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Abstract
Further results on the airborne mapping of hailswaths with both fixed beam and scanning IR radiometers are described. It was ascertained that the scanning radiometer made a valuable contribution toward the determination of the structure of the hailswath. The results show that the haliswath derived previously from fixed beam data was similar to the one derived from extensive manner data. Two hailswaths mapped in June 1971 were studied extensively. The dimensions, orientation and fine-structure of the hailswaths, as revealed by IR radiometry, are discussed.
Abstract
Further results on the airborne mapping of hailswaths with both fixed beam and scanning IR radiometers are described. It was ascertained that the scanning radiometer made a valuable contribution toward the determination of the structure of the hailswath. The results show that the haliswath derived previously from fixed beam data was similar to the one derived from extensive manner data. Two hailswaths mapped in June 1971 were studied extensively. The dimensions, orientation and fine-structure of the hailswaths, as revealed by IR radiometry, are discussed.
Abstract
Stationary linear perturbation responses to Northern Hemisphere orography are calculated in a quasi-geostrophic barotropic model in solid-body rotation. The stationary mountain torque induced by these perturbations is then used to construct graphical solutions to the steady-state wave, mean-flow interaction problem. It is shown that multiple solutions exist in the system and are near either the forcing equilibrium of the zonal forcing or near the resonance points in the system. Some of these near-resonance solutions have blocklike configurations with a confluence zone upstream from a large-amplitude structure consisting of a high at high latitudes and a low at low latitudes. These blocklike configurations are shown to be near stable solutions of the system. Time-dependent calculations show that the initial state and the zonal forcing equilibrium are important in determining the long-term time evolution of the system.
Abstract
Stationary linear perturbation responses to Northern Hemisphere orography are calculated in a quasi-geostrophic barotropic model in solid-body rotation. The stationary mountain torque induced by these perturbations is then used to construct graphical solutions to the steady-state wave, mean-flow interaction problem. It is shown that multiple solutions exist in the system and are near either the forcing equilibrium of the zonal forcing or near the resonance points in the system. Some of these near-resonance solutions have blocklike configurations with a confluence zone upstream from a large-amplitude structure consisting of a high at high latitudes and a low at low latitudes. These blocklike configurations are shown to be near stable solutions of the system. Time-dependent calculations show that the initial state and the zonal forcing equilibrium are important in determining the long-term time evolution of the system.
Abstract
Stationary equilibrium states induced by orography and zonal beating are calculated in a simple non-linear quasi-geostrophic baroclinic model. For a specific vector wavenumber and for sufficiently large orography, multiple equilibrium states are found. The states are either near a resonance point in the system or are at the zonal forcing equilibrium. These multiple solutions occur because the heat transport and mountain torque are nonlinear functions of the zonal streamfunction. Near the zonal forcing equilibrium the transports are nearly zero and near the resonance point they become large enough to balance the zonal heating and friction.
Only some of these near-resonant states are stable; the state at the zonal forcing equilibrium is unstable, mainly due to baroclinic instability. Near resonance, the amplitudes of the stationary eddies depend upon the strength of the zonal forcing; a stronger zonal forcing moves the solutions closer to a resonance point, which drastically increases the amplitudes of the perturbations and leaves the zonal mean quantities virtually unaffected. The solutions become more complicated when several wavenumbers and modes are considered. Some time-dependent calculations are discussed.
Abstract
Stationary equilibrium states induced by orography and zonal beating are calculated in a simple non-linear quasi-geostrophic baroclinic model. For a specific vector wavenumber and for sufficiently large orography, multiple equilibrium states are found. The states are either near a resonance point in the system or are at the zonal forcing equilibrium. These multiple solutions occur because the heat transport and mountain torque are nonlinear functions of the zonal streamfunction. Near the zonal forcing equilibrium the transports are nearly zero and near the resonance point they become large enough to balance the zonal heating and friction.
Only some of these near-resonant states are stable; the state at the zonal forcing equilibrium is unstable, mainly due to baroclinic instability. Near resonance, the amplitudes of the stationary eddies depend upon the strength of the zonal forcing; a stronger zonal forcing moves the solutions closer to a resonance point, which drastically increases the amplitudes of the perturbations and leaves the zonal mean quantities virtually unaffected. The solutions become more complicated when several wavenumbers and modes are considered. Some time-dependent calculations are discussed.
