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Allen J. Lenzen, Donald R. Johnson, and Robert Atlas

Abstract

Quasi-Lagrangian diagnostics of mass, angular momentum, water vapor, and kinetic energy are evaluated for four different Goddard Laboratory for Atmospheres model simulations of the Queen Elizabeth II storm of 9–11 September 1978 to study the impact of Seasat-A satellite Scatterometer (SASS) winds and horizontal resolution in numerical prediction. In a four-way comparison, the diagnostics investigate the impact of including dealiased SASS winds in the initial conditions of the model and doubling the horizontal resolution on 36 h simulations of the QE II storm. The largest impact on the simulation stemmed from doubling the model's horizontal resolution from 4° × 5° to 2° × 2.5°. The increased resolution resulted in a storm track much closer to that observed, a much deeper surface development, a stronger mass circulation, stronger heating, and stronger increase of angular momentum. The inclusion of SASS data resulted in an approximately 2–3-mb-deeper surface cyclone for both the 2° × 2.5° and 4° × 5° resolution simulations. The inclusion also led to substantial increases in the horizontal mass circulation and heating for the 2° × 2.5° simulation. During the early explosive deepening phase of the cyclone, the inward lateral transport of water vapor in lower layers was larger in the 2° × 2.5° SASS than in the 2° × 2.5° NOSASS (exclusion of SASS surface winds) simulation. During the period of most rapid development, the results from the SASS simulation revealed a larger generation of kinetic energy throughout the troposphere and increased outward transport of kinetic energy in upper layers.

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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 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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Jason A. Otkin, William E. Lewis, Allen J. Lenzen, Brian D. McNoldy, and Sharanya J. Majumdar

Abstract

In this study, cycled forecast experiments were performed to assess the ability of different cloud microphysics and cumulus parameterization schemes in the Hurricane Weather Research and Forecasting (HWRF) Model to accurately simulate the evolution of the cloud and moisture fields during the entire life cycle of Hurricane Edouard (2014). The forecast accuracy for each model configuration was evaluated through comparison of observed and simulated Geostationary Operational Environmental Satellite-13 (GOES-13) infrared brightness temperatures and satellite-derived tropical cyclone intensity estimates computed using the advanced Dvorak technique (ADT). Overall, the analysis revealed a large moist bias in the mid- and upper troposphere during the entire forecast period that was at least partially due to a moist bias in the initialization datasets but was also affected by the microphysics and cumulus parameterization schemes. Large differences occurred in the azimuthal brightness temperature distributions, with two of the microphysics schemes producing hurricane eyes that were much larger and clearer than observed, especially for later forecast hours. Comparisons to the forecast 10-m wind speeds showed reasonable agreement (correlations between 0.58 and 0.74) between the surface-based intensities and the ADT intensity estimates inferred via cloud patterns in the upper troposphere. It was also found that model configurations that had the smallest differences between the ADT and surface-based intensities had the most accurate track and intensity forecasts. Last, the cloud microphysics schemes had the largest impact on the forecast accuracy.

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

Abstract

The purpose of this study is to briefly describe the global atmospheric University of Wisconsin (UW) hybrid isentropic–eta coordinate (UW θη) model and document results from a 14-yr climate simulation. The model, developed through modification of the UW hybrid isentropic–sigma (θσ) coordinate model, employs a vertical coordinate that smoothly varies from terrain following at the earth's surface to isentropic coordinates in the middle to upper troposphere. The UW θη model eliminates the discrete interface in the UW θσ model between the PBL expressed in sigma coordinates and the free atmosphere expressed in isentropic coordinates. The smooth transition of the modified model retains the excellent transport characteristics of the UW θσ model while providing for straightforward application of data assimilation techniques, use of higher-order finite-difference schemes, and implementation on massively parallel computing platforms.

This study sets forth the governing equations and describes the vertical structure employed by the UW θη model after which the results from a 14-yr climate simulation detail the model's simulation capabilities. Relative to reanalysis data and other fields, the dominant features of the global circulation, including seasonal variability, are well represented in the simulations, thus demonstrating the viability of the hybrid model for extended-length integrations. Overall the study documents that no insurmountable barriers exist to simulation of climate utilizing hybrid isentropic coordinate models. Additional results from two numerical experiments examining conservation demonstrate a high degree of numerical accuracy for the UW θη model in simulating reversibility and potential vorticity transport over a 10-day period that corresponds with the global residence time of water vapor.

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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

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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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Thomas J. Greenwald, R. Bradley Pierce, Todd Schaack, Jason Otkin, Marek Rogal, Kaba Bah, Allen Lenzen, Jim Nelson, Jun Li, and Hung-Lung Huang

Abstract

In support of the Geostationary Operational Environmental Satellite R series (GOES-R) program, the Cooperative Institute for Meteorological Satellite Studies (CIMSS) at the University of Wisconsin–Madison is generating high quality simulated Advanced Baseline Imager (ABI) radiances and derived products in real time over the continental United States. These data are mainly used for testing data-handling systems, evaluating ABI-derived products, and providing training material for forecasters participating in GOES-R Proving Ground test bed activities. The modeling system used to generate these datasets consists of advanced regional and global numerical weather prediction models in addition to state-of-the-art radiative transfer models, retrieval algorithms, and land surface datasets. The system and its generated products are evaluated for the 2014 Pacific Northwest wildfires; the 2013 Moore, Oklahoma, tornado; and Hurricane Sandy. Simulated aerosol optical depth over the Front Range of Colorado during the Pacific Northwest wildfires was validated using high-density Aerosol Robotic Network (AERONET) measurements. The aerosol, cloud, and meteorological modeling system used to generate ABI radiances was found to capture the transport of smoke from the Pacific wildfires into the Front Range of Colorado and true-color imagery created from these simulated radiances provided visualization of the smoke plumes. Evaluation of selected simulated ABI-derived products for the Moore tornado and Hurricane Sandy cases was done using real-time GOES sounder/imager products produced at CIMSS. Results show that simulated ABI moisture and atmospheric stability products, cloud products, and red–green–blue (RGB) airmass composite imagery are well suited as proxy ABI data for user preparedness.

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