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H. C. Davies and C. H. Bishop

Abstract

Perturbations of the classical Eady model are treated in terms of the system's two intrinsic baroclinic edge waves. This provides a simple quantitative example of the wave coupling interpretation of quasigeostrophic instability and a compact framework for examining the rudiments of upper level–lower level dynamical interaction.

The reformulation consolidates and extends a series of earlier theoretical results: the existence of transient growth at wavenumbers beyond the Eady cutoff scale, the disparity between different measures of the maximum instantaneous growth rate with the highest values being associated with thermal (pressure) development at large (small) wavelengths, the existence of maximum instantaneous thermal growth rates substantially exceeding that of the Eady normal modes, and the vertical alignment of the couplet most favorable for initial rapid development–quadrature phase of the thermal (pressure) components for optimum thermal (pressure) growth.

There is also diversity in the finite time evolution of couplets. Short wavelength couplets undergo a periodic temporal development with comparatively mild amplitude changes. Longer-scale couplets asymptote toward the counterpart Eady normal mode. The latter achieve maximum thermal growth in a stipulated time if the relative phase of the couplet transits symmetrically through the quadrature configuration, and the fastest growing couplet can typically sustain a thermal amplitude doubling in ∼6 hours and a fivefold increase in ∼24 hours. During such development the eastward thermal slope of the very long (intermediate) scale couplets become less (more) inclined to the vertical.

It is further shown that a coherent packet of edge wave couplets can evolve rapidly (∼1 day) from a suitably shaped initial disturbance composed predominantly of either ultralong or intermediate-scale waves. The vertical structure of the emerging intermediate-scale packet is akin to that of observed atmospheric developments.

The edge wave formulation is also used to explore the effect of interior PV perturbations. Consideration of the influence of an idealized, but elemental, potential vorticity distribution upon a surface edge wave leads to inferences regarding the cyclogenetic potential of certain atmospheric flow structures.

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A. Barcilon and C. H. Bishop

Abstract

The evolution of waves in a basic state containing a constant vertical shear and a smaller constant horizontal shear is considered. The “PV-thinking” associated with counterpropagating Rossby potential vorticity (PV) edge waves found at the horizontal boundaries is used to interpret the evolution of the waves.

The presence of the barotropic shear introduces a time-dependent y wavenumber, which, in turn, makes the total horizontal wavenumber a function of time. For properly configured initial (x, y) wavenumbers, the horizontal wavenumber decreases at first. This decrease induces an increase in the scale of the disturbances and a growth associated with downgradient momentum fluxes. The PV edge waves grow by mutual interactions when properly phase shifted. This growth is due to a downgradient flux of heat.

These ideas are illustrated on a paradigm of type-B cyclogenesis. The nonlinear dynamics is also computed in the spirit of a weakly nonlinear analysis. This simple weakly nonlinear model captures the asymmetry between westward tilts in the vertical of geopotential minima and maxima found in the fully nonlinear evolution of baroclinic waves on cyclonically and anticyclonically sheared jets.

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G. Abramowitz and C. H. Bishop

Abstract

Obtaining multiple estimates of future climate for a given emissions scenario is key to understanding the likelihood and uncertainty associated with climate-related impacts. This is typically done by collating model estimates from different research institutions internationally with the assumption that they constitute independent samples. Heuristically, however, several factors undermine this assumption: shared treatment of processes between models, shared observed data for evaluation, and even shared model code. Here, a “perfect model” approach is used to test whether a previously proposed ensemble dependence transformation (EDT) can improve twenty-first-century Coupled Model Intercomparison Project (CMIP) projections. In these tests, where twenty-first-century model simulations are used as out-of-sample “observations,” the mean-square difference between the transformed ensemble mean and “observations” is on average 30% less than for the untransformed ensemble mean. In addition, the variance of the transformed ensemble matches the variance of the ensemble mean about the “observations” much better than in the untransformed ensemble. Results show that the EDT has a significant effect on twenty-first-century projections of both surface air temperature and precipitation. It changes projected global average temperature increases by as much as 16% (0.2°C for B1 scenario), regional average temperatures by as much as 2.6°C (RCP8.5 scenario), and regional average annual rainfall by as much as 410 mm (RCP6.0 scenario). In some regions, however, the effect is minimal. It is also found that the EDT causes changes to temperature projections that differ in sign for different emissions scenarios. This may be as much a function of the makeup of the ensembles as the nature of the forcing conditions.

