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Peter Bartello and Stephen J. Thomas

Abstract

The purpose of this paper is to ascertain the cost-effectiveness of semi-Lagrangian advection schemes for a wide variety of geophysical flows at all scales. The approach used is first to determine the minimum computational overhead associated with these schemes and then to examine temporal variability in the Lagrangian and Eulerian frames by employing simple turbulent cascade phenomenologies. The goal is to evaluate whether the Lagrangian variability is sufficiently slower than that of the Eulerian frame to overcome the computational overhead. It is found that the most efficient semi-Lagrangian schemes require a factor of 5–10 times more floating point operations per grid point per time step than the classic second-order leapfrog scheme.

In the enstrophy cascade of 2D or quasigeostrophic turbulence, evolution of flow quantities is considerably slower in the Lagrangian frame and semi-Lagrangian advection schemes can be very cost-effective. In an energy cascade such as the Kolmogorov range of 3D turbulence or the inverse cascade of QG or 2D turbulence, the Lagrangian evolution remains slower than the Eulerian evolution. However, the difference is very much less than in the enstrophy cascade. Since the computational overhead of semi-Lagrangian schemes is considerable, they are at best marginally cost-effective at current resolutions for these flows, which prevail in the atmosphere at scales below 300–400 km. In the presence of stationary forcing fields in the Eulerian frame, the time step must respect the advective timescale even in the Lagrangian frame, at length scales where the forcing is significant. Here semi-Lagrangian schemes are not recommended.

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Thomas M. Hamill and Stephen J. Colucci

Abstract

Motivated by the success of ensemble forecasting at the medium range, the performance of a prototype short-range ensemble forecast system is examined. The ensemble dataset consists of 15 case days from September 1995 through January 1996. There are 15 members of the ensemble, 10 from an 80-km version of the eta model and five from the regional spectral model. Initial conditions include various in-house analyses available at the National Centers for Environmental Prediction as well as bred initial conditions interpolated from the medium-range forecast ensemble. Forecasts from the 29-km mesoeta model were archived as well for comparison.

The performance of the ensemble is first evaluated by the criterion of “uniformity of verification rank.” Assuming a perfect forecast model, equally plausible initial conditions, and the verification is a plausible member of the ensemble, these imply the verification when pooled with the 15 ensemble forecasts and sorted is equally likely to occur in each of the 16 ranks. Hence, over many independent samples, a histogram of the rank distribution should be nearly uniform. Using data from the ensemble forecasts, rank distributions were populated and found to be nonuniform. This was determined to be largely a result of model and initial condition deficiencies and not problems with the verification data. The uniformity of rank distributions varied with atmospheric baroclinicity for midtropospheric forecast variables but not for precipitation forecasts.

Examination of the error characteristics of individual ensemble members showed that the assumption of identical errors for each member is not met with this particular ensemble configuration, primarily because of the use of both bred and nonbred initial conditions in this test. Further, there were both differences in the accuracy of eta and regional spectral model bred member forecasts.

The performance of various summary forecasts from the ensemble such as its mean showed that the ensemble can generate forecasts that have similar or lower error than forecasts from the 29-km mesoeta, which was approximately equivalent in computational expense. Also, by combining the ensemble forecasts with rank information from other cases, reliable ensemble precipitation forecasts could be created, indicating the potential for useful probabilistic forecasts of quantitative precipitation from the ensemble.

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Thomas S. Ehrmann and Stephen J. Colucci

Abstract

A dry-core idealized general circulation model with a stratospheric polar vortex in the Northern Hemisphere is run with a combination of simplified topography and imposed tropospheric temperature perturbations, each located in the Northern Hemisphere with a zonal wavenumber of 1. The phase difference between the imposed temperature wave and the topography is varied to understand what effect this has on the occurrence of polar vortex displacements. Geometric moments are used to identify the centroid of the polar vortex for the purposes of classifying whether or not the polar vortex is displaced. Displacements of the polar vortex are a response to increased tropospheric wave activity. Compared to a model run with only topography, the likelihood of the polar vortex being displaced increases when the warm region is located west of the topography peak, and decreases when the cold region is west of the topography peak. This response from the polar vortex is due to the modulation of vertically propagating wave activity by the temperature forcing. When the southerly winds on the western side of the topographically forced anticyclone are collocated with warm- or cold-temperature forcing, the vertical wave activity flux in the troposphere becomes more positive or negative, respectively. This is in line with recent reanalysis studies that showed that anomalous warming west of the surface pressure high, in the climatological standing wave, precedes polar vortex disturbances.

