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  • 1
    Publication Date: 2023-07-28
    Description: 〈title xmlns:mml="http://www.w3.org/1998/Math/MathML"〉Abstract〈/title〉〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉The Lagrangian representation of fluid flows offers a natural perspective to study many kinds of physical mechanisms. By contrast, the Eulerian representation is more convenient from a diagnostic point of view. This article attempts to combine elements of both worlds by proposing an Eulerian method that allows one to extract Lagrangian information about the atmospheric flow. The method is based on the offline advection of passive tracer fields and includes a relaxation term. The latter device allows one to run the integration in a continuous fashion without the need for reinitialization. As a result one obtains accumulated Lagrangian information, for example, about the recent parcel displacement or the recent parcel‐based diabatic heating, at each point of an Eulerian grid at any time step. The method is implemented with a pseudospectral algorithm suitable for gridded global atmospheric data and compared with the more traditional trajectory method. The method's utility is demonstrated on the basis of a few examples, which relate to cloud formation and the development of temperature anomalies. The examples highlight that the method provides a convenient diagnostic of parcel‐based changes, paving an intuitive way to explore the physical processes involved. Due to its gridpoint‐based nature, the proposed method can be applied to large data sets in a straightforward and computationally efficient manner, suggesting that the method is particularly useful for climatological analyses.〈/p〉
    Description: 〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉The Lagrangian representation of fluid flows offers the most natural perspective to study many kinds of physical mechanisms; by contrast, the Eulerian representation is more convenient from a diagnostic point of view. This article attempts to combine elements of both worlds by proposing an Eulerian method that allows one to extract Lagrangian information about the atmospheric flow. The method enables one to easily produce a sequence of maps showing accumulated Lagrangian changes. 〈boxed-text position="anchor" id="qj4453-blkfxd-0001" content-type="graphic" xml:lang="en"〉〈graphic position="anchor" id="jats-graphic-1" xlink:href="urn:x-wiley:00359009:media:qj4453:qj4453-toc-0001"〉 〈/boxed-text〉〈/p〉
    Description: Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659
    Keywords: ddc:551.5 ; air‐parcel approach ; atmospheric fluid dynamics ; atmospheric transport ; Eulerian tracer technique ; Lagrangian analysis ; Lagrangian tracking ; synoptic‐scale meteorology ; trajectories
    Language: English
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  • 2
    Publication Date: 2023-07-25
    Description: 〈title xmlns:mml="http://www.w3.org/1998/Math/MathML"〉Abstract〈/title〉〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉Local ensemble transform Kalman filters (LETKFs) allow explicit calculation of the Kalman gain, and by this the contribution of individual observations to the analysis field. Though this is a known feature, the information on the analysis contribution of individual observations (partial analysis increment) has not been used as systematic diagnostic up to now despite providing valuable information. In this study, we demonstrate three potential applications based on partial analysis increments in the regional modelling system of Deutscher Wetterdienst and propose their use for optimising LETKF data assimilation systems, in particular with respect to satellite data assimilation and localisation. While exact calculation of partial analysis increments would require saving the large, five‐dimensional ensemble weight matrix in the analysis step, it is possible to compute an approximation from standard LETKF output. We calculate the Kalman gain based on ensemble analysis perturbations, which is an approximation in the case of localisation. However, this only introduces minor errors, as the localisation function changes very gradually among nearby grid points. On the other hand, the influence of observations always depends on the presence of other observations and settings for the observation error and for localisation. However, the influence of observations behaves approximately linearly, meaning that the assimilation