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Alain Joly and Alan J. Thorpe

Abstract

The stability of the steady two-dimensional horizontal shear front to geostrophic disturbances in the along-front direction is examined within the framework of semi-geostrophic theory. The basic state corresponds to the geostrophic along-front flow at any time during the nonlinear evolution of a two-dimensional Eady wave. The matrix resulting from the stability analysis can be transformed into a weakly nondiagonal form. Its structure shows that the selection of the most unstable along-front wavenumber is independent of the “intensity” of the front. The growth rate is a linear function of this amplitude. The most unstable along-front mode is a modified Eady mode stationary with respect to the front. It draws a fraction of its energy from the shear. For smaller along-front wavelengths, the solution is dominated by propagating modes near the boundaries. These are also baroclinic, with a larger contribution from the basic kinetic energy and much smaller growth rates. It is apparent that the existence of a vorticity maximum at fronts, however large, is not sufficient to produce the observed small scale of frontal waves. Anomalous potential vorticity at the front is necessary to provide a deep zone of large horizontal shear and hence the reduced horizontal scale of waves.

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Craig H. Bishop and Alan J. Thorpe

Abstract

It has been shown that lower tropospheric potential vorticity zones formed during moist deformation frontogenesis will support growing waves if at some time the frontogenesis ceases. In this paper, the ways in which these waves are affected by the frontogenetic process are identified.

Observations show that fronts in the eastern Atlantic commonly feature saturated ascent regions characterized by zero moist potential vorticity. Furthermore, in many cases the horizontal temperature gradient in the lowest one to two kilometers of the atmosphere is rather weak. These features are incorporated in an analytical archetype. The dynamical implications of saturated ascent in conditions of zero moist potential vorticity are represented in the model by assuming that adiabatic temperature changes are precisely balanced by diabatic tendencies. The observed small temperature gradient at low levels is represented in the model by taking it to be zero in the lowest two kilometers. Consequently, the forcing of the low-level moist ageostrophic vortex stretching that strengthens the low-level potential vorticity anomaly is confined to middle and upper levels.

A semianalytical initial value solution for the linear development of waves on the evolving low-level potential vorticity anomaly is obtained. The waves approximately satisfy the inviscid primitive equations whenever the divergent part of the perturbation is negligible relative to the rotational part. The range of nonmodal wave developments supported by the front is summarized using RT phase diagrams. This analysis shows that the most dramatic effects of frontogenesis on frontal wave growth are due to (a) the increase in time of the potential vorticity and hence potential instability of the flow and (b) the increase in time of the alongfront wavelength relative to the width of the strip. An optimally growing streamfunction wave is described. Finally, a diagnostic technique suitable for identifying small amplitude frontal waves in observational data is described.

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Hannah R. Pomroy and Alan J. Thorpe

Abstract

The existence and production of reduced upper-tropospheric potential vorticity (RUPV) by heating is considered. An objective technique is used that identifies anomalies of PV arising from a particular physical process (here latent heat release). The evolution of two RUPV anomalies and a related diabatically increased lower-tropospheric PV (ILPV) anomaly occurring during Intensive Observing Period One of the cyclones from the Fronts and Atlantic Storm Track Experiment (FASTEX) is examined using model analyses, sounding data, and trajectory calculations. Three distinct airflows are identified emanating from the ILPV anomaly each with a different evolution. Results show that RUPV anomalies exist in the atmosphere and, in a weaker form, in numerical models.

The dynamical role of RUPV anomalies is examined using a nonlinear balance PV inversion and reruns of the U.K. Meteorological Office Limited Area Model. This shows that instantaneously the flow and temperature perturbations associated with RUPV anomalies are of at least comparable magnitude and extent to those induced by a similar positive anomaly. Over time one RUPV anomaly is seen to have a significant effect upon the development of its parent low. This low is more compact and more rapidly developing in the absence of the anomaly. The effect of the positive anomaly is also significant, but removing it has only a short-term effect as the anomaly quickly reforms. These results show that it is important to consider the role of RUPV in the PV model of a midlatitude cyclone.

