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Philip D. Thompson

Abstract

This paper is concerned with calculating the nonlinear transfer and partition of energy in a triad of interacting modes of a two-dimensional viscous flow, driven by random sources and sinks of vorticity. Our approach to the problem lies in deriving a moment expansion from the Fokker-Planck equation for the equilibrium probability distribution of a large ensemble of such flows. For sufficiently small values of a set of dimensionless “ordering-parameters,” depending only on given external conditions, the moment expansion is convergent. A remarkably simple relation between the fourth and fifth moments leads to a tractable “sixth- moment discard” closure, which is in some respects similar to the “eddy-damped, quasi-normal” approximation, but has a clearer theoretical basis.

The accuracy of the “sixth-moment discard” closure is judged by comparing the theoretically-derived kinetic energy and energy-transfer spectra with those constructed from a large ensemble of numerical integrations of the original evolution equations. For nonhomogencous forcing corresponding to “ordering parameters” only slightly less than unity, the theoretical and numerical results agree to within about 5%.

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Philip D. Thompson

Abstract

A method is proposed whereby incorrect analyses at two successive times may be optimally adjusted to maintain dynamical consistency with a given prediction model. It is shown that, in the ensemble average, the mean-square error of the adjusted analyses is half that of the original analyses.

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Philip D. Thompson
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Philip D. Thompson

Abstract

Starting with the vorticity equation for barotropic flow, we derive a system of stochastic differential equations that determines the time-evolution of the local variance of vorticity error originating in a large ensemble of initial states containing random and statistically isotropic initial errors. Those equations show that the local growth or decay of error variance depends primarily on the detailed structure of the true vorticity field; in general, the most rapid growth of error can be expected in concentrated regions of strong vorticity gradient.

Those stochastic differential equations provide the basis for a simple method of stochastic-dynamic prediction. It requires only a modest increase over the total volume of computation for deterministic prediction.

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Werner A. Baum and Philip D. Thompson

Soviet developments in long-range weather forecasting are described and evaluated. Part I (by W. A. Baum), dealing with non-dynamical methods, is based entirely on a literature survey. Part II (by P. D. Thompson), dealing with dynamical methods, is based partially on direct contact with Russian colleagues.

Operational forecasts based upon the synoptic-empirical Multanovsky method, as modified during the last generation, appear to have been unsuccessful. This apparent failure, only very recently admitted, seems to stem in part from an almost blind adherence to the complex and somewhat mystical Multanovsky philosophy. There are definite indications that a sharp break with the past took place in the mid-fifties, but it is too soon to discern a clear trend or to estimate the impact of this break on operational capabilities. No attempts appear to have been made to apply modern statistical approaches to the problem.

Soviet understanding of the basic theory of dynamical long-range prediction does not seem to surpass ours. However, Russian meteorologists have been relatively forward-looking in the application of dynamical methods on an experimental or routine basis. Forecasts of surface mean monthly temperature anomalies, for the Eurasian continent, have been prepared by dynamical methods since 1952. Their accuracy appears not significantly different from that of subjective forecasts.

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Owen E. Thompson, Philip A. Arkin, and William D. Bonner

Abstract

A comprehensive summary of diurnal wind variations in the midwestern region of the United States is presented. Analyses are based on seven summers of four per day soundings at Fort Worth, Tex., Topeka, Kan., and International Falls, Minn. It is found that the diurnal oscillations are most prominent at Fort Worth, of significant amplitude at Topeka, and, although of lesser amplitude, still detectable at International Falls. An analysis is made of the forcing required to account for that part of the wind oscillation which cannot be attributed to Coriolis effects. This analysis indicates that the forcing is comparatively small at Fort Worth when the wind oscillations are largest owing to a resonance there with natural inertial oscillations. Significant forcing is present at higher latitude stations even though the manifestation of the forcing in the wind field is somewhat smaller in amplitude. The data suggest that forcing mechanisms at low and high attitudes may propagate to cause wind oscillations in the middle levels.