of other observations primarily decreases the magnitude of the influence, but it does not change the overall structure of the partial analysis increments. This means that the calculation of partial analysis increments can be used as an efficient diagnostic to investigate the three‐dimensional influence of observations in the assimilation system. Furthermore, the diagnostic can be used to detect whether the influence of additional experimental observations is in accordance with other observations without conducting computationally expensive single‐observation experiments. Last but not least, the calculation can be used to approximate the influence an observation would have when applying different assimilation settings.〈/p〉
    Keywords: ddc:551.5 ; analysis influence ; convective‐scale ; ensemble data assimilation ; localisation ; NWP ; satellite data assimilation
    Language: English
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  • 3
    Publication Date: 2023-07-25
    Description: 〈title xmlns:mml="http://www.w3.org/1998/Math/MathML"〉Abstract〈/title〉〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉For both the meso‐ and synoptic scales, reduced mathematical models give insight into their dynamical behaviour. For the mesoscale, the weak temperature gradient approximation is one of several approaches, while for the synoptic scale the quasigeostrophic theory is well established. However, the way these two scales interact with each other is usually not included in such reduced models, thereby limiting our current perception of flow‐dependent predictability and upscale error growth. Here, we address the scale interactions explicitly by developing a two‐scale asymptotic model for the meso‐ and synoptic scales with two coupled sets of equations for the meso‐ and synoptic scales respectively. The mesoscale equations follow a weak temperature gradient balance and the synoptic‐scale equations align with quasigeostrophic theory. Importantly, the equation sets are coupled via scale‐interaction terms: eddy correlations of mesoscale variables impact the synoptic potential vorticity tendency and synoptic variables force the mesoscale vorticity (for instance due to tilting of synoptic‐scale wind shear). Furthermore, different diabatic heating rates—representing the effect of precipitation—define different flow characteristics. With weak mesoscale heating relatable to precipitation rates of 〈mml:math id="jats-math-1" display="inline" overflow="scroll"〉〈mml:mrow〉〈mml:mi〉𝒪〈/mml:mi〉〈mml:mo stretchy="false"〉(〈/mml:mo〉〈mml:mn〉6〈/mml:mn〉〈mml:mspace width="0.3em"/〉〈mml:mtext〉mm〈/mml:mtext〉〈mml:mo〉·〈/mml:mo〉〈mml:msup〉〈mml:mrow〉〈mml:mi mathvariant="normal"〉h〈/mml:mi〉〈/mml:mrow〉〈mml:mrow〉〈mml:mo form="prefix"〉−〈/mml:mo〉〈mml:mn〉1〈/mml:mn〉〈/mml:mrow〉〈/mml:msup〉〈mml:mo stretchy="false"〉)〈/mml:mo〉〈/mml:mrow〉〈/mml:math〉, the mesoscale dynamics resembles two‐dimensional incompressible vorticity dynamics and the upscale impact of the mesoscale on the synoptic scale is only of a dynamical nature. With a strong mesosocale heating relatable to precipitation rates of 〈mml:math id="jats-math-2" display="inline" overflow="scroll"〉〈mml:mrow〉〈mml:mi〉𝒪〈/mml:mi〉〈mml:mo stretchy="false"〉(〈/mml:mo〉〈mml:mn〉60〈/mml:mn〉〈mml:mspace width="0.3em"/〉〈mml:mtext〉mm〈/mml:mtext〉〈mml:mo〉·〈/mml:mo〉〈mml:msup〉〈mml:mrow〉〈mml:mi mathvariant="normal"〉h〈/mml:mi〉〈/mml:mrow〉〈mml:mrow〉〈mml:mo form="prefix"〉−〈/mml:mo〉〈mml:mn〉1〈/mml:mn〉〈/mml:mrow〉〈/mml:msup〉〈mml:mo stretchy="false"〉)〈/mml:mo〉〈/mml:mrow〉〈/mml:math〉, divergent motions and three‐dimensional effects become relevant for the mesoscale dynamics and the upscale impact also includes thermodynamical effects.〈/p〉
    Description: 〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉We develop a two‐scale asymptotic model for the meso‐ and synoptic scales following a weak temperature gradient balance and quasigeostrophic theory, but with explicit scale interactions and dependent on the mesoscale diabatic heating. With weak mesoscale heating, the mesoscale dynamics resembles 2D incompressible vorticity dynamics and the upscale impact on the synoptic scale is only of a dynamical nature. With strong mesoscale heating, divergent motions and 3D effects become relevant for the mesoscale and the upscale impact also includes thermodynamical effects. 〈boxed-text position="anchor" id="qj4456-blkfxd-0001" content-type="graphic" xml:lang="en"〉〈graphic position="anchor" id="jats-graphic-1" xlink:href="urn:x-wiley:00359009:media:qj4456:qj4456-toc-0001"〉