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C. H. Bishop and E. Heifetz

Abstract

The role of the continuous spectrum and its associated potential vorticity (PV) in absolute instability are investigated in the context of a semi-infinite version of Eady’s basic state. This flow crudely resembles the zonally averaged midlatitude atmosphere. The disturbances are composed of a zero PV part and a nonzero PV part. A closed form analytic solution is described that features a localized wave packet whose streamfunction field expands and amplifies in an absolutely unstable way. However, since an examination of the PV field associated with this disturbance reveals that the linear amplification of the localized streamfunction wave packet is induced by a nonlocalized PV field, it is clear that the seed for the expansion of the streamfunction wave packet lies not within the wave packet but upstream of the wave packet. While this precise analytic solution allows for the identification of the upstream PV anomalies, any sort of measurement error would render these upstream PV anomalies invisible. Thus, observations would be incapable of distinguishing an absolute instability seeded by PV anomalies generated within the confines of the streamfunction wave packet from the absolute instability described by the authors’ solution.

The general initial value solution is analyzed, and it is found that this apparent absolute instability is not a peculiarity of this particular solution. Absolutely unstable wave packets will be “naturally selected” over geophysically relevant timescales to dominate the flows that emerge from random disturbances to the idealized basic state. In Eady’s basic state, which is bounded aloft by a rigid lid, the natural selection mechanism only operates at wavelengths at which the normal modes of Eady’s basic state are neutral. It is suggested that an atmospheric counterpart of this natural selection process may be responsible for the medium-scale upper- and lower-tropospheric waves that have recently been identified in the observational record.

The authors prove that the group velocity of a streamfunction field attributable to eastward moving PV anomalies may, in fact, be westward.

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S. J. Majumdar, C. H. Bishop, B. J. Etherton, and Z. Toth

Abstract

The practical application of the ensemble transform Kalman filter (ET KF), used in recent Winter Storm Reconnaissance (WSR) programs by the National Centers for Environmental Prediction (NCEP), is described. The ET KF assesses the value of targeted observations taken at future times in improving forecasts for preselected critical events. It is based on a serial assimilation framework that makes it an order of magnitude faster than its predecessor, the ensemble transform technique. The speed of the ET KF enabled several different forecast scenarios to be assessed for targeting during recent WSR programs.

Each potential observational network is broken down into idealized routine and adaptive components. The adaptive component represents a predesigned flight track along which GPS dropwindsondes are released. For a large number of flight tracks, the ET KF estimates the forecast error reducing effects of these observations (via the “signal variance”). The track that maximizes the average forecast signal variance within a selected verification region is deemed optimal for targeting. Secondary flight tracks can also be chosen using serial assimilation, by calculating the signal variance for each flight track given that the primary track had already been selected.

For the second consecutive year the ET KF was able to estimate, via a statistical rescaling, the variance of NCEP signal realizations produced by the dropwindsonde data. A monotonic increasing relationship between the ET KF signal variance and the reduction in NCEP forecast error variance due to the targeted observations was then deduced for the operational 2001 WSR program.

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I. Szunyogh, Z. Toth, R. E. Morss, S. J. Majumdar, B. J. Etherton, and C. H. Bishop

Abstract

In this paper, the effects of targeted dropsonde observations on operational global numerical weather analyses and forecasts made at the National Centers for Environmental Prediction (NCEP) are evaluated. The data were collected during the 1999 Winter Storm Reconnaissance field program at locations that were found optimal by the ensemble transform technique for reducing specific forecast errors over the continental United States and Alaska. Two parallel analysis–forecast cycles are compared; one assimilates all operationally available data including those from the targeted dropsondes, whereas the other is identical except that it excludes all dropsonde data collected during the program.

It was found that large analysis errors appear in areas of intense baroclinic energy conversion over the northeast Pacific and are strongly associated with errors in the first-guess field. The “signal,” defined by the difference between analysis–forecast cycles with and without the dropsonde data, propagates at an average speed of 30° per day along the storm track to the east. Hovmöller diagrams and eddy statistics suggest that downstream development plays a significant role in spreading out the effect of the dropsondes in space and time. On average, the largest rms surface pressure errors are reduced by 10%–20% associated with the eastward-propagating leading edge of the signal. The dropsonde data seem to be more effective in reducing forecast errors when zonal flow prevails over the eastern Pacific. Results from combined verification statistics (based on surface pressure, tropospheric winds, and precipitation amount) indicate that the dropsonde data improved the forecasts in 18 of the 25 targeted cases, while the impact was negative (neutral) in only 5 cases.