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1st. Lt. Philip D. Thompson, A. C.
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Gregory C. Johnson, Rick Lumpkin, Simone R. Alin, Dillon J. Amaya, Molly O. Baringer, Tim Boyer, Peter Brandt, Brendan R. Carter, Ivona Cetinić, Don P. Chambers, Lijing Cheng, Andrew U. Collins, Cathy Cosca, Ricardo Domingues, Shenfu Dong, Richard A. Feely, Eleanor Frajka-Williams, Bryan A. Franz, John Gilson, Gustavo Goni, Benjamin D. Hamlington, Josefine Herrford, Zeng-Zhen Hu, Boyin Huang, Masayoshi Ishii, Svetlana Jevrejeva, John J. Kennedy, Marion Kersalé, Rachel E. Killick, Peter Landschützer, Matthias Lankhorst, Eric Leuliette, Ricardo Locarnini, John M. Lyman, John J. Marra, Christopher S. Meinen, Mark A. Merrifield, Gary T. Mitchum, Ben I. Moat, R. Steven Nerem, Renellys C. Perez, Sarah G. Purkey, James Reagan, Alejandra Sanchez-Franks, Hillary A. Scannell, Claudia Schmid, Joel P. Scott, David A. Siegel, David A. Smeed, Paul W. Stackhouse, William Sweet, Philip R. Thompson, Joaquin A. Triñanes, Denis L. Volkov, Rik Wanninkhof, Robert A. Weller, Caihong Wen, Toby K. Westberry, Matthew J. Widlansky, Anne C. Wilber, Lisan Yu, and Huai-Min Zhang
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Gregory C. Johnson, Rick Lumpkin, Tim Boyer, Francis Bringas, Ivona Cetinić, Don P. Chambers, Lijing Cheng, Shenfu Dong, Richard A. Feely, Baylor Fox-Kemper, Eleanor Frajka-Williams, Bryan A. Franz, Yao Fu, Meng Gao, Jay Garg, John Gilson, Gustavo Goni, Benjamin D. Hamlington, Helene T. Hewitt, William R. Hobbs, Zeng-Zhen Hu, Boyin Huang, Svetlana Jevrejeva, William E. Johns, Sato Katsunari, John J. Kennedy, Marion Kersalé, Rachel E. Killick, Eric Leuliette, Ricardo Locarnini, M. Susan Lozier, John M. Lyman, Mark A. Merrifield, Alexey Mishonov, Gary T. Mitchum, Ben I. Moat, R. Steven Nerem, Dirk Notz, Renellys C. Perez, Sarah G. Purkey, Darren Rayner, James Reagan, Claudia Schmid, David A. Siegel, David A. Smeed, Paul W. Stackhouse, William Sweet, Philip R. Thompson, Denis L. Volkov, Rik Wanninkhof, Robert A. Weller, Caihong Wen, Toby K. Westberry, Matthew J. Widlansky, Josh K. Willis, Lisan Yu, and Huai-Min Zhang
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Molly Baringer, Mariana B. Bif, Tim Boyer, Seth M. Bushinsky, Brendan R. Carter, Ivona Cetinić, Don P. Chambers, Lijing Cheng, Sanai Chiba, Minhan Dai, Catia M. Domingues, Shenfu Dong, Andrea J. Fassbender, Richard A. Feely, Eleanor Frajka-Williams, Bryan A. Franz, John Gilson, Gustavo Goni, Benjamin D. Hamlington, Zeng-Zhen Hu, Boyin Huang, Masayoshi Ishii, Svetlana Jevrejeva, William E. Johns, Gregory C. Johnson, Kenneth S. Johnson, John Kennedy, Marion Kersalé, Rachel E. Killick, Peter Landschützer, Matthias Lankhorst, Tong Lee, Eric Leuliette, Feili Li, Eric Lindstrom, Ricardo Locarnini, Susan Lozier, John M. Lyman, John J. Marra, Christopher S. Meinen, Mark A. Merrifield, Gary T. Mitchum, Ben Moat, Didier Monselesan, R. Steven Nerem, Renellys C. Perez, Sarah G. Purkey, Darren Rayner, James Reagan, Nicholas Rome, Alejandra Sanchez-Franks, Claudia Schmid, Joel P. Scott, Uwe Send, David A. Siegel, David A. Smeed, Sabrina Speich, Paul W. Stackhouse Jr., William Sweet, Yuichiro Takeshita, Philip R. Thompson, Joaquin A. Triñanes, Martin Visbeck, Denis L. Volkov, Rik Wanninkhof, Robert A. Weller, Toby K. Westberry, Matthew J. Widlansky, Susan E. Wijffels, Anne C. Wilber, Lisan Yu, Weidong Yu, and Huai-Min Zhang
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