    Description: German Research Foundation (DFG)
    Keywords: ddc:551.5 ; asymptotics ; atmospheric dynamics ; mesoscale ; multiscale scale interactions ; quasigeostrophic ; synoptic scale
    Language: English
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  • 4
    Publication Date: 2024-05-30
    Description: 〈title xmlns:mml="http://www.w3.org/1998/Math/MathML"〉Abstract〈/title〉〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉The Intertropical Convergence Zone (ITCZ) is a central component of the atmospheric general circulation, but remarkably little is known about the dynamical and thermodynamical structure of the convergence zone itself. This is true even for the structure of the low‐level convergence that gives the ITCZ its name. Following on from the major international field campaigns in the 1960s and 1970s, we performed extensive atmospheric profiling of the Atlantic ITCZ during a ship‐based measurement campaign aboard the research vessel 〈italic toggle="no"〉SONNE〈/italic〉 in summer 2021. Combining data collected during our north–south crossing of the ITCZ with reanalysis data shows the ITCZ to be a meridionally extended region of intense precipitation, with enhanced surface convergence at its edges rather than in the center. Based on the location of these edges, we construct a composite view of the structure of the Atlantic ITCZ. The ITCZ, far from being simply a region of enhanced deep convection, has a rich inner life, that is, a rich dynamical and thermodynamic structure that changes throughout the course of the year, and has a northern edge that differs systematically from the southern edge.〈/p〉
    Description: Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347
    Description: Horizon 2020 Framework Programme CONSTRAIN http://dx.doi.org/10.13039/100010661
    Description: https://doi.org/10.5281/ZENODO.7051674
    Description: https://doi.org/10.24381/cds.adbb2d47
    Keywords: ddc:551.5 ; ITCZ ; Atlantic ; convergence ; observations ; reanalysis
    Language: English
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  • 5
    Publication Date: 2022-10-04
    Description: We review the widely used concepts of “buoyancy” and “convective available potential energy” (CAPE) in relation to deep convection in tropical cyclones and discuss their limitations. A fact easily forgotten in applying these concepts is that the buoyancy force of an air parcel, as often defined, is non‐unique because it depends on the arbitrary definition of a reference density field. However, when calculating CAPE, the buoyancy of a lifted air parcel is related to the specific reference density field along a vertical column passing through that parcel. Both concepts can be generalized for a vortical flow and to slantwise ascent of a lifted air parcel in such a flow. In all cases, the air parcel is assumed to have infinitely small dimensions. In this article, we explore the consequences of generalizing buoyancy and CAPE for buoyant regions of finite size that perturb the pressure field in their immediate environment. Quantitative calculations of effective buoyancy, defined as the sum of the conventional buoyancy and the static vertical perturbation pressure gradient force induced by it, are shown for buoyant regions of finite width. For a judicious choice of reference density, the effective buoyancy per unit mass is essentially a unique force, independent of the reference density, but its distribution depends on the horizontal scale of the buoyant region. A corresponding concept of “effective CAPE” is introduced and its relevance to deep convection in tropical cyclones is discussed. The study is conceived as a first step to understanding the decreasing ability of inner‐core deep convection in tropical cyclones to ventilate the mass of air converging in the frictional boundary layer as the vortex matures and decays.
    Description: The buoyancy force of an infinitesimally small air parcel is non‐unique, depending on the arbitrary definition of a reference density field. When calculating the “convective available potential energy” (CAPE), the buoyancy of a lifted air parcel is related to the reference density field along a vertical column passing through that parcel. We generalize buoyancy and CAPE for buoyant regions of finite size that perturb the pressure field in their immediate environment and discuss the relevance to deep convection in tropical cyclones.
