Ten sites of severe coastal erosion in Puerto Rico have been studied by using a series of aerial photographs from 1936, 1950-51, 1962-63, 1971, and 1977 (Fig. 1) . The flights were all made during winter months and the photographs were reproduced at scales of 1:10 000 1:15 000, and 1:20 000. Because of scale limitations inherent in the original aerial photographs, many reported measures of coastal erosion cannot be supported by the data. A practical limit of definition on aerial photographs for the human eye is 0.5 mm, which means that the smallest field distance that can be measured on a 1:20 000 photograph is 10 meters. Since each study is a comparison of one photograph with another, the value must be doubled to 20 meters as there are two sources of error. To improve the accuracy of interpretation, photographs for the sites in Puerto Rico were enlarged to a scale of 1:5000, which allows comparison between two photographs of a five meter change in shoreline. The photographs were taken from 6 to 14 years apart, so between each set we can measure an annual change of about 0.5 meter.
Tadical distortion should have a minimal effect since the coastal sites in this study are of low relief. Tilt error was checked and found to be minimal. The stage of tide at the time of photography can be a factor if the slope of the beach is low or the tidal range large. This was not a serious problem at the study sites, but to minimize the effect, where possible the loss of features above the water-line has been used as a measure of erosional loss.
The rate of erosion of a beach is not necessarily constant with time and there are accelerations, decelerations, and even reversals to a condition of accretion. Taking two points in time cannot provide information on changes in rate, and may in fact produce totally inaccurate results. Since five sets of photographs have been used, covering a forty year span of time, trends can be examined. The analyses show that rates of erosion are indeed variable, but trends of gain or loss seem to be consistent, and are comparable with other measurements where they are available.
Area D has been the site of the most rapid erosion. Between 1962 and 1971, there was a rapid loss of shoreline at the rate of 7.2 meters per year (Fig. 3) . The offshore bathymetry study by the Corps of Engineers (Fig. 4) shows a loss of sediment offshore that is consistent with the loss of the protective shoal at point D in the 1950 photograph.
From 1971 to 1977, the straightened shoreline at D had a reduced rate of erosion of 1.7 meters per year. The area is still being eroded as seen in field observations (Fig. 5) , but at a reduced rate. It is possible that the shoreline is adjusting to a situation of relative stability under the present wave regime. Waves approach from the southeast and are refracted to a northward direction. This sets up a north transport of the beach and nearshore sands. Even though the wave orthogonals indicate a general dispersal of energy, there is a concentration just south of where the point was located, which has led to reshaping of the coast.
Areas C and D are both being eroded at the present time at rates of 1.0 and 0.5 meters per year, respectively. The only period of accretion was between 1950 and 1963. There have been individual attempts at fill with concrete and rock debris which have not been effective. The value of the land makes structural remedies questionable for this area. Recommendations were made to the Coastal Zone Management Program that similar areas of low cost development be made hazard warning areas in which expensive development could be discouraged.3
Visual inspection shows numbers of palm trees in the water and portions of the cliff that are about to collapse. The prospect is for continued erosion. There is some development of houses along the shore and sale of lots so that more can be expected. This area is an excellent example of the need to establish erosion hazard warning criteria and urbanization planning to avoid the need for expensive shoreline control measures.
Measurements from the 1950, 1971, and 1977 aerial photographs show a rate of erosion on the east of Punta Salinas of 2.1 meters per year from 1950 to 1971 and 1.65 meters per year to 1977 (Fig. 9) . Ground surveys taken between 1962 and 1973 give a rate of erosion of 1.4 meters per year, so that the determinations seem compatible. The west side of the tombolo has been eroding at an average rate of 1.8 meters per year from 1950 to 1977. The total loss between the two arrows of Figure 8 for the 27 year period has been about 100 meters - almost 4 meters per year. In 1950 there was a width of 175 meters and in 1977, there was only 75 meters remaining. The refraction of waves results in a complex pattern of sediment movement, but the transport is essentially to the south from each side of the tombolo. There is no replenishment source of sand for the beaches, so erosion should continue in the present wave regime
Area C has changed in response to fill and dredge operations rather than a natural transport system (Fig. 11) . Areas A and B have continued to erode. In area A, the rate from 1950 to 1977 was 1.7 meters per year. Urbanization that existed in 1950 was abandoned by 1962. Between 1950 and 1962, the mouth of the river also shifted, introducing new hydrodynamic conditions. In area B, there was relative stability between 1950 and 1962, followed by erosion at the rate of 1.0 meters per year from 1962 to 1977.
The southern part of the bay is undeveloped, but west of the present river mouth the coast is highly developed and is an area of critical erosion problems. There was a loss of more than 15 meters of shoreline between 1950 and 1977, but the rate of erosion has been slowed by rip-rap and boulder wall construction to protect the town.
This area is protected by offshore shoals of eolianite that serve to break wave action. Whether there has been a loss of eolianite or a change in wave direction, there does seem to be a new set of conditions that have led to increased erosion. The oblique photograph can only be used for an approximation, but the 1971 aerial photograph shows a ratio of 1:1 for borrow pit width and shoreline between the pit and the sea. The barrier was approximately 135 meters wide in 1971. The ratio is now 2:1, meaning that the barrier is only 75 to 80 meters wide.
Wave and current dynamics were altered by addition of a jetty and harbor, but there was erosion even before construction. Between 1951 and 1962, area A was relatively stable, but area B and C were eroding at 1.25 and 2.25 meters per year (Fig. 19) . Between 1962 and 1971, area A eroded at 2.5 meters per year. The rate of erosion was less in area B, with a rate of 0.75 meters per year. Area C continued to erode at 2.25 meters per year.
Investigation of erosion by examination of the aerial photographs shows a relatively stable shoreline between 1971 and 1977. Only a shore area shows retreat of the shoreline. Field investigation supports this observation. There has been some undercutting of the cliff shoreline and some toppling of new trees, but the rate is reduced. The offshore area between the shoreline and the line of offshore shoals is now shallow and acts as a buffer to wave action. East of the jetty, there is marked erosion that continues to the site of the abandoned Las Mareas schoolhouse (Fig. 20) . The school had a playground including a baseball field on the seaward side when it was constructed. Between 1936 and 1977 there was a 30 meter loss of shoreline at an average annual rate of 0.75 meters (Fig. 19).