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Fred M. Reames and Tom H. Zapotocny

Abstract

The University of Wisconsin hybrid isentropic–sigma (θ–σ) coordinate channel model and the nominally identical sigma (σ) model are used to test the relative capabilities of nine trace constituent transport algorithms. The nine are “standard” second-order finite differencing, the standard with two local “borrow and fill” fixers, the standard with a global fixer, four conservative flux-integrated approaches, and the conservation of second-order moments (CSOM). Transport of two analytically specified initial trace constituent distributions is simulated within a common initial atmosphere, which includes a baroclinically amplifying synoptic-scale wave. Two different vertical resolution θ–σ models and four vertical resolution σ models provide excellent test beds for comparison of the transport algorithms because their 48-h predictions of standard synoptic fields are virtually identical.

Although no analytic solution exists against which detailed comparisons can be made, the constraint of adiabatic conditions for a continuum provides that the maximum of a trace constituent within explicit or implicit isentropic layers of a model should be conserved throughout the simulations, and that the area between any two trace constituent contours on an isentropic surface should remain constant. With these conditions as bases of comparison, several results are unambiguous. First, in the σ models the standard with fixers is better than the other schemes except for the CSOM at the highest resolution. Second, in the θ–σ models, the piecewise parabolic and CSOM schemes produce results approximately as accurate as the standard with fixers. Third, when comparing all algorithms, models, resolutions, and distributions, the CSOM scheme produces the most consistent results. Finally, for a large majority of the cases, the θ–σ models perform more accurately than the σ models with respect to the conservation of constituent extrema.

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Fred M. Reames and Tom H. Zapotocny

Abstract

Part I of this paper examined nine trace constituent advection algorithms as applied in channel versions of the University of Wisconsin hybrid isentropic–sigma (θ–σ) and sigma (σ) models. This paper examines the performance of 12 semi-Lagrangian transport (SLT) algorithms in the same models. The interpolants of trace constituent include second- through twelfth-order Lagrangian, an overlapping polynomial, a quasi-monotonic scheme, and two sixth-order schemes that employ derivative estimates. Additional experiments are performed that emulate the SLT algorithm in the NCAR Community Climate Model 2. As in Part I, these three-dimensional simulations are under adiabatic conditions so that conservation of the initial trace constituent maximum on an isentropic surface, and conservation of the areas between any two constituent contours, can be used as objective measures of SLT algorithm accuracy. Further, the experiments provide comparisons not only between the different SLT formulations but also between their performance in models using θ and σ coordinates.

Similar to Part I, an important result of the experiments is that comparison of algorithms is most revealing under three-dimensional transport within a baroclinic wave in which vertical transport is important. The experiments also show 1) that the “cascade” interpolation scheme is a reasonable method of greatly reducing computation time in SLT without affecting accuracy; 2) that “shape-preserving” interpolation schemes reduce accuracy in both the θ–σ and σ models; and 3) that Lagrangian interpolants of tenth and twelfth order do not significantly improve results. Comparisons to results in Part I suggest that the conservation of second-order moments advection scheme is the most consistent of all options tested.

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William H. Raymond, Gary S. Wade, and Tom H. Zapotocny

Abstract

Imager channel 3 (at 6.7 μm) on the Geostationary Operational Environmental Satellite (GOES) is particularly sensitive to water vapor in the atmosphere. Channel-3 data from both clear and cloudy regions are used in a new assimilation scheme to improve the initial upper-tropospheric moisture fields for modeling and numerical weather prediction purposes. In this assimilation, the navigated and calibrated radiance (brightness temperature) observations from GOES are used in combination with a forward radiative transmittance model and a numerical optimization procedure to produce modifications to the upper-tropospheric moisture field. All modifications are made proportional to the contribution weighting function, which is associated with the forward radiative model. Cloudy regions are given special consideration. When processed by a forward radiative transfer model, the assimilated moisture fields are shown to correlate better with GOES observations both initially and in 24- and 48-h forecasts. Additional merits of the proposed assimilation technique, which does not require an adjoint or linearization, are discussed.

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William H. Raymond, Gary S. Wade, and Tom H. Zapotocny

Abstract

An unsolved problem with water vapor wind estimates from the upper-tropospheric 6.7-μm water vapor band on the Geostationary Operational Environmental Satellite (GOES) Imager (channel 3) is its exact placement in the vertical column. Satellite water vapor observations are known to be depth-averaged assessments of the upper-tropospheric moisture. Details about the effective averaging of upper-tropospheric observations, valid for GOES or those of other satellite platforms, are not retrieved as part of the observation. However, details about the vertical placement can be accurately estimated from forward radiative models that mimic the instrument spectral characteristics. A new method has been developed to assimilate satellite radiances or brightness temperatures directly into a numerical forecast model. A by-product of the new scheme is knowledge of the weighting functions that describe the assignment value given to each vertical layer. As a consequence, given water vapor wind data, these weighting functions allow the guessed wind field to be “intelligently” modified. In this study the vertical and horizontal characteristics of these weighting functions are examined. Statistics for a 16-day period are presented that show how weighted average wind components from the initial model forecast fields, computed using the weighting functions, compare with GOES water vapor wind observations.

