Temporal and spatial bias in the estimation of shoreline rate‐of‐change statistics from beach survey information

Abstract

Abstract Specification of setback requirements for beach protection may require an allowance for demonstrable shoreline change, particularly shoreline recession (Geary and Lord, 1981; MacRae, 1987). However, estimates of shoreline rate‐of‐change are reputedly biased by the procedures used to monitor shoreline movements (Tanner, 1978; Leatherman, 1983) and to calculate the rates‐of‐change (Morton, 1978). In the latter context, variation in estimated rates‐of‐change due to temporal and spatial attributes of beach survey records have been investigated for two sets of records: time‐series describing monthly changes in the width of the beach for 245 months on each of six profile stations at Scarborough Beach in Western Australia; and 138 monthly observations at each of 18 profile stations on Warilla Beach, New South Wales. In the analysis each time‐series was specified in three ways. First, the rate‐of‐change estimates were identified as linear trends calculated by least‐squares techniques applied to blocks of data representing 5 years of shoreline change. The 5‐year block was utilized as a statistical window and moved, month by month, through the time‐series from beginning to end. Second, the procedure was repeated for 10‐year blocks of record, but only for time‐series from Scarborough Beach. Third, effects due to extending the survey record were investigated by incrementing the first 5‐year time‐series on a month‐by‐month basis and recalculating the trend after each increment. Results of the analyses show that trends based on 5‐year records of monthly beach surveys are substantially affected by short‐term fluctuations, in the width of the beach or in the volume of sediment. Here, short‐term fluctuations are those of less than 24 months duration. At Scarborough the beach alternated between erosional and depositional states, with the depositional condition prevailing. A maximum progradation rate of 8.2 m/yr and a recession rate of 2.4 m/yr occurred during different 5‐year intervals on the same profile station. These were significantly different from the overall, secular progradation rate (2.8 m/yr) for that profile. Similar disparities were obtained for other profile stations at Scarborough, and also for changes in the volume of sediment on Warilla Beach. The disparity was suppressed, but by no means eliminated, in estimates based on a 10‐year‐long record. The length of record required to suppress the high‐frequency effects was at least 10 years; in this instance equivalent to 120 data points in the time‐series describing shoreline change. Very few detailed beach survey records match this requirement. The observations from Scarborough and Warilla indicate that there is also considerable spatial variability in shoreline rates‐of‐change, estimated over a common time‐span and for different profile stations on the beach. At Warilla, for example, profiles are less variable on the southern part of the beach, where the beach is backed by a rock wall, than those recorded for the northern, more open, and unprotected section of the beach. The results confirm earlier observations that survey records from small segments of beach cannot be used to accurately portray variation on the beach as a whole. This is especially true where parts of the beach are protected by engineering works.