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.

The genetic signature of Neolithic in Greece

The Neolithic is characterized by the transition from a subsistence economy, based on hunting and gathering, to one based on food producing. This important change was paralleled by one of the most significant demographic increase in the recent history of European populations. The earliest Neolithic sites in Europe are located in Greece. However, the debate regarding the colonization route followed by the Middle-eastern farmers is still open. Based on archaeological, archaeobotanical, craniometric and genetic data, two main hypotheses have been proposed. The first implies the maritime colonization of North-eastern Peloponnesus from Crete, whereas the second points to an island hopping route that finally brought migrants to Central Greece. To test these hypotheses using a genetic approach, 206 samples were collected from the two Greek regions proposed as the arrival point of the two routes (Korinthian district and Euboea). Expectations for each hypothesis were compared with empirical observations based on the analysis of 60 SNPs and 26 microsatellite loci of Y-chromosome and mitochondrial DNA hypervariable region I. The analysis of Y-chromosome haplogroups revealed a strong genetic affinity of Euboea with Anatolian and Middle-eastern populations. The inferences of the time since population expansion suggests an earlier usage of agriculture in Euboea. Moreover, the haplogroup J2a-M410, supposed to be associated with the Neolithic transition, was observed at higher frequency and variance in Euboea showing, for both these parameters, a decreasing gradient moving from this area. The time since expansion estimates for J2a-M410 was found to be compatible with the Neolithic and slightly older in Euboea. The analysis of mtDNA resulted less informative. However, a higher genetic affinity of Euboea with Anatolian and Middle-eastern populations was confirmed. These results taken as a whole suggests that the most probable route followed by Neolithic farmers during the colonization of Greece was the island hopping route.