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Todd K. Schaack and Donald R. Johnson

Abstract

Three-dimensional global distributions of atmospheric heating are estimated for January and July of the 3-year period 1986–88 from the ECMWF/TOGA assimilated datasets. Emphasis is placed on the interseasonal and interannual variability of heating both locally and regionally. Large fluctuations in the magnitude of heating and the disposition of maxima/minima in the Tropics occur over the 3-year period. This variability, which is largely in accord with anomalous precipitation expected during the ENSO cycle, appears realistic. In both January and July, interannual differences of 1.07−1.5 K day−1 in the vertically averaged heating occur over the tropical Pacific. These interannual regional differences are substantial in comparison with maximum monthly averaged Heating rates of 2.0−2.5 K day−1. In the extratropics, the most prominent interannual variability occurs along the wintertime North Atlantic cyclone track.

Vertical profiles of heating from selected regions also reveal large interannual variability. Clearly evident is the modulation of the heating within tropical regions of deep moist convection associated with the evolution of the ENSO cycle. The beating integrated over continental and oceanic basins emphasizes the impact of land and ocean surfaces on atmospheric energy balance and depicts marked interseasonal and interannual large-scale variability.

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Ming-Ying Wei and Todd K. Schaack

Abstract

Based on surface pressure and terrain height analyses from the National Meteorological Center, mountain torques are calculated for January, April, July and October 1979 during the First GARP Global Experiment. The zonally integrated mountain torques are generally in good agreement with previous studies. For all four months, positive torque exists in the tropical latitudes as well as in the polar and subtropical latitudes of the Northern Hemisphere; negative torque exists in northern middle latitudes and most of the Southern Hemisphere. An exception occurs in July when the mountain torque is negative between 5 and 25°N and positive in the Southern Hemisphere subtropics. Over latitudes where large terrain variation exists such as near 20°S due to the Andes, the estimate obtained in this study is larger in magnitude than that from previous work. The difference is due to the differences in both grid resolution and the particular atmospheric data and topography selected.

The meridional profiles of individual continental mountain torques are examined to illustrate geographical contributions to the net zonal torque. The positive mountain torque in northern high latitudes is due mainly to North America and Greenland. Both North America and Eurasia contribute to the sink of angular momentum in northern middle latitudes and the source in the subtropical latitudes. The negative torque between 5 and 25°N in July is due to the influence of the Indian monsoon trough on Arabia and Africa. The negative mountain torque over South America dominates the positive torque over Africa and Australia in the Southern Hemisphere in January and October.

Although the monthly averaged zonally integrated mountain torque assumes lesser importance when compared to the frictional torque, regional mountain torque at the synoptic time scale is quite large and can have considerable influence on the large scale circulation. Hemispheric torques are in qualitative agreement with previous work. Due to the partial cancellation of hemispheric torques and the variances in mountain torque which can result from different computing methods and grid distribution, no conclusive statement is drawn in regard to the global mountain torques during FGGE.

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Martin P. Hoerling, Todd K. Schaack, and Allen J. Lenzen

Abstract

Using a mathematical formulation of stratospheric-tropospheric (ST) exchange, the cross-tropopause mass flux is diagnosed globally for January 1979. Contributions by physical mechanisms including the diabatic transport and the quasi-horizontal adiabatic transport along isentropes that intersect the tropopause surface are evaluated. Both thermal and dynamical definitions of the tropopause are used.

Two regions of zonally integrated mass flux into the stratosphere are found, one over tropical latitudes associated with diabatic transports, and a second over subpolar latitudes associated with adiabatic transports. The ingress to the stratosphere in each of the latitude bands 50°–70°N and 40°–70°S is as intense as that occurring over the tropics, a feature of the global budget not previously documented. Compensating mass outflow from the stratosphere occurs mainly over midlatitudes near axes of strong upper-level westerlies.

Large zonal asymmetries are found in the regional patterns of ST exchange. Consistent with the concept of a stratosphere fountain, the tropical inflow to the stratosphere is maximized over the Australasian monsoon. The midlatitude mass outflow tends to be concentrated along stationary wave troughs, roughly in the vicinity of cyclogenetic areas. A mass transport into the stratosphere occurs downstream and poleward of the troughs. The extratropical pattern of time-averaged cross-tropopause mass flux thus appears to be interpretable within the framework of simple physical models on three-dimensional airmass trajectories in baroclinic disturbances.