Abstract
National Meteorological Center dynamical extended-range forecasts of daily as well as time means of lower tropospheric thickness (700 mb height minus 1000 mb height) are analyzed in this paper. Daily forecasts show significant skill until about 11 days when they are in distinguishable from randomly selected states. Forecasts of time averages show significant skill for almost all averages, especially if the appropriate averaging period of the forecast is selected. The correlation between the forecast average over the first 10 days and the observed average over the 30-day period starting at the same time is about 0.25. No better way of forecasting the 30-day average, on average, was found for this data. Large variations in skill occur with the most skilful periods corresponding to decreased baroclinicity. Composite states of high and low skill show that over the United States 30-day means that have a warm west coast with high pressure aloft and a cold cut coast with low pressure aloft is predicted best by the model. Predictability analyses in which the model is compared with itself rather than with the observations indicate an even greater potential predictability.
Abstract
National Meteorological Center dynamical extended-range forecasts of daily as well as time means of lower tropospheric thickness (700 mb height minus 1000 mb height) are analyzed in this paper. Daily forecasts show significant skill until about 11 days when they are in distinguishable from randomly selected states. Forecasts of time averages show significant skill for almost all averages, especially if the appropriate averaging period of the forecast is selected. The correlation between the forecast average over the first 10 days and the observed average over the 30-day period starting at the same time is about 0.25. No better way of forecasting the 30-day average, on average, was found for this data. Large variations in skill occur with the most skilful periods corresponding to decreased baroclinicity. Composite states of high and low skill show that over the United States 30-day means that have a warm west coast with high pressure aloft and a cold cut coast with low pressure aloft is predicted best by the model. Predictability analyses in which the model is compared with itself rather than with the observations indicate an even greater potential predictability.
Abstract
Nonlinear responses to fixed and seasonally varying surface temperature anomalies in a two-level hemispheric time-dependent coupled atmosphere-surface mixed layer model are described. Linear stationary models that are equivalent to the nonlinear time-dependent model are used to analyze these responses. A model linearized around the climatological zonal state of the time dependent model and forced by anomalous surface temperatures does not provide a reasonable estimate for the anomalous responses, which are considerably underestimated. Better responses are obtained when the anomalous stationary nonlinear eddy fluxes are included in a model linearized around the full climatology. However, this latter model is overly sensitive, and anomalous responses are a small residual balance to the forcing by the surface temperature anomalies and the anomalous transient eddy fluxes. To better understand these linear responses, an eigenanalysis of the climatological state is performed. Seasonal anomalies appear to be dominated by one characteristic pattern near resonance which can be associated with a slowly growing coupled atmosphere-ocean instability.
Abstract
Nonlinear responses to fixed and seasonally varying surface temperature anomalies in a two-level hemispheric time-dependent coupled atmosphere-surface mixed layer model are described. Linear stationary models that are equivalent to the nonlinear time-dependent model are used to analyze these responses. A model linearized around the climatological zonal state of the time dependent model and forced by anomalous surface temperatures does not provide a reasonable estimate for the anomalous responses, which are considerably underestimated. Better responses are obtained when the anomalous stationary nonlinear eddy fluxes are included in a model linearized around the full climatology. However, this latter model is overly sensitive, and anomalous responses are a small residual balance to the forcing by the surface temperature anomalies and the anomalous transient eddy fluxes. To better understand these linear responses, an eigenanalysis of the climatological state is performed. Seasonal anomalies appear to be dominated by one characteristic pattern near resonance which can be associated with a slowly growing coupled atmosphere-ocean instability.
Abstract
Stationary planetary waves are investigated with severely-truncated quasi-geostrophic models extending from the surface to 100 km. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers (∼4 or 5) occur with an equivalent barotropic structure. In the presence of Ekman friction and Newtonian damping these stationary waves have associated with them a mountain torque and temperature transport which can influence the zonal flow. In time-dependent calculations it is shown that this wave-zonal flow interaction is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Here high and low refer to large and small values of the zonal wind.
Resonant zonal wavenumbers of lower wavenumber (∼2 or 3) also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere; still lower quasi-resonant wavenumbers also occur with two nodes in the vertical. These waves destabilize the wave-zonal flow interaction on both the high and low sides of the resonance peak. This instability depends upon the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.
Abstract
Stationary planetary waves are investigated with severely-truncated quasi-geostrophic models extending from the surface to 100 km. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers (∼4 or 5) occur with an equivalent barotropic structure. In the presence of Ekman friction and Newtonian damping these stationary waves have associated with them a mountain torque and temperature transport which can influence the zonal flow. In time-dependent calculations it is shown that this wave-zonal flow interaction is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Here high and low refer to large and small values of the zonal wind.
