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A three-dimensional electric-analog model of the Long Island groundwater system constructed by the U.S. Geological Survey in the early 1970's was used as the basis for developing a digital, three-dimensional finite-difference model. The digital model was needed to provide faster modifications and more rapid solutions to water-management questions. Results generated by the two models are depicted as potentiometricsurface maps of the upper glacial and Magothy aquifers. Results compare favorably for all parts of Long Island except the northwestern part, where hydrologic discontinuities are most prevalent and which the two models represent somewhat differently. The mathematical and hydrologic principles used in development of ground-water models, and the procedures for calibration and acceptance, are presented in nontechnical terms. INTRODUCTION Long Island, N.Y., a part of the New York metropolitan area, has grown rapidly since World War II. Although the western part of the island obtains water from elsewhere, Nassau, Suffolk, and parts of Queens Counties (fig. 2) are totally dependent on local ground water for their supply. Because acreage and natural resources needed for growth and development on Long Island are restricted, as on any island, land managers and planners are faced with many types of decisions as to the best use of these resources. At present, much work is being done to develop accurate methods and equipment to provide information and to evaluate future alternatives in environmental questions. Since 1932, the U.S. Geological Survey, in cooperation with local and State agencies, has been studying and monitoring the water resources of Long Island. In the mid-1960's, the Geological Survey began to develop an electric analog model of the Long Island aquifer system to predict how the ground-water system would respond to alternative water-management proposals. The resulting information has been important in answering questions concerning local ground-water resources. Before 1965, the most reliable method of ground-water modeling was the electric-analog model (a physical-mathematical model), which is based on the analogy between the flow of electricity and the flow of water. With sufficient data and proper calibration, such a model can indicate ground-water flow at any locality within the modeled area. Subsequently, the Geological Survey constructed and tested a large, complex electric-analog model of the Long Island ground-water system (Getzen, 1977). This model was used successfully for several years to predict the response of the ground-water system to a variety of management alternatives (Kimmel and Harbaugh, 1976; Harbaugh and Reilly, 1976). Although the model proved useful and yielded satisfactory results, it has inherent disadvantages. It was large and cumbersome, the measurement of electrical values on the model was time consuming, and modifying the model electrically for alternative types of tests was even more time consuming. Since the late 1960's, the speed and versatility of digital computers in solving complex mathematical problems has increased, and the cost of such computations has decreased accordingly. At the same time, the quantity of data that can be stored and manipulated has increased. Thus, it soon became evident that the electric-analog model's capability to predict the response of the ground-water system to stresses could be enhanced by use of a digital model, which, in addition, would provide greater versatility and wider applications. The hydraulic values used in the electric-analog model were used as a basis for developing the digital model. The digital model, which solves hydrologic equations to indicate water levels at selected localities, provides more rapid solutions to hydrologic questions than the analog model and is more easily modified as new information becomejs,available. In addition, the digital model can simulate certain aspects of the ground-water system more accurately than the analog model. Purpose and Scope The purpose of this report is to (1) explain the concepts and procedures used in developing a ground-water model, and (2) compare the operation and results of the analog and digital models of the Long Island ground-water system. The first sections of this report describe the principles of modeling and explain the similarities and differences between the electric analog-model representation of a real hydrologic system and the numerical (digital) model representation. The steps in designing a model are introduced to explain the development of a model from problem definition to solution; a short discussion of ground-water hydrology is included also. Those interested in a more comprehensive discussion of the principles of ground-water flow may refer to Bennett (1976). The latter sections of the report trace the transition of ground-water modeling on Long Island from the analog to the digital technique. Although the analog representation was able to answer many questions about the Long Island ground-water