TY - JOUR A1 - Kuhlbrodt, Till A1 - Névir, Peter T1 - Low-order point vortex models of atmospheric blocking N2 - Conceptual models of blocking structures are constructed by reducing the twodimensional atmospheric vorticity field to a few point vortices. The flow is assumed to be barotropic and divergence-free, and a blocking event is represented by a point vortex dipole. The focus is here on the motion of the blocking dipole under the influence of the zonal mean flow. This is modelled in three different ways: A dipole embedded in a latitude-dependent zonal mean flow exhibits neutrally stable oscillations; their period is estimated analytically. A cyclonic point vortex approaching from upstream can either pass the dipole or break it up, so that an $Omega$-shaped pattern of three vortices emerges. The stationarity of a blocking between two troughs is modelled by four point vortices. These low-order point vortex models are compared with the dynamics of real blockings in case studies. Despite their high degree of simplification, those models reproduce the kinematics of blocking events properly. This results from the discretization of the flow to its actual physical states, the vortices, in contrast to the common, purely mathematical discretization to grid points. Thus, point vortex dynamics are proposed to be a powerful completion of continuous fluid dynamics in explaining blocking events. Y1 - 2000 ER - TY - JOUR A1 - Kuhlbrodt, Till A1 - Titz, Sven Holger A1 - Feudel, Ulrike A1 - Rahmstorf, Stefan T1 - A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing N2 - Aspects of open ocean deep convection variability are explored with a two-box model. In order to place the model in a region of parameter space relevant to the real ocean, it is fitted to observational data from the Labrador Sea. A systematic fit to OWS Bravo data allows us to determine the model parameters and to locate the position of the Labrador Sea on a stability diagram. The model suggests that the Labrador Sea is in a bistable regime where winter convection can be either ?on? or ?off?, with both these possibilities being stable climate states. When shifting the surface buoyancy forcing slightly to warmer or fresher conditions, the only steady solution is one without winter convection. We then introduce short-term variability by adding a noise term to the surface temperature forcing, turning the box model into a stochastic climate model. The surface forcing anomalies generated in this way induce jumps between the two model states. These state transitions occur on the interannual to decadal timescale. Changing the average surface forcing towards more buoyant conditions lowers the frequency of convection. However, convection becomes more frequent with stronger variability in the surface forcing. As part of the natural variability, there is a non-negligible probability for decadal interruptions of convection. The results highlight the role of surface forcing variability for the persistence of convection in the ocean. Y1 - 2001 SN - 1616-7341 ER - TY - JOUR A1 - Kuhlbrodt, Till A1 - Monahan, A. H. T1 - Stochastic stability of open-ocean deep convection N2 - Open-ocean deep convection is a highly variable and strongly nonlinear process that plays an essential role in the global ocean circulation. A new view of its stability is presented here, in which variability, as parameterized by stochastic forcing, is central. The use of an idealized deep convection box model allows analytical solutions and straightforward conceptual understanding while retaining the main features of deep convection dynamics. In contrast to the generally abrupt stability changes in deterministic systems, measures of stochastic stability change smoothly in response to varying forcing parameters. These stochastic stability measures depend chiefly on the residence times of the system in different regions of phase space, which need not contain a stable steady state in the deterministic sense. Deep convection can occur frequently even for parameter ranges in which it is deterministically unstable; this effect is denoted wandering unimodality. The stochastic stability concepts are readily applied to other components of the climate system. The results highlight the need to take climate variability into account when analyzing the stability of a climate state Y1 - 2003 SN - 0022-3670 ER - TY - JOUR A1 - Titz, Sven Holger A1 - Kuhlbrodt, Till A1 - Feudel, Ulrike T1 - Grid geometry effects on convection in ocean climate models : a conceptual study N2 - Ocean convection is a highly non-linear and local process. Typically, a small-scale phenomenon of this kind entails numerical problems in the modelling of ocean circulation. One of the tasks to solve is the improvement of convection parameterization schemes, but the question of grid geometry also plays a considerable role. Here, this question is studied in the context of global ocean models coupled to an atmosphere model. Such ocean climate models have mostly structured, coarsely resolved grids. Using a simple conceptual two-layer model, we compare the discretization effects of a rectangular grid with those of a grid with hexagonal grid cells, focussing on average properties of the ocean. It turns out that systematic errors tend to be clearly smaller with the hexagonal grid. In a hysteresis experiment with the atmospheric boundary condition as a hysteresis parameter, the spatially averaged behaviour shows nonnegligible artificial steps for quadratic grid cells. This bias is reduced with the hexagonal grid. The same holds for the directional sensitivity (or horizontal anisotropy) which is found for different angles of the advection velocity. The grid with hexagonal grid cells shows much more isotropic results. From the limited viewpoint of these test experiments, it seems that the hexagonal grid (i.e. icosahedral-hexagonal grids on the sphere) is recommendable for ocean climate models. (C) 2003 Elsevier Ltd. All rights reserved Y1 - 2004 SN - 1463-5003 ER - TY - JOUR A1 - Lind, P. G. A1 - Titz, Sven Holger A1 - Kuhlbrodt, Till A1 - Corte-Real, J. A. M. A1 - Kurths, Jürgen A1 - Gallas, J. A. C. A1 - Feudel, Ulla T1 - Coupled bistable maps : a tool to study convection parameterization in ocean models N2 - We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling Y1 - 2004 SN - 