Review of The 3-D Global Spatial Data Model by Earl F. Burkholder: CRC Press. Boca Raton, Fla.; 2008; ISBN: 978-1-4200-6301-1. Price: $95.96.

This book provides a complete set of mathematical formulas needed to

This complete set of equations, combined in a single computer program, has been named the Global Spatial Data Model (GSDM), by the writer. Observational data considered include surface mark-to-mark observations (horizontal and vertical angles, distances, azimuths), orthometric height differences from leveling, and Cartesian coordinates and coordinate differences from GPS.

The GSDM is an outstanding means for combining all types of measurements where the following conditions are met:

Given the time variability of NAD83 coordinates, one can expect to use GSDM directly in conjunction with NAD-83 related coordinates only with local (urban areas or small county) networks in the eastern United States. For larger-scale NAD83 networks, even in the eastern United States, to maintain $1\mathrm{cm}$ accuracy desired by many surveyors, over times of decades, would require reduction of observations to a common time epoch before entering them into a GSDM.

Conversion to a common time epoch will always be required if ITRF or WGS84 coordinates are used and few-centimeter accuracy is desired. While conversion between coordinate systems using HTDP does not introduce error into observations, the error in conversion to a common time epoch must be included in the error budget.

Another point that is discussed, but may be overlooked by the reader, is that observed angles using, for example, a total station are relative to a plane perpendicular to the local gravity vector at a station, not the ellipsoidal normal at that point. Deflection of the vertical corrections may be needed to produce the differential north, east and up ellipsoidal normal components discussed in Appendix A of the book.

Chapter 1 is an essential guide to the rest of the book. It gives a brief summary of each of the 22 sets of equations that make up the GSDM and graphically illustrates how these equations fit together. The chapter also summarizes the covariance matrices used to provide the accuracy information for the various types of observations and coordinates.

Chapter 2 briefly introduces the four types of coordinates to be considered: Earth-centered Cartesian, ellipsoidal, State Plane, and local tangent plane, as well as the observation types that will be considered.

Chapter 3 is one of several chapters containing what might be called ancillary information. This chapter can be characterized as a short summary of basic mathematics, including arithmetic, algebra, plane and spherical geometry, trigonometry, calculus, the use of matrices, and probability and statistics. One cannot, of course, learn mathematics from these 42 pages, but they can serve as handy references to forgotten concepts.

Chapters 4 and 6 go into detail about geometry relevant to development of the necessary GSDM equations. Chapter 4 discusses basic 2D and 3D Cartesian geometry, including circular and spiral curves. Chapter 6 covers ellipsoidal coordinates. It begins with the transformations in both directions between Cartesian and ellipsoidal coordinates. It then covers computations on an ellipsoid in going back and forth between latitudes and longitudes and angles, distances, and azimuths.

Chapter 5, another ancillary chapter, is a summary of the field of geodesy, including an interesting short history of the development of geodesy.

Chapter 7 is a nonmathematical discussion of datums, including currently relevant datums and coordinate systems, namely NAD83, WGS84, and the ITRF coordinate systems. The reader cannot depend on this chapter to understand coordinate systems and datums. I found it misleading in places. For example, the importance of time variability is underestimated, and also it is not made clear that the ITRF coordinate systems are fundamental and the NAD83 and WGS84 Cartesian coordinates are derived from ITRF coordinates.

Chapter 8 covers physical geodesy, giving the relation between ellipsoidal, orthometric, and geoid heights and specifying how height systems fit into the GSDM.

Chapter 9 is another ancillary chapter, giving a discussion of how GPS positioning works.

Chapter 10 is a detailed development of the equations used in the GSDM to transform between ellipsoidal latitude and longitude and State Plane coordinates. Map projections considered in discussing State Plane coordinates are Mercator, Oblique Mercator, and Lambert Conformal.

Chapter 11 begins with a discussion of why the GSDM was developed, but the bulk of the chapter is a numerical example of the covariance matrices for a small observation network.

The final chapter, Chapter 12, covers issues involved in using the GSDM. There are three appendices. Appendix A gives the rotation matrices needed to convert from Cartesian coordinate differences between two points to local, north, east, and up coordinate differences. Appendix B gives the constants needed to derive the NAD83 State Plane coordinates. Appendix C gives a numeric example of the computation of network accuracy and local accuracy as defined by the National Geodetic Survey.

I would be remiss if I did not finish with two other comments. First, the book gives many numerical examples of computations throughout. While some may consider this unnecessary, I feel it gives a reader who was originally unfamiliar with certain equations a much better feeling for the computations.

Finally, for better or worse, I am not sure which, this is the only book I have ever encountered where there are more entries in the table of contents than there are pages in the book.