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Craig H. Bishop and Alan J. Thorpe

Abstract

In this paper, the role of horizontal deformation and the associated frontogenetic ageostrophic circulation in suppressing the development of nonlinear waves is assessed. Unless linear barotropic frontal waves can become nonlinear, the associated horizontal transports of momentum will not be sufficient to halt frontogenesis or to create nonlinear mixing processes such as vortex roll-up. The analysis of Dritschel et al. suggests that such nonlinear phenomena will not occur if the wave slope remains small. For the linear model described in Part I, a simple relationship between optimal wave slope amplification over a specified time period and the amplification of an initially isolated edge wave is found. Using this relationship, the mechanisms by which strain affects the dependence of optimal wave slope amplification on wavelength and the time of entry of disturbances to the front are investigated. It is found that waves entering the frontal zone when it is intense can experience greater steepening than those appearing earlier in the development of the front. The most rapidly growing waves enter the front with a wavelength about three times the width of the front. As the front collapses, the ratio of wavelength to frontal width rapidly increases. For strain rates greater than 0.6 × 10−5 s−1, the model predicts that wave slope amplification greater than a factor of e is impossible.

The variation of optimal growth with wavenumber and the time of entry of disturbances to the front is explained using diagnostics based on a mathematical model of Bretherton's qualitative description of wave growth in terms of the interaction of counterpropagating edge waves. These diagnostics yield a simple formula for the frontogenesis rate required to completely eliminate wave steepening. For the front considered in Part I, the formula predicts that no amplification is possible for strain rates greater than one-quarter of the Coriolis parameter. Diagnostics of this sort may aid attempts to predict, from the large-scale forcing, the minimum attainable cross-frontal scale of a front.

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Alan J. Thorpe, Hans Volkert, and Dietrich Heimann

Abstract

Observations from the German Front Experiment are presented here that show the existence—in conditions with a dominant flow component parallel to the main Alpine chain—of a mesoscale region to the north of the Alps where the absolute and potential vorticity (PV) are substantially negative. These structures exist before the front arrives to the Alps and appear to be affected little by the passage of the front. A dynamical explanation for these and other mesoscale structures is sought by considering a simple unsheared airflow impinging on the Alps from the west. A linear frictionless model for the steady-state response is used as well as a full nonlinear numerical model with and without friction. A vastly simplified Alpine orography is considered as well as one that adequately describes its mesoscale detail.

The results show that the frictionless linear dynamics lead to a zone north of the Alps with anticyclonic vorticity but with uniform (positive) potential vorticity. With boundary-layer processes included in a nonlinear simulation substantial PV anomalies are produced. This leads to negative PV, and absolute vorticity, north of the Alps and positive PV south of the Alps. The region of PV anomalies in the model bears a suggestive similarity to that in the observations. The PV structures are attributed to frictional processes acting in a boundary layer that acquires a slope due to the sloping mountain sides. This mechanism only operates in this situation.

Other mesoscale aspects of the flow are discussed in regions around the Alps for which we have as yet no detailed observational evidence; for example, there is strong flow retardation immediately downstream of the orography. An important conclusion is that the Alps, in conditions of parallel flow, are a significant source of potential vorticity anomalies in the lower troposphere. These are advected away from the orography and must be an important part of the tropospheric PV budget.

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Douglas J. Parker and Alan J. Thorpe

Abstract

It is shown here that there exists a regime of balanced frontogenesis that is forced almost entirely by the diabatic hating due to convection at a front. This theory is explored in the context of the two-dimensional semigeostrophic equations with an Eady basic state: convection is parameterized to be dependent on the low-level moisture convergence of the cross-frontal ageostrophic flow, in accordance with recent diagnostic studies. The significant result is that the growth rate of the convective frontal system becomes independent of the total wavelength of the domain once the diabatic heating exceeds a relatively large threshold magnitude. In this regime the frontal zone has a width and structure dependent on the heating magnitude but not on the wavelength. The system is described as “solitary” or “isolated” since the dynamics are self-contained and independent of the far field.

The energetics of the system have a diabatic conversion that is an order of magnitude greater than that due to the large-scale alongfront temperature gradient. The large-scale forcing is, however, necessary as a catalyst in maintaining a weak ageostrophic convergence that allows the convective heating to be triggered. The constraint of alongfront geostrophic balance means that convective forcing alone cannot maintain frontogenesis. It is suggested that the dynamics exhibited by the convectively dominated front may also be important in the study of midlatitude squall lines.

The propagation and dynamics of the front are interpreted in terms of the notion of a “diabatic Rossby wave.”