While uncertainties concerning quantitative aspects of the global ST exchange remain, qualitative confirmation of the mass-transport diagnostics is found in independent studies of trace atmospheric constituents. In particular, the finding of mass inflow to the stratosphere at subpolar latitudes is consistent with satellite and aircraft measurements of high water vapor mixing ratios in the low stratosphere over these regions.

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Todd K. Schaack, Allen J. Lenzen, and Donald R. Johnson

Abstract

Global distributions of atmospheric heating for January 1979 are estimated from two Global Weather Experiment (GWE) Level III datasets generated at the Goddard Laboratory for Atmospheres (GLA). One set utilized data from the full GWE observing system (to be denoted SAT), while the other excluded information either measured or transmitted by satellite (to be denoted NOSAT). These two distributions of heating are compared with the ones predicted by the forecast model (MODEL) during the above SAT and NOSAT GWE assimilations and another one predicted during a wintertime climate simulation (CLIMATE) of the GLA GCM. Through intercomparison of the five distributions, this study with an emphasis on satellite-derived information investigates the global distribution of atmospheric heating and the impact of observations on the diagnostic estimates of heating derived from assimilated datasets.

The spatial patterns of heat sources and sinks north of 40°S estimated from the SAT and NOSAT datasets are similar and are consistent with physical and climatological considerations and in general agreement with estimates derived from other GWE data. South of 40°S the relative accuracy of the distributions is uncertain. Substantial differences between the two estimates occur in tropical oceanic regions of deep convection and over the central North Pacific. Over the North Pacific the SAT results depict a mid-latitude oceanic storm track extending from the coast of Asia to the east of the dateline, while the NOSAT heating is confined to the western Pacific. In tropical-subtropical oceanic regions of deep convection, differences occur in the intensity of heating and in the disposition of heating maxima. Overall, the results indicate a substantial impact of satellite information on diagnostic estimates of heating in regions where there is a paucity of conventional observations. Although there are uncertainties, the addition of satellite data provides information on the atmosphere's wind and temperature structure that is important for estimation of the global distribution of heating and energy exchange.

The comparison of the SAT and NOSAT diagnostic and corresponding MODEL distributions indicates that in Northern Hemisphere middle latitudes the assimilation of observed data substantially impacted the diagnostic estimates of heating. In tropical latitudes, these comparisons imply a larger influence of the assimilation model's predicted heating on the resulting diagnostic estimates in the NOSAT than in the SAT assimilation. The substantial departure of the NOSAT and SAT MODEL distributions from the climatological heating of the GLA model (CLIMATE) is an indication of the effect of observations on the ensemble of forecasts during the GWE assimilations and provides additional documentation of the impact of observed data on the diagnosed heating distributions.

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Martin P. Hoerling, Todd K. Schaack, and Allen J. Lenzen

Abstract

The European Center for Medium Range Weather Forecasts (ECMWF) level IIIb dataset is used to construct global pressure analyses of the tropopause surface during January 1979. Two methods are employed: a dynamical method based on isentropic potential vorticity (IPV) and a thermal method based on lapse rate criteria. Regional tropopause pressure analyses are extracted from the global analyses and compared against distributions derived from rawinsonde data. The coarse vertical resolution of the ECMWF data compromises the ability to resolve abrupt stability changes between the troposphere and stratosphere and impacts tropopause analyses using both methods. Sensitivity of the derived tropopause pressures to a range of IPV and lapse rate thresholds is examined. For the assimilated dataset employed herein, 3.5 IPV units represent an optimal value for tropopause analysis outside the tropics. Modification of the WMO lapse rate criteria does not significantly improve tropopause analysis globally.

Both methods capture the large-scale features of the radiosonde-reported tropopause surface in the regional analyses, although each approach has limitations. The spatial structure and temporal evolution of the dynamically determined tropopause surface within a developing extratropical cyclone is found to be superior to that based on lapse rate criteria, while only the lapse rate method is a viable approach in the tropics.

