An Introduction to Numerical Weather Prediction Techniques

T. N. Krishnamurti, Lahouari Bounoua

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351467056
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Meteorology & Climatology

An Introduction to Numerical Weather Prediction Techniques is unique in the meteorological field as it presents for the first time theories and software of complex dynamical and physical processes required for numerical modeling. It was first prepared as a manual for the training of the World Meteorological Organization's programs at a similar level. This new book updates these exercises and also includes the latest data sets.
This book covers important aspects of numerical weather prediction techniques required at an introductory level. These techniques, ranging from simple one-dimensional space derivative to complex numerical models, are first described in theory and for most cases supported by fully tested computational software. The text discusses the fundamental physical parameterizations needed in numerical weather models, such as cumulus convection, radiative transfers, and surface energy fluxes calculations.
The book gives the user all the necessary elements to build a numerical model. An Introduction to Numerical Weather Prediction Techniques is rich in illustrations, especially tables showing outputs from each individual algorithm presented. Selected figures using actual meteorological data are also used.
This book is primarily intended for senior-level undergraduates and first-year graduate students in meteorology. It is also excellent for individual scientists who wish to use the book for self-study. Scientists dealing with geophysical data analysis or predictive models will find this book filled with useful techniques and data-processing algorithms.

1

Introduction

This is an introductory workbook on numerical weather prediction methodology. It is written for the senior level undergraduates and first year graduate levels in meteorology. The size of this text is deliberately limited to 13 chapters so that the material could be covered in a one semester laboratory course. A synoptic laboratory with terminals for use of each student is desirable for such a course. This book is also suitable for individual scientists who wish to undertake it for self learning.

The text came about from a training manual the senior author wrote for the World Meteorological Organization in 1982 which interested a wide audience of students and scientists from many educational and research centers around the world. The present text has been extensively revised, extended and worked out with newer data sets. A diskette is provided with the text that carries these sample data sets and the codes.

This workbook starts out with an introduction to finite difference methodology. Space differencing techniques include first, second and fourth order schemes, the treatment of Laplacian and Jacobian operations and solutions of Poisson and Helmholtz type equations. An entire section in this chapter is devoted to the description of a wide variety of most popular time differencing schemes encountered in numerical weather prediction. The stability conditions for each individual scheme are also discussed.

Chapter 3 enumerates a number of techniques on the computation of vertical velocity. The vertical velocity is not an observed meteorological variable, and in most cases its estimation involves the calculation of the horizontal wind divergence. Small uncertainties in horizontal wind measurements cause large errors in the estimation of the vertical velocity. Understanding of the methods for the calculation of vertical velocity is an important issue.

Chapter 4 describes two powerful and popular methods of computing the streamfunctions and velocity potential, namely the relaxation and the Fourier transform techniques. It also introduces the wind pressure relationship. Unlike the middle latitudes, where the geostrophic constraint is important, in the tropics one can see the departures from the geostrophic law by exploring a number of what are called “balance” relationships. Here one solves for the pressure given a wind field. This chapter shows how the pressure field is deduced from the linear and the nonlinear balance laws.

Chapter 5, on objective analysis, introduces four methods for data analysis that range from the simple polynomial approach to optimal interpolation. They illustrate how raw data can be analyzed over an array of grid points.

The physical processes are fairly important in the evolution of weather. Chapter 6 introduces basic physical concepts relevant to numerical weather prediction. Basically, the use of moisture variables in meteorology is introduced together with some algorithms describing their computational aspects. Some principles on stability are also introduced.

A simple convective model illustrating the evolution of buoyancy driven dry thermal is provided as an introduction to convective modelling. The complex subject of cumulus parameterization is introduced in Chapter 7. Some of the most common schemes for the determination of rainfall rates resulting from cumulus convection are presented. The chapter also includes a section on large scale condensation.

The planetary boundary layer is an important component that needs to be modeled. In Chapter 8 the best way to model the fluxes of momentum, heat and moisture from the earth’s surface (land as well as ocean) is sought. This chapter presents several methods for the calculation of these fluxes. There is a constant flux layer some tens of meters deep next to the earth’s surface. The calculation of the surface fluxes as well as their vertical distribution is presented.

Chapter 9 introduces the radiative transfer calculations. The treatment of short and long wave irradiances, the role of clouds, the energy balance at the earth’s surface and the issue of the diurnal change are presented. Only an elementary treatment of this important physical process is highlighted.

In Chapter 10 a simple barotropic model is introduced. For tropical applications the streamfunction of the flows is the basic dependent variable and is obtained from the analyzed wind field. This forecast model makes use of the principle of conservation of absolute vorticity. This is generally regarded as a first useful model for learning numerical weather prediction. This model has practical applicability over certain parts of the tropics (e.g., Eastern Atlantic and West Africa).

A second numerical weather prediction model based on the principle of conservation of potential vorticity is presented in Chapter 11. Here the reader is introduced to the first primitive equations model. The forecast of the wind as well as the geopotential height is performed at a single level.

Diagnostic calculation from model output is an important area. This helps in the interpretation of model output. If the forecasts are skillful in simulating a phenomenon such as a storm then the diagnostic studies can tell us something about the lifecycle of a phenomenon. If the forecast is poor, the diagnostic calculations performed on the model output and on the analyzed (observed) fields can provide some reasons for the model’s failure. These are essential ingredients for developing the numerical weather prediction capability and are addressed in Chapter 12.

Chapter 13 enumerates some recent satellite and model-based data sets that have relevance to numerical weather prediction.

It is important to note that many of the illustrations shown in this textbook cannot be reproduced without a graphical software. Furthermore, because the tables presented in the text have been edited, they will not be reproduced exactly by the software. The software included inside the text has also been edited for presentation.

The students taking this course should have some background in elementary dynamic, physical and synoptic meteorology. In addition, a good working knowledge of the Fortran language is a requirement. The following are helpful recommended texts.

1.  Wallace and Hobbs, 1977: Atmospheric Science.

2.  Holton, 1992: An Introduction to Dynamic Meteorology.

3.  Houghton, 1985: Physical Meteorology.

4.  Nyhoff and Leestma, 1988: Fortran 77 for Engineers and Scientists.

2

Finite Differences

In meteorology, the fundamental equations governing the atmospheric circulation appear, in general, to consist of sets of non-linear partial differential equations which do not have analytical solutions and are solved using numerical methods. The most common operations encountered during the solution of these equations are of the type of first and second derivative, Jacobian and Laplacian. These operators are spatial derivatives and require the knowledge of the variabl...