A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

A study on the fluid dynamics of domestic Gas burners

Domestic gas burners are investigated experimentally and numerically in order to further understand the fluid dynamics processes that drive the cooking appliance performances. In particular, a numerical simulation tool has been developed in order to predict the onset of two flame instabilities which may deteriorate the performances of the burner: the flame back and flame lift. The numerical model has been firstly validated by comparing the simulated flow field with a data set of experimental measurements. A prediction criterion for the flame back instability has been formulated based on isothermal simulations without involving the combustion modelization. This analysis has been verified by a Design Of Experiments investigation performed on different burner prototype geometries. On the contrary, the formulation of a prediction criterion regarding the flame lift instability has required the use of a combustion model in the numerical code. In this analysis, the structure and aerodynamics of the flame generated by a cooking appliance has thus been characterized by experimental and numerical investigations, in which, by varying the flow inlet conditions, the flame behaviour was studied from a stable reference case toward a complete blow-out.

Studio di fenomeni d'instabilità gravitativa sui fondali marini, con particolare riferimento all'isola di Stromboli

In the last decade the interest for submarine instability grew up, driven by the increasing exploitation of natural resources (primary hydrocarbons), the emplacement of bottom-lying structures (cables and pipelines) and by the development of coastal areas, whose infrastructures increasingly protrude to the sea. The great interest for this topic promoted a number of international projects such as: STEAM (Sediment Transport on European Atlantic Margins, 93-96), ENAM II (European North Atlantic Margin, 96-99), GITEC (Genesis and Impact of Tsunamis on the European Coast 92-95), STRATAFORM (STRATA FORmation on Margins, 95-01), Seabed Slope Process in Deep Water Continental Margin (Northwest Gulf of Mexico, 96-04), COSTA (Continental slope Stability, 00-05), EUROMARGINS (Slope Stability on Europe’s Passive Continental Margin), SPACOMA (04-07), EUROSTRATAFORM (European Margin Strata Formation), NGI's internal project SIP-8 (Offshore Geohazards), IGCP-511: Submarine Mass Movements and Their Consequences (05-09) and projects indirectly related to instability processes, such as TRANSFER (Tsunami Risk ANd Strategies For the European region, 06-09) or NEAREST (integrated observations from NEAR shore sourcES of Tsunamis: towards an early warning system, 06-09). In Italy, apart from a national project realized within the activities of the National Group of Volcanology during the framework 2000-2003 “Conoscenza delle parti sommerse dei vulcani italiani e valutazione del potenziale rischio vulcanico”, the study of submarine mass-movement has been underestimated until the occurrence of the landslide-tsunami events that affected Stromboli on December 30, 2002. This event made the Italian Institutions and the scientific community more aware of the hazard related to submarine landslides, mainly in light of the growing anthropization of coastal sectors, that increases the vulnerability of these areas to the consequences of such processes. In this regard, two important national projects have been recently funded in order to study coastal instabilities (PRIN 24, 06-08) and to map the main submarine hazard features on continental shelves and upper slopes around the most part of Italian coast (MaGIC Project). The study realized in this Thesis is addressed to the understanding of these processes, with particular reference to Stromboli submerged flanks. These latter represent a natural laboratory in this regard, as several kind of instability phenomena are present on the submerged flanks, affecting about 90% of the entire submerged areal and often (strongly) influencing the morphological evolution of subaerial slopes, as witnessed by the event occurred on 30 December 2002. Furthermore, each phenomenon is characterized by different pre-failure, failure and post-failure mechanisms, ranging from rock-falls, to turbidity currents up to catastrophic sector collapses. The Thesis is divided into three introductive chapters, regarding a brief review of submarine instability phenomena and related hazard (cap. 1), a “bird’s-eye” view on methodologies and available dataset (cap. 2) and a short introduction on the evolution and the morpho-structural setting of the Stromboli edifice (cap. 3). This latter seems to play a major role in the development of largescale sector collapses at Stromboli, as they occurred perpendicular to the orientation of the main volcanic rift axis (oriented in NE-SW direction). The characterization of these events and their relationships with successive erosive-depositional processes represents the main focus of cap.4 (Offshore evidence of large-scale lateral collapses on the eastern flank of Stromboli, Italy, due to structurally-controlled, bilateral flank instability) and cap. 5 (Lateral collapses and active sedimentary processes on the North-western flank of Stromboli Volcano), represented by articles accepted for publication on international papers (Marine Geology). Moreover, these studies highlight the hazard related to these catastrophic events; several calamities (with more than 40000 casualties only in the last two century) have been, in fact, the direct or indirect result of landslides affecting volcanic flanks, as observed at Oshima-Oshima (1741) and Unzen Volcano (1792) in Japan (Satake&Kato, 2001; Brantley&Scott, 1993), Krakatau (1883) in Indonesia (Self&Rampino, 1981), Ritter Island (1888), Sissano in Papua New Guinea (Ward& Day, 2003; Johnson, 1987; Tappin et al., 2001) and Mt St. Augustine (1883) in Alaska (Beget& Kienle, 1992). Flank landslide are also recognized as the most important and efficient mass-wasting process on volcanoes, contributing to the development of the edifices by widening their base and to the growth of a volcaniclastic apron at the foot of a volcano; a number of small and medium-scale erosive processes are also responsible for the carving of Stromboli submarine flanks and the transport of debris towards the deeper areas. The characterization of features associated to these processes is the main focus of cap. 6; it is also important to highlight that some small-scale events are able to create damage to coastal areas, as also witnessed by recent events of Gioia Tauro 1978, Nizza, 1979 and Stromboli 2002. The hazard potential related to these phenomena is, in fact, very high, as they commonly occur at higher frequency with respect to large-scale collapses, therefore being more significant in terms of human timescales. In the last chapter (cap. 7), a brief review and discussion of instability processes identified on Stromboli submerged flanks is presented; they are also compared with respect to analogous processes recognized in other submerged areas in order to shed lights on the main factors involved in their development. Finally, some applications of multibeam data to assess the hazard related to these phenomena are also discussed.

