A review of the cumulus parameterization problem is presented with an emphasis on its conceptual aspects covering the history of the underlying ideas, major problems existing at present, and possible directions and approaches for future climate models. Since its introduction in the early 1960s, there have been decades of controversies in posing the cumulus parameterization problem. In this paper, it is suggested that confusion between budget and advection considerations is primarily responsible for the controversies. It is also pointed out that the performance of parameterization schemes can be better understood if one is not bound by their authors' justifications. The current trend in posing cumulus parameterization is away from deterministic diagnostic closures, including instantaneous adjustments, toward prognostic or nondeterministic closures, including relaxed and/or triggered adjustments. A number of questions need to be answered, however, for the merit of this trend to be fully utilized. M...

The Cumulus Parameterization Problem: Past, Present, and Future

The influence of the direction of storm motion on the azimuthal distribution of electrified convection in 35 Atlantic basin tropical cyclones from 1985 to 1999 was examined using data from the National Lightning Detection Network. In the inner 100 km, flashes most often occurred in the front half of storms, with a preference for the right-front quadrant. In the outer rainbands (r = 100–300 km), flashes occurred predominantly to the right of motion, although the maximum remained in the right-front quadrant. The results are shown to be consistent with previous studies of asymmetries in rainfall, radar reflectivity, and vertical motion with respect to tropical cyclone motion. The motion effect has been attributed to the influence of asymmetric friction in the tropical cyclone boundary layer. The authors previously found a strong signature in the azimuthal distribution of lightning with respect to vertical wind shear. Because both effects show clearly, vertical wind shear and storm motion must themse...

The Relationship between Storm Motion, Vertical Wind Shear, and Convective Asymmetries in Tropical Cyclones

We present numerical-model experiments to investigate the dynamics of tropical-cyclone amplification and its predictability in three dimensions. For the prototype amplification problem beginning with a weak-tropical-storm-strength vortex, the emergent flow becomes highly asymmetric and dominated by deep convective vortex structures, even though the problem as posed is essentially axisymmetric. The asymmetries that develop are highly sensitive to the boundary-layer moisture distribution. When a small random moisture perturbation is added in the boundary layer at the initial time, the pattern of evolution of the flow asymmetries is changed dramatically, and a non-negligible spread in the local and azimuthally-averaged intensity results. We conclude, first, that the flow on the convective scales exhibits a degree of randomness, and only those asymmetric features that survive in an ensemble average of many realizations can be regarded as robust; and secondly, that there is an intrinsic uncertainty in the prediction of maximum intensity using either maximum-wind or minimum-surface-pressure metrics. There are clear implications for the possibility of deterministic forecasts of the mesoscale structure of tropical cyclones, which may have a major impact on the intensity and on rapid intensity changes.

Some other aspects of vortex structure are addressed also, including vortex-size parameters, and sensitivity to the inclusion of different physical processes or higher spatial resolution. We investigate also the analogous problem on a β-plane, a prototype problem for tropical-cyclone motion. A new perspective on the putative role of the wind--evaporation feedback process for tropical-cyclone intensification is offered also.

The results provide new insight into the fluid dynamics of the intensification process in three dimensions, and at the same time suggest limitations of deterministic prediction for the mesoscale structure. Larger-scale characteristics, such as the radius of gale-force winds and β-gyres, are found to be less variable than their mesoscale counterparts. Copyright © 2008 Royal Meteorological Society

Tropical-cyclone intensification and predictability in three dimensions

: We review the four main paradigms of tropical cyclone intensification that have emerged over the past five decades, discussing the relationship between them and highlighting their strengths and weaknesses. A major focus is on a new paradigm articulated in a series of recent papers using observations and high- resolution, three-dimensional, numerical model simulations. Unlike the three previous paradigms, all of which assumed axial symmetry, the new one recognises the presence of localised, buoyant, rotating deep convection that grows in the rotation-rich environment of the incipient storm, thereby greatly amplifying the local vorticity. It exhibits also a degree of randomness that has implications for the predictability of local asymmetric features of the developing vortex. While surface moisture fluxes are required for intensification, the postulated evaporation-wind feedback process that forms the basis of an earlier paradigm is not. Differences between spin up in three-dimensional and axisymmetric numerical models are discussed also. In all paradigms, the tangential winds above the boundary layer are amplified by the convectively-induced inflow in the lower troposphere in conjunction with the approximate material conservation of absolute angular momentum. This process acts also to broaden the outer circulation. Azimuthally-averaged fields from high-resolution model simulations have highlighted a second mechanism for amplifying the mean tangential winds. This mechanism, which is coupled to the first via boundary-layer dynamics, involves the convergence of absolute angular momentum within the boundary layer, where this quantity is not materially conserved, but where air parcels are displaced much further radially in - wards than air parcels above the boundary layer. It explains why the maximum tangential winds occur in the boundary layer and accounts for the generation of supergradient wind speeds there.

http://www.bom.gov.au/jshess/docs/2014/montgomery.pdf

Paradigms for Tropical Cyclone Intensification

Tropical-Cyclone Intensification and Predictability in Three Dimensions

A three-layer shallow-water numerical model is used to study the motion of tropical-cyclone-like vortices in a westerly baroclinic current. the structure of the vortex and its environment are chosen to be representative of real tropical cyclones. Numerical experiments with and without convection are discussed. Several different environmental flows are considered.



