Víctor J. García-Garrido

Bio: Víctor J. García-Garrido is an academic researcher from University of Alcalá. The author has contributed to research in topics: Phase space & Hamiltonian system. The author has an hindex of 12, co-authored 42 publications receiving 414 citations. Previous affiliations of Víctor J. García-Garrido include Spanish National Research Council & Autonomous University of Madrid.

A Theoretical Framework for Lagrangian Descriptors

Abstract: This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by i...

Lagrangian coherent structure assisted path planning for transoceanic autonomous underwater vehicle missions.

Abstract: Transoceanic Gliders are Autonomous Underwater Vehicles (AUVs) for which there is a developing and expanding range of applications in open-seas research, technology and underwater clean transport. Mature glider autonomy, operating depth (0–1000 meters) and low energy consumption without a CO2 footprint enable evolutionary access across ocean basins. Pursuant to the first successful transatlantic glider crossing in December 2009, the Challenger Mission has opened the door to long-term, long-distance routine transoceanic AUV missions. These vehicles, which glide through the water column between 0 and 1000 meters depth, are highly sensitive to the ocean current field. Consequently, it is essential to exploit the complex space-time structure of the ocean current field in order to plan a path that optimizes scientific payoff and navigation efficiency. This letter demonstrates the capability of dynamical system theory for achieving this goal by realizing the real-time navigation strategy for the transoceanic AUV named Silbo, which is a Slocum deep-glider (0–1000 m), that crossed the North Atlantic from April 2016 to March 2017. Path planning in real time based on this approach has facilitated an impressive speed up of the AUV to unprecedented velocities resulting in major battery savings on the mission, offering the potential for routine transoceanic long duration missions.

A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370

Abstract: . The disappearance of Malaysia Airlines flight MH370 on the morning of 8 March 2014 is one of the great mysteries of our time. Perhaps the most relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out for roughly 2 months following the crash. Difficulties in the search efforts, due to the uncertainty of the plane's final impact point and the time that had passed since the accident, bring the question on how the debris scattered in an always moving ocean, for which there are multiple data sets that do not uniquely determine its state. Our approach to this problem is based on the use of Lagrangian descriptors (LD), a novel mathematical tool coming from dynamical systems theory that identifies dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the Australian Maritime Safety Authority (AMSA), and determining regions where one might have expected impact debris to be located, which were not subjected to any exploration.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

Abstract: Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization

Abstract: If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

The major stratospheric final warming in 2016: dispersal of vortex air and termination of Arctic chemical ozone loss

Abstract: . The 2015/16 Northern Hemisphere winter stratosphere appeared to have the greatest potential yet seen for record Arctic ozone loss. Temperatures in the Arctic lower stratosphere were at record lows from December 2015 through early February 2016, with an unprecedented period of temperatures below ice polar stratospheric cloud thresholds. Trace gas measurements from the Aura Microwave Limb Sounder (MLS) show that exceptional denitrification and dehydration, as well as extensive chlorine activation, occurred throughout the polar vortex. Ozone decreases in 2015/16 began earlier and proceeded more rapidly than those in 2010/11, a winter that saw unprecedented Arctic ozone loss. However, on 5–6 March 2016 a major final sudden stratospheric warming ("major final warming", MFW) began. By mid-March, the mid-stratospheric vortex split after being displaced far off the pole. The resulting offspring vortices decayed rapidly preceding the full breakdown of the vortex by early April. In the lower stratosphere, the period of temperatures low enough for chlorine activation ended nearly a month earlier than that in 2011 because of the MFW. Ozone loss rates were thus kept in check because there was less sunlight during the cold period. Although the winter mean volume of air in which chemical ozone loss could occur was as large as that in 2010/11, observed ozone values did not drop to the persistently low values reached in 2011. We use MLS trace gas measurements, as well as mixing and polar vortex diagnostics based on meteorological fields, to show how the timing and intensity of the MFW and its impact on transport and mixing halted chemical ozone loss. Our detailed characterization of the polar vortex breakdown includes investigations of individual offspring vortices and the origins and fate of air within them. Comparisons of mixing diagnostics with lower-stratospheric N2O and middle-stratospheric CO from MLS (long-lived tracers) show rapid vortex erosion and extensive mixing during and immediately after the split in mid-March; however, air in the resulting offspring vortices remained isolated until they disappeared. Although the offspring vortices in the lower stratosphere survived longer than those in the middle stratosphere, the rapid temperature increase and dispersal of chemically processed air caused active chlorine to quickly disappear. Furthermore, ozone-depleted air from the lower-stratospheric vortex core was rapidly mixed with ozone rich air from the vortex edge and midlatitudes during the split. The impact of the 2016 MFW on polar processing was the latest in a series of unexpected events that highlight the diversity of potential consequences of sudden warming events for Arctic ozone loss.