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John W. Nielsen-Gammon
and
Daniel Keyser

Abstract

Effective stratification can be interpreted as the resistance to upward motion of saturated air parcels experiencing condensation. Previously published expressions for effective stratification conflict with each other, and the most widely distributed expression contains an O(1) error. A derivation of effective stratification is presented that exposes its physical interpretation and that reveals the origin of the flaw in the incorrect derivation.

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Altuğ Aksoy
,
Fuqing Zhang
, and
John W. Nielsen-Gammon

Abstract

The performance of the ensemble Kalman filter (EnKF) in forced, dissipative flow under imperfect-model conditions is investigated through simultaneous state and parameter estimation where the source of model error is the uncertainty in the model parameters. A two-dimensional, nonlinear, hydrostatic, nonrotating, and incompressible sea-breeze model is used for this purpose with buoyancy and vorticity as the prognostic variables and a square root filter with covariance localization is employed. To control filter divergence caused by the narrowing of parameter variance, a “conditional covariance inflation” method is devised. Up to six model parameters are subjected to estimation attempts in various experiments. While the estimation of single imperfect parameters results in error of model variables that is indistinguishable from the respective perfect-parameter cases, increasing the number of estimated parameters to six inevitably leads to a decline in the level of improvement achieved by parameter estimation. However, the overall EnKF performance in terms of the error statistics is still superior to the situation where there is parameter error but no parameter estimation is performed. In fact, compared with that situation, the simultaneous estimation of six parameters reduces the average error in buoyancy and vorticity by 40% and 46%, respectively.

Several aspects of the filter configuration (e.g., observation location, ensemble size, radius of influence, and parameter variance limit) are found to considerably influence the identifiability of the parameters. The parameter-dependent response to such factors implies strong nonlinearity between the parameters and the state of the model and suggests that a straightforward spatial covariance localization does not necessarily produce optimality.

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David A. Gold
and
John W. Nielsen-Gammon

Abstract

Observational and modeling studies have shown that shear and instability are powerful predictors of the likelihood of severe weather and tornadoes. To the extent that upper-tropospheric forecast errors can be described as potential vorticity (PV) anomalies on the forecasted PV field, knowing (and being able to quantify) the effects of such errors on shear and instability would allow forecasters to anticipate the effects of those errors on the likely mode of severe weather. To test the sensitivity of the severe convective environment to PV fluctuations, a PV inversion framework is adopted that utilizes nonlinear balance. The observed PV field is modified in a way that mimics realistic perturbations of trough intensity, location, or shape. Soundings, including moisture profiles, are reconstructed from the balanced geopotential height field assuming that air parcels conserve mixing ratio while their isentropic surfaces are displaced upward or downward by the addition of anomalous PV. Unperturbed balanced soundings agree reasonably well with full, unbalanced soundings, and differences are attributable to departures from nonlinear balance in areas of strong vorticity or acceleration. Balanced vertical wind profiles do not include the effects of friction, so the vertical shear of the balanced wind departs unacceptably from total shear within the lowest 1 km of the troposphere. The balanced wind perturbations are added to the total analyzed shear profile to estimate the effect of PV perturbations on shear and storm-relative helicity. By this process, the importance of typical or hypothesized upper-tropospheric forecast errors may be addressed in an idealized, case-study, or operational context.

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John W. Nielsen-Gammon
and
David A. Gold

Abstract

Idealized numerical experiments are conducted to understand the effect of upper-tropospheric potential vorticity (PV) anomalies on an environment conducive to severe weather. Anomalies are specified as a single isolated vortex, a string of vortices analogous to a negatively tilted trough, and a pair of string vortices analogous to a position error in a negatively tilted trough. The anomalies are placed adjacent to the tropopause along a strong upper-level jet at a time just prior to a major tornado outbreak and inverted using the nonlinear balance equations.

In addition to the expected destabilization beneath and adjacent to a cyclonic PV anomaly, the spatial pattern of the inverted balanced streamfunction and height fields is distorted by the presence of the horizontal PV gradient along the upper-tropospheric jet stream. Streamfunction anomalies are elongated in the cross-jet direction, while height and temperature anomalies are elongated in the along-jet direction. The amplitude of the inverted fields, as well as the changes in CAPE associated with the inverted temperature perturbations, are linearly proportional to the amplitudes of the PV anomalies themselves, and the responses to complex PV perturbation structures are approximated by the sum of the responses to individual simple PV anomalies. This is true for the range of PV amplitudes tested, which was designed to mimic typical 6-h forecast or analysis errors and produced changes in CAPE beneath the trough of well over 100 J kg−1. Impacts on inverted fields are largest when the PV anomaly is on the anticyclonic shear side of the jet, where background PV is small, compared with the cyclonic shear side of the jet, where background PV is large.

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David A. Gold
and
John W. Nielsen-Gammon

Abstract

Nonlinear balance potential vorticity (PV) inversion is used to diagnose the sensitivity of the severe convective parameter space to the amplitude of a subsynoptic-scale PV anomaly on 13 March 1990, a day on which a significant tornado outbreak impacted the Great Plains. PV surgery is used to both amplify and remove the PV anomaly, and the contemporaneous impact on various convective parameters is subsequently quantified by using piecewise PV inversion to compute the changes in those parameters attributable to each PV alteration. It is found that amplifying the anomaly increases the CAPE by amounts typically ranging from 20% to 30% within the atmospheric columns experiencing the maximum PV increase. Ascent is increased slightly downshear of the PV anomaly, consistent with extant conceptual models governing synoptic-scale forcing for vertical motion. Amplifying the PV anomaly increases deep-layer shear over the southern half of the outbreak region and reduces storm-relative helicity over the northern half, primarily through changes in the estimated storm motion vector. Removing the anomaly produces complementary changes of the opposite sign. Thresholds of several commonly used convective parameters are chosen on the basis of prior empirical studies, and the horizontal displacement of these threshold contours produced by the PV alterations reveals that relatively modest subsynoptic-scale PV changes would not likely change the predominant convective mode during the Hesston outbreak.