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Alan J. Thorpe, Hans Volkert, and Michał J. Ziemiański

Two lines of thinking concerning fluid rotation—using either vorticity or circulation—emerged from the nineteenth-century work of Helmholtz and Thomson (Lord Kelvin), respectively. Vilhelm Bjerknes introduced an extension of Kelvin's ideas on circulation into geophysics. In this essay a historical perspective will be given on what has become known as the “Bjerknes circulation theorem.” Bjerknes wrote several papers on this topic, the first being in 1898. As Bjerknes noted, a Polish physicist, Ludwik Silberstein, had previously published an equivalent result concerning vorticity generation in 1896. Silberstein's work had built on an earlier paper by J. R. Schiitz in 1895. In his 1898 paper Bjerknes describes many possible applications of the theorem to meteorology and oceanography including to extratropical cyclones, a subject that made his “Bergen School” famous.

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Kerry A. Emanuel, Maurizio Fantini, and Alan J. Thorpe

Abstract

In the semigeostrophic system, the growth rate of baroclinic waves varies with the inverse square root of the potential vorticity, which acts as the effective static stability. Recent observations in the ascent regions of middle latitude cyclones show that the effective potential vorticity for saturated air is very near zero. In this paper we examine the structure and rate of growth of baroclinic cyclones when the effective potential vorticity is small for upward (saturated) displacements but large in regions of descent. Analytic solutions for two-dimensional disturbances in a two-layer semigeostrophic model and numerical simulations using a multilevel semigeostrophic model show that when the effective potential vorticity is small in regions of upward motion, growth rates are modestly increased and the region of ascent intensifies and collapses onto a thin ascending sheet. In the limit of zero moist potential vorticity the fastest growing wave has a finite growth rate which is about 2.5 times the dry value while the horizontal scale is reduced by a factor of about 0.6 compared to the dry modes. The asymmetry associated with condensation heating leads to frontal collapse first at the surface, rather than at both boundaries as in the dry case. In contrast to the analytic model, the numerical simulations allow the effect of (dry) potential vorticity evolution due to the latent heat release to be included. The anomalies of potential vorticity are advected horizontally through the wave, enhancing the low-level and diminishing the upper-level cyclonic vorticity and static stability in both the saturated and unsaturated regions of the flow.

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Douglas B. Clark, Christopher M. Taylor, and Alan J. Thorpe

Abstract

The surface fluxes of heat and moisture in semiarid regions are sensitive to spatial variability of soil moisture caused by convective rainfall. Under conditions typical of the Sahel, this variability may persist for several days after a storm, during which time it modifies the overlying boundary layer. A model of the land surface is used to quantify the dependence of surface fluxes of heat and moisture on antecedent rainfall amount, time since rainfall, and surface properties. Next, a coupled model of the land and atmosphere is used to characterize the boundary layer variability that results from this surface variability, and its dependence on factors including the length scale of the surface variability. Finally, two- and three-dimensional modeling of squall lines is used to examine the sensitivity of rainfall to boundary layer variability. Boundary layer variability tends to be greater for surface variability on long length scales, but squall-line rainfall shows the strongest response for anomalies on small length scales, comparable to that of the convection. As a result, the feedback between soil moisture and rainfall will be strongest at an intermediate scale.

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Linus Magnusson, Jean-Raymond Bidlot, Simon T. K. Lang, Alan Thorpe, Nils Wedi, and Munehiko Yamaguchi

Abstract

On 30 October 2012 Hurricane Sandy made landfall on the U.S. East Coast with a devastating impact. Here the performance of the ECMWF forecasts (both high resolution and ensemble) are evaluated together with ensemble forecasts from other numerical weather prediction centers, available from The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) archive. The sensitivity to sea surface temperature (SST) and model resolution for the ECMWF forecasts are explored. The results show that the ECMWF forecasts provided a clear indication of the landfall from 7 days in advance. Comparing ensemble forecasts from different centers, the authors find the ensemble forecasts from ECMWF to be the most consistent in the forecast of the landfall of Sandy on the New Jersey coastline. The impact of the warm SST anomaly off the U.S. East Coast is investigated by running sensitivity experiments with climatological SST instead of persisting the SST anomaly from the analysis. The results show that the SST anomaly had a small effect on Sandy’s track in the forecast, but the forecasts initialized with the warm SST anomaly feature a more intense system in terms of the depth of the cyclone, wind speeds, and precipitation. Furthermore, the role of spatial resolution is investigated by comparing four global simulations, spanning from TL159 (150 km) to TL3999 (5 km) horizontal resolution. Forecasts from 3 and 5 days before the landfall are evaluated. While all resolutions predict Sandy’s landfall, at very high resolution the tropical cyclone intensity and the oceanic wave forecasts are greatly improved.

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