Michael C. Morgan

Using Tropopause Maps to Diagnose Midlatitude Weather Systems

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.

Evolution of Analysis Error and Adjoint-Based Sensitivities: Implications for Adaptive Observations

The structure and evolution of analysis error and adjoint-based sensitivities [potential enstrophy initial singular vectors (SVs) and gradient sensitivities of the forecast error to initial conditions] are compared following a cyclone development in a three-dimensional quasigeostrophic channel model. The results show that the projection of the evolved SV onto the forecast error increases during the evolution. Based on the similarities of the evolved SV to the forecast error, use of the evolved SV is suggested as an adaptive observation strategy. The use of the evolved SV strategy for adaptive observations is evaluated by performing observation system simulation experiments using a three-dimensional variational data assimilation scheme under the perfect model assumption. Adaptive strategies using the actual forecast error, gradient sensitivity, and initial SV are also tested. The observation system simulation experiments are implemented for five simulated synoptic cases with two different observation spacings and three different configurations of adaptive observation location densities (sparse, dense, and mixed), and the impact of the adaptive strategies is compared with that of the nonadaptive, fixed observations. The impact of adaptive strategies varies with the observation density. For a small number of observations, several of the adaptive strategies tested reduce forecast error more than the nonadaptive strategy. For a large number of observations, it is more difficult to reduce forecast errors using adaptive observations. The evolved SV strategy performs as well as or better than the adjoint-based strategies for both observation densities. The impact of using the evolved SVs rather than the adjoint-based sensitivities for adaptive observation purposes is larger in the situation of a large number of observation stations for which the forecast error reduction by adjointbased adaptive strategies is difficult.

A Potential Vorticity and Wave Activity Diagnosis of Optimal Perturbation Evolution

Abstract A diagnosis of singular vector (SV) evolution (computed for the L2 streamfunction norm) in the Eady model using potential vorticity (PV) and Eliassen–Palm (E–P) flux diagnostics is performed. In addition, a partitioning of the vertical component of the E–P flux vector based on the results of the piecewise PV inversion is introduced to better elucidate the fundamental mechanisms for SV amplification. The initial PV structures of the Eady model SVs on both the long- and shortwave sides of the Eady model shortwave cutoff are characterized by initially upshear tilted interior PV anomalies. The results of the PV and the E–P flux diagnostics for optimal perturbations reveal a three-stage process for the SV evolution: 1) a superposition of interior PV anomalies (diagnosed by a positive vertical component of the E–P flux), 2) a subsequent intensification (characterized by maxima in the E–P flux near the boundaries) of the SV boundary potential temperature anomalies (BTAs) by winds attributed to interior ...

The Impact of Outflow Environment on Tropical Cyclone Intensification and Structure

Abstract In this study, the impacts of regions of weak inertial stability on tropical cyclone intensification and peak strength are examined. It is demonstrated that weak inertial stability in the outflow layer minimizes an energy sink of the tropical cyclone secondary circulation and leads to more rapid intensification to the maximum potential intensity. Using a full-physics, three-dimensional numerical weather prediction model, a symmetric distribution of environmental inertial stability is generated using a variable Coriolis parameter. It is found that the lower the value of the Coriolis parameter, the more rapid the strengthening. The lower-latitude simulation is shown to have a significantly stronger secondary circulation with intense divergent outflow against a comparatively weak environmental resistance. However, the impacts of differences in the gradient wind balance between the different latitudes on the core structure cannot be neglected. A second study is then conducted using an asymmetric iner...

Dependence of Singular Vector Structure and Evolution on the Choice of Norm

A diagnosis of singular vector (SV) evolution in the Eady model for the potential enstrophy and energy norms is performed using potential vorticity (PV) inversion and Eliassen‐Palm (E‐P) flux diagnostics, and compared with the SV evolution for the streamfunction variance norm. The diagnostics reveal that the mechanism for SV amplification depends on the initial relative magnitudes of the interior PV and boundary temperature anomalies (BTAs). In addition, the relative magnitudes of the initial PV and BTAs are dependent on the norm chosen, the length scale of the perturbation, and the length of the optimization interval. If the initial contribution of the PV to a given norm is larger than the contribution of the BTAs to that norm, then the SV evolution in that norm is governed by the baroclinic superposition of the interior PV followed by an amplification of the BTAs by winds attributed to the interior PV. In the other case, the mutual interaction of BTAs governs the SV evolution. The initial interior PV is most important for the energy and streamfunction variance SVs, but is less important for the potential enstrophy SVs. Excluding the longwave (i.e., wavelengths longer than the Eady instability cutoff ) enstrophy norm SVs, for the shortwave SVs and for long optimization times, the importance of the initial interior PV is most apparent. In the view of targeted observations, the sensitive regions indicated by the SV analysis can be identified with particular mechanisms for SV development. The forecast measure may be considered sensitive in some regions in the sense that the forecast measure exhibits a large response to small changes in the initial conditions in those regions. The potential enstrophy norm is identified as being dynamically sensitive at the boundaries in contrast to the energy and streamfunction variance norm in the midtroposphere. It is suggested that subjective PV diagnosis of sensitivity may be viewed as being consistent with an objective diagnosis of sensitivity using potential enstrophy norm SVs.