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Stephen J. Colucci and Thomas S. Ehrmann

Abstract

A climatology of the anticyclone that commonly appears over the Aleutian Islands in the wintertime Northern Hemisphere stratosphere is presented. Applying a geometric moments technique to a reanalysis dataset and updating a previously published definition, 68 Aleutian high (AH) events have been identified during 35 winter (October–March) seasons (1979/80–2013/14), or about 2 events per season. The events lasted an average of approximately 33 days. Thirteen of the 68 AH events each temporally and spatially coincided with tropospheric blocking identified with a wave-breaking definition, while 41 of the AH onsets each coincided with a persistently positive geopotential height anomaly in the troposphere. Also, 41 of the 68 AH events each coincided with or were followed by an objectively defined disturbance (split or displacement) to the stratospheric polar vortex. Finally, 47 of these disturbance events were each preceded by an AH onset, such that in almost all winters (33 out of 35), an early season AH was followed by a later-season polar vortex disturbance (PVD).

Potential vorticity (PV) inversion revealed that the geopotential height rises associated with composite AH onset were forced primarily by anticyclonic PV increases in the stratosphere, with the troposphere providing a lesser contribution. Poleward eddy heat fluxes in the stratosphere preceded and especially followed composite AH onset, consistent with the findings that composite AH onset was forced primarily by anticyclonic PV increases in the stratosphere and that many AH onsets were each followed by a PVD onset.

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Thomas M. Hamill and Stephen J. Colucci

Abstract

The accuracy of short-range probabilistic forecasts of quantitative precipitation (PQPF) from the experimental Eta–Regional Spectral Model ensemble is compared with the accuracy of forecasts from the Nested Grid Model’s model output statistics (MOS) over a set of 13 case days from September 1995 through January 1996. Ensembles adjusted to compensate for deficiencies noted in prior forecasts were found to be more skillful than MOS for all precipitation categories except the basic probability of measurable precipitation. Gamma distributions fit to the corrected ensemble probability distributions provided an additional small improvement.

Interestingly, despite the favorable comparison with MOS forecasts, this ensemble configuration showed no ability to “forecast the forecast skill” of precipitation—that is, the ensemble was not able to forecast the variable specificity of the ensemble probability distribution from day-to-day and location-to-location. Probability forecasts from gamma distributions developed as a function of the ensemble mean alone were as skillful at PQPF as forecasts from distributions whose specificity varied with the spread of the ensemble. Since forecasters desire information on forecast uncertainty from the ensemble, these results suggest that future ensemble configurations should be checked carefully for their presumed ability to forecast uncertainty.

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Ramachandran D. Nair, Stephen J. Thomas, and Richard D. Loft

Abstract

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are approximated by a Lax–Friedrichs scheme. A third-order total variation diminishing Runge–Kutta scheme is applied for time integration, without any filter or limiter. Numerical results are reported for the standard shallow water test suite. The numerical solutions are very accurate, there are no spurious oscillations in test case 5, and the model conserves mass to machine precision. Although the scheme does not formally conserve global invariants such as total energy and potential enstrophy, conservation of these quantities is better preserved than in existing finite-volume models.

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Ramachandran D. Nair, Stephen J. Thomas, and Richard D. Loft

Abstract

A conservative transport scheme based on the discontinuous Galerkin (DG) method has been developed for the cubed sphere. Two different central projection methods, equidistant and equiangular, are employed for mapping between the inscribed cube and the sphere. These mappings divide the spherical surface into six identical subdomains, and the resulting grid is free from singularities. Two standard advection tests, solid-body rotation and deformational flow, were performed to evaluate the DG scheme. Time integration relies on a third-order total variation diminishing (TVD) Runge–Kutta scheme without a limiter. The numerical solutions are accurate and neither exhibit shocks nor discontinuities at cube-face edges and vertices. The numerical results are either comparable or better than a standard spectral element method. In particular, it was found that the standard relative error metrics are significantly smaller for the equiangular as opposed to the equidistant projection.

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Thomas J. Greenwald, Graeme L. Stephens, Sundar A. Christopher, and Thomas H. Vonder Haar

Abstract

The large-scale spatial distribution and temporal variability of cloud liquid water path (LWP) over the world's oceans and the relationship of cloud LWP to temperature and the radiation budget are investigated using recent satellite measurements from the Special Sensor Microwave/Imager(SSM/1),the Earth Radiation Budget Experiment (ERBE), and the International Satellite Cloud Climatology Project (ISCCP). Observations of cloud liquid water on a 2.5° × 2.5° grid are used over a 53-month period beginning July 1987 and ending in December 1991.

