Abstract: The purpose of the present study is to use a new method of empirical model error correction, developed by Danforth et al. in 2007, based on estimating the systematic component of the nonperiodic errors linearly dependent on the anomalous state. The method uses singular value decomposition (SVD) to generate a basis of model errors and states. It requires only a time series of errors to estimate covariances and uses negligible additional computation during a forecast integration. As a result, it should be suitable for operational use at a relatively small computational expense. The method is tested with the Lorenz ’96 coupled system as the truth and an uncoupled version of the same system as a model. The authors demonstrate that the SVD method explains a significant component of the effect that the model’s unresolved state has on the resolved state and shows that the results are better than those obtained with Leith’s empirical correction operator. The improvement is attributed to the fact that the SVD truncation effectively reduces sampling errors. Forecast improvements of up to 1000% are seen when compared with the original model. The improvements come at the expense of weakening ensemble spread.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).