We conclude that the pressure of the tropopause surface can be determined globally using ECMWF assimilated data. The preliminary results are encouraging and suggest that it is feasible to proceed beyond sounding analyses and case studies for determining the tropopause position. We view this to be an important first step toward implementing global studies of stratospheric–tropospheric exchange.

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Martin P. Hoerling, Todd K. Schaack, and Donald R. Johnson

Abstract

Simulations of the global distribution of heating (the sum of latent, sensible, short and longwave radiation) are presented for January and July using the R15 NCAR Community Climate Model (CCM). The vertical and horizontal distributions of heating predicted by an earlier version of the CCM (CCM0B) are contrasted with those predicted by the current version of the CCM (CCMI) in which substantial revisions were made in the physical parameterizations of convective, radiative, and sensible heating. The results are compared with climatological studies of atmospheric heating and with recent diagnostic analyses of heating during the Global Weather Experiment (GWE).

The dominant heat sources in the CCM simulations of January and July are located over Indonesia-Southeast Asia in broad agreement with the primary feature of the observed Asian monsoon; however, several marked distinctions between the vertically averaged heating distributions for CCM0B and CCM1 occur. During January, centers of maximum heating are located farther south of the equator in CCM1 than in CCM0B. This southward shift in CCM1 is accompanied by strong heating along the South Pacific and South Atlantic convergence zones. These latter features are largely absent in CCM0B. Additionally, CCM1 heating over the monsoon regions of southern Africa and South America is nearly double that found in CCM0B. Similarly, during July, CCM1 heating in the monsoon regions of northern Africa, the western Pacific, and Central America is nearly double that observed in CCM0B.

With fixed boundary conditions (e.g., sea surface temperatures, soil moisture, sea ice extent, and snow cover) in the perpetual simulations, the interannual variability of heating is due entirely to internal model dynamics. The interannual variability of both January and July heating is larger in CCM1 than in CCM0B. Regions of maximum interannual variability in both CCM0B and CCM1 are found in the vicinity of the principal tropical heat source regions. This variability is associated primarily with in situ fluctuations in the intensity of regional heating centers, while geographical displacements appear to be of secondary importance.

Major differences are found between the vertical distributions of heating for CCM0B and CCM1. These stem largely from changes in physical parameterizations, in particular a change in the prescribed critical relative humidity for condensation by moist stable and unstable adiabatic adjustment from 80% in CCM0B to 100% in CCM1, and a replacement of dry convective adjustment-in CCM0B by vertical diffusion of heat and moisture in CCM1. In the tropics, maximum heating occurs in the lower troposphere in CCM0B, while strongest heating occurs in the mid- to upper troposphere in CCM1. In the storm tracks of extratropical latitudes, heating is confined below 800 mb in CCM0B, while heating of appreciable magnitude extends above 500 mb in CCM1. The vertical distribution of heating in CCM1 agrees favorably with diagnosed distributions for the GWE, while the CCM0B heating distribution does not.

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Paul Spaete, Donald R. Johnson, and Todd K. Schaack

Abstract

Using data generated from a model simulation, the exchange of mass between the stratosphere and the troposphere is estimated for the Presidents' Day storm during a 24-h period beginning at 1500 UTC 18 February 1979. This 24-h interval coincided with a strongly developed tropopause depression and the onset of explosive surface cyclogenesis. The initial part of the study consists of identifying a surface of isentropic potential vorticity (IPV) to represent the tropopause. The 3.0-IPV-unit surface is chosen since the pressure distribution on this surface closely matches the tropopause pressures reported by radiosonde stations. The IPV surface portrays the depression of the tropopause associated with the polar-front jet and trough system accompanying the baroclinic amplification of the Presidents' Day storm.

Using a quasi-Lagrangian transport model, stratospheric–tropospheric mass exchange is estimated for the region including and immediately adjacent to the tropopause depression. The estimated mass transport from the stratosphere to the troposphere for the 24-h period is 5 × 1014 kg. The transport from the troposphere to the stratosphere is 2 × 1014 kg yielding a net transport across the tropopause of 3 × 1014 kg from the stratosphere to the troposphere. These results are confirmed by a second, independent model simulation.

