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## Abstract

The kinematic technique of representing three-dimensional vertical circulations in baroclinic disturbances in terms of a vector streamfunction (referred to as the psi vector) recently proposed by the authors is placed in the context of quasigeostrophic (QG) theory. A diagnostic equation is derived for the psi vector from which the vertical velocity and the irrotational part of the ageostrophic velocity can be inferred. It is shown that, for domains that are periodic or unbounded horizontally, the psi vector is forced dynamically by the irrotational part of the **Q** vector. It is further shown for such domains that the vertical shear of the nondivergent part of the ageostrophic velocity is proportional to the nondivergent part of the **Q** vector. This, in principle, completes the diagnosis of the vertical velocity and the total ageostrophic velocity from the mass field, along with diabatic and frictional effects in the thermodynamic and momentum equations.

It is demonstrated that the projection of the psi-vector equation onto the cross-front vertical plane leads to a generalization of the QG form of the Sawyer-Eliassen equation applicable to three-dimensional flows. The forcing of the scalar streamfunction for the transverse (cross-front) circulation comprises not only the confluence and horizontal shear terms from the two-dimensional case, but additional terms involving the component of the vertical velocity associated with the vertical circulation in the alongfront direction and the nondivergent component of the ageostrophic velocity in the cross-front plane. These additional terms vanish in the two-dimensional case, wherein the vertical circulation is confined to the cross-front plane and the nondivergent part of the ageostrophic velocity is restricted to the alongfront direction.

The diagnostic methodologies for the total ageostrophic flow and for the generalized Sawyer-Eliassen equation are illustrated through applications to upper-level and surface frontal zones simulated in an *f*-plane primitive equation (PE) channel model of a finite-amplitude baroclinic wave. It is found that discrepancies in the sense of the cross-contour flow in jet-entrance and jet-exit regions between the QG-diagnosed ageostrophic flow and that simulated by the PE model can be traced to differences in the nondivergent part of the ageostrophic flow. Qualitative consistency is found, however, in the comparison between the QG irrotational ageostrophic flow and its PE counterpart, suggesting the utility of QG diagnoses of the vertical motion field in the vicinity of curved jet-front systems, where the geostrophic-momentum approximation may break down locally. In the generalized Sawyer-Eliassen equation, it is found that the confluence and horizontal shear forcing terms are dominant, but tend to be opposed by the term involving the component of the nondivergent part of the ageostrophic flow in the cross-front plane. The dominance of these “two-dimensional” forcing terms motivates a comparison between the diagnosed frontal circulations and those obtained in previous two-dimensional front-ogenesis models. This comparison addresses the extent to which idealized frontogenetical mechanisms involving confluence and horizontal shear carry over to less restrictive, three-dimensional contexts.

## Abstract

The kinematic technique of representing three-dimensional vertical circulations in baroclinic disturbances in terms of a vector streamfunction (referred to as the psi vector) recently proposed by the authors is placed in the context of quasigeostrophic (QG) theory. A diagnostic equation is derived for the psi vector from which the vertical velocity and the irrotational part of the ageostrophic velocity can be inferred. It is shown that, for domains that are periodic or unbounded horizontally, the psi vector is forced dynamically by the irrotational part of the **Q** vector. It is further shown for such domains that the vertical shear of the nondivergent part of the ageostrophic velocity is proportional to the nondivergent part of the **Q** vector. This, in principle, completes the diagnosis of the vertical velocity and the total ageostrophic velocity from the mass field, along with diabatic and frictional effects in the thermodynamic and momentum equations.

It is demonstrated that the projection of the psi-vector equation onto the cross-front vertical plane leads to a generalization of the QG form of the Sawyer-Eliassen equation applicable to three-dimensional flows. The forcing of the scalar streamfunction for the transverse (cross-front) circulation comprises not only the confluence and horizontal shear terms from the two-dimensional case, but additional terms involving the component of the vertical velocity associated with the vertical circulation in the alongfront direction and the nondivergent component of the ageostrophic velocity in the cross-front plane. These additional terms vanish in the two-dimensional case, wherein the vertical circulation is confined to the cross-front plane and the nondivergent part of the ageostrophic velocity is restricted to the alongfront direction.

