Thomas Frisius

Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air

Abstract The local mass balance equations of cloudy air are formulated for a model system composed of dry air, water vapor, and four categories of water condensate particles, as typically adopted for numerical weather prediction and climate models. The choice of the barycentric velocity as reference motion provides the most convenient form of the total mass continuity equation. Mass transfer across the earth’s surface due to precipitation and evaporation causes a nonvanishing barycentric vertical velocity ws and is proportional to the local difference between evaporation rate and rain plus snow rate. Hence ws vanishes only in the special situation that evaporation and precipitation balance exactly. Alternative concepts related to different reference motions are reviewed. However, the choice of the barycentric velocity turns out to be advantageous for several reasons. The implication of the nonvanishing total mass transport across the earth’s surface is estimated from model simulations for two extreme weat...

A Mechanism for the Barotropic Equilibration of Baroclinic Waves

Abstract The barotropic instability of finite amplitude waves is suggested as a mechanism for explaining the equilibration of a baroclinic wave growing in a meridionally independent vertical shear flow. A quasigeostrophic two-layer channel model on an f-plane is used to give evidence for this hypothesis. Three solutions with different flow symmetries are adopted for the analysis. Numerical simulations reveal that the flow symmetry of the initial small amplitude perturbation can have a large impact on wave structure evolution and energetics. The flow symmetry of the first solution forces the wave to excite symmetric life cycles with baroclinic growth and baroclinic decay. The flow symmetries of the other solutions enable the wave to undergo an asymmetric life cycle with baroclinic growth followed by a barotropic decay that occurs when the fundamental wave has a sufficiently large aspect ratio. Accordingly, a linear-stability analysis of a steady barotropic wave reveals an increasing destabilization with in...

An Extended Model for the Potential Intensity of Tropical Cyclones

AbstractEmanuel’s theory of hurricane potential intensity (E-PI) makes use of the assumption that slantwise convective instability vanishes in a steady-state vortex of a tropical cyclone. In the framework of an extended mathematical potential intensity model it is shown that relaxing this assumption and including an eye results in a larger maximum wind speed compared to that of the predictions made by E-PI. Previous studies by Bryan and Rotunno demonstrate that the effect of unbalanced flow considerably contributes to maximum winds in excess of E-PI (“superintensity”). The authors argue that the proposed mechanism induced by convective instability provides another possible explanation for simulated and observed tropical cyclones exceeding E-PI in addition to flow imbalance. Further evidence for the relevance of conditional instability in mature tropical cyclones to superintensity is given by the fact that convective available potential energy arises in numerical simulations of tropical cyclones. This is d...

The Impact of Gradient Wind Imbalance on Potential Intensity of Tropical Cyclones in an Unbalanced Slab Boundary Layer Model

The assumption of gradient wind balance is customarily made so as to derive the theoretical upper-bound intensity of a mature tropical cyclone. Emanuel’s theory of hurricane potential intensity (E-PI) makes use of this assumption, whereas more recent studies by Bryan and Rotunno demonstrate that the effect of unbalanced flow can result in maximum winds that are well in excess of E-PI (superintensity). The existence of supergradient winds has been verified in a slab boundary layer model developed by Smith. Here, the authors apply the slab boundary layer model within the framework of classical E-PI theory to investigate the sensitivity of supergradient winds to the radius of maximum gradient wind (RMGW) and four nondimensional model parameters. The authors find that the Rossby number, the drag coefficient, and the modified Rankine decayparameterallhaveaconsiderableinfluenceonthestrengthoftheunbalancedflow.Incontrast,theratio of surface exchange coefficients has little noticeable effect on superintensity. The inclusion of horizontal momentum diffusion leads to a weaker superintensity, but the qualitative features of the model remain similar.To furtherelucidatethesefindings,theauthorsusetheboundarylayermodeltoexaminethemodified E-PI theoryproposedby Emanueland Rotunno.Theyassumea constantRichardsonnumberforthe outflow. The boundary layer model driven by the modified E-PI solution depends on just three model parameters rather than the four parameters used in the classical E-PI framework. Despite this apparent advantage, the resultsobtainedintheframeworkofthemodifiedE-PIarelessrealisticthanthosecomputedwiththeclassical E-PI approach.

Dynamical system analysis of a low-order tropical cyclone model

ABSTRACT Tropical cyclone dynamics is investigated by means of a conceptual box model. The tropical cyclone (TC) is divided into three regions, the eye, eyewall and ambient region. The model forms a low-order dynamical system of three ordinary differential equations. These are based on entropy budget equations comprising processes of surface enthalpy transfer, entropy advection, convection and radiative cooling. For tropical ocean parameter settings, the system possesses four non-trivial steady state solutions when the sea surface temperature (SST) is above a critical value. Two steady states are unstable while the two remaining states are stable. Bifurcation diagrams provide an explanation why only finite-amplitude perturbations above a critical SST can transform into TCs. Besides SST, relative humidity of the ambient region forms an important model parameter. The surfaces that describe equilibria as a function of SST and relative humidity reveal a cusp-catastrophe where the two non-trivial equilibria split into four. Within the model regime of four equilibria, cyclogenesis becomes very unlikely due to the repelling and attracting effects of the two additional equilibria. The results are in qualitative agreement with observations and evince the relevance of the simple model approach to the dynamics of TC formation and its maximum potential intensity.