    Keywords: ddc:551.5
    Language: English
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  • 6
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    John Wiley & Sons, Ltd | Chichester, UK
    Publication Date: 2022-10-04
    Description: New cross‐validation diagnostics have been derived by further partitioning well‐established impact diagnostics. They are related to consistency relations, the most prominent of which indicates whether the first‐guess departures of a given observation type pull the model state into the direction of the verifying data (when processed with the ensemble estimated model error covariances). Alternatively, this can be regarded as cross‐validation between model error covariance estimates from the ensemble (which are used in the data assimilation system) and estimates diagnosed directly from the observations. A statistical cross‐validation tool has been developed that includes an indicator of statistical significance as well as a normalization that makes the statistical comparison largely independent from the total number of data and the closeness of their collocation. We also present a version of these diagnostics related to single‐observation experiments that exploits the same consistency relations but is easier to compute. Diagnostics computed within the Deutscher Wetterdienst's localized ensemble transform Kalman filter (LETKF) are presented for various kinds of bins. Results from well‐established in‐situ measurements are taken as a benchmark for more complex observations. Good agreement is found for radio‐occultation bending angle measurements, whereas atmospheric motion vectors are generally also beneficial but substantially less optimal than the corresponding in‐situ measurements. This is consistent with reported atmospheric motion vector height assignment problems. To illustrate its potential, a recent example is given where the method allowed identifying bias problems of a subgroup of aircraft measurements. Another diagnostic relationship compares the information content of the analysis increments with a theoretical optimum. From this, the information content of the LETKF increments is found to be considerably lower than those of the deterministic hybrid ensemble–variational system, which is consistent with the LETKF's limitation to the comparably low‐dimensional ensemble space for finding the optimal analysis.
    Description: New cross‐validation diagnostics are presented, allowing to test the consistent use of different observation types in the data assimilation system. The figure gives an example in which these new diagnostics allowed identification of the detrimental impact of a group of aircraft measurements (which as a consequence has now been blacklisted in the Deutscher Wetterdienst's operational system). More precisely, brown colors in this plot indicate regions where these aircraft measurements pulled the analysis state away from radiosonde observations.
    Keywords: ddc:551.5
    Language: English
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  • 7
    Publication Date: 2022-10-06
    Description: Trade wind convection organises into a rich spectrum of spatial patterns, often in conjunction with precipitation development. Which role spatial organisation plays for precipitation and vice versa is not well understood. We analyse scenes of trade‐wind convection scanned by the C‐band radar Poldirad during the EUREC4A field campaign to investigate how trade‐wind precipitation fields are spatially organised, quantified by the cells' number, mean size, and spatial arrangement, and how this matters for precipitation characteristics. We find that the mean rain rate (i.e., the amount of precipitation in a scene) and the intensity of precipitation (mean conditional rain rate) relate differently to the spatial pattern of precipitation. Whereas the amount of precipitation increases with mean cell size or number, as it scales well with the precipitation fraction, the intensity increases predominantly with mean cell size. In dry scenes, the increase of precipitation intensity with mean cell size is stronger than in moist scenes. Dry scenes usually contain fewer cells with a higher degree of clustering than moist scenes do. High precipitation intensities hence typically occur in dry scenes with rather large, few, and strongly clustered cells, whereas high precipitation amounts typically occur in moist scenes with rather large, numerous, and weakly clustered cells. As cell size influences both the intensity and amount of precipitation, its importance is highlighted. Our analyses suggest that the cells' spatial arrangement, correlating mainly weakly with precipitation characteristics, is of second‐order importance for precipitation across all regimes, but it could be important for high precipitation intensities and to maintain precipitation amounts in dry environments.
    Description: We analyse scenes of trade‐wind convection scanned by the C‐band radar Poldirad during the EUREC4A field campaign to investigate how trade‐wind precipitation fields are spatially organised, quantified by the cells' number, mean size, and spatial arrangement, and how this matters for precipitation characteristics. We conclude that the cells' size is important for both the amount and intensity of precipitation, whereas the cells' spatial arrangement is of second‐order importance for precipitation across all regimes, but possibly important for precipitation in dry environments.
