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245

Elsevier Science Publishers B.V., Amsterdam--Printed in The Netherlands

Book Reviews ATMOSPHERIC SCIENCE L. Bengtsson, M. Ghil and E. K~llen (Editors), 1981 .Dynamic Methodology. Data Assimilation Methods. Applied Mathematical Sciences, 36. Springer-Verlag, New York, ix + 330 pp., DM 44.00, approx. US $20.50 (paperback). The European Centre for Medium Range Weather Forecasts has conducted annually for some years seminars focussing on current problems in large scale numerical weather prediction. The seminar in 1980 was devoted to procedures of data assimilation and the present book contains seven of the lectures from that seminar. Data assimilation reprosents a merging of two traditionally separate functions in the process of numerical m e t e o r o l o g y , i.e., o b j e c t i v e n u m e r i c a l analyses and numerical weather prediction. The commonly used term of four-dimensional data assimilation acknowledges this explicitly; this term refers to intermittent merging of data of both conventional synoptic and space-based asynoptic observations with the continuing integration of the numerical prediction model thereby prov i d i n g an analysis of data arbitrarily distributed both in space and time. The seven lectures in the book have been well chosen and highlight both the current procedures and requirements in data assimilation and development currently in progress. The first paper, " A n Overview of Meteorological Data Assimilation" by P. Morel

0012-8252/84/$03.00

(France) provides an introductory statement of the problems in data assimilation alluding to matters dealt with in more detail in companion contributions. The following lecture, " A Review of Methods for Objective Analysis" by N. Gustavsson (Sweden) presents a very comprehensive and informative review of objective numerical analysis. The developments in the past 30 years leading from two-dimensional univariate to three-dimensional multivariate analysis schemes are developed very clearly and discussed with reference to current practice at a number of operational centres throughout the world. " T h e Normal Mode Approach in the Initialization Problem", is the third paper of the book and is contributed by R. Daley (U.S.A.). This lecture provides an excellent review of the normal mode analysis of the primitive equations and illustrates its particular relevance in numerical weather prediction. The procedures of linear, non-linear and variationally constrained normal mode initialization are all considered clearly and informatively. The fourth contribution, "Assimilation of Asynoptic Data and the Initialization Problem", is by K. Bube and M, Ghil (U.S.A.). This paper presents a theoretical analysis of problems central to the understanding of current assimilation procedures. The frame-work is that of the shallow water equations and questions considered include the uniqueness of initial value problems in the absence of complete observations of all variables and

© 1984 Elsevier Science Publishers B.V,

246 the extent to which intermittent updating of the

quantities

observed

overcomes

in meteorological analysis.

de-

This volume is a very valuable contribu-

ficiency in the observational data base. The

tion to the literature of numerical meteorol-

Bounded Derivative Principle is discussed and used to illustrate the close relationship between assimilation and initialization.

ogy. The lectures by Gustavsson, Daley and Kanamitsu should be of particular interest to the specialist practitioners; those by Ghil et

"Application of Estimation Theory to Numerical Weather Prediction" by M. Ghil et al. (U.S.A.) is the fifth contribution and con-

al. and Talagrand of particular interest in clarifying the theoretical problems of data assimilation. I would recommend the volume,

s i d e r s the a p p l i c a t i o n of Kalman (or Kalman-Bucy) filtering in data assimilation. The lecture is the most mathematical in the

additionally, to students in this field and to those involved in using numerical analyses from major meteorological centres such as ECMWF.

volume and presents a unified picture of analysis and initialization within the context of a modified Kalman-Bucy filter adopting a

W. Bourke, Melbourne, Vic.

dynamic constraint. This contribution reflects some current theoretical research in this area rather than consensus of application. The sixth contribution, " C o n v e r g e n c e of

L. Bengtsson and J. Lighthill (Editors), 1981. Intense Atmospheric Vortices. Proceedings

Assimilation Procedures" by O. Talagrand

of the Joint Symposium ( I U T A M / I U G G ) held at Reading (U.K.), July 1 4 - 1 7 , 1981.

(France) addresses mathematics of 'identical twin' experiments in linearized shallow water

Springer-Verlag, Berlin, 1982, xii + 326 pp. (1995 figs.), DM56.00, US$23.40 (softcover).

equations and then demonstrates convergence of intermittent updating in a non-linear model. This paper and that of Ghil and Bube are complementary and provide a theoretical insight into current practices. The final contribution from the seminar

In the lower 5 km or so of the earth's atmosphere, the pressure field consists primarily of a transient network of depressions

series is the lecture "Some Climatological and Energy Budget Calculations using the FGGE IIIB Analyses During January 1979" by M. Kanamitsu (Japan). This contribution presents an assessment of the analyses produced by the data assimilation scheme of

terns of airflow. Low-pressure systems vary in diameter from a few tens of metres to a few thousand kilometres; high-pressure systems, because of the different balance of

ECMWF for the month of January 1979 from the First GARP Global Experiment. Characteristics of January 1979 mean fields are

The lower atmosphere, therefore, consists of a relatively shallow envelope of air in

compared to long term climatological means for both hemispheres and for the tropics. Deficiencies in tropical divergence patterns are identified as due to the lack of diabatic heating in the non-linear normal model initialization. The unique possibilities of the enhanced observational data base of the global experiments are apparent from the paper's discussion; diagnostic studies of the global circulation from the ECMWF analyses testify to the successful application of data assimilation in handling the voluminous data base, which is inhomogeneous in both space and time and error characteristics. An appendix to the volume is a reprint of the pioneering study of A. Eliassen (Norway) in 1954 on the use of statistical interpolation

and anticyclones, and air moves around these centres of high and low pressure in a multiplicitly of predominantly circular pat-

forces operating on moving air in different pressure field, are generally much larger.

which are embedded a changing spatial and time pattern of individual rotations. Of particular importance are the very intense rotations or vortices such has tornadoes and tropical cyclones, known locally as hurricanes, typhoons, cyclones or willy-willies. Tornadoes average no more than a few hundred metres in diameter; hurricanes are mostly from 80 to 800 km across. These intense low-pressure systems are almost invariably associated with extreme and destructive weather in low and middle latitudes and it is thereby of great economic and social importance to improve our understanding and if possible our ability to forecast the form and development of such systems. In recent years, improved surveillance and analytical techniques, such as weather satellites,

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