The mass transport from stratosphere to troposphere across the 3.0-IPV surface coincides with descending air, often referred to as the “dry airstream,” arcing counterclockwise around the polar-front jet and trough system from northwest to east. Reverse transport from the troposphere to the stratosphere occurs northeast of the depression and agrees with trajectories of air parcels within the end region of rising “conveyer belts."

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Donald R. Johnson, Allen J. Lenzen, Tom H. Zapotocny, and Todd K. Schaack

Abstract

A challenge common to weather, climate, and seasonal numerical prediction is the need to simulate accurately reversible isentropic processes in combination with appropriate determination of sources/sinks of energy and entropy. Ultimately, this task includes the distribution and transport of internal, gravitational, and kinetic energies, the energies of water substances in all forms, and the related thermodynamic processes of phase changes involved with clouds, including condensation, evaporation, and precipitation processes.

All of the processes noted above involve the entropies of matter, radiation, and chemical substances, conservation during transport, and/or changes in entropies by physical processes internal to the atmosphere. With respect to the entropy of matter, a means to study a model’s accuracy in simulating internal hydrologic processes is to determine its capability to simulate the appropriate conservation of potential and equivalent potential temperature as surrogates of dry and moist entropy under reversible adiabatic processes in which clouds form, evaporate, and precipitate. In this study, a statistical strategy utilizing the concept of “pure error” is set forth to assess the numerical accuracies of models to simulate reversible processes during 10-day integrations of the global circulation corresponding to the global residence time of water vapor. During the integrations, the sums of squared differences between equivalent potential temperature θ e numerically simulated by the governing equations of mass, energy, water vapor, and cloud water and a proxy equivalent potential temperature e numerically simulated as a conservative property are monitored. Inspection of the differences of θ e and e in time and space and the relative frequency distribution of the differences details bias and random errors that develop from nonlinear numerical inaccuracies in the advection and transport of potential temperature and water substances within the global atmosphere.

A series of nine global simulations employing various versions of Community Climate Models CCM2 and CCM3—all Eulerian spectral numerics, all semi-Lagrangian numerics, mixed Eulerian spectral, and semi-Lagrangian numerics—and the University of Wisconsin—Madison (UW) isentropic-sigma gridpoint model provides an interesting comparison of numerical accuracies in the simulation of reversibility. By day 10, large bias and random differences were identified in the simulation of reversible processes in all of the models except for the UW isentropic-sigma model. The CCM2 and CCM3 simulations yielded systematic differences that varied zonally, vertically, and temporally. Within the comparison, the UW isentropic-sigma model was superior in transporting water vapor and cloud water/ice and in simulating reversibility involving the conservation of dry and moist entropy. The only relative frequency distribution of differences that appeared optimal, in that the distribution remained unbiased and equilibrated with minimal variance as it remained statistically stationary, was the distribution from the UW isentropic-sigma model. All other distributions revealed nonstationary characteristics with spreading and/or shifting of the maxima as the biases and variances of the numerical differences of θ e and e amplified.

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Donald R. Johnson, Allen J. Lenzen, Tom H. Zapotocny, and Todd K. Schaack

Abstract

The objectives of this study are 1) to provide the framework for an in-depth statistical analysis of the numerical uncertainties in the simulation of conservation of entropy, potential vorticity, and like properties under appropriate modeling constraints, and 2) to illustrate the discriminating nature of the analysis in an application that isolates internal numerical inaccuracies in the simulation of reversible atmospheric processes. In an earlier study the authors studied the pure error sum of squares function as a quadratic measure of uncertainties by summing the squared differences between equivalent potential temperature as simulated by the nonlinear governing equations for mass, energy, water vapor, and cloud water and its counterpart simulated as a trace constituent. Within the experimental design to examine a model's capabilities to conserve the moist entropy, the continuum equations demand that the differences between equivalent potential temperature θ e and proxy equivalent potential temperature e vanish at all discrete model information points throughout the 10-day simulation. The differences that develop provide a measure of numerical inaccuracies in the simulation of reversibility.

