Abstract: The purpose of the present study is to explore the feasibility of estimating and correcting systematic model errors using a simple and efficient procedure, inspired by papers by Leith as well as DelSole and Hou, that could be applied operationally, and to compare the impact of correcting the model integration with statistical corrections performed a posteriori. An elementary data assimilation scheme (Newtonian relaxation) is used to compare two simple but realistic global models, one quasigeostrophic and one based on the primitive equations, to the NCEP reanalysis (approximating the real atmosphere). The 6-h analysis corrections are separated into the model bias (obtained by time averaging the errors over several years), the periodic (seasonal and diurnal) component of the errors, and the nonperiodic errors. An estimate of the systematic component of the nonperiodic errors linearly dependent on the anomalous state is generated.Forecasts corrected during model integration with a seasonally dependent estimate of the bias remain useful longer than forecasts corrected a posteriori. The diurnal correction (based on the leading EOFs of the analysis corrections) is also successful. State-dependent corrections using the full-dimensional Leith scheme and several years of training actually make the forecasts worse due to sampling errors in the estimation of the covariance. A sparse approximation of the Leith covariance is derived using univariate and spatially localized covariances. The sparse Leith covariance results in small regional improvements, but is still computationally prohibitive. Finally, singular value decomposition is used to obtain the coupled components of the correction and forecast anomalies during the training period. The corresponding heterogeneous correlation maps are used to estimate and correct by regression the state-dependent errors during the model integration. Although the global impact of this computationally efficient method is small, it succeeds in reducing state-dependent model systematic errors in regions where they are large. The method requires only a time series of analysis corrections to estimate the error covariance and uses negligible additional computation during a forecast. As a result, it should be suitable for operational use at relatively small computational expense.
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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).