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Richard Rotunno
,
William C. Skamarock
, and
Chris Snyder

Abstract

A comparative analysis of simulations of baroclinic waves with and without surface drag is presented, with particular reference to surface features. As in recent studies, the present simulations show that, compared to simulations with no drag, those with surface drag are less inclined to develop a secluded warm sector, and that drag weakens the warm front while the cold front remains strong. The authors demonstrate that analogous effects occur when Ekman pumping is used in nonlinear quasigeostrophic numerical simulations of unstable baroclinic waves in a channel. However, since the quasigeostrophic model produces symmetric highs and lows in the unstable baroclinic wave, the cold and warm fronts are therefore also symmetric and hence equally affected by the Ekman pumping. The different effect that friction has on the warm front with respect to the cold front in the primitive-equation simulations is fundamentally related to the tendency for the lows to be strong and narrow and the highs weak and broad, and for the warm front to form just north of, and extend eastward from, the low, while the cold front extends between the high and the low. The authors’ thesis is that the Ekman pumping associated with the low, at the location where the warm front would form in the absence of surface friction, acts to resist the formation of the warm front, while the cold front, positioned between the high and the low where Ekman pumping associated with the baroclinic wave is weak, is therefore relatively unaffected.

Given the weakness of Ekman pumping associated with the baroclinic wave in the vicinity of the incipient cold front, the present simulations indicate that cold frontogenesis occurs in the drag case in much the same way as in the no-drag case. Present analysis shows that the horizontal advection creating the cold front is a combination of geostrophic and ageostrophic effects. A portion of the ageostrophic frontogenesis is a response to geostrophic frontogenesis, as in the case without surface drag; however with surface drag, a significant portion of the cross-front ageostrophic flow is due to the Ekman layer associated with the front itself.

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Richard Rotunno
,
William C. Skamarock
, and
Chris Snyder

Abstract

Using a primitive equation (PE) model, we revisit two canonical flows that were previously studied using a semigeostrophic equation (SG) model. In a previous paper, the authors showed that the PE and the SG models can have significantly different versions of the large-scale dynamics—here they report on the implications of this difference for frontogenesis. The program for the study of frontogenesis developed by B. J. Hoskins and collaborators is followed to show how, in the PE version of the canonical cases, the surface warm front develops before the cold front, and why the upper-level front is a long, nearly continuous feature going from ridge to trough. The frontogenesis experienced by an air parcel is computed following the parcel to illustrate better the mechanisms involved. As the present calculations are carried out longer than most previous ones, the relation of the upper frontogenesis to the formation of the upper-level “cutoff” cyclone is also examined. Trajectory and three-dimensional graphical analyses show, with respect to the latter, the extreme distortions of the isentropic surfaces and mixing-induced variations in the potential vorticity field.

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Chris Snyder
,
William C. Skamarock
, and
Richard Rotunno

Abstract

A nonhydrostatic numerical model is used to simulate two-dimensional frontogenesis forced by either horizontal deformation or shear. Both inviscid frontogenesis prior to frontal collapse and frontogenesis with horizontal diffusion following collapse are considered. The numerical solutions generally agree well with semigeostrophic (SG) theory, though differences can be substantial for intense fronts. Certain deviations from SG that have been previously discussed in the literature area, upon closer examination, associated with spurious gravity waves produced by inadequate resolution or by the initialization of the numerical model. Even when spurious waves are eliminated, however, significant deviations from SG still exist: gravity waves are emitted by the frontogenesis when the cross-front scale becomes sufficiently small, and higher-order corrections to SG may also be present. In the postcollapse solutions (where they are most prominent), the emitted waves are stationary with respect to the front and lead to a band of increased low-level ascent just ahead of the surface front. It is suggested here that, when small, the deviations from SG arise as the linear forced response to the cross-front accelerations neglected by SG.

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Gregory J. Hakim
,
Chris Snyder
, and
David J. Muraki

Abstract

Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind, and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeostrophic dynamics, in particular, have cyclone–anticyclone symmetry.

In order to explore these and related problems, a novel small Rossby number approximation is introduced to the primitive equations applied to a simple model of the tropopause in continuously stratified fluid. This model resolves dynamics that give rise to vortical asymmetries, while retaining both the conceptual simplicity of quasigeostrophic dynamics and the computational economy of two-dimensional flows. The model contains no depth-independent (barotropic) flow, and thus may provide a useful comparison to two-dimensional flows dominated by this flow component.

Solutions for random initial conditions (i.e., freely decaying turbulence) exhibit vortical asymmetries typical of tropopause observations, with strong localized cyclones, and weaker diffuse anticyclones. Cyclones cluster around a distinct length scale at a given time, whereas anticyclones do not. These results differ significantly from previous studies of cyclone–anticyclone asymmetry in the shallow-water primitive equations and the periodic balance equations. An important source of asymmetry in the present solutions is divergent flow associated with frontogenesis and the forward cascade of tropopause potential temperature variance. This thermally direct flow changes the mean potential temperature of the tropopause, selectively maintains anticyclonic filaments relative to cyclonic filaments, and appears to promote the merger of anticyclones relative to cyclones.

