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- Author or Editor: DAVID WILLIAMSON x
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Abstract
Numerical experiments designed to investigate trade-offs among meteorological variables and between space and time in observing systems are conducted using the six-layer global circulation model of the National Center for Atmospheric Research (NCAR). The error growth characteristics of the NCAR model are first discussed in view of their effect on periodically updating historical data.
The updating experiments are divided into two groups. In the first group, “observed” temperature data with and without errors are periodically inserted into the model to recover the wind field. The root mean square (rms) error of the wind field is reduced by updating temperature and it approaches an asymptotic level which depends on the magnitude of the random errors in the “observed” temperature field. In the second group, “observed” wind data with and without errors are periodically updated to recover the temperature field. The rms error of the temperature field is reduced by updating winds. The asymptotic level depends on the magnitude of errors in the “observed” wind field. The results of wind updating were found to be sensitive to a slight change in the prediction model.
The scale and latitude dependence of the adaptation of meteorological variables forced by updating is also investigated. The wind is shown to adjust to temperature updating better at higher latitudes and for larger scales. The temperature adjusts to wind updating better for smaller scales, but not necessarily at lower latitudes.
Abstract
Numerical experiments designed to investigate trade-offs among meteorological variables and between space and time in observing systems are conducted using the six-layer global circulation model of the National Center for Atmospheric Research (NCAR). The error growth characteristics of the NCAR model are first discussed in view of their effect on periodically updating historical data.
The updating experiments are divided into two groups. In the first group, “observed” temperature data with and without errors are periodically inserted into the model to recover the wind field. The root mean square (rms) error of the wind field is reduced by updating temperature and it approaches an asymptotic level which depends on the magnitude of the random errors in the “observed” temperature field. In the second group, “observed” wind data with and without errors are periodically updated to recover the temperature field. The rms error of the temperature field is reduced by updating winds. The asymptotic level depends on the magnitude of errors in the “observed” wind field. The results of wind updating were found to be sensitive to a slight change in the prediction model.
The scale and latitude dependence of the adaptation of meteorological variables forced by updating is also investigated. The wind is shown to adjust to temperature updating better at higher latitudes and for larger scales. The temperature adjusts to wind updating better for smaller scales, but not necessarily at lower latitudes.
Abstract
Updating experiments performed with 5° and 2.5° versions of the NCAR Global Circulation Model are described. Either wind or temperature is updated. Little difference in the asymptotic error of the induced field is found between updating the 5° model with data generated by the 5° model and updating the 2.5° model with data generated by the 2.5° model. This similarity is expected since both models are shown to have similar error growth rates. When the 5° model is updated with data generated by the 2.5° model, the error in the induced field approaches a much larger asymptote. However, this asymptotic error is still less than that of randomly chosen states. The larger asymptotic error is attributed to the rapid error accumulation in a 5° model forecast when compared to data generated by the 2.5° model.
Abstract
Updating experiments performed with 5° and 2.5° versions of the NCAR Global Circulation Model are described. Either wind or temperature is updated. Little difference in the asymptotic error of the induced field is found between updating the 5° model with data generated by the 5° model and updating the 2.5° model with data generated by the 2.5° model. This similarity is expected since both models are shown to have similar error growth rates. When the 5° model is updated with data generated by the 2.5° model, the error in the induced field approaches a much larger asymptote. However, this asymptotic error is still less than that of randomly chosen states. The larger asymptotic error is attributed to the rapid error accumulation in a 5° model forecast when compared to data generated by the 2.5° model.
Abstract
The large-scale transient components of atmospheric flow have been studied for many years. Observational studies indicate that large amplitude regularly westward propagating waves appear episodically in the atmosphere. These waves have spatial structures and frequencies enticingly similar to those of external Rossby modes obtained theoretically from the linearized baroclinic equations.
