William Duffy Stephen M. Dickson
USING GRID AND GRAPH TO QUANTIFY AND DISPLAY SHORELINE CHANGEABSTRACT When faced with displaying subtle shoreline changes, coastal geologists are often forced to choose between two compromises. They can use very large scale maps that capture the detail but display only a limited portion of the shoreline at a time. Or they can average the change for various shoreline segments and display these less detailed data in graphic form next to a map of the coast. This paper will describe a methodology for preparing and displaying shoreline change data digitized from ortho-corrected aerial photographs of Maine's coast. By using GRID and the Arcplot GRAPH commands, all the detail of the original data is maintained on maps of a reasonable scale. Once the data are in this format, it is also easy to resample them at various intervals for use in erosion rate models being used to develop coastal setback zones in Maine. INTRODUCTION Coastal erosion is a problem throughout the U.S., occurring on both the east and west coasts, the Gulf shore, and the Great lakes. In Maine the worst coastal erosion often occurs during "nor'easters"; winter storms usually lasting six or more hours and characterized by strong northeasterly winds. Rising sea-levels and poorly-sited coastal development acerbate the problem. In 1992 the Maine Geological Survey (MGS) received a grant from the Maine State Planning Office under the Coastal Zone Management Act of 1972 to develop a series of maps identifying regions of high coastal erosion in Maine. These maps and the data used to create them would document the rate of coastal erosion and be used to develop coastal setback zones in Maine. DATA COLLECTION The Maine Geological Survey began the study by collecting sets of circa 1950 and 1990 aerial photographs for 30 Maine beaches. Using a computerized analytic stereoplotter system at the University of Maine, the 1:5000 to 1:30,000 scale film diapositives were magnified 16x and the seaward dune vegetation lines were digitized. All data were converted to UTM coordinates using known ground control points and standard aerotriangulation and orthophoto correction techniques. These methods produced sets of 1950 and 1990 coastline data for each beach. Comparisons between common points on each set of photos showed positional accuracy of one meter or better. Finally, using the DXFARC command the coastline data were converted to ArcInfo coverages. USING GRAPH AND GRID While the coastline coverages for a particular beach contained highly detailed positional data, it was difficult to see subtle changes at anything other than large scales. We decided that a better way to display the detail recorded in these data was to use the GRAPH commands in the ArcInfo Arcplot module. GRAPH commands use two fields from an attribute table as the X and Y coordinates of a line or area graph. To display the attributes, the user specifies a GRAPH EXTENT which sets the length of each axis in page units. By specifying a large value for one axis with respect to the other, the data displayed can be stretched to make subtle changes visible. With the coastline erosion data, we wanted to use the length of the coastline as the Y-axis and the change in coastline positions between 1950 and 1990 as the X-axis. The tricky question was how to get this change information from the two coastline arcs. In most vector based GIS software, like ArcInfo, arcs and polygons have topology, i.e., they have information attached to them which record their beginning and end points, and left and right sides (for arcs) or their inside and outside (for polygons). Topology makes it possible to assign addresses to a street arc or to find how many addresses there are within a town polygon. However, topology gives us no information as to what is going on in the empty space around an arc or outside a polygon. Information is only recorded for the coordinates that form the arc or polygon. In the GRID module of ArcInfo information is not tied to specific features like arcs or polygons. Instead, all data are referenced to a fixed location or cell whose size is defined by the user. Individual cells can be coded with values just as arcs or polygons are; however, there is no empty space in a grid coverage, all cells contain at least the coordinates of their location. Because of this, we can move anywhere in a grid coverage and get information such as "How far am I from the nearest cell coded as 1950?" And this was precisely the question we needed to ask. MAKING GRIDS To the uninitiated creating and manipulating grids can be a daunting task. However, with a little experience, using grids soon becomes second nature. With simple commands, grids can be created from arc or polygon coverages and vise versa. A new grid can be created by applying one or more statistical or logical functions to another grid. A third grid can be created by simply adding two other grids. Grids provide a set of powerful tools for the analysis of geographic data that vary continuously over a region. In the first step of our analysis, the LINEGRID command was used to convert both coastline coverages to grids with a one meter cell size. In the resulting grids, cells which fell at the position of the 1950 or 1990 coastline were coded as "1950" and "1990", respectively. All other cells were coded as NODATA. Next, the EUCDISTANCE function was used to create a new grid from the 1950 coastline grid. This function calculates the distance of every cell in the new grid to the nearest occurrence of a specified value in the original grid. In this case the specified value was the code "1950" in the 1950 coastline grid. The resulting grid looks like a buffer around the original 1950 coastline grid (Figure 1). However, unlike a buffer polygon, this buffer was composed of individual cells, each of which contained a distance value.