    Description: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy—EXC 2037 'CLICCS—Climate, Climatic Change, and Society'
    Description: https://doi.org/10.25326/217
    Description: https://doi.org/10.25326/79
    Keywords: ddc:551.5
    Language: English
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  • 8
    Publication Date: 2022-10-06
    Description: The stochastically perturbed parametrisation tendency (SPPT) scheme is a well‐established technique in ensemble forecasting to address model uncertainty by introducing perturbations into the tendencies provided by the physics parametrisations. The magnitude of the perturbations scales with the local net parametrisation tendency, resulting in large perturbations where diabatic processes are active. Rapidly ascending air streams, such as warm conveyor belts (WCBs) and organized tropical convection, are often driven by cloud diabatic processes and are therefore prone to such perturbations. This study investigates the effects of SPPT and initial condition perturbations on rapidly ascending air streams by computing trajectories in sensitivity experiments with the European Centre for Medium‐Range Weather Forecasts (ECMWF) ensemble prediction system, which are set up to disentangle the effects of initial conditions and physics perturbations. The results demonstrate that SPPT systematically increases the frequency of rapidly ascending air streams. The effect is observed globally, but is enhanced in regions where the latent heating along the trajectories is larger. Despite the frequency changes, there are only minor modifications to the physical properties of the trajectories due to SPPT. In contrast to SPPT, initial condition perturbations do not affect WCBs and tropical convection systematically. An Eulerian perspective on vertical velocities reveals that SPPT increases the frequency of strong upward motions compared with experiments with unperturbed model physics. Consistent with the altered vertical motions, precipitation rates are also affected by the model physics perturbations. The unperturbed control member shows the same characteristics as the experiments without SPPT regarding rapidly ascending air streams. We make use of this to corroborate the findings from the sensitivity experiments by analyzing the differences between perturbed and unperturbed members in operational ensemble forecasts of ECMWF. Finally, we give an explanation of how symmetric, zero‐mean perturbations can lead to a unidirectional response when applied in a nonlinear system.
    Description: The stochastically perturbed parametrisation tendencies (SPPT) scheme is used at ECMWF to perturb the model physics and introduces state‐dependent perturbations into the parametrisation tendencies. The frequency of rapidly ascending air streams is systematically enhanced when SPPT is active. This effect is stronger when the latent heating is large (panel a), and is therefore more pronounced in the Tropics than in the Extratropics. In contrast, the impact of SPPT on the physical properties of the air streams, such as the latent heat release, is very small (panel b).
    Description: Helmholtz Young Investigator Group ‘Sub‐ Seasonal Predictability: Understanding the Role of Diabatic Outflow’
    Keywords: ddc:551.5
    Language: English
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  • 9
    Publication Date: 2024-01-15
    Description: The formation of low stratus cloud over idealized hills is investigated using numerical model simulations. The main driver for the cloud formation is radiative cooling due to outgoing longwave radiation. Despite a purely horizontal flow, the advection terms in the prognostic equations for heat and moisture produce vertical mixing across the upper cloud edge, leading to a loss of cloud water content. This behavior is depicted via a budget analysis. More precisely, this spurious mixing is caused by the diffusive error of the advection scheme in regions where the sloping surfaces of the terrain‐following vertical coordinate intersect the cloud top. This study shows that the intensity of the (spurious) numerical diffusion depends strongly on the horizontal resolution, the order of the advection schemes, and the choice of scalar advection scheme. A large‐eddy simulation with 4‐m horizontal resolution serves as a reference. For horizontal resolutions of a few hundred meters and simulations carried out with a model setup as used in numerical weather prediction, a strong reduction of the simulated liquid‐water path is observed. In order to keep the (spurious) numerical diffusion at coarser resolutions small, at least a fifth‐order advection scheme should be used. In the present case, a weighted essentially nonoscillatory scalar advection scheme turns out to increase the numerical diffusion along a sharp cloud edge compared with an upwind scheme. Furthermore, the choice of vertical coordinate has a strong impact on the simulated liquid‐water path over orography. With a modified definition of the sigma coordinate, it is possible to produce cloud water where the classical sigma coordinate does not allow any cloud formation.
    Description: Diffusive errors of the advection scheme reduce the cloud water content of low stratus over idealized hills. This is due to the terrain‐following vertical coordinate and depends strongly on the horizontal resolution. Orographic features should be represented by at least 𝒪(10) grid points and a fifth‐order advection scheme (or higher) should be used. A weighted essentially nonoscillatory scalar advection scheme increases numerical diffusion along a sharp cloud edge compared with an upwind scheme. Modifying the definition of the sigma coordinate leads to a strong gain in the simulated liquid‐water path.
