shoreline retreat collides with shoreline development, a state of "critical 

 erosion" is achieved. Shoreline retreat is due to many causes but a major one 

 is rising sea- level and indications are that the rise will continue for the 

 foreseeable future. 



The usual response to critical erosion on America's shore is stabiliza- 

 tion; halting of shoreline retreat by engineering means. Such stabilization 

 of America's shore has been successful in increasing the length of life of 

 buildings built adjacent to the beach. However, stabilization in the long run 

 (50 years +) and sometimes in a much shorter time frame has resulted in severe 

 degradation of the recreational beach area. Dollar costs of halting shoreline 

 retreat by stabilization is very high. Replacement of the beach by pumping in 

 new sand costs about 1 million dollars or more per shoreline mile each time it 

 is done and it must be carried out repeatedly commonly in 3 to 10 year inter- 

 vals. Another approach, the building of seawalls, costs between $100 to $600 

 per linear open ocean shoreline ft. Combining these cost figures with the 

 2,000 mile figure of critically eroding shoreline gives some idea of the mag- 

 nitude of the potential economic crisis on the American shoreline if we con- 

 tinue to stabilize. 



Stabilization costs can be justified for major coastal cities or harbor 

 entrances (Chicago, Galveston, Miami Beach, Coney Island, the Columbia River 

 entrance, for example), but stabilization of most American shores is not jus- 

 tifiable in the broader scope of national interest. Numerous projects involv- 

 ing public and private money along virtually all developed coastal and lake 

 shores presently threaten most of America's recreational shoreline. 



The consequences of responding to rising sea-level by shoreline stabili- 

 zation are so serious that we urge immediate measures to explore totally new 

 approaches to shoreline management. Such approaches may even involve drastic 

 and unpopular measures such as assuming that building adjacent to the beach 

 are temporary or expendable. Equally important, the new approach to shoreline 

 management must incorporate the very significant advances in geologic under- 

 standing of shoreline processes that have occurred during the last decades. 

 In the past the American public has been largely unappraised and unaware of 

 the long range environmental and dollar costs of shoreline stabilization. 

 There is a critical and immediate need for the public to know the direction in 

 which American shoreline management is leading. (Modified Summary). 



268 PINTER, N. and GARDNER, T. W. 1989. "Construction of a Polynomial 

 Model of Glacio-Eustatic Fluctuation: Estimating Paleo-Sea-Levels 

 Continuously Through Time," Geology . Vol 17, No. 4, pp 295-298. 



Sea- level curves for the late Quaternary are typically reconstructed 

 with data from reef tracts and terraces preserved along actively uplifting 

 coastline, recording highstands, and in some cases lowstands, of the world's 

 oceans through time. As a result, sea- level curves reconstructed from these 

 data are fixed at the maxima (highstands) and minima (lowstands) , but either 

 make no predictions about the intervening time or use arbitrary or free-hand 

 methods of interpolation. These curves fail to meet the need of many 

 applications of sea-level data for continuous, quantitative information. 



A new method for calculating sea- levels during intervening times 

 produces a polynomial expression of sea-level through time. LaGrange 

 polynomial interpolation is used to fit a series of fourth-order equations to 



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