Slope stability analysis by multi-temporal DEMs and 3D modelling: The 2002 and 2007 Stromboli landslide events

Natural hazard related to the volcanic activity represents a potential risk factor, particularly in the vicinity of human settlements. Besides to the risk related to the explosive and effusive activity, the instability of volcanic edifices may develop into large landslides often catastrophically destructive, as shown by the collapse of the northern flank of Mount St. Helens in 1980. A combined approach was applied to analyse slope failures that occurred at Stromboli volcano. SdF slope stability was evaluated by using high-resolution multi-temporal DTMMs and performing limit equilibrium stability analyses. High-resolution topographical data collected with remote sensing techniques and three-dimensional slope stability analysis play a key role in understanding instability mechanism and the related risks. Analyses carried out on the 2002–2003 and 2007 Stromboli eruptions, starting from high-resolution data acquired through airborne remote sensing surveys, permitted the estimation of the lava volumes emplaced on the SdF slope and contributed to the investigation of the link between magma emission and slope instabilities. Limit Equilibrium analyses were performed on the 2001 and 2007 3D models, in order to simulate the slope behavior before 2002-2003 landslide event and after the 2007 eruption. Stability analyses were conducted to understand the mechanisms that controlled the slope deformations which occurred shortly after the 2007 eruption onset, involving the upper part of slope. Limit equilibrium analyses applied to both cases yielded results which are congruent with observations and monitoring data. The results presented in this work undoubtedly indicate that hazard assessment for the island of Stromboli should take into account the fact that a new magma intrusion could lead to further destabilisation of the slope, which may be more significant than the one recently observed because it will affect an already disarranged deposit and fractured and loosened crater area. The two-pronged approach based on the analysis of 3D multi-temporal mapping datasets and on the application of LE methods contributed to better understanding volcano flank behaviour and to be prepared to undertake actions aimed at risk mitigation.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Magma injections and destabilization of basaltic volcanoes: a numerical study. Application to La Reunion (Indian ocean, France) and Stromboli (Tyrrhenian sea, Italy)