Resonant zonal wavenumbers of lower wavenumber (∼2 or 3) also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere; still lower quasi-resonant wavenumbers also occur with two nodes in the vertical. These waves destabilize the wave-zonal flow interaction on both the high and low sides of the resonance peak. This instability depends upon the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.
Abstract
Linear prediction models applicable to a basic nonlinear two-level quasi-geostrophic model and extended range forecasting are described. One prediction model is linearized around the nonlinear model baroclinic climatological state and solved via an expansion in normal modes. The skill of these predictions are superior to persistence forecasts of daily events for at least 20 days and time averages for at least 90 days. As might be expected, initial states that project strongly onto the linear baroclinic model slow modes provide skillful forecasts at long forecast lags (seasons), which thus provides a prediction of the quality of the prediction and a possible explanation as to why persistence and forecast skill have been found to be correlated at long lags.
An equivalent method for partitioning extended range forecast quality is provided via an EOF expansion. Initial states strongly projecting onto the first and dominant EOF mode are predicted best by the linear baroclinic model. This dominant EOF mode is very similar to the first eigenmode calculated from the linear baroclinic climatological operator.
An alternative linear prediction method is to construct an empirical linear operator from the anomalies. This latter empirical method provides the greatest forecast skill for both dependent and independent datasets. Moreover, the dominant empirical linear prediction mode is again similar to the dominant mode calculated from the EOF expansion and the linear baroclinic model.
Abstract
Linear prediction models applicable to a basic nonlinear two-level quasi-geostrophic model and extended range forecasting are described. One prediction model is linearized around the nonlinear model baroclinic climatological state and solved via an expansion in normal modes. The skill of these predictions are superior to persistence forecasts of daily events for at least 20 days and time averages for at least 90 days. As might be expected, initial states that project strongly onto the linear baroclinic model slow modes provide skillful forecasts at long forecast lags (seasons), which thus provides a prediction of the quality of the prediction and a possible explanation as to why persistence and forecast skill have been found to be correlated at long lags.
An equivalent method for partitioning extended range forecast quality is provided via an EOF expansion. Initial states strongly projecting onto the first and dominant EOF mode are predicted best by the linear baroclinic model. This dominant EOF mode is very similar to the first eigenmode calculated from the linear baroclinic climatological operator.
An alternative linear prediction method is to construct an empirical linear operator from the anomalies. This latter empirical method provides the greatest forecast skill for both dependent and independent datasets. Moreover, the dominant empirical linear prediction mode is again similar to the dominant mode calculated from the EOF expansion and the linear baroclinic model.
Abstract
The stationary nonlinear response to perturbation heating is calculated in a highly truncated, two-level baroclinic model. For certain values of the intrinsic parameters and forcing, multiple equilibrium states exist. For a specific zonal and meridional wavelength, three equilibrium states are present: two are near a resonant point and one is near the zonal forcing equilibrium. Only one of these is ever stable, namely, the one where the zonal wind is on the low side of the resonant point; this state has a relatively small zonal wind and relatively large stationary perturbations. The equilibrium point on the high side of resonance is unstable mainly due to resonant instability and the equilibrium point near the forcing equilibrium is unstable mainly due to baroclinic unstability. Different equilibria are obtained for each vector wavenumber because the resonant value of the zonal wind decreases with decreasing wavelength.
Abstract
The stationary nonlinear response to perturbation heating is calculated in a highly truncated, two-level baroclinic model. For certain values of the intrinsic parameters and forcing, multiple equilibrium states exist. For a specific zonal and meridional wavelength, three equilibrium states are present: two are near a resonant point and one is near the zonal forcing equilibrium. Only one of these is ever stable, namely, the one where the zonal wind is on the low side of the resonant point; this state has a relatively small zonal wind and relatively large stationary perturbations. The equilibrium point on the high side of resonance is unstable mainly due to resonant instability and the equilibrium point near the forcing equilibrium is unstable mainly due to baroclinic unstability. Different equilibria are obtained for each vector wavenumber because the resonant value of the zonal wind decreases with decreasing wavelength.
Abstract
A two-level spherical quasi-geostrophic model is formulated for predictability experiments. The stationary external forcing for this model is calculated from observations. Both barotropic and baroclinic forcings are required in order to achieve a realistic model climatology. Realistic transient behavior is also present in the model. The most notable difference is that the observed transient kinetic energy has more energy in the smallestscales.
