Introduction and comments on books

Atmospheric modeling, data assimilation and predictability (Kalnay)

Nowadays, everyday weather forecast is based on an activity called "numerical weather prediction" (NWP). NWP is numerical simulation of behavior of the atmosphere based on dynamics and physics of the atmosphere. But this is only half of the story. Initial conditions of the simulations must be based on observations. Observations are not perfect, some of them being even worse than NWP forecasts. The process to prepare the initial conditions for NWP by achieving the best mix of observations and forecasts is called "data assimilation", because it resembles the behavior of organisms that take nutrients and build their bodies. Even if we tentatively assume that observations themselves are jobs of a different tribe, understanding of NWP is not complete without understanding of data assimilation. A textbook of NWP including the topic of data assimilation has been long awaited, and this book by Prof. Kalnay is very welcome.

The author is now a professor of the University of Maryland, but perhaps best known as the leader of the NCEP/NCAR Reanalysis project (Kalnay et al., 1996) -- a great achievement of data assimilation. The publisher aptly included this book in "graduate textbooks". This book consists of the chapters:

  1. Historical overview of numerical weather prediction
  2. The continuous equations
  3. Numerical discretization of the equations of motion
  4. Introduction to the parameterization of subgrid-scale physical processes
  5. Data assimilation
  6. Atmospheric predictability and ensemble forecasting.

Historical materials in Chapter 1 are mostly drawn from writings of the late Jule Charney (the author's Ph.D. thesis advisor) in the early days of NWP, and from the history of NWP at U.S. National Centers for Environmental Prediction (formerly called National Meteorological Center) where the author worked. This chapter also introduces topics appearing in the later chapters.

Chapter 2 is a summary of sets of dynamic (including thermodynamic) equations used for NWP models. Probably readers need to consult a textbook of atmospheric dynamics such as Holton (2004) --the author suggests James (1994)-- for proper understanding of the equations. Nevertheless a chapter is necessary in order to introduce notations and technical terms appearing in following chapters.

The equations introduced in Chapter 2 are partial differential equations (PDEs), but computer programs (numerical ones) can handle only finite numbers. The methods for discrete approximations of PDEs are taught in Chapter 3. Finite difference methods for discretization of time, and both finite difference methods and "spectral" (orthogonal function expansion) methods for discretization of space are explained.

The physics behind the NWP models is not only dynamics. Absorption and emission of radiation (electromagnetic waves in visible and infra-red wavelengths) as well as condensation of water vapor are also important. In addition, collective effects of dynamics in such scales that are not resolved by the spatial discretization of the model should be taken into account. Chapter 4 deals with these issues. But this chapter is only 9 pages long! It does not mean that these issues are marginal. Surely, dealing these subjects properly would make the volume of the textbook more than double. It seems to be a wise choice to write just the relevance of physical processes and references. Nevertheless, this choice seems to be biased towards middle latitudes. For the tropics (or even in warm temperate zone in summer), condensation coupled with sub-grid convection should not be dealt so lightly.

[[Though I have not examined so closely, I think that the books of Krishnamurti and Bounoua (1996) and Krishnamurti et al. (1997) are recommendable to those who want to learn about global-scale NWP with emphasis on the tropics. The former book includes introduction to "objective analysis" (a term referring to relatively crude forms of "data assimilation"), while the latter book concentrates on the simulation model. These books contain more concrete examples, of Fortran codes in the former and of mathematical formula for spectral and finite difference schemes in the latter, that comprise a certain single NWP system. On the other side, the variety of NWP systems discussed in these books is not so wide as in Kalnay's book.]]

Chapter 5 explains methods for data assimilation. It is assumed that readers are familiar with linear algebra (matrices) and basics of multivariate statistics. The methods mainly discussed are "optimal interpolation" (OI) and "three-dimensional variational method" (3D-VAR). "Four-dimensional variational method" (4D-VAR) is briefly mentioned as one of "advanced methods" together with "ensemble Kalman filtering" etc. But this book is useful for readers who want to understand 4D-VAR as well. The concept of "adjoint models" which is essential component of 4D-VAR is extensively explained in Chapter 6 and Appendix B.

The limit to NWP is caused by the nature of atmospheric dynamics that is called "chaotic" by modern applied mathematicians (see Lorenz, 1993). Insignificant difference in the initial condition can grow large. Beyond the practical limit of deterministic prediction, however, something might be said in a stochastic sense. Ensemble forecasting is an attempt to make partially stochastic prediction by doing multiple deterministic forecasts from slightly different initial conditions. These issues are discussed in Chapter 6.

This book concisely introduces so many subjects. Consequently description of most of the subjects are short. Therefore I do not recommend it for self-study in isolated situation. The book seems to serve best when used by an instructor who has some experience in these subjects (but perhaps not so experienced as Prof. Kalnay or having insufficient time to write a textbook). Also it may be useful for a new staff member of an operational or research institution where an atmospheric model is used, to fill the gap between textbooks of atmospheric dynamics and the specific technical document of the model (or the program code of the model itself).

[[Japanese readers should also see an introduction of this book in Japanese (Miyoshi, 2003).]]


2004-Jun-11; minor revision 2005-Mar-13; moved here 2009-Feb-09

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