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.

Understanding block rotation of strike-slip fault zones: Paleomagnetic and structural approach

This thesis is focused on the paleomagnetic rotation pattern inside the deforming zone of strike-slip faults, and the kinematics and geodynamics describing it. The paleomagnetic investigation carried out along both the LOFZ and the fore-arc sliver (38º-42ºS, southern Chile) revealed an asymmetric rotation pattern. East of the LOFZ and adjacent to it, rotations are up to 170° clockwise (CW) and fade out ~10 km east of fault. West of the LOFZ at 42ºS (Chiloé Island) and around 39°S (Villarrica domain) systematic CCW rotations have been observed, while at 40°-41°S (Ranco-Osorno domain) and adjacent to the LOFZ CW rotations reach up to 136° before evolving to CCW rotations at ~30 km from the fault. These data suggest a directed relation with subduction interface plate coupling. Zones of high coupling yield to a wide deforming zone (~30 km) west of the LOFZ characterized by CW rotations. Low coupling implies a weak LOFZ and a fore-arc dominated by CCW rotations related to NW-sinistral fault kinematics. The rotation pattern is consistent with a quasi-continuous crust kinematics. However, it seems unlikely that the lower crust flux can control block rotation in the upper crust, considering the cold and thick fore-arc crust. I suggest that rotations are consequence of forces applied directly on both the block edges and along the main fault, within the upper crust. Farther south, at the Austral Andes (54°S) I measured the anisotropy of magnetic susceptibility (AMS) of 22 Upper Cretaceous to Upper Eocene sites from the Magallanes fold-thrust belt internal domains. The data document continuous compression from the Early Cretaceous until the Late Oligocene. AMS data also show that the tectonic inversion of Jurassic extensional faults during the Late Cretaceous compressive phase may have controlled the Cenozoic kinematic evolution of the Magallanes fold-thrust belt, yielding slip partitioning.