In the present study, the episode of 10–28 January 1979 is studied by expanding global objective analyses into the normal modes of a global baroclinic quasi-geostrophic model linearized about the observed nonseparable zonal mean wind field. Several coherent regularly propagating waves are found. One of the most significant of these (the R3 1 or 16 day mode) is examined in detail. Although the observed structure is similar in some ways to the theoretically derived structure, there are important discrepancies. These discrepancies are examined more closely using upper air soundings from Antarctica.
The experimental results suggest that for the episode of 10–28 January 1979 the identification of the observed regularly propagating 16 day wave with the theoretically derived R3 1 mode is doubtful and more sophisticated explanations may be required.
Abstract
The large-scale transient components of atmospheric flow have been studied for many years. Observational studies indicate that large amplitude regularly westward propagating waves appear episodically in the atmosphere. These waves have spatial structures and frequencies enticingly similar to those of external Rossby modes obtained theoretically from the linearized baroclinic equations.
In the present study, the episode of 10–28 January 1979 is studied by expanding global objective analyses into the normal modes of a global baroclinic quasi-geostrophic model linearized about the observed nonseparable zonal mean wind field. Several coherent regularly propagating waves are found. One of the most significant of these (the R3 1 or 16 day mode) is examined in detail. Although the observed structure is similar in some ways to the theoretically derived structure, there are important discrepancies. These discrepancies are examined more closely using upper air soundings from Antarctica.
The experimental results suggest that for the episode of 10–28 January 1979 the identification of the observed regularly propagating 16 day wave with the theoretically derived R3 1 mode is doubtful and more sophisticated explanations may be required.
Abstract
Numerical models for the prediction of atmospheric motions are described by a finite number of coupled ordinary differential equations. We formally solve the initial-value problem for small-amplitude perturbations on some basic state as described by the prediction system. The solution and hence initial conditions are expressed as a sum over the normal modes of oscillation of the perturbation equations. The question as to which modes describe the evolution of meteorologically significant information may be answered for models which are used not only for prediction but also for climate simulation. Those modes which have a much larger amplitude in noisy real data than in climate simulation studies can be filtered from the initial data. The expansion of grid-point data into the normal modes of a model thus allows filtering in a more selective and rational fashion than has been possible using classical initialization procedures. Such an expansion also allows comparison of numerical simulation studies with spectral studies of actual free modes in the atmosphere. As an example of the model expansion procedure, we describe the application of a finite-difference approximation to the dynamics of a two-layer ocean model on a rotating sphere. In the limit of infinitesimal grid interval, the expansion of initial data is given by the Hough functions of tidal theory. For a finite grid interval, it is necessary to consider not only modes related to the Hough modes but also computational modes specific to the finite-difference equations employed. Examples of the eigenfrequencies and eigenfunctions for a basic state at rest are compared with those obtained assuming a basic state with a latitudinally varying zonal wind.
Abstract
Numerical models for the prediction of atmospheric motions are described by a finite number of coupled ordinary differential equations. We formally solve the initial-value problem for small-amplitude perturbations on some basic state as described by the prediction system. The solution and hence initial conditions are expressed as a sum over the normal modes of oscillation of the perturbation equations. The question as to which modes describe the evolution of meteorologically significant information may be answered for models which are used not only for prediction but also for climate simulation. Those modes which have a much larger amplitude in noisy real data than in climate simulation studies can be filtered from the initial data. The expansion of grid-point data into the normal modes of a model thus allows filtering in a more selective and rational fashion than has been possible using classical initialization procedures. Such an expansion also allows comparison of numerical simulation studies with spectral studies of actual free modes in the atmosphere. As an example of the model expansion procedure, we describe the application of a finite-difference approximation to the dynamics of a two-layer ocean model on a rotating sphere. In the limit of infinitesimal grid interval, the expansion of initial data is given by the Hough functions of tidal theory. For a finite grid interval, it is necessary to consider not only modes related to the Hough modes but also computational modes specific to the finite-difference equations employed. Examples of the eigenfrequencies and eigenfunctions for a basic state at rest are compared with those obtained assuming a basic state with a latitudinally varying zonal wind.
