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P. F. J. Lermusiaux
A. R. Robinson


A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean–atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients.

Schemes for filtering and smoothing via ESSE are derived. The data–forecast melding minimizes variance in the error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is based on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures are made. The theoretical and practical advantages of ESSE are discussed. The concepts introduced by the subspace approach are as useful as the practical benefits. The formalism forms a theoretical basis for the intercomparison of reduced dimension assimilation methods and for the validation of specific assumptions for tailored applications. The subspace approach is useful for a wide range of purposes, including nonlinear field and error forecasting, predictability and stability studies, objective analyses, data-driven simulations, model improvements, adaptive sampling, and parameter estimation.

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Robert J. Trapp
Karen A. Kosiba
James N. Marquis
Matthew R. Kumjian
Stephen W. Nesbitt
Joshua Wurman
Paola Salio
Maxwell A. Grover
Paul Robinson
, and
Deanna A. Hence


On 10 November 2018, during the RELAMPAGO field campaign in Argentina, South America, a thunderstorm with supercell characteristics was observed by an array of mobile observing instruments, including three Doppler on Wheels radars. In contrast to the archetypal supercell described in the Glossary of Meteorology, the updraft rotation in this storm was rather short lived (~25 min), causing some initial doubt as to whether this indeed was a supercell. However, retrieved 3D winds from dual-Doppler radar scans were used to document a high spatial correspondence between midlevel vertical velocity and vertical vorticity in this storm, thus providing evidence to support the supercell categorization. Additional data collected within the RELAMPAGO domain revealed other storms with this behavior, which appears to be attributable in part to effects of the local terrain. Specifically, the IOP4 supercell and other short-duration supercell cases presented had storm motions that were nearly perpendicular to the long axis of the Sierras de Córdoba Mountains; a long-duration supercell case, on the other hand, had a storm motion nearly parallel to these mountains. Sounding observations as well as model simulations indicate that a mountain-perpendicular storm motion results in a relatively short storm residence time within the narrow zone of terrain-enhanced vertical wind shear. Such a motion and short residence time would limit the upward tilting, by the left-moving supercell updraft, of the storm-relative, antistreamwise horizontal vorticity associated with anabatic flow near complex terrain.

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