The diagnostic methodologies for the total ageostrophic flow and for the generalized Sawyer-Eliassen equation are illustrated through applications to upper-level and surface frontal zones simulated in an *f*-plane primitive equation (PE) channel model of a finite-amplitude baroclinic wave. It is found that discrepancies in the sense of the cross-contour flow in jet-entrance and jet-exit regions between the QG-diagnosed ageostrophic flow and that simulated by the PE model can be traced to differences in the nondivergent part of the ageostrophic flow. Qualitative consistency is found, however, in the comparison between the QG irrotational ageostrophic flow and its PE counterpart, suggesting the utility of QG diagnoses of the vertical motion field in the vicinity of curved jet-front systems, where the geostrophic-momentum approximation may break down locally. In the generalized Sawyer-Eliassen equation, it is found that the confluence and horizontal shear forcing terms are dominant, but tend to be opposed by the term involving the component of the nondivergent part of the ageostrophic flow in the cross-front plane. The dominance of these “two-dimensional” forcing terms motivates a comparison between the diagnosed frontal circulations and those obtained in previous two-dimensional front-ogenesis models. This comparison addresses the extent to which idealized frontogenetical mechanisms involving confluence and horizontal shear carry over to less restrictive, three-dimensional contexts.

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## Abstract

In a recent paper on the kinematics of frontogenesis, Keyser et al. conjectured that partitioning the **Q** vector into along- and cross-isentrope components yields vertical-motion patterns that are respectively cellular and banded—the former on the scale of the baroclinic disturbance and the latter on the scale of the embedded frontal zones. This conjecture is examined diagnostically through solution of the quasigeostrophic omega equation, using the output from a nearly adiabatic and frictionless *f*-plane primitive equation channel model of the evolution of a baroclinic disturbance to finite amplitude. The results of the present study support the proposed conjecture, suggesting the following interpretation of the characteristic comma structure of the vertical-motion field in midlatitude baroclinic disturbances: The comma shape arises from the modification or distortion of a wave-scale dipole pattern by frontal-scale asymmetries. The dipole is associated with the along-isentrope component of the **Q** vector, reflecting the wavelike pattern in the potential temperature field within the baroclinic disturbance; the asymmetries are associated with the cross-isentrope component of the **Q** vector, reflecting the presence of frontal zones within the baroclinic disturbance.

## Abstract

In a recent paper on the kinematics of frontogenesis, Keyser et al. conjectured that partitioning the **Q** vector into along- and cross-isentrope components yields vertical-motion patterns that are respectively cellular and banded—the former on the scale of the baroclinic disturbance and the latter on the scale of the embedded frontal zones. This conjecture is examined diagnostically through solution of the quasigeostrophic omega equation, using the output from a nearly adiabatic and frictionless *f*-plane primitive equation channel model of the evolution of a baroclinic disturbance to finite amplitude. The results of the present study support the proposed conjecture, suggesting the following interpretation of the characteristic comma structure of the vertical-motion field in midlatitude baroclinic disturbances: The comma shape arises from the modification or distortion of a wave-scale dipole pattern by frontal-scale asymmetries. The dipole is associated with the along-isentrope component of the **Q** vector, reflecting the wavelike pattern in the potential temperature field within the baroclinic disturbance; the asymmetries are associated with the cross-isentrope component of the **Q** vector, reflecting the presence of frontal zones within the baroclinic disturbance.

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## Abstract

The problem of representing vertical circulations in frontal zones is reexamined with the objective of devising a methodology sufficiently general to apply in situations where these circulations are no longer confined to the cross-front (transverse) vertical plane and therefore must be viewed as fully dimensional. The proposed methodology, which builds upon the earlier work of Hoskins and Draghici and of Eliassen, consists of adopting a vector streamfunction that describes the vertical velocity and the horizontal irrotational flow. This generalized streamfunction, referred to as the *psi vector*, may be determined uniquely from the vertical velocity field over a limited region provided that suitable lateral boundary conditions on the velocity potential for the irrotational part of the horizontal velocity can be specified. A key property of the psi vector is that its projections onto arbitrary orthogonal vertical planes yield two independent vertical circulations, providing an objective means for separating a three-dimensional vertical circulation into cross- and alongfront components.