    Description: Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659
    Description: Hans Ertel Centre for Weather Research
    Keywords: ddc:551.5 ; advection ; fog ; low stratus ; resolution ; rolling terrain ; vertical coordinate
    Language: English
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  • 10
    Publication Date: 2022-03-31
    Description: Aerosol can affect clouds in various ways. Beside the microphysical impact of aerosol particles on cloud formation, the interference of aerosol with atmospheric radiation leads to changes in local heating, surface fluxes and thus mesoscale circulations, all of which may also modify clouds. Rather little is known about these so‐called semi‐direct effects in realistic settings – a reason why this study investigates the impact of absorbing aerosol particles on cloud and radiation fields over Germany. Using advanced high‐resolution simulations with grid spacings of 312 and 625 m, numerical experiments with different aerosol optical properties are contrasted using purely scattering aerosol as a control case and realistic absorbing aerosol as a perturbation. The combined effect of surface dimming and atmospheric heating induces positive temperature and negative moisture anomalies between 800 and 900 hPa, impacting low‐level cloud formation. Decreased relative humidity as well as increased atmospheric stability below clouds lead to a reduction of low‐level cloud cover, liquid water path and precipitation. It is further found that direct and semi‐direct effects of absorbing aerosol forcing have similar magnitudes and contribute equally to a reduction of net radiation at the top of the atmosphere.
    Description: Atmospheric aerosol particles can absorb solar radiation, altering the thermal structure of the atmosphere and surface fluxes. Using advanced high‐resolution simulations over Germany with grid spacings of 312 and 625 m, we find that boundary‐layer absorbing aerosol reduces low‐level cloud cover, liquid water path and precipitation. Direct and semi‐direct effects have similar magnitudes and contribute equally to a positive absorbing aerosol forcing.
    Description: German Ministry for Education and Research EU Horizon 2020 project CONSTRAIN
    Description: https://cera-www.dkrz.de/WDCC/ui/cerasearch/entry?acronym=DKRZ_LTA_1174_ds00001
    Keywords: ddc:551.5
    Language: English
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  • 11
    Publication Date: 2022-03-29
    Description: An idealized, three‐dimensional, numerical simulation of tropical cyclone evolution in a quiescent environment on an f‐plane is used to explore aspects of the cyclone's life cycle in the context of the rotating‐convection paradigm. In the 20‐day simulation, the vortex undergoes a life cycle including a gestation period culminating in genesis, a rapid intensification phase, a mature phase, a transient decay and re‐intensification phase, a second mature phase and a rapid decay phase. During much of the life cycle, the flow evolution is highly asymmetric, although important aspects of it can be understood within an azimuthally averaged framework, central to which are a boundary‐layer control mechanism and a new ventilation diagnostic. The boundary‐layer control mechanism provides an explanation for the gradual expansion of the inner core of the vortex. The ventilation diagnostic characterizes the ability of deep convection within a given radius to evacuate the mass of air ascending out of the boundary layer within that radius. The transient decay and re‐intensification phase is not associated with an eyewall replacement cycle, but rather with a hitherto undescribed process in which the eyewall becomes fragmented as a rainband complex forms beyond it. This process is interpreted as an interplay between the boundary layer and ventilation. The final rapid decay of the vortex results from the ever increasing difficulty of deep convection to ventilate the air exiting the boundary layer. Any unventilated air flows radially outwards in the lower troposphere and leads to spin‐down because of the approximate conservation of mean absolute angular momentum. If found in real cyclones, such transience or final decay might be erroneously attributed to ambient vertical wind shear. The results support the hypothesis that, even in a quiescent environment, isolated tropical cyclone vortices are intrinsically transient and never reach a globally steady state.
    Description: A three‐dimensional, idealized numerical simulation of tropical cyclone evolution on an f‐plane is used to explore aspects of the cyclone's life cycle in the framework of the rotating‐convection paradigm. In the simulation, which lasts for 20 days, the vortex undergoes a life cycle that includes a gestation period cultimating in genesis, a rapid intensification period, a mature stage followed by a transient decay and re‐intensification stage, a second mature stage and a final rapid decay stage. The results support the hypothesis that, even in a quiescent environment on an f‐plane, isolated tropical cyclone vortices are intrinsically transient and never reach a globally steady state.
    Description: U.S. Office of Naval Research http://dx.doi.org/10.13039/100000006
    Description: German Research Council
    Keywords: ddc:551.5
    Language: English
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