system, it gave rise to certain questions as to (a) reliability of the data that had been used in constructing the model, and (b) the lack of data from some localities. Getzen (1977, p. 19-31) gives a detailed discussion of the Long Island analog-model design principles and the simulation of Long Island ground-water hydrology. This report includes a comparison of results from the digital and the analog models and a discussion of the acceptability of the numerical model as evidence that the transition to the numerical simulation technique was done accurately and that reliable results can be obtained. The result of this conversion is an acceptable digital model that can yield results faster and allow for more flexibility in stressing and updating the model. Acknowledgments The authors are deeply indebted to 0. L. Franke, whose enthusiasm and technical knowledge were invaluable in quantitatively describing the Long Island flow system and in preparing this general report, and to R. T. Getzen, whose work (Getzen, 1977) forms the foundation of this report. GROUND-WATER MODELING ON LONG ISLAND Developing a Ground-Water Model A model is an approximate representation of some aspect of a real system. A ground-water model of the type discussed in this report, is designed to indicate the patterns of flow within the ground-water system by solving equations that describe the system. Thus, a ground-water flow model incorporates only those aspects of the natural system that directly affect the movement of ground water. Hydrologic systems are modeled for two main reasons to provide information on how the system functions and to predict how the system will respond to given stresses. Thus, a model constructed properly can be useful in planning for the management of water resources. However, because a model is based on approximate, rather than exact, values, its predictions are only as accurate as the data and assumptions used in its construction and operation. A general procedure for developing a ground-water flow model from concept to final calibrated model is shown as a flow chart in figure 1. In step 1, the problem to be modeled is defined. The problem must be formulated in adequate detail to allow systematic development of the model. Because the problem cannot be solved through direct measurements, the solution must rely on mathematical equations which will describe the ground-water flow. DEFINE PROBLEM DEVELOP CONCEPTUAL FORMULATION OF HYDROLOGIC SYSTEM IN TERMS OF PROBLEM TO BE SOLVED MAKE GENERAL ASSUMPTIONS THAT WILL SIMPLIFY SOLUTION OF PROBLEM WHILE RETAINING SUFFICIENT DETAIL TO PROVIDE ACCURATE ANSWER DESIGN SOLUTION TECHNIQUE CHECK SOLUTION TECHNIQUE TO INSURE IT IS CORRECT MAKE CORRECTIONS COLLECT DATA NEEDED TO SOLVE PROBLEM APPLY DATA TO SOLUTION TECHNIQUE (THIS is NOW A MODEL OF THE SYSTEM) CHECK MODEL RESULTS AGAINST HISTORICAL INFORMATION TO INSURE THAT DATA ARE ACCURATE AND SUFFICIENT TO SOLVE PROBLEM (CALIBRATION STAGE) GO BACK AND COLLECT MORE COMPLETE AND ACCURATE DATA MODEL IS CALIBRATED AND SHOULD BE CHECKED AGAINST ANOTHER SET OF HISTORICAL DATA (iF HISTORICAL DATA ARE UNAVAILABLE FOR A CHECK/ A LOWER CONFIDENCE LEVEL WILL BE PLACED ON MODEL RESULTS) 10 MODEL CAN BE USED TO SOLVE THE PROBLEM Figure 1. Flow chart showing steps in designing a ground-water model. The second step, the conceptual formulation of the hydrologic system and its components, is the most important one in the modeling process because this step determines which characteristics of the flow system are to be incorporated. A correct concept allows for a true, although approximate, mathematical representation of the flow system; otherwise the model will produce an incorrect solution to the problem. Once a concept of the hydrologic system has been developed, the mathematical formulation and solution techniques can be derived (steps 2-5) and values representing the hydraulic characteristics of the system (step 6) can be input into the model. The combination of the solution technique and the hydraulic data (step 7) constitute an approximate representation (or model) of the natural system. Model results are then checked against actual historical measurements to see if the model f s solutions are accurate; if the model reproduces the historical information incorrectly, more complete or more accurate data are needed. This phase of the model development, in which the model response is compared with historical data to check the applicability of the selected hydrologic coefficients, is called the calibration stage (step 8). This phase is repeated and the data adjusted until a good match between values measured in the real system and those produced by the model is attained. However, if possible, the model should be checked against another set of historical data (other than the calibration data) to assure that the calibration match was not coincidental. The difference between a calibrated model and an

A comparison of analog and digital modeling techniques for simulating three-dimensional ground-water flow on Long Island, New York