STR. [Available at http://wrf-model.org/wrfadmin/docs/arw_v2.pdf]
Smagorinski, J., J. L. Halloway, Jr., and G. D. Hembree, 1967. Prediction experiments with a general circulation model. Proceed. Int'l. Sympo. Dynamics Large Scale Atmospheric Processes, Nauka, Moscow, USSR, 70–134.
, and , 2003. Tests of an ensemble Kalman filter for convective-scale data assimilation. Mon. Wea. Rev., 131, 1663–77.CrossRefGoogle Scholar
, 1986. Dynamic normal mode initialization. J. Meteor. Soc. Japan, 64, 623–32.CrossRefGoogle Scholar
, , , , and , 1999. Using ensembles for short-range forecasting. Mon. Wea. Rev., 127, 433–46.2.0.CO;2>CrossRefGoogle Scholar
, 1970. Variational initialization of the balance equation. J. Appl. Meteor., 9, 732–39.2.0.CO;2>CrossRefGoogle Scholar
and , 1996. Comparison of thermodynamic retrieval by the adjoint method with the traditional retrieval method. Mon. Wea. Rev., 124, 308–24.2.0.CO;2>CrossRefGoogle Scholar
, 1972. On the damping of high-frequency motions in four-dimensional assimilation of meteorological data. J. Atmos. Sci., 29, 1571–4.2.0.CO;2>CrossRefGoogle Scholar
, 1988. Implicit normal mode initialization. Mon. Wea. Rev., 116, 1013–1031.2.0.CO;2>CrossRefGoogle Scholar
and , 2005. Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS Experiments. Mon. Wea. Rev., 133, 1789–1807.CrossRefGoogle Scholar
and , 1993. Operational ensemble prediction at the National Meteorological Center: Practical aspects. Weather and Forecasting, 8, 379–98.2.0.CO;2>CrossRefGoogle Scholar
, 2000. High-order monotonic numerical diffusion and smoothing. Mon. Wea. Rev. 128, 2853–64.2.0.CO;2>CrossRefGoogle Scholar
and , 2006. A high-resolution modeling study of the 24 May 2002 case during IHOP. Part I: Numerical simulation and general evolution of the dryline and convection. Mon. Wea. Rev., 134, 149–71.CrossRefGoogle Scholar
, , and , 2006. An OSSE framework based on the ensemble square-root Kalman filter for evaluating impact of data from radar networks on thunderstorm analysis and forecast. J. Atmos. Ocean Tech., 23, 46–66.CrossRefGoogle Scholar
, , and , 2006a. Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation, Part I: Perfect model experiments. Mon. Wea. Rev., 134, 722–36.CrossRefGoogle Scholar
, , and , 2006b. Mesoscale predictability of an extreme warm-season rainfall event. Weather and Forecasting, 21, 149–66.CrossRefGoogle Scholar
and , 1996. Rainfall assimilation through an optimal control of initial and boundary conditions in a limited-area mesoscale model. Mon. Wea. Rev., 124, 2859–82.2.0.CO;2>CrossRefGoogle Scholar