0218-1274 ER - TY - THES A1 - Kuhlbrodt, Till T1 - Stability and variability of open-ocean deep convection in deterministic and stochastic simple models N2 - Die Tiefenkonvektion ist ein wesentlicher Bestandteil der Zirkulation im Nordatlantik. Sie beeinflusst den nordwärtigen Wärmetransport der thermohalinen Zirkulation. Ein Verständnis ihrer Stabilität und Variabilität ist daher nötig, um Klimaveränderungen im Bereich des Nordatlantiks einschätzen zu können. Diese Arbeit hat zum Ziel, das konzeptionelle Verständnis der Stabilität und der Variabilität der Tiefenkonvektion zu verbessern. Beobachtungsdaten aus der Labradorsee zeigen Phasen mit und ohne Tiefenkonvektion. Ein einfaches Modell mit zwei Boxen wird an diese Daten angepasst. Das Ergebnis legt nahe, dass die Labradorsee zwei koexistierende stabile Zustände hat, einen mit regelmäßiger Tiefenkonvektion und einen ohne Tiefenkonvektion. Diese Bistabilität ergibt sich aus einer positiven Salzgehalts-Rückkopplung, deren Ursache ein Netto-Süßwassereintrag in die Deckschicht ist. Der konvektive Zustand kann schnell instabil werden, wenn der mittlere Antrieb sich hin zu wärmeren oder weniger salzhaltigen Bedingungen ändert. Die wetterbedingte Variabilität des externen Antriebs wird durch die Addition eines stochastischen Antriebsterms in das Modell eingebaut. Es zeigt sich, dass dann die Tiefenkonvektion häufig an- und wieder ausgeschaltet wird. Die mittlere Aufenthaltszeit in beiden Zuständen ist ein Maß ihrer stochastischen Stabilität. Die stochastische Stabilität hängt in glatter Weise von den Parametern des Antriebs ab, im Gegensatz zu der deterministischen (nichtstochastischen) Stabilität, die sich abrupt ändern kann. Sowohl das Mittel als auch die Varianz des stochastischen Antriebs beeinflussen die Häufigkeit von Tiefenkonvektion. Eine Abnahme der Konvektionshäufigkeit, als Reaktion auf eine Abnahme des Salzgehalts an der Oberfläche, kann zum Beispiel durch eine Zunahme der Variabilität in den Wärmeflüssen kompensiert werden. Mit einem weiter vereinfachten Box-Modell werden einige Eigenschaften der stochastischen Stabilität analytisch untersucht. Es wird ein neuer Effekt beschrieben, die wandernde Monostabilität: Auch wenn die Tiefenkonvektion aufgrund geänderter Parameter des Antriebs kein stabiler Zustand mehr ist, kann der stochastische Antrieb immer noch häufig Konvektionsereignisse auslösen. Die analytischen Gleichungen zeigen explizit, wie die wandernde Monostabilität sowie andere Effekte von den Modellparametern abhängen. Diese Abhängigkeit ist für die mittleren Aufenthaltszeiten immer exponentiell, für die Wahrscheinlichkeit langer nichtkonvektiver Phasen dagegen nur dann, wenn diese Wahrscheinlichkeit gering ist. Es ist zu erwarten, dass wandernde Monostabilität auch in anderen Teilen des Klimasystems eine Rolle spielt. Insgesamt zeigen die Ergebnisse, dass die Stabilität der Tiefenkonvektion in der Labradorsee sehr empfindlich auf den Antrieb reagiert. Die Rolle der Variabilität ist entscheidend für ein Verständnis dieser Empfindlichkeit. Kleine Änderungen im Antrieb können bereits die Häufigkeit von Tiefenkonvektionsereignissen deutlich mindern, was sich vermutlich stark auf das regionale Klima auswirkt. N2 - Deep convection is an essential part of the circulation in the North Atlantic Ocean. It influences the northward heat transport achieved by the thermohaline circulation. Understanding its stability and variability is therefore necessary for assessing climatic changes in the area of the North Atlantic. This thesis aims at improving the conceptual understanding of the stability and variability of deep convection. Observational data from the Labrador Sea show phases with and without deep convection. A simple two-box model is fitted to these data. The results suggest that the Labrador Sea has two coexisting stable states, one with regular deep convection and one without deep convection. This bistability arises from a positive salinity feedback that is due to the net freshwater input into the surface layer. The convecting state can easily become unstable if the mean forcing shifts to warmer or less saline conditions. The weather-induced variability of the external forcing is included into the box model by adding a stochastic forcing term. It turns out that deep convection is then switched "on" and "off" frequently. The mean residence time in either state is a measure of its stochastic stability. The stochastic stability depends smoothly on the forcing parameters, in contrast to the deterministic (non-stochastic) stability which may change abruptly. The mean and the variance of the stochastic forcing both have an impact on the frequency of deep convection. For instance, a decline in convection frequency due to a surface freshening may be compensated for by an increased heat flux variability. With a further simplified box model some stochastic stability features are studied analytically. A new effect is described, called wandering monostability: even if deep convection is not a stable state due to changed forcing parameters, the stochastic forcing can still trigger convection events frequently. The analytical expressions explicitly show how wandering monostability and other effects depend on the model parameters. This dependence is always exponential for the mean residence times, but for the probability of long nonconvecting phases it is exponential only if this probability is small. It is to be expected that wandering monostability is relevant in other parts of the climate system as well. All in all, the results demonstrate that the stability of deep convection in the Labrador Sea reacts very sensitively to the forcing. The presence of variability is crucial for understanding this sensitivity. Small changes in the forcing can already significantly lower the frequency of deep convection events, which presumably strongly affects the regional climate. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2003 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam. KW - Labradorsee ; Thermohaline Konvektion ; Stochastisches Modell KW - Stochastische dynamische Systeme KW - Nichtlineare Dynamik KW - Bistabilität KW - Nordatlantik KW - Stochastic dynamical systems KW - Nonlinear dynamics KW - Bistability KW - North Atlantic Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000622 ER -