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Fuqing Zhang
,
Naifang Bei
,
Richard Rotunno
,
Chris Snyder
, and
Craig C. Epifanio

Abstract

A recent study examined the predictability of an idealized baroclinic wave amplifying in a conditionally unstable atmosphere through numerical simulations with parameterized moist convection. It was demonstrated that with the effect of moisture included, the error starting from small random noise is characterized by upscale growth in the short-term (0–36 h) forecast of a growing synoptic-scale disturbance. The current study seeks to explore further the mesoscale error-growth dynamics in idealized moist baroclinic waves through convection-permitting experiments with model grid increments down to 3.3 km. These experiments suggest the following three-stage error-growth model: in the initial stage, the errors grow from small-scale convective instability and then quickly [O(1 h)] saturate at the convective scales. In the second stage, the character of the errors changes from that of convective-scale unbalanced motions to one more closely related to large-scale balanced motions. That is, some of the error from convective scales is retained in the balanced motions, while the rest is radiated away in the form of gravity waves. In the final stage, the large-scale (balanced) components of the errors grow with the background baroclinic instability. Through examination of the error-energy budget, it is found that buoyancy production due mostly to moist convection is comparable to shear production (nonlinear velocity advection). It is found that turning off latent heating not only dramatically decreases buoyancy production, but also reduces shear production to less than 20% of its original amplitude.

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Rebecca E. Morss
,
Kerry A. Emanuel
, and
Chris Snyder

Abstract

Adaptive sampling uses information about individual atmospheric situations to identify regions where additional observations are likely to improve weather forecasts of interest. The observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network. In this study, observing strategies are explored in a simulated idealized system with a three-dimensional quasigeostrophic model and a realistic data assimilation scheme. Using simple error norms, idealized adaptive observations are compared to nonadaptive observations for a range of observation densities.

The results presented show that in this simulated system, the influence of both adaptive and nonadaptive observations depends strongly on the observation density. For sparse observation networks, the simple adaptive strategies tested are beneficial: adaptive observations can, on average, reduce analysis and forecast errors more than the same number of nonadaptive observations, and they can reduce errors by a given amount using fewer observational resources. In contrast, for dense observation networks it is much more difficult to benefit from adapting observations, at least for the data assimilation method used here. The results suggest that the adaptive strategies tested are most effective when the observations are adapted regularly and frequently, giving the data assimilation system as many opportunities as possible to reduce errors as they evolve. They also indicate that ensemble-based estimates of initial condition errors may be useful for adaptive observations. Further study is needed to understand the extent to which the results from this idealized study apply to more complex, more realistic systems.

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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder
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Lotte Bierdel
,
Chris Snyder
,
Sang-Hun Park
, and
William C. Skamarock

Abstract

Under assumptions of horizontal homogeneity and isotropy, one may derive relations between rotational or divergent kinetic energy spectra and velocities along one-dimensional tracks, such as might be measured by aircraft. Two recent studies, differing in details of their implementation, have applied these relations to the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset and reached different conclusions with regard to the mesoscale ratio of divergent to rotational kinetic energy. In this study the accuracy of the method is assessed using global atmospheric simulations performed with the Model for Prediction Across Scales, where the exact decomposition of the horizontal winds into divergent and rotational components may be easily computed. For data from the global simulations, the two approaches yield similar and very accurate results. Errors are largest for the divergent component on synoptic scales, which is shown to be related to a very dominant rotational mode. The errors are, in particular, sufficiently small so that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly. The proposed technique thus provides a strong observational check of model results with existing large commercial aircraft datasets. The results do, however, show a significant dependence on the height and latitude ranges considered, and the disparate conclusions drawn from previous applications to MOZAIC data may result from the use of different subsets of the data.

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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder

Abstract

Recent papers by the authors demonstrated the possible influence of initial errors of small amplitude and scale on the numerical prediction of the “surprise” snowstorm of 24–25 January 2000. They found that initial errors grew rapidly at scales below 200 km, and that the rapid error growth was dependent on moist processes. In an attempt to generalize these results from a single case study, the present paper studies the error growth in an idealized baroclinic wave amplifying in a conditionally unstable atmosphere. The present results show that without the effects of moisture, there is little error growth in the short-term (0–36 h) forecast error (starting from random noise), even though the basic jet used here produces a rapidly growing synoptic-scale disturbance. With the effect of moisture included, the error is characterized by upscale growth, basically as found by the authors in their study of the numerical prediction of the surprise snowstorm.

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L. Mark Berliner
,
Zhan-Qian Lu
, and
Chris Snyder

Abstract

Suppose that one has the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of “adaptive observations” is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptive observations problem found in the literature are reviewed and interpreted from the optimal statistical design viewpoint. In addition, a numerical example, using the 40-variable model of Lorenz and Emanuel, suggests that some other proposed approaches may often be close to the optimal solution, at least in this highly idealized model.

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