In calculations on a northern-hemisphere f-plane without convection, anomalies of upper-layer potential vorticity (PV) have a major influence on the vortex motion in the middle layer. This is true even in numerical experiments that include a PV-gradient in the middle layer associated with an upper-level westerly jet. For example, when a broad anticyclone is included in the upper layer, the middle-layer vortex moves initially to the east-northeast. If the middle-layer PV-gradient were the dominant factor, the middle-layer vortex would, instead, move to the south-east. When there is no middle-layer PV-gradient, the middle-layer vortex is deflected to the right of the environmental shear vector if the upper-layer vortex is cyclonic and to the left of the environmental shear vector if the upper-layer vortex is anticyclonic. the size of the vortex affects the drift velocity, but has a negligible effect on the drift direction.



Calculations incorporating a convective parametrization based on that developed by Ooyama (1969) show that an initially weak vortex can intensify to hurricane strength in a conditionally neutral environment. This calculation underscores the importance of surface fluxes in Ooyama's scheme and subsequent schemes based on it, as it shows that the scheme does not rely necessarily on a large amount of convective instability in the initial state.



In calculations on a northern-hemisphere f-plane with an upper-level westerly jet and convection, the middle-layer vortex moves to the south-east because of the middle-layer PV-gradient. When the middle-layer PV-gradient is removed but the convection retained, the middle-layer vortex moves first to the south-east and then to the northeast. In this case the motion of the middle-layer vortex is controlled by the upper-layer PV-anomaly. At early times, the vertical shear tilts the vortex towards the east so that the western side of the upper-layer cyclonic core lies above the middle-layer vortex centre. Consequently, the upper-layer cyclonic core induces a southward component to the flow across the middle-layer vortex centre. As time proceeds, the upper-layer westerlies advect the broad anticyclonic outer part of the upper vortex over the middle-layer vortex centre, inducing a northward component across its centre.



Relatively minor changes to the convective parametrization have a relatively large effect on the motion of the vortex. Changing the way the parametrized clouds transport momentum, changes the structure of the upper-layer vortex. Changes to the pattern of PV in the upper layer in turn affect the middle-layer flow attributable to it. the effect of the upper-layer PV on the motion of the middle-layer vortex is weakened when the outflow from a tropical cyclone is confined to a comparatively shallow upper layer as is commonly observed.

The effects of convection and baroclinicity on the motion of tropical‐cyclone‐like vortices

A three-layer shallow-water model with a convection parametrization is used to study the track deflections of slow-moving hurricanes on a β-plane as they approach straight coastlines of different orientations with respect to north, or as they cross to a cooler or warmer body of water. In the landfall experiments, the land surface is level and is characterized by an abrupt increase of the drag coefficient and zero evaporation. the tracks of a 72 h integration on a β-plane are compared with an ocean control experiment.

It is found that the divergent flow in the boundary layer in regions of offshore winds is responsible for the observed track deflections. In this region middle-layer air descends into the boundary layer and increases the positive potential-vorticity anomaly in the middle layer. In the case of land conditions to the west of the vortex, the maximum potential-vorticity anomaly extends less to the north of the vortex centre and results in a more southerly track than in the ocean control case. If land conditions are specified in the north, the positive potential-vorticityasymmetry maximum extends more to the north-west and results in a northward deflection of the track. On the other hand, land conditions to the north-west of the initial vortex centre do not significantly change the location of the asymmetry, and therefore the track deflection is small. the magnitude of the track deflections, as well as the drift speed, increases when the roughness of the land is increased. It is significant that track deflections commence about 20 h before landfall, reaching a value of about 150 km at the time of landfall.

Compared with landfalling hurricanes, track deflections of model hurricanes which drift into a region of different sea surface temperature (SST) are smaller and are a result of intensity changes of the vortex circulation. the maximum wind speed at the time of landfall increases if a region of higher SST is located adjacent to the coastline.

Klaus Dengler

Papers

The effects of convection and baroclinicity on the motion of tropical‐cyclone‐like vortices

A numerical study of the effects of land proximity and changes in sea surface temperature on hurricane tracks