Shoreline Modeling and Erosion Prediction

This paper presents a shoreline-erosion prediction model of Lake Erie that can forecast shoreline changes from annual to 10-year increments. It was developed by using historical bluffline data of years 1973, 1990, 1994, and 2000 at Lake Erie provided by NOAA and local government agencies. The relationships among these historical shorelines are analyzed using a least-squares method. Erosion rates are then derived from shoreline changes. In addition, other influential factors such as changes in terrain and water-levels are also considered in the model. INTRODUCTION In coastal regions the natural forces that cause shoreline changes are embodied in waves, currents, wind and other factors. The backward movement of land due to actions of these forces is termed erosion. The loss of coastal land properties, submergence of beaches and structures near the shore are direct consequences of these coastal erosion processes. Most of the coastal regions in the United States are suffering from erosion. The direct financial and resource loss caused by this natural process makes it a significant problem that needs to be researched. In order to increase the possibility of overcoming the effect of the erosion process, attempts must be made to predict its occurrence and make research results publicly available. Shoreline changes can be used as a good indicator of occurrence of coastal erosion. Accurate information is required regarding the past and present movement of the shoreline in order to take preventive actions against loss of infrastructure along the shores. One of the most important factors in any shoreline change analysis is the consistency of the shoreline model applied from one coastal region to another. All the natural forces responsible for shoreline movement are the functions of space and time because the intensities of these activities change according to geographic location and seasonal variations. The main challenge in shoreline prediction modeling has been to create models with sophisticated spatio-temporal numerical analysis which can generate testable predictions about the functioning of a coastal erosion system (Fletcher et al., 2003). In the presence of modern GIS technology, these models will have greater reliability, accuracy, and analyzing/visualization capability. In the past, errors in the process of identifying shoreline positions and digitization, as well as the absence of spatio-temporal tools for analyzing the trend of shoreline changes, were among the potential causes for restricting the ability of models to provide defensible shoreline change rate evaluations. There is certainly a need for revision of such prediction models due to the evolution of technologies and the increasing need for such models. The first requirement is to choose a shoreline indicator for coastal mapping purposes. The primary requirement in choosing an indicator should be its easy identification in the coastal area and on aerial photographs. Morton and Speed (1998) and Pajak and Leatherman (2002) mentioned some of these shoreline indicators including bluff edges, vegetation lines, high water marks, beach crust, dune crust, beach scarp, etc. Due to the scope of the research project, the top bluff edge is chosen in this research as the shoreline indicator based on its visibility on aerial photographs. In shoreline change modeling, various mathematical models have been proposed. An empirical model is used in bluffline modeling which does not involve sand transportation (Ali, 2003). In this empirical model shorelines are identified in increasing order of time (from past to future) and then the relationship between the time and the shoreline position changes is analyzed by using a numerical method. Bluffline modeling would become unstable in the presence of sand transportation due to its impermanency as sand can be transported back into the water. Moreover, the lack of involvement of sand transportation in the empirical model makes it easier to implement. However, it is reasonable to assume that by modeling the shoreline position changes we are taking the underlying coastal erosion processes into account because all of the changes in the geometry of the shoreline are the end result of erosion phenomena. The Division of Geological Survey in the Ohio Department of Natural Resources (ODNR) proposed and implemented a technique for creating the correspondence between the available shoreline indicators by creating transects at a master shoreline. Here, the master shoreline implies a shoreline with a good quality. Once these transects are created, then the rates of shoreline change are derived on these transects. By using these change rates, the future shoreline position can be derived. Another approach, the End Point rate (EPR) method, presented by Liu (1998) and Galgano and Douglas (2000), is based on an empirical equation which shows that the future position of a shoreline can be derived by a linear relationship between past shoreline positions and time. The change rate (m) and intercept (c) involved in this model are derived by a line (y = mx+c) extracted from the points on the earliest and latest available shorelines (y and x represent the shoreline position and time respectively). This model may not be applied widely because of the absence of positional quality information and due to undesirable results for short periods, for instance, less than eighty years (Galgano and Douglas, 2000). Models described in the above paragraph assume the determination of future shorelines is based on modeling points on past shorelines. The shoreline change prediction based on some chosen points from shoreline depictions cannot be fully justified because these points do not guarantee the continuity of the shoreline. A shoreline is a continuous and dynamic feature; a model for shoreline change analysis must maintain the continuity of the shoreline. In this regard, Liu (1998) and Li et al. (2001) presented a method for shoreline change modeling and analysis by using a dynamic segmentation concept. This approach preserves the continuity of the shoreline by dividing the shoreline into various line segments. These line segments are continuous due to the fact that the end location of the first segment would be the same as the start location of the second segment, and so on. This paper implements the dynamic segmentation approach by modeling the changes with line segments of available past shorelines. ANALYTICAL MODEL: ASSUMPTIONS AND METHODLOGY The shape of a bluffline with a reasonable length is generally irregular and cannot be expressed using analytical functions. To apply any numerical modeling approach in the analysis of the bluffline change, its geometry should be expressed under some assumptions. We divide a bluffline A1An+1 into a finite number (n) of segments A1A2, A2A3, A3A4, ..., AnAn+1 which are defined by their starting and ending points A1 (x1, y1), A2 (x2, y2), A3 (x3, y3), A4 (x4, y4), ..., An (xn, yn), An+1(xn+1, yn+1). Moreover, these segments with small spatial extents can be approximated to linear segments A1A2, A2A3, A3A4, ..., AnAn+1 (Figure 1). In implementing the linear approximation on all the available blufflines of different times, a standardized parameterization method is used (Schmidley, 1996). According to this method each of the curves is normalized onto the interval of [0, 1] by considering their length equal to 1. These normalized curves are then divided into the same number of line segments. The ending points of these line segments are defined by their normalized coordinates. The same division of each bluffline will ensure the line segments of a bluffline have the same constant length. The graphical representation for this procedure is shown in Figure 2, where the lengths of two blufflines A1An+1 (time t =k) and A1An+1 (time t =k+m) are normalized to 1 and equal-length line segments A1A2, Ap-1Ap, ..., AnAn+1 and A1A2, Ap-1Ap, ..., AnAn+1 are created on both normalized blufflines. The next step is to derive correspondences among blufflines. Setting up a correspondence between two blufflines is equivalent to deriving the correlation A1 A2 A3 A4 (x1, y1) (x2, y2) (x3, y3) (x4, y4) (xn, yn) An An+1 (xn+1, yn+1) Figure 1. Linear approximation of the bluffline between every pair of divided line segments on both blufflines, for instance, A1A2 and A1 A2, or Ap-1Ap and Ap-1 Ap. Thus, the bluffline change analysis is reduced to a problem of identifying parameters which are responsible for the change of the same line segment on different blufflines and establishing a method to predict the variability of these parameters in temporal dimension. For example, modeling the change of a pair of the line segments Sm and Sm (Ap1Ap and Ap-1Ap ) on different blufflines A1An+1 (time t =k) and A1An+1 (time t =k+m) can be treated as a subproblem for the entire bluffline change analysis (Figure 2). Figure 2. Concept of basic unit model in the analysis of bluffline change Figure 3. Transformation of one line segment to another line segment (Ali, 2003) Identification of Parameters of Line Segments The transformation from one line segment to another line segment includes translation, rotation and scale changes. Three basic parameters can be identified as translation (∆ T), rotation ( ∆ R) and scale change (∆ S). In two-dimensional space, translation is composed of two subchanges (∆ x and ∆ y), i.e., change in the x direction and O x1 x3 x2 x4 C D