University of Connecticut DigitalCommons@UConn Peer-reviewed Articles 12-1-2004 What Does Height Really Mean? Part I: Introduction Thomas H. Meyer University of Connecticut, [email protected] Daniel R. Roman National Geodetic Survey David B. Zilkoski National Geodetic Survey Follow this and additional works at: http://digitalcommons.uconn.edu/thmeyer_articles Recommended Citation Meyer, Thomas H.; Roman, Daniel R.; and Zilkoski, David B., "What Does Height Really Mean? Part I: Introduction" (2004). Peer- reviewed Articles. Paper 2. http://digitalcommons.uconn.edu/thmeyer_articles/2 This Article is brought to you for free and open access by DigitalCommons@UConn. It has been accepted for inclusion in Peer-reviewed Articles by an authorized administrator of DigitalCommons@UConn. For more information, please contact [email protected]. Land Information Science What does height really mean? Part I: Introduction Thomas H. Meyer, Daniel R. Roman, David B. Zilkoski ABSTRACT: This is the first paper in a four-part series considering the fundamental question, “what does the word height really mean?” National Geodetic Survey (NGS) is embarking on a height mod- ernization program in which, in the future, it will not be necessary for NGS to create new or maintain old orthometric height benchmarks. In their stead, NGS will publish measured ellipsoid heights and computed Helmert orthometric heights for survey markers. Consequently, practicing surveyors will soon be confronted with coping with these changes and the differences between these types of height. Indeed, although “height’” is a commonly used word, an exact definition of it can be difficult to find. These articles will explore the various meanings of height as used in surveying and geodesy and pres- ent a precise definition that is based on the physics of gravitational potential, along with current best practices for using survey-grade GPS equipment for height measurement. Our goal is to review these basic concepts so that surveyors can avoid potential pitfalls that may be created by the new NGS height control era. The first paper reviews reference ellipsoids and mean sea level datums. The second paper reviews the physics of heights culminating in a simple development of the geoid and explains why mean sea level stations are not all at the same orthometric height. The third paper introduces geopotential numbers and dynamic heights, explains the correction needed to account for the non-parallelism of equipotential surfaces, and discusses how these corrections were used in NAVD 88. The fourth paper presents a review of current best practices for heights measured with GPS. Preliminaries National Geodetic Survey is responsible for the federal framework and is continually developing he National Geodetic Survey (NGS) is new tools and techniques using new technology responsible for the creation and main- to more effectively and efficiently establish this tenance of the United State’s spatial framework, i.e., GPS and Continually Operating Treference framework. In order to address unmet Reference System (CORS). The agency is work- spatial infrastructure issues, NGS has embarked ing with partners to transfer new technology so on a height modernization program whose “… the local requirements can be performed by the most desirable outcome is a unified national posi- private sector under the supervision of the NGS tioning system, comprised of consistent, accurate, (National Geodetic Survey 1998). and timely horizontal, vertical, and gravity control Instead of building new benchmarks, NGS has networks, joined and maintained by the Global implemented a nation-wide network of continu- Positioning System (GPS) and administered by ously operating global positioning system (GPS) the National Geodetic Survey” (National Geodetic reference stations known as the CORS, with the Survey 1998). As a result of this program, NGS is intent that CORS shall provide survey control working with partners to maintain the National in the future. Although GPS excels at providing Spatial Reference System (NSRS). horizontal coordinates, it cannot directly measure In the past, NGS performed high-accuracy an orthometric height; GPS can only directly pro- surveys and established horizontal and/or verti- vide ellipsoid heights. However, surveyors and cal coordinates in the form of geodetic latitude engineers seldom need ellipsoid heights, so NGS and longitude and orthometric height. The has created highly sophisticated, physics-based, mathematical software models of the Earth’s grav- Thomas H. Meyer, Department of Natural Resources ity field (Milbert 1991; Milbert and Smith 1996; Management and Engineering, University of Connecticut, Storrs, Smith and Milbert 1999; Smith and Roman 2001) CT 06269-4087. Tel: (860) 486-2840; Fax: (860) 486-5480. that are used in conjunction with ellipsoid heights E-mail: <[email protected]>. Daniel R. Roman, to infer Helmert orthometric heights (Helmert National Geodetic Survey, 1315 East-West Highway, Silver 1890). As a result, practicing surveyors, mappers, Springs, MD 20910. E-mail: <[email protected]>. David and engineers working in the United States may B. Zilkoski, National Geodetic Survey, 1315 East-West Highway, be working with mixtures of ellipsoid and ortho- Silver Springs, MD 20910. E-mail: <[email protected]>. metric heights. Indeed, to truly understand the Surveying and Land Information Science, Vol. 64, No.4, 2004, pp. 223-233 output of all these height conversion programs, This first paper in the series is introductory. Its one must come to grips with heights in all their purpose is to explain why a series of this nature is forms, including elevations, orthometric heights, relevant and timely, and to present a conceptual ellipsoid heights, dynamic heights, and geopoten- framework for the papers that follow. It contains a tial numbers. review of reference ellipsoids, mean sea level, and According to the Geodetic Glossary (National the U.S. national vertical datums. Geodetic Survey 1986), height is defined as, “The The second paper is concerned with gravity. distance, measured along a perpendicular, between It presents a development of the Earth’s gravity a point and a reference surface, e.g., the height of forces and potential fields, explaining why the an airplane above the ground.” Although this defi- force of gravity does not define level surfaces, nition seems to capture the intuition behind height whereas the potential field does. The deflection very well, it has a (deliberate) ambiguity regarding of the vertical, level surfaces, the geoid, plumb the reference surface (datum) from which the mea- lines, and geopotential numbers are defined and surement was made. explained. Heights fall broadly into two categories: those It is well known that the deflection of the verti- that employ the Earth’s gravity field as their datum cal causes loop misclosures for horizontal traverse and those that employ a reference ellipsoid as their surveys. What seems to be less well known is that datum. Any height referenced to the Earth’s grav- there is a similar situation for orthometric heights. ity field can be called a “geopotential height,’’ As will be discussed in the second paper, geoid and heights referenced to a reference ellipsoid undulations affect leveled heights such that, in are called “ellipsoid heights.” These heights are the absence of orthometric corrections, the eleva- not directly interchangeable; they are referenced tion of a station depends on the path taken to the to different datums and, as will be explained in station. This is one cause of differential leveling subsequence papers, in the absence of site-specific loop misclosure. The third paper in this series gravitation measurements there is no rigorous will explain the causes of this problem and how transformation between them. This is a situation dynamic heights are the solution. analogous to that of the North American Datum of The fourth paper of the series is a discussion of 1983 (NAD83) and the North American Datum of height determination using GPS. GPS measure- 1927 (NAD27)— two horizontal datums for which ments that are intended to result in orthometric there is no rigorous transformation. heights require a complicated set of datum trans- The definitions and relationships between eleva- formations, changing ellipsoid heights to ortho- tions, orthometric heights, dynamic heights, geopo- metric heights. Full understanding of this process tential numbers, and ellipsoid heights are not well and the consequences thereof requires knowledge understood by many practitioners. This is perhaps of all the information put forth in this review. As not too surprising, given the bewildering amount was mentioned above, NGS will henceforth pro- of jargon associated with heights. The NGS glos- vide the surveying community with vertical control sary contains 17 definitions with specializations for that was derived using these methods. Therefore, “elevation,” and 23 definitions with specializations for we feel that practicing surveyors can benefit from “height,” although nine of these refer to other (mostly a series of articles whose purpose is to lay out the elevation) definitions. It is the purpose of this series, information needed to understand this process then, to review these concepts with the hope that the and to use the results correctly. reader will have a better and deeper understanding The current article proceeds as follows. The next of what the word “height” really means. section provides a review