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Tom H. Zapotocny, Donald R. Johnson, and Fred M. Reames

Abstract

The description of a global version of the University of Wisconsin (UW) hybrid isentropic-sigma (θ − σ) model and the results from an initial numerical weather prediction experiment are presented in this paper. The main objectives of this initial test are to 1) discuss θ − σ model development and computer requirements, 2) demonstrate the ability of the UW θ − σ model for global numerical weather prediction using realistic orography and parameterized physical processes, and 3) compare the transport of an inert trace constituent against a nominally “identical” sigma (σ) coordinate model. Initial and verifying data for the 5-day simulations presented in this work were supplied by the Goddaird Earth Observing System (GEOS-1) data assimilation system. The time period studied is 1–6 February 1985.

This validation experiment demonstrates that the global UW θ − σ model produces a realistic 5-day simulation of the mass and momentum distributions when compared to both the identical σ model and GEOS-1 verification. Root-mean-square errors demonstrate that the θ − σ model is slightly more accurate than the nominally identical σ model with respect to standard synoptic variables. Of particular importance, the UW θ − σ model displays a distinct advantage over the conventional σ model with respect to the prognostic simulation of inert trace constituent transport in amplifying baroclinic waves of the extratropics. This is especially true in the upper troposphere and stratosphere where the spatial integrity and conservation of an inert trace constituent is severely compromised in the a model compared to the θ − σ model.

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Tom H. Zapotocny, Donald R. Johnson, and Fred M. Reames

Abstract

In an initial effort in regional numerical weather prediction, results from the University of Wisconsin isentropic-sigma (UW θ−σ) hybrid model and an “identical” sigma model are compared. The two main objectives are to demonstrate the capability of the UW θ−σ model for regional numerical weather prediction and to identify advantages of the hybrid model in simulating atmospheric water vapor transport and precipitation relative to the sigma model.

The 72-h simulations produced by the two models extend over a region covering the western Pacific Ocean, North America, and the western Atlantic Ocean. The simulations begin at 0000 UTC 13 January 1979, a period during which an intense Chicago blizzard (sometimes called the Mayor Jane Byrne storm) develops over the central United States. This period also includes the rapid development of a cyclone in the western Pacific Ocean.

Results using the Global Weather Experiment (GWE) ECMWF level IIIB data as initial and verification data indicate that both models produce reasonable and similar 72-b simulations, with the UW θ−σ model mass and momentum distributions being slightly more accurate than the sigma model. Of particular importance for the Chicago blizzard is that the UW θ−σ model more accurately simulates water vapor transport northward from the Gulf of Mexico and westward from the Atlantic Ocean. As a result, the hybrid model more accurately simulates observed precipitation, especially over the northeastern United States and southeastern Canada.

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Tom H. Zapotocny, Fred M. Reames, R. Bradley Pierce, Donald R. Johnson, and Bart J. Wolf

Abstract

The main goals of this paper are 1) to demonstrate the feasibility of incorporating a prognostic equation for water vapor and diabatic processes in the University of Wisconsin θσ model discussed in Part I, 2) to document methods applied to overcome difficulties stemming from the inclusion of moist processes and 3) to present results illustrating the effects of latent heat release on baroclinic development. The results confirm earlier studies that a prognostic equation for water vapor and the diabatic component of latent heat release may be included in a hybrid model. However, the modifications made in this study were important for eliminating spurious supersaturation and release of latent heat within grid volumes emerging and submerging through the interface between sigma and isentropic model domains. The results demonstrate the hybrid model's robust nature and potential for use in prediction.

For this demonstration, model simulations of an analytically specified synoptic-scale wave that amplified baroclinically under dry and moist conditions are compared. Simulations with and without a hydrological component show that the overall effect of latent heat release is to markedly enhance cyclo- and frontogenesis. The resultant pattern of precipitation is coherent, and the structure of the developing wave is consistent with the concepts of self-development. No detrimental effects are evident in either the structure or processes resulting from the inclusion of moist processes and the presence of an interface between sigma and isentropic model domains.

