Download Variational Methods in Geosciences by YOSHI K. SASAKI (Eds.) PDF

By YOSHI K. SASAKI (Eds.)

The previous couple of many years have visible a excellent progress within the use of variational tools, essentially the most vintage and chic equipment in actual and mathematical sciences, as robust instruments of optimization and numerical research. The great accumulation of knowledge at the use of variational equipment within the zone of the geosciences, which include meteorology, oceanography, hydrology, geophysics and seismology, indicated the necessity for the 1st symposium on Variational tools in Geosciences to be equipped and held in Norman on October 15-17, 1985. the worth of this symposium used to be greater through the variety of stimulating and informative papers provided

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Variational Methods in Geosciences

The previous couple of many years have noticeable a incredible progress within the use of variational tools, essentially the most vintage and chic equipment in actual and mathematical sciences, as strong instruments of optimization and numerical research. The great accumulation of data at the use of variational equipment within the sector of the geosciences, together with meteorology, oceanography, hydrology, geophysics and seismology, indicated the necessity for the 1st symposium on Variational equipment in Geosciences to be geared up and held in Norman on October 15-17, 1985.

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Ray, P . , Z i e g l e r , C, W. Bumgarner and S e r a f i n , R. (1980): S i n g l e and m u l t i p l e d o p p l e r - r a d a r o b s e r v a t i o n s of t o r n a d i c s t o r m s . Mon. Wea. R e v . , 108, 1607-1625. S a s a k i , Y . K . , 1955: A fundamental study of t h e numerical p r e d i c t i o n based on the v a r i a t i o n a l p r i n c i p l e . J . Meteor. S o c . J a p a n , 33, 262-275. S a s a k i , Y . K . , 1958: An o b j e c t i v e a n a l y s i s based on t h e v a r i a t i o n a l method.

USE OF VARIATIONAL METHODS TO ENFORCE 'A POSTERIORI' CONSERVATION OF INTEGRAL INVARIANTS Sasaki (1975, 1976) proposed a variational approach for enforcing 'a p o s t e r i o r i ' c o n s t r a i n t s of mass and t o t a l energy c o n s e r v a t i o n when s o l v i n g the shallow-water equations. B a y l i s s and I s a a c s o n (1975) and I s a a c s o n (1977) i n d e ­ pendently proposed to 1 i n e a r i z e the c o n s e r v a t i v e c o n s t r a i n t s about the p r e d i c t e d v a l u e s by a g r a d i e n t method a l s o w i t h the view of e n f o r c i n g i n t e g r a l conservation.

O p t i m i z . Theory and Appl. V o l . 3 . 5, 3 6 1 - 3 8 1 . Navon, I . M . , 1981: Implementation of a p o s t e r i o r i methods f o r e n f o r c i n g c o n ­ s e r v a t i o n of p o t e n t i a l enstrophy and mass i n d i s c r e t i z e d s h a l l o w - w a t e r e q u a t i o n models. Mon. Wea. R e v . , V o l . 109, 946-958. Navon, I . M . , 1982a: A p o s t e r i o r i numerical techniques f o r e n f o r c i n g s i m u l t a nious c o n s e r v a t i o n of i n t e g r a l i n v a r i a n t s upon f i n i t e - d i f f e r e n c e s h a l l o w water e q u a t i o n s models.

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