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S. J. Majumdar, S. D. Aberson, C. H. Bishop, R. Buizza, M. S. Peng, and C. A. Reynolds

Abstract

Airborne adaptive observations have been collected for more than two decades in the neighborhood of tropical cyclones, to attempt to improve short-range forecasts of cyclone track. However, only simple subjective strategies for adaptive observations have been used, and the utility of objective strategies to improve tropical cyclone forecasts remains unexplored. Two objective techniques that have been used extensively for midlatitude adaptive observing programs, and the current strategy based on the ensemble deep-layer mean (DLM) wind variance, are compared quantitatively using two metrics. The ensemble transform Kalman filter (ETKF) uses ensembles from NCEP and the ECMWF. Total-energy singular vectors (TESVs) are computed by the ECMWF and the Naval Research Laboratory, using their respective global models. Comparisons of 78 guidance products for 2-day forecasts during the 2004 Atlantic hurricane season are made, on both continental and localized scales relevant to synoptic surveillance missions. The ECMWF and NRL TESV guidance identifies similar large-scale target regions in 90% of the cases, but are less similar to each other in the local tropical cyclone environment (56% of the cases) with a more stringent criterion for similarity. For major hurricanes, all techniques usually indicate targets close to the storm center. For weaker tropical cyclones, the TESV guidance selects similar targets to those from the ETKF (DLM wind variance) in only 30% (20%) of the cases. ETKF guidance using the ECMWF ensemble is more like that provided by the NCEP ensemble (and DLM wind variance) for major hurricanes than for weaker tropical cyclones. Minor differences in these results occur when a different metric based on the ranking of fixed storm-relative regions is used.

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C. A. Reynolds, M. S. Peng, S. J. Majumdar, S. D. Aberson, C. H. Bishop, and R. Buizza

Abstract

Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

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R. H. Langland, Z. Toth, R. Gelaro, I. Szunyogh, M. A. Shapiro, S. J. Majumdar, R. E. Morss, G. D. Rohaly, C. Velden, N. Bond, and C. H. Bishop

The objectives and preliminary results of an interagency field program, the North Pacific Experiment (NORPEX), which took place between 14 January and 27 February 1998, are described. NORPEX represents an effort to directly address the issue of observational sparsity over the North Pacific basin, which is a major contributing factor in short-range (less than 4 days) forecast failures for land-falling Pacific winter-season storms that affect the United States, Canada, and Mexico. The special observations collected in NORPEX include approximately 700 targeted tropospheric soundings of temperature, wind, and moisture from Global Positioning System (GPS) dropsondes obtained in 38 storm reconnaissance missions using aircraft based primarily in Hawaii and Alaska. In addition, wind data were provided every 6 h over the entire North Pacific during NORPEX, using advanced and experimental techniques to extract information from multispectral geostationary satellite imagery. Preliminary results of NORPEX data impact studies using the U.S. Navy and National Weather Service forecast models include reductions of approximately 10% in mean 2-day forecast error over western North America (30°–60°N, 100°–130°W) from assimilation of targeted dropsonde and satellite wind data (when measured against control forecasts that contain no special NORPEX observations). There are local reductions of up to 50% in 2-day forecast error for individual cases, although some forecasts are degraded by the addition of the special dropsonde or satellite wind data. In most cases, the positive impact of the targeted dropsonde data on short-range forecast skill is reduced when the full set of advanced satellite wind data is already included in the model analyses. The NORPEX dataset is being used in research to improve objective methods for targeting observations, to study the “mix” of in situ and space-based observations, and to understand the structure and dynamics of fast-growing errors that limit our ability to provide more accurate forecasts of Pacific winter storms.

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Craig H. Bishop, Daniel Hodyss, Peter Steinle, Holly Sims, Adam M. Clayton, Andrew C. Lorenc, Dale M. Barker, and Mark Buehner

Abstract

Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the model grid spacing, (iii) and/or there are many variable types associated with each grid point, (iv) and/or 4D ensemble covariances are employed.

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