Predictability experiments have an initial rms doubling time of approximately two days. This growth rate along with an initial error of about l/2 the initial error of present operational models produces an rms error equal to the climatological rms error and a correlation of 0.5 on about day 12 of the forecast. At the largest scales, this limiting point is reached shortly thereafter. The error continues to grow at a decreasing rate until at about 30 days the forecast skill is extremely small and comparable to the skill of a persistence forecast.
Various time averages at various lags were examined for skill in the extended range. Filters that weighted most strongly the initial forecast days.were shown to provide increased skill. At the furthest limits (60-day time averages), filters improve the skill of prediction by an amount comparable to that which a numerical forecast is an improvement over a persistence forecast. A window filter improves forecasts of time averages by simply eliminating forecast days beyond about day 15. Besides the overall limit, no stable geographical or spectralvariations in the cutoff time could be determined from the limited sample of forecasts described in this paper.
Abstract
A two-level spherical quasi-geostrophic model is formulated for predictability experiments. The stationary external forcing for this model is calculated from observations. Both barotropic and baroclinic forcings are required in order to achieve a realistic model climatology. Realistic transient behavior is also present in the model. The most notable difference is that the observed transient kinetic energy has more energy in the smallestscales.
Predictability experiments have an initial rms doubling time of approximately two days. This growth rate along with an initial error of about l/2 the initial error of present operational models produces an rms error equal to the climatological rms error and a correlation of 0.5 on about day 12 of the forecast. At the largest scales, this limiting point is reached shortly thereafter. The error continues to grow at a decreasing rate until at about 30 days the forecast skill is extremely small and comparable to the skill of a persistence forecast.
Various time averages at various lags were examined for skill in the extended range. Filters that weighted most strongly the initial forecast days.were shown to provide increased skill. At the furthest limits (60-day time averages), filters improve the skill of prediction by an amount comparable to that which a numerical forecast is an improvement over a persistence forecast. A window filter improves forecasts of time averages by simply eliminating forecast days beyond about day 15. Besides the overall limit, no stable geographical or spectralvariations in the cutoff time could be determined from the limited sample of forecasts described in this paper.
Abstract
Forecasts of time averages of 1–10 days in duration by an operational numerical weather prediction model are documented for the global 500 mb height field in spectral space. The error growth of this model is compared to the error growth in a simple idealized model. Useful forecast intervals for time averages are about twice the useful forecast intervals of instantaneous events. The skill of the forecasts for time averages can be increased still further by ignoring numerical weather prediction model forecasts of instantaneous events past certain stopping point. The window of useful forecast time, for the predictions of ten-day averages considered here, is approximately one week.
The documented transient spectra have the largest values in the planetary scales, along with the largest variability. The error spectra grow from a relatively flat initial spectra to an asymptotic spectral shape similar to the transient spectra. The largest increase in error occurs on the initial day. Temporal variations in the numerical weather forecasts have a large high frequency component. Some notable systematic errors are present; when these errors are removed the time of useful skill for daily forecasts is improved by 6–12 hours and the time of useful skill for forecasts of time averages is improved by 1–2 days. Statistical filters also improve the forecasts although, except for removing systematic errors, they are not likely to prove useful for independent forecasts.
Abstract
Forecasts of time averages of 1–10 days in duration by an operational numerical weather prediction model are documented for the global 500 mb height field in spectral space. The error growth of this model is compared to the error growth in a simple idealized model. Useful forecast intervals for time averages are about twice the useful forecast intervals of instantaneous events. The skill of the forecasts for time averages can be increased still further by ignoring numerical weather prediction model forecasts of instantaneous events past certain stopping point. The window of useful forecast time, for the predictions of ten-day averages considered here, is approximately one week.
The documented transient spectra have the largest values in the planetary scales, along with the largest variability. The error spectra grow from a relatively flat initial spectra to an asymptotic spectral shape similar to the transient spectra. The largest increase in error occurs on the initial day. Temporal variations in the numerical weather forecasts have a large high frequency component. Some notable systematic errors are present; when these errors are removed the time of useful skill for daily forecasts is improved by 6–12 hours and the time of useful skill for forecasts of time averages is improved by 1–2 days. Statistical filters also improve the forecasts although, except for removing systematic errors, they are not likely to prove useful for independent forecasts.