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David A. Gold
and
John W. Nielsen-Gammon

Abstract

A potential vorticity (PV) diagnostic framework is used to explore the sensitivity of the 3 May 1999 Oklahoma City tornado outbreak to the strength of a particular PV anomaly proximate to the geographical region experiencing the tornado outbreak. The results derived from the balanced PV diagnosis agree broadly with those obtained previously in a numerical simulation of the same event, while offering additional insight into the nature of the sensitivity. Similar to the findings of other cases, the balanced diagnosis demonstrates that intensifying (removing) the PV anomaly of interest increases (decreases) the balanced CAPE over the southwestern portion of the outbreak region, reduces (increases) the storm-relative helicity, and increases (reduces) ascent. The latter finding, coupled with the results of the modeling study, demonstrates that intensifying a PV anomaly proximate to an outbreak environment can increase the likelihood that more widespread and possibly less tornadic convection will ensue. The overall results of the balanced diagnosis complement those of other case studies, leading to the formulation of a conceptual model that broadly anticipates how the convective regime will respond to changes in intensity of upper-tropospheric weather features.

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Richard C. Igau
and
John W. Nielsen-Gammon

Abstract

The evolution of the southerly low-level jet (LLJ) during a return flow event is studied using output from the Penn State/NCAR Mesoscale Model (Version 4). Three geographically different southerly LLJs develop in the simulation: one over the southern Plains of the United States, a second southwest of Brownsville, Texas, and a third over the western Gulf of Mexico. The LLJ over the Plains is found to form first as an inertial oscillation and later as a response to lee troughing and an elevated mixed layer that develops over the region. Over Mexico, the temperature structure over the Altiplanicie Mexicana (Mexican High Plain) is responsible for a locally intense low-level pressure gradient east of the High Plain which remains nearly stationary over two diurnal cycles. The LLJ over the western Gulf of Mexico results largely from topographic blocking of the low-level southerly flow by the eastern end of the Neovolcanic Cordillera northwest of Veracruz, Mexico.

The evolution of the lower troposphere over the southern Plains resembles the Carlson and Ludlam conceptual model for a severe storm environment, but the structure of the return flow is complex. When midlevel westerlies are weak, mesoscale and boundary layer processes govern the development of LLJs. As the west and southwesterly winds increase with an approaching upper-level disturbance, synoptic influences overwhelm the mesoscale processes leading to a single, larger-scale LLJ.

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Michael C. Morgan
and
John W. Nielsen-Gammon

Abstract

The use of potential vorticity (PV) allows the efficient description of the dynamics of nearly balanced atmospheric flow phenomena, but the distribution of PV must be simply represented for ease in interpretation. Representations of PV on isentropic or isobaric surfaces can be cumbersome, as analyses of several surfaces spanning the troposphere must be constructed to fully apprehend the complete PV distribution.

Following a brief review of the relationship between PV and nearly balanced flows, it is demonstrated that the tropospheric PV has a simple distribution, and as a consequence, an analysis of potential temperature along the dynamic tropopause (here defined as a surface of constant PV) allows for a simple representation of the upper-tropospheric and lower-stratospheric PV. The construction and interpretation of these tropopause maps, which may be termed “isertelic” analyses of potential temperature, are described. In addition, techniques to construct dynamical representations of the lower-tropospheric PV and near-surface potential temperature, which complement these isertelic analyses, are also suggested. Case studies are presented to illustrate the utility of these techniques in diagnosing phenomena such as cyclogenesis, tropopause folds, the formation of an upper trough, and the effects of latent heat release on the upper and lower troposphere.

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John W. Nielsen-Gammon
and
David M. Schultz

Abstract

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Jason A. Sippel
,
John W. Nielsen-Gammon
, and
Stephen E. Allen

Abstract

This study explores the extent to which potential vorticity (PV) generation and superposition were relevant on a variety of scales during the genesis of Tropical Storm Allison. Allison formed close to shore, and the combination of continuous Doppler radar, satellite, aircraft, and surface observations allows for the examination of tropical cyclogenesis in great detail.

Preceding Allison’s genesis, PV superposition on the large scale created an environment where decreased vertical shear and increased instability, surface fluxes, and low-level cyclonic vorticity coexisted. This presented a favorable environment for meso-α-scale PV production by widespread convection and led to the formation of surface-based, meso-β-scale vortices [termed convective burst vortices (CBVs)]. The CBVs seemed to form in association with intense bursts of convection and rotated around each other within the meso-α circulation field. One CBV eventually superposed with a mesoscale convective vortex (MCV), resulting in a more concentrated surface vortex with stronger pressure gradients.

The unstable, vorticity-rich environment was also favorable for the development of even smaller, meso-γ-scale vortices that formed within the cores of deep convective cells. Several meso-γ-scale convective vortices were present in the immediate vicinity when a CBV developed, and the smaller vortices may have contributed to the formation of the CBV. The convection associated with the meso-γ vortices also fed PV into existing CBVs.

Much of the vortex behavior observed in Allison has been documented or simulated in studies of other tropical cyclones. Multiscale vortex formation and interaction may be a common aspect of many tropical cyclogenesis events.

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