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Tom H. Zapotocny, James A. Jung, John F. Le Marshall, and Russ E. Treadon

Abstract

Observing system experiments are used to quantify the contributions to the forecast made by conventional in situ and remotely sensed satellite data. The impact of each data type is assessed by comparing the analyses and forecasts based on an observing system using all data types. The analysis and forecast model used for these observing system experiments is the National Centers for Environmental Prediction (NCEP) Global Data Assimilation/Forecast System (GDAS/GFS). The case studies chosen consist of 45-day periods during January–February 2003 and August–September 2003. During these periods, a T254–64 layer version of NCEP’s Global Spectral Model was used. The control run utilizes NCEP’s operational database and consists of all data types routinely assimilated in the GDAS. The two experimental runs have either all the conventional in situ data denied (NoCon) or all the remotely sensed satellite data denied (NoSat). Differences between the control and experimental runs are accumulated over the 45-day periods and analyzed to demonstrate the forecast impact of these data types through 168 h. Anomaly correlations, forecast impacts, and hurricane track forecasts are evaluated for both experiments. Anomaly correlations of geopotential height are evaluated over the polar caps and midlatitudes of both the Northern and Southern Hemispheres for spectral waves 1–20. Forecast impacts related to conventional meteorological parameters are evaluated. The parameters examined include geopotential height, precipitable water, temperature, the u component of the wind, wind vector differences, and relative humidity. Comparisons are made on multiple pressure levels extending from 10 to 1000 hPa. Hurricane track forecasts are evaluated during August and September for both the Atlantic and eastern Pacific basins. The results demonstrate a positive forecast impact from both the conventional in situ and remotely sensed satellite data during both seasons in both hemispheres. The positive forecast impacts from the conventional and satellite data are of similar magnitude in the Northern Hemisphere; however, the contribution to forecast quality from satellite data is considerably larger than the conventional data in the Southern Hemisphere. The importance of satellite data also generally increases at longer forecast times relative to conventional data. Finally, the accuracy of hurricane track forecasts benefits from the inclusion of both conventional and satellite data.

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James A. Jung, Tom H. Zapotocny, John F. Le Marshall, and Russ E. Treadon

Abstract

Observing system experiments (OSEs) during two seasons are used to quantify the important contributions made to forecast quality from the use of the National Oceanic and Atmospheric Administration’s (NOAA) polar-orbiting satellites. The impact is measured by comparing the analysis and forecast results from an assimilation–forecast system using one NOAA polar-orbiting satellite with results from using two and three polar-orbiting satellites in complementary orbits.

The assimilation–forecast system used for these experiments is the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System–Global Forecast System (GDAS–GFS). The case studies chosen consist of periods during January–February and August–September 2003. Differences between the forecasts are accumulated over the two seasons and are analyzed to demonstrate the impact of these satellites.

Anomaly correlations (ACs) and geographical forecasts (FIs) are evaluated for all experimental runs during both seasons. The anomaly correlations are generated using the standard NCEP verification software suite and cover the polar regions (60°–90°) and midlatitudes (20°–80°) of each hemisphere. The rms error for 850- and 200-hPa wind vector differences are shown for the tropical region (20°N–20°S). The geographical distribution of forecast impact on geopotential heights, relative humidity, precipitable water, and the u component of wind are also examined.

The results demonstrate that the successive addition of each NOAA polar-orbiting satellite increases forecast quality. The use of three NOAA polar-orbiting satellites generally provides the largest improvement to the anomaly correlation scores in the polar and midlatitude regions. Improvements to the anomaly correlation scores are also realized from the use of two NOAA polar-orbiting satellites over only one. The forecast improvements from two satellites are generally smaller than if using three satellites, consistent with the increase in areal coverage obtained with the third satellite.

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Donald R. Johnson, Tom H. Zapotocny, Fred M. Reames, Bart J. Wolf, and R. Bradley Pierce

Abstract

The primary objectives of this study are threefold: 1) to compare simulators of dry and moist baroclinic development from 10-and 22-layer hybrid isentropic-sigma coordinate models with those from 11-, 27-, and 35-layer sigma coordinate models; 2) to examine the ability of the models to transport water vapor and simulate equivalent potential temperature θe; and 3) to compare predictions of the timing, location, and amount of precipitation. A model's capability to predict precipitation sterns from the accuracy of its simulation of the joint distribution of mass, potential temperature, and water vapor throughout the model domain. In a series of experiments to compare simulations of precipitation, several analytic distributions of water vapor are specified initially. The water vapor distributions include a “cylinder”extending vertically throughout the atmosphere and “lenses” within isentropic, sigma, and isobaric layers. The effect of increased horizontal resolution are also studied.

Results indicate that when the relative humidity is vertically uniform through a substantial extent of the atmosphere, all the models produce very similar precipitation distributions. However, when water vapor is confined to relatively shallow layers, the ability of the sigma coordinate models to simulate the timing, location, and amount of precipitation is severely compromised. Furthermore, the 10-layer hybrid model conserves θe to a higher degree of accuracy and simulates a more realistic evolution of precipitation even when compared to results from sigma models with increased vertical and horizontal resolution. In all instances, the experiments demonstrate that advantages reside in prediction of precipitation with the hybrid model. Both theoretical and conceptual bases for thew differences are provided.

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