An atmospheric balanced model of an axisymmetric vortex with zero potential vorticity

This paper presents an atmospheric axisymmetric balanced model for a zero potential vorticity vortex that is vertically confined between two frictional boundary layers. Zero potential vorticity has the consequence that the potential temperature does not vary on angular momentum surfaces. This leads to neutrality with respect to symmetric instability. The axisymmetric balanced model conserves this flow property when the diabatic heating and the torque also do not vary on angular momentum surfaces. With these conditions and a transformation to the potential radius coordinates, the model reduces to prognostic equations for the physical radii at the lower and upper boundaries. The knowledge of these radii is sufficient to deduce all dynamic fields of the axisymmetric vortex. Analytical solutions can be obtained for vanishing viscosity and a prescribed heating profile. However, these solutions may reveal a frontal collapse in a finite time. This circumstance can be avoided by the inclusion of a horizontal diffusion term within the boundary layers. Then, the model produces a vortex resembling a tropical cyclone for a typical heating profile. It is suggested that the model might be used for a better conceptual understanding of tropical cyclogenesis.

The Theoretician's Clouds—Heavier or Lighter than Air? On Densities in Atmospheric Thermodynamics

AbstractThreefold densities may be introduced into atmospheric thermodynamics. For rainless clouds the general indirect or implicit conclusion is that they are denser than moist air under the same circumstances, although in a classic treatise a different conclusion was reached, to the effect that cloudy air (containing water and/or ice) is less dense than moist air under the same pressure and temperature. By reconsidering carefully different ways of determining densities, any doubts that may linger after reading the scant literature dealing explicitly with the density of a cloud are dispelled.

The Development of a Cyclone–Anticyclone Asymmetry within a Growing Baroclinic Wave

Abstract This study examines the cyclone–anticyclone asymmetry within idealized baroclinic waves. For this purpose a primitive equation (PE) model and a quasigeostrophic (QG) model are used. The Rossby number appears to be an essential external parameter for the cyclone–anticyclone asymmetry. Consequently, the Rossby number effect on nonlinear baroclinic waves is a central point of this study. First, the baroclinic stability of a vertically antisymmetric dipole jet flow is analyzed. Increasing the Rossby number in the PE model has the effect that the eddies of the fastest growing normal mode are tilted toward the northwest–southeast direction. The increase of this tilt is almost proportional to the Rossby number and arises due to leading-order corrections to the QG model. The nonlinear development of the fastest growing normal mode is simulated for various Rossby numbers. The PE model simulations exhibit the development of strong cyclones and weak anticyclones even when the cyclonic and anticyclonic shear...

The Impact of Gradient Wind Imbalance on Tropical Cyclone Intensification within Ooyama’s Three-Layer Model

AbstractThis paper addresses the validity of the gradient wind balance approximation during the intensification phase of a tropical cyclone in Ooyama’s three-layer model. For this purpose, the sensitivity to various model modifications is examined, given by the inclusion of (i) unbalanced dynamics in the free atmosphere, (ii) unbalanced dynamics in the slab boundary layer, (iii) a height-parameterized boundary layer model, and (iv) a rigid lid. The most rapid intensification occurs when the model employs the unbalanced slab boundary layer, while the simulation with the balanced boundary layer reveals the slowest intensification. The simulation with the realistic height-parameterized boundary layer model exhibits an intensification rate that lies in between. Intensification is induced by a convective ring in all experiments, but a distinct contraction of the radius of maximum gradient wind only takes place with unbalanced boundary layer dynamics. In all experiments the rigid lid and the balance approximati...

Dynamical system properties of an axisymmetric convective tropical cyclone model

The dynamical system behaviour of tropical cyclones and their potential intensity with a view to sea surface temperature, tropospheric temperature stratification and tropospheric moisture content is investigated in the axisymmetric convective model HURMOD. The model results exhibit the existence of a fixed-point attractor associated with a strong tropical cyclone. Moreover, the initial vortex strength forms an amplitude threshold to cyclogenesis. Above this threshold, the size of the tropical cyclone and its intensity are independent of the initial vortex strength and its horizontal extent. Below the amplitude threshold, cyclogenesis does not occur and the system approaches an atmospheric state of rest. In case one allows for a deviation of the tropospheric stratification from moist-neutral conditions, the modelling results reveal the existence of bifurcations with the sea surface temperature representing the bifurcation parameter: As the sea surface temperature decreases and the storm weakens, the fixed-point attractor turns first into a limit cycle indicating a Hopf-bifurcation and then gives way to a steady-state of lower intensity, before the intensity oscillation becomes chaotic, and finally the tropical storm dies. The amplitude threshold and the sea surface temperature range, within which the system exhibits bifurcation points, are sensitive to the reference value of relative humidity and the reference tropospheric temperature stratification. If the reference troposphere is presumed to be moist-neutral, the dynamical behaviour of the modelled tropical cyclone does not change within the range of tropical sea surface temperature, and the tropical cyclone only slightly weakens with decreasing sea surface temperature, without any abrupt changes in intensity. Apart from the existence of Hopf-bifurcations, these findings are qualitatively similar to results gained from a low-order model presented in a precursory study.