In this extension of the earlier study, the first consideration is to examine zonal–vertical cross sections of the differences, relative frequency distributions of the differences, and the vertical structure of systematic differences. Subsequently, through an analysis of variance, the sum of squares is partitioned into three components: the squared deviations of differences from an area mean difference, the square of the deviation of the mean difference from the global mean difference, and the square of the global mean difference. In the situation where biases vanish in all three components, a theoretical development based on the uniqueness of a distribution with its moment-generating function suggests that the nearer the empirical relative frequency distribution of pure error differences is to the classical triangular distribution of the differences of two random variates, the closer the model's simulation is to the optimum accuracy feasible in ensuring reversibility and appropriate conservation of moist entropy. A final consideration is to place the random and systematic components of differences within a probability perspective in which the normal distribution is utilized to assess whether the magnitude of the average difference exceeds that expected to develop from the presence of the random component.

The focus of the application in this study assesses the capabilities of several models to simulate the conservation of moist entropy and reversibility of moist-adiabatic processes over a period of 10 days. The assessment includes four different versions of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM) and the University of Wisconsin (UW) hybrid isentropic-sigma (θσ) model. The assessment from the 10-day simulations focuses on the temporal evolution of the global sum of squares of the differences of equivalent potential temperature and its trace and the three components. In the case of all models expressed in sigma coordinates, the global sum of squares as simulated exceeds the global sum of squares from the UW θσ model. The partitioning into three components of variance revealed different structures of average differences resulting from errors in vertical exchange, and also different magnitudes of the random component among the CCM models. In contrast, the component sum of squares in the UW θσ model simulation was minimal, except for small global and area average differences stemming from transport across the interface between the isentropic and sigma domains of the model in the low troposphere. The empirical relative frequency distribution for the pure error differences in the UW θσ model tends to equilibrate and be triangular in form as would be expected from statistical theory in which the random variate is given by the difference of two variates, each of which is drawn from a uniform distribution of random errors.

In conclusion, the combination of the methods developed in the earlier study and this paper provides a robust strategy for the global assessments of numerical accuracies in simulating reversibility within weather and climate predictions throughout the model domain globally and also regionally.

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Tom H. Zapotocny, Allen J. Lenzen, Donald R. Johnson, Todd K. Schaack, and Fred M. Reames

Abstract

Five- and 10-day inert trace constituent distributions prognostically simulated with the University of Wisconsin (UW) hybrid isentropic–sigma (θσ) model, the nominally identical UW sigma (σ) model, and the National Center for Atmospheric Research Community Climate Model 2 (CCM2) are analyzed and compared in this study. The UW θσ and σ gridpoint models utilize the flux form of the primitive equations, while CCM2 is based on the spectral representation and uses semi-Lagrangian transport (SLT) for trace constituents. Results are also compared against a version of the CCM that uses spectral transport for the trace constituent. These comparisons 1) contrast the spatial and temporal evolution of the filamentary transport of inert trace constituents simulated with the UW θσ and σ models against a “state of the art” GCM under both isentropic and nonisentropic conditions and 2) examine the ability of the models to conserve the initial trace constituent maximum value during 10-day integrations.

Results show that the spatial distributions of trace constituent evolve in a similar manner, regardless of the transport scheme or model type. However, when compared to the UW θσ model’s ability to simulate filamentary structure and conserve the initial trace constituent maximum value, results from the other models in this study indicate substantial spurious dispersion. The more accurate conservation demonstrated with the UW θσ model is especially noticeable within extratropical amplifying baroclinic waves, and it stems from the dominance of two-dimensional, quasi-horizontal isentropic exchange processes in a stratified baroclinic atmosphere. This condition, which largely precludes spurious numerical dispersion associated with vertical advection, is unique to isentropic coordinates. Conservation of trace constituent maxima in sigma coordinates suffers from the complexity of, and inherent need for, resolving three-dimensional transport in the presence of vertical wind shear during baroclinic amplification, a condition leading to spurious vertical dispersion. The experiments of this study also indicate that the shape-preserving SLT scheme used in CCM2 further reduces conservation of the initial maximum value when compared to the spectral transport of trace constituents, although the patterns are more coherent and the Gibbs phenomenon is eliminated.

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