The highest values of cloud liquid water (greater than 0.13 kg m−2) occur largely along principal routes of northern midlatitude storm and in area dominated by tropical convection. The zonally averaged structure is distinctly trimodal, where maxima appear in the midlatitudes and near the equator. The avenge marine cloud LWP over the globe is estimated to he about 0.113 kg m−2. Its highest seasonal variability is typically between 15% and 25% of the annual mean but in certain locations can exceed 30%. Comparisons of cloud LWP to temperature for low clouds during JJA and DJF of 1990 show significant positive correlations at colder temperatures and negative correlations at warmer temperatures. The correlations also exhibit strong seasonal and regional variation.

Coincident and collocated observations of cloud LWP from the SSM/I and albedo measurements from the Earth Radiation Budget Satellite (ERBS) and the NOAA-10 satellite are compared for low clouds in the North Pacific and North Atlantic. The observed albedo-LWP relationships correspond reasonably well with theory, where the average cloud effective radius (re) is 11.1 μm and the standard deviation is 5.2 μm. The large variability in the inferred values of re suggests that other factors may be important in the albedo-LWP relationships. In terms of the effect of the LWP on the net cloud forcing, the authors find that a 0.05 kg m−2 increase in LWP (for LWP >0.2 kg m−2) results in a −25 W m−2 change in the net cloud forcing at a solar zenith angle of 75°.

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Stephen M. Strader, Walker S. Ashley, Thomas J. Pingel, and Andrew J. Krmenec

Abstract

This study examines how tornado risk and societal exposure interact to create tornado disaster potential in the United States. Finescale historical and projected demographic data are used in a set of region-specific Monte Carlo tornado simulations to reveal how societal development has shaped, and will continue to shape, tornado disaster frequency and consequences. Results illustrate that although the U.S. Midwest contains the greatest built-environment exposure and the central plains experience the most significant tornadoes, the midsouth contains the greatest tornado disaster potential. This finding is attributed to the relatively elevated tornado risk and accelerated growth in developed land area that characterizes the midsouth region. Disaster potential is projected to amplify in the United States due to increasing built-environment development and its spatial footprint in at-risk regions. In the four regions examined, both average annual tornado impacts and associated impact variability are projected to be as much as 6 to 36 times greater in 2100 than 1940. Extreme annual tornado impacts for all at-risk regions are also projected to nearly double during the twenty-first century, signifying the potential for greater tornado disaster potential in the future. The key lesson is that it is the juxtaposition of both risk and societal exposure that drive disaster potential. Mitigation efforts should evaluate changes in tornado hazard risk and societal exposure in light of land-use planning, building codes, and warning dissemination strategies in order to reduce the effects of tornadoes and other environmental hazards.

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David L. Randel, Thomas H. Vonder Haar, Mark A. Ringerud, Graeme L. Stephens, Thomas J. Greenwald, and Cynthia L. Combs

A comprehensive and accurate global water vapor dataset is critical to the adequate understanding of water vapor's role in the earth's climate system. To begin to satisfy this need, the authors have produced a blended dataset made up of global, 5-yr (1988–92), l°x 1° spatial resolution, atmospheric water vapor (WV) and liquid water path products. These new products consist of both the daily total column-integrated composites and a multilayered WV product at three layers (1000–700, 700–500, 500–300 mb). The analyses combine WV retrievals from the Television and Infrared Operational Satellite (TIROS) Operational Vertical Sounder (TOVS), the Special Sensor Microwave/Imager, and radiosonde observations. The global, vertical-layered water vapor dataset was developed by slicing the blended total column water vapor using layer information from TOVS and radiosonde. Also produced was a companion, over oceans only, liquid water path dataset. Satellite observations of liquid water path are growing in importance since many of the global climate models are now either incorporating or contain liquid water as an explicit variable. The complete dataset (all three products) has been named NVAP, an acronym for National Aeronautics and Space Administration Water Vapor Project.

This paper provides examples of the new dataset as well as scientific analysis of the observed annual cycle and the interannual variability of water vapor at global, hemispheric, and regional scales. A distinct global annual cycle is shown to be dominated by the Northern Hemisphere observations. Planetary-scale variations are found to relate well to recent independent estimates of tropospheric temperature variations. Maps of regional interannual variability in the 5-yr period show the effect of the 1992 ENSO and other features.

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