The psi-vector methodology is applied to surface and upper-level frontal zones simulated in an *f* plane primitive equation channel model of a finite-amplitude baroclinic wave in which all diabatic and frictional influences are neglected except for horizontal diffusion. Both along and cross-front vertical circulations are diagnosed and interpreted for upper-level frontal zones associated with jet streams and jet streaks situated within curved flowed and for surface fronts possessing attributes of observed warm and cold fronts. In all of these frontal systems, the transverse vertical circulation is dominant in the sense that the cross-front component of the vertical velocity is larger in magnitude than the corresponding alongfront component. The lateral scale of the cross-front circulation is of a frontal dimension, whereas the scale of the alongfront circulation is characteristic of the baroclinic wave. The orientations of the cross-front circulations relative to the respective frontal zones are broadly consistent with those discussed in earlier two-dimensional models. These findings support interpretations 1) that three- dimensional vertical circulations in midiatitude cyclones may be viewed conceptually as a superposition of vertical circulations associated with the baroclinic wave and with the embedded fronts, and 2) that confluence and horizontal shear forcing mechanisms, although strictly applicable to two-dimensional frontogenesis models, may carry over to describe transverse vertical circulations in three-dimensional systems.

## Abstract

The problem of representing vertical circulations in frontal zones is reexamined with the objective of devising a methodology sufficiently general to apply in situations where these circulations are no longer confined to the cross-front (transverse) vertical plane and therefore must be viewed as fully dimensional. The proposed methodology, which builds upon the earlier work of Hoskins and Draghici and of Eliassen, consists of adopting a vector streamfunction that describes the vertical velocity and the horizontal irrotational flow. This generalized streamfunction, referred to as the *psi vector*, may be determined uniquely from the vertical velocity field over a limited region provided that suitable lateral boundary conditions on the velocity potential for the irrotational part of the horizontal velocity can be specified. A key property of the psi vector is that its projections onto arbitrary orthogonal vertical planes yield two independent vertical circulations, providing an objective means for separating a three-dimensional vertical circulation into cross- and alongfront components.

The psi-vector methodology is applied to surface and upper-level frontal zones simulated in an *f* plane primitive equation channel model of a finite-amplitude baroclinic wave in which all diabatic and frictional influences are neglected except for horizontal diffusion. Both along and cross-front vertical circulations are diagnosed and interpreted for upper-level frontal zones associated with jet streams and jet streaks situated within curved flowed and for surface fronts possessing attributes of observed warm and cold fronts. In all of these frontal systems, the transverse vertical circulation is dominant in the sense that the cross-front component of the vertical velocity is larger in magnitude than the corresponding alongfront component. The lateral scale of the cross-front circulation is of a frontal dimension, whereas the scale of the alongfront circulation is characteristic of the baroclinic wave. The orientations of the cross-front circulations relative to the respective frontal zones are broadly consistent with those discussed in earlier two-dimensional models. These findings support interpretations 1) that three- dimensional vertical circulations in midiatitude cyclones may be viewed conceptually as a superposition of vertical circulations associated with the baroclinic wave and with the embedded fronts, and 2) that confluence and horizontal shear forcing mechanisms, although strictly applicable to two-dimensional frontogenesis models, may carry over to describe transverse vertical circulations in three-dimensional systems.

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## Abstract

Recent diagnostic studies using retrievals from the Visible Infrared Spin-Scan Radiometer (VISSR) Atmospheric Sounder (VAS) indicate that there are limitations of gestationary satellite sounding data (poor vertical resolution of temperature and moisture profiles) as well as advantages (fine horizontal resolution and time resolution better than the conventional network and polar-orbiting satellites). A simulation experiment is presented which tests a procedure that assimilates temperature soundings from geostationary satellites using a method developed by Gal-Chen. The method takes advantage of the strength of this observing system (Increased temporal and horizontal resolution) while avoiding its major weakness (poor vertical resolution). The assimilation technique is based on multiple insertions of satellite data over an analysis cycle. In the experiment, the insertion rate is varied from every half hour as an upper limit to every six hours as a lower limit. In the updating procedure, we ensure that the fine vertical structure that might be generated by the model is not destroyed by the coarse vertical resolution of the inserted satellite data. At the same time, the model is constrained to reproduce thickness compatible with those that would be inferred from the satellite sounding (assuming the radiance measurements are exact). The results of these simulation experiments indicate that, for the case of a baroclinically unstable wave, considerable improvements in the short-range forecast (⩽48 h) may be realized if geostationary satellite data is inserted with a frequency near 1 h during a 6-h analysis cycle compared with a single insertion. On the assumption that cloud cover would limit the ability to obtain satellite soundings, an experiment was conducted showing that, while poor vertical resolution apparently can be tolerated, a nearly complete horizontal coverage is necessary to maintain the positive impact on the numerical simulations. This implies that in order to make geostationary satellite data useful for initializing numerical models, microwave sounding channels should be considered for geostationary orbit so that frequent observations of the surface-500 mb thickness can be estimated for cloud-covered (but nonprecipitating) areas as well.