Figure 1. Euclidean Distance Grid. Grid cells have been color coded to reflect distance from 1953 shoreline. A third grid was then created by intersecting the distance grid with the 1990 coastline grid created earlier. The intersection was done using the conditional statement: "If the coastline grid cell contains the code "1990" put the value of the distance grid at that location in the new grid, otherwise put a NODATA value there". The result of this statement was a grid containing the distance to the nearest 1950 cell at the position of each 1990 cell. The final step was to convert this last grid back to an arc using the GRIDLINE command. Unlike the original coverage, which contained only a few arcs connected at pseudonodes, this new arc coverage consisted of hundreds of short arcs, approximately one meter in length, connected at pseudonodes. Each of the short arcs represented the 1990 coastline position and contained a code for its distance from the 1950 coastline. While the above procedure may seem complicated, it required only five commands to execute. BACK TO GRAPH AND MAPS The resulting arc coverage contained the change in coastline position between 1950 and 1990 (the X-axis information) for each segment of its length (the Y-axis information). This information could now be used to produce a graph showing both the obvious and subtle changes in coastline position in 40 years. An example of one map and graph is shown in Figure 2.
Figure 2. Camp Ellis Beach, Saco, Maine. The 1991 coastline position is shown in black, the 1953 coastline is green. North is to the left and a portion of a large jetty, built to stabilize the mouth of the Saco River, is shown at the south end (right) of the beach. The graph shows the extent of erosion which has taken place over 38 years. Most of the beach shows a net loss of material. The two major areas of accretion are due to seawall construction made in an attempt delay the retreat of the shoreline near houses. The building footprints, shown in dark green, were digitized prior to 1991 and since then three buildings have been destroyed during winter storms. Many fine details are apparent on the graph in Figure 2 which are hard to see on the adjacent map. Using the graph data, average erosion rates can be calculated for individual beaches making it possible to compare coastal changes in different regions. In addition, the graph data can be resampled and averaged based on various criteria, such as vegetation type or beach orientation. CONCLUSIONS The GRID and GRAPH techniques described above have substantially increased the amount and improved the quality of data being extracted from an arc data set. At the same time, the display of the data in a graphic form shows clearly the extent of the coastal erosion problem in Maine. We hope these data can be used to improve public policy on coastal hazards related to coastline change. ACKNOWLEDGMENT This project was made possible by financial assistance from the Maine Geological Survey, Department of Conservation, and from a grant through the Maine State Planning Office under the Coastal Zone Management Act of 1972, as amended, pursuant to Award #NA37OZ0263-01 administered by the Office of Ocean & Coastal Resource Management of the National Oceanic and Atmospheric Administration. Data for this project were gathered by the Department of Geological Sciences and the Department of Survey Engineering at the University of Maine. Data analysis and map production were done at the Maine Office of Geographic Information Systems. William Duffy, Programmer Analyst Maine Office of Geographic Information Systems Station #22, 71 Hospital St. Augusta, ME 04333 Telephone: (207) 287-6375 Fax: (207) 287-7641 E-mail firstname.lastname@example.org Stephen M. Dickson, Marine Geologist Maine Geological Survey, Dept. of Conservation Station #22 Augusta, ME 04333 Telephone: (207) 287-2801 Fax: (207) 287-2353