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.

La psicologia della Gestalt. Ricerche teoriche e sperimentali sulla percezione sonora e musicale (1890-1939)

The aim of the present work is a historical survey on Gestalt trends in psychological research between late 19th and the first half of 20th century with privileged reference to sound and musical perception by means of a reconsideration of experimental and theoretical literature. Ernst Mach and Christian von Ehrenfels gave rise to the debate about Gestaltqualität which notably grew thanks to the ‘Graz School’ (Alexius Meinong, Stephan Witasek, Anton Faist, Vittorio Benussi), where the object theory and the production theory of perception were worked out. Stumpf’s research on Tonpsychologie and Franz Brentano’s tradition of ‘act psychology’ were directly involved in this debate, opposing to Wilhelm Wundt’s conception of the discipline; this clearly came to light in Stumpf’s controversy with Carl Lorenz and Wundt on Tondistanzen. Stumpf’s concept of Verschmelzung and his views about consonance and concordance led him to some disputes with Theodor Lipps and Felix Krueger, lasting more than two decades. Carl Stumpf was responsible for education of a new generation of scholars during his teaching at the Berlin University: his pupils Wolfgang Köhler, Kurt Koffka and Max Wertheimer established the so-called ‘Berlin School’ and promoted the official Gestalt theory since the 1910s. After 1922 until 1938 they gave life and led together with other distinguished scientists the «Psychologische Forschung», a scientific journal in which ‘Gestalt laws’ and many other acoustical studies on different themes (such as sound localization, successive comparison, phonetic phenomena) were exposed. During the 1920s Erich Moritz von Hornbostel gave important contributions towards the definition of an organic Tonsystem in which sound phenomena could find adequate arrangement. Last section of the work contains descriptions of Albert Wellek’s studies, Kurt Huber’s vowel researches and aspects of melody perception, apparent movement and phi-phenomenon in acoustical field. The work contains also some considerations on the relationships among tone psychology, musical psychology, Gestalt psychology, musical aesthetics and musical theory. Finally, the way Gestalt psychology changed earlier interpretations is exemplified by the decisive renewal of perception theory, the abandon of Konstanzannahme, some repercussions on theory of meaning as organization and on feelings in musical experience.