## Abstract

Recent diagnostic studies using retrievals from the Visible Infrared Spin-Scan Radiometer (VISSR) Atmospheric Sounder (VAS) indicate that there are limitations of gestationary satellite sounding data (poor vertical resolution of temperature and moisture profiles) as well as advantages (fine horizontal resolution and time resolution better than the conventional network and polar-orbiting satellites). A simulation experiment is presented which tests a procedure that assimilates temperature soundings from geostationary satellites using a method developed by Gal-Chen. The method takes advantage of the strength of this observing system (Increased temporal and horizontal resolution) while avoiding its major weakness (poor vertical resolution). The assimilation technique is based on multiple insertions of satellite data over an analysis cycle. In the experiment, the insertion rate is varied from every half hour as an upper limit to every six hours as a lower limit. In the updating procedure, we ensure that the fine vertical structure that might be generated by the model is not destroyed by the coarse vertical resolution of the inserted satellite data. At the same time, the model is constrained to reproduce thickness compatible with those that would be inferred from the satellite sounding (assuming the radiance measurements are exact). The results of these simulation experiments indicate that, for the case of a baroclinically unstable wave, considerable improvements in the short-range forecast (⩽48 h) may be realized if geostationary satellite data is inserted with a frequency near 1 h during a 6-h analysis cycle compared with a single insertion. On the assumption that cloud cover would limit the ability to obtain satellite soundings, an experiment was conducted showing that, while poor vertical resolution apparently can be tolerated, a nearly complete horizontal coverage is necessary to maintain the positive impact on the numerical simulations. This implies that in order to make geostationary satellite data useful for initializing numerical models, microwave sounding channels should be considered for geostationary orbit so that frequent observations of the surface-500 mb thickness can be estimated for cloud-covered (but nonprecipitating) areas as well.

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## Abstract

Evaluations of operational TIROS-N and NOAA-6 temperature soundings over North America are presented for an early January 1980 period one month after completion of the First GARP Global Experiment. In addition to collocated comparisons, synoptic analyses derived only from satellite data and model forecasts initialized from these analyses are compared with those obtained from conventional data. The collocated results, similar to those presented by Phillips *et al*. (1979) and Schlatter (1981) from TIROS-N soundings, show maximum sounding errors new the surface and tropopause. The analysis comparisons further illustrate that thermal gradients inferred from satellite soundings are too weak, with NOAA-6 gradients slightly weaker than TIROS-N gradients. Difference fields between satellite and conventional thickness analyses propagate eastward with the synoptic patterns, strongly suggesting a correlation of satellite sounding errors to synoptic patterns. These anomalies are also retained in model forecasts started from satellite analyses. These results stress the importance of properly defining the error characteristics of satellite soundings before incorporating them into analysis-forecast systems.

## Abstract

Evaluations of operational TIROS-N and NOAA-6 temperature soundings over North America are presented for an early January 1980 period one month after completion of the First GARP Global Experiment. In addition to collocated comparisons, synoptic analyses derived only from satellite data and model forecasts initialized from these analyses are compared with those obtained from conventional data. The collocated results, similar to those presented by Phillips *et al*. (1979) and Schlatter (1981) from TIROS-N soundings, show maximum sounding errors new the surface and tropopause. The analysis comparisons further illustrate that thermal gradients inferred from satellite soundings are too weak, with NOAA-6 gradients slightly weaker than TIROS-N gradients. Difference fields between satellite and conventional thickness analyses propagate eastward with the synoptic patterns, strongly suggesting a correlation of satellite sounding errors to synoptic patterns. These anomalies are also retained in model forecasts started from satellite analyses. These results stress the importance of properly defining the error characteristics of satellite soundings before incorporating them into analysis-forecast systems.