Diagnosis of Optimal Perturbation Evolution in the Eady Model

Abstract The structure and evolution of Eady model singular vector (SV, also referred to as optimal perturbation) streamfunction perturbations are described using a combination of two different partitions of the vector subspace describing all possible streamfunction perturbations. A modal partitioning of the SV perturbation streamfunction (expressing the SV streamfunction as a linear combination of modal structures) is used to ascribe the roles and relative importance of the continuum modes (CMs) and the discrete normal modes (NMs) in SV initial structure and subsequent evolution. In addition, a potential vorticity (PV) partitioning of the SV perturbation streamfunction into parts attributed to the SV PV and the SV boundary thermal anomalies (BTAs) is employed. The structures of the CMs and NMs are described in terms of their characteristic perturbation PV and BTAs. Modal decomposition of the SVs reveals that for all zonal wavenumbers (k), the NMs have the largest projection coefficients (with magnitudes ...

Using Piecewise Potential Vorticity Inversion to Diagnose Frontogenesis. Part I: A Partitioning of the Q Vector Applied to Diagnosing Surface Frontogenesis and Vertical Motion

Abstract The technique of piecewise potential vorticity (PV) inversion is used to identify the nondivergent wind fields attributed to upper-, middle-, and lower-tropospheric PV anomalies in addition to the irrotational wind with the goal of diagnosing the respective wind fields’ frontogenetic potentialities. Frontogenesis is diagnosed using a piecewise separation of the Q vector into parts associated with the partitioned wind field. Partitioned geostrophic Q vectors are used to diagnose the vertical motion attributed to the upper-, middle-, and lower-tropospheric PV anomalies. Insight gained from this new diagnostic technique is demonstrated by examining a particular case of extratropical marine cyclogenesis resulting from the interaction of an upper-tropospheric short-wave trough with a surface thermal wave. In the early stages of development, the largest contributor to surface frontogenesis was associated with winds attributed to the lower-tropospheric thermal wave. As the cyclone matured, the contribut...

Interpretation of the Structure and Evolution of Adjoint-Derived Forecast Sensitivity Gradients

A 36-h adjoint-based forecast sensitivity study of three response functions defined in the lower troposphere—average temperature in an isolated region of the upper Midwest (R1), meridional temperature difference (R2), and average zonal component of the wind (R3)—is conducted with the goal of providing a synoptic and dynamic interpretation of the sensitivity gradient structure and evolution. In addition to calculating and interpreting the sensitivity gradients with respect to basic model variables along the model forecast trajectory, a technique is outlined that allows for the calculation of the sensitivity gradients with respect to variables derivable from the model state vector (including geopotential, relative vorticity, and divergence), and a method for visualizing the sensitivities with respect to the horizontal components of the wind is proposed and demonstrated. The sensitivity of R1 to all model and derived variables revealed that R1 was controlled by nearly adiabatic processes associated with the addition or generation of temperature perturbations upstream of the region in which R1 was defined. For R2, the sensitivity gradients revealed the well-known influence of confluent horizontal flow and vertical tilting of isentropes to increase the north–south temperature gradient over the region within which R2 was defined. The sensitivity of R3 to the components of the horizontal wind reveals that simply adding or generating an upstream zonal wind perturbation is insufficient to change the zonal wind at 36 h as these wind perturbations upstream of the domain within which R3 is defined are torqued by the Coriolis force as they are advected toward the domain. These results suggest adjoint-derived sensitivities of quasi-conserved response functions may be more easily interpretable than sensitivities calculated for nonconserved response functions.

Application of adjoint-derived forecast sensitivities to the 24-25 January 2000 U.S. east coast snowstorm

Abstract The 24–25 January 2000 eastern United States snowstorm was noteworthy as operational numerical weather prediction (NWP) guidance was poor for lead times as short as 36 h. Despite improvements in the forecast of the surface cyclone position and intensity at 1200 UTC 25 January 2000 with decreasing lead time, NWP guidance placed the westward extent of the midtropospheric, frontogenetically forced precipitation shield too far to the east. To assess the influence of initial condition uncertainties on the forecast of this event, an adjoint model is used to evaluate forecast sensitivities for 36- and 48-h forecasts valid at 1200 UTC 25 January 2000 using as response functions the energy-weighted forecast error, lower-tropospheric circulation about a box surrounding the surface cyclone, 750-hPa frontogenesis, and vertical motion. The sensitivities with respect to the initial conditions for these response functions are in general very similar: geographically isolated, maximized in the middle and lower tr...

Exploring the Structure of Regional Climate Scenarios by Combining Synoptic and Dynamic Guidance and GCM Output

A set of regional climate scenarios is constructed for two study regions in North America using a combination of GCM output and synoptic‐dynamical reasoning. The approach begins by describing the structure and components of a climate scenario and identifying the dynamical determinants of large-scale and regional climate. Expert judgement techniques are used to categorize the tendencies of these elements in response to increased greenhouse forcing in climate model studies. For many of the basic dynamical elements, tendencies are ambiguous, and changes in sign (magnitude, position) can usually be argued in either direction. A set of climate scenarios is produced for winter and summer, emphasizing the interrelationships among dynamical features, and adjusting GCM results on the basis of known deficiences in GCM simulations of the dynamical features. The scenarios are qualitative only, consistent with the level of precision afforded by the uncertainty in understanding of the dynamics, and in order to provide an outline of the reasoning and chain of contingencies on which the scenarios are based. The three winter scenarios outlined correspond roughly to a north‐south displacement of the stationary wave pattern, to an increase in amplitude of the pattern, and to a shift in phase of the pattern. These scenarios illustrate that small changes in the dynamics can lead to large changes in regional climate in some regions, while other regions are apparently insensitive to some of the large changes in dynamics that can be plausibly hypothesized. The dynamics of summer regional climate changes are even more difficult to project, though thermodynamic considerations allow some more general conclusions to be reached in this season. Given present uncertainties it is difficult to constrain regional climate projections.