Most basaltic volcanoes are affected by recurrent lateral instabilities during their evolution. Numerous factors have been shown to be involved in the process of flank destabilization occurring over long periods of time or by instantaneous failures. However, the role of these factors on the mechanical behaviour and stability of volcanic edifices is poorly-constrained as lateral failure usually results from the combined effects of several parameters. Our study focuses on the morphological and structural comparison of two end-member basaltic systems, La Reunion (Indian ocean, France) and Stromboli (southern Tyrrhenian sea, Italy). We showed that despite major differences on their volumes and geodynamic settings, both systems present some similarities as they are characterized by an intense intrusive activity along well-developed rift zones and recurrent phenomena of flank collapse during their evolution. Among the factors of instability, the examples of la Reunion and Stromboli evidence the major contribution of intrusive complexes to volcano growth and destruction as attested by field observations and the monitoring of these active volcanoes. Classical models consider the relationship between vertical intrusions of magma and flank movements along a preexisting sliding surface. A set of published and new field data from Piton des Neiges volcano (La Reunion) allowed us to recognize the role of subhorizontal intrusions in the process of flank instability and to characterize the geometry of both subvertical and subhorizontal intrusions within basaltic edifices. This study compares the results of numerical modelling of the displacements associated with high-angle and low-angle intrusions within basaltic volcanoes. We use a Mixed Boundary Element Method to investigate the mechanical response of an edifice to the injection of magmatic intrusions in different stress fields. Our results indicate that the anisotropy of the stress field favours the slip along the intrusions due to cointrusive shear stress, generating flank-scale displacements of the edifice, especially in the case of subhorizontal intrusions, capable of triggering large-scale flank collapses on basaltic volcanoes. Applications of our theoretical results to real cases of flank displacements on basaltic volcanoes (such as the 2007 eruptive crisis at La Reunion and Stromboli) revealed that the previous model of subvertical intrusions-related collapse is a likely mechanism affecting small-scale steeply-sloping basaltic volcanoes like Stromboli. Furthermore, our field study combined to modelling results confirms the importance of shallow-dipping intrusions in the morpho-structural evolution of large gently-sloping basaltic volcanoes like Piton de la Fournaise, Etna and Kilauea, with particular regards to flank instability, which can cause catastrophic tsunamis.

Solving the cooling flow problem through mechanical AGN feedback

A fundamental gap in the current understanding of collapsed structures in the universe concerns the thermodynamical evolution of the ordinary, baryonic component. Unopposed radiative cooling of plasma would lead to the cooling catastrophe, a massive inflow of condensing gas toward the centre of galaxies, groups and clusters. The last generation of multiwavelength observations has radically changed our view on baryons, suggesting that the heating linked to the active galactic nucleus (AGN) may be the balancing counterpart of cooling. In this Thesis, I investigate the engine of the heating regulated by the central black hole. I argue that the mechanical feedback, based on massive subrelativistic outflows, is the key to solving the cooling flow problem, i.e. dramatically quenching the cooling rates for several billion years without destroying the cool-core structure. Using an upgraded version of the parallel 3D hydrodynamic code FLASH, I show that anisotropic AGN outflows can further reproduce fundamental observed features, such as buoyant bubbles, cocoon shocks, sonic ripples, metals dredge-up, and subsonic turbulence. The latter is an essential ingredient to drive nonlinear thermal instabilities, which cause cold gas condensation, a residual of the quenched cooling flow and, later, fuel for the AGN feedback engine. The self-regulated outflows are systematically tested on the scales of massive clusters, groups and isolated elliptical galaxies: in lighter less bound objects the feedback needs to be gentler and less efficient, in order to avoid drastic overheating. In this Thesis, I describe in depth the complex hydrodynamics, involving the coupling of the feedback energy to that of the surrounding hot medium. Finally, I present the merits and flaws of all the proposed models, with a critical eye toward observational concordance.

Lateral spreading and associated slope processes in fractured rock slabs

Landslides of the lateral spreading type, involving brittle geological units overlying ductile terrains, are a common occurrence in the sandstone and limestone plateaux of the northern Apennines of Italy. These instability phenomena can become particularly risky, when historical towns and cultural heritage sites built on the top of them are endangered. Neverthless, the mechanisms controlling the developing of related instabilities, i.e. toppling and rock falls, at the edges of rock plateaux are not fully understood yet. In addition, the groundwater flow path developing at the contact between the more permeable units, i.e. the jointed rock slab, and the relatively impermeable clay-rich units have not been already studied in details, even if they may play a role in this kind of instability processes, acting as eventual predisposing and/or triggering factors. Field survey, Terrestrial Laser Scanner and Close Range Photogrammetry techniques, laboratory tests on the involved materials, hydrogeological monitoring and modelling, displacements evaluation and stability analysis through continuum and discontinuum numerical codes have been performed on the San Leo case study, with the aim to bring further insights for the understanding and the assessment of the slope processes taking place in this geological context. The current research permitted to relate the aquifer behaviour of the rocky slab to slope instability processes. The aquifer hosted in the fractured slab leads to the development of perennial and ephemeral springs at the contact between the two units. The related piping erosion phenomena, together with slope processes in the clay-shales led to the progressive undermining of the slab. The cliff becomes progressively unstable due to undermining and undergoes large-scale landslides due to fall or topple.