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Analyses and forecasts for the first 2 weeks of the Genesis of Atlantic Lows Experiment (GALE) are described. These fields were produced using the National Meteorological Center (NMC) Regional Analysis and Forecast System (RAFS). Two sets of analyses and forecasts were constructed: one using the NMC operational database only (Level IIIa), and one using the NMC data merged with high-density observations taken during GALE (Level IIIb).

During the first 14 days of GALE, supplemental data were collected throughout two Intensive Observing Periods (IOPs). Comparisons of the Level IIIa and IIIb analyses over the GALE observing region in the southeastern United States indicated a worsening of the geopotential height analysis at operational NWS rawinsonde sites using the supplemental IIIb data. This was caused by inconsistencies in the height measurements at the high-density GALE rawinsonde sites. Such patterns were not observed in the wind and temperature analyses.

During IOP No. 1, the Level IIIa and IIIb Nested Grid Model (NGM) forecasts were nearly identical. For IOP No. 2, one forecast cycle saw an improvement in the Level IIIb forecasts due to offshore GALE dropwindsonde data, while another was improved by the inclusion of late-arriving rawinsonde data in the IIIb analysis. The inland, high-density GALE soundings, however, had a negligible impact on NGM forecasts during the entire 12-day period.

Analyses and forecasts for the first 2 weeks of the Genesis of Atlantic Lows Experiment (GALE) are described. These fields were produced using the National Meteorological Center (NMC) Regional Analysis and Forecast System (RAFS). Two sets of analyses and forecasts were constructed: one using the NMC operational database only (Level IIIa), and one using the NMC data merged with high-density observations taken during GALE (Level IIIb).

During the first 14 days of GALE, supplemental data were collected throughout two Intensive Observing Periods (IOPs). Comparisons of the Level IIIa and IIIb analyses over the GALE observing region in the southeastern United States indicated a worsening of the geopotential height analysis at operational NWS rawinsonde sites using the supplemental IIIb data. This was caused by inconsistencies in the height measurements at the high-density GALE rawinsonde sites. Such patterns were not observed in the wind and temperature analyses.

During IOP No. 1, the Level IIIa and IIIb Nested Grid Model (NGM) forecasts were nearly identical. For IOP No. 2, one forecast cycle saw an improvement in the Level IIIb forecasts due to offshore GALE dropwindsonde data, while another was improved by the inclusion of late-arriving rawinsonde data in the IIIb analysis. The inland, high-density GALE soundings, however, had a negligible impact on NGM forecasts during the entire 12-day period.

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## Abstract

A full description of the ModelE version of the Goddard Institute for Space Studies (GISS) atmospheric general circulation model (GCM) and results are presented for present-day climate simulations (ca. 1979). This version is a complete rewrite of previous models incorporating numerous improvements in basic physics, the stratospheric circulation, and forcing fields. Notable changes include the following: the model top is now above the stratopause, the number of vertical layers has increased, a new cloud microphysical scheme is used, vegetation biophysics now incorporates a sensitivity to humidity, atmospheric turbulence is calculated over the whole column, and new land snow and lake schemes are introduced. The performance of the model using three configurations with different horizontal and vertical resolutions is compared to quality-controlled in situ data, remotely sensed and reanalysis products. Overall, significant improvements over previous models are seen, particularly in upper-atmosphere temperatures and winds, cloud heights, precipitation, and sea level pressure. Data–model comparisons continue, however, to highlight persistent problems in the marine stratocumulus regions.

## Abstract

A full description of the ModelE version of the Goddard Institute for Space Studies (GISS) atmospheric general circulation model (GCM) and results are presented for present-day climate simulations (ca. 1979). This version is a complete rewrite of previous models incorporating numerous improvements in basic physics, the stratospheric circulation, and forcing fields. Notable changes include the following: the model top is now above the stratopause, the number of vertical layers has increased, a new cloud microphysical scheme is used, vegetation biophysics now incorporates a sensitivity to humidity, atmospheric turbulence is calculated over the whole column, and new land snow and lake schemes are introduced. The performance of the model using three configurations with different horizontal and vertical resolutions is compared to quality-controlled in situ data, remotely sensed and reanalysis products. Overall, significant improvements over previous models are seen, particularly in upper-atmosphere temperatures and winds, cloud heights, precipitation, and sea level pressure. Data–model comparisons continue, however, to highlight persistent problems in the marine stratocumulus regions.