A cost-precision model for marine environmental monitoring, based on time-integrated averages

Ongoing marine monitoring programs are seldom designed to detect changes in the environment between different years, mainly due to the high number of samples required for a sufficient statistical precision. We here show that pooling over time (time integration) of seasonal measurements provides an efficient method of reducing variability, thereby improving the precision and power in detecting inter-annual differences. Such data from weekly environmental sensor profiles at 21 stations in the northern Bothnian Sea was used in a cost-precision spatio-temporal allocation model. Time-integrated averages for six different variables over 6 months from a rather heterogeneous area showed low variability between stations (coefficient of variation, CV, range of 0.6-12.4%) compared to variability between stations in a single day (CV range 2.4-88.6%), or variability over time for a single station (CV range 0.4-110.7%). Reduced sampling frequency from weekly to approximately monthly sampling did not change the results markedly, whereas lower frequency differed more from results with weekly sampling. With monthly sampling, high precision and power of estimates could therefore be achieved with a low number of stations. With input of cost factors like ship time, labor, and analyses, the model can predict the cost for a given required precision in the time-integrated average of each variable by optimizing sampling allocation. A following power analysis can provide information on minimum sample size to detect differences between years with a required power. Alternatively, the model can predict the precision of annual means for the included variables when the program has a pre-defined budget. Use of time-integrated results from sampling stations with different areal coverage and environmental heterogeneity can thus be an efficient strategy to detect environmental differences between single years, as well as a long-term temporal trend. Use of the presented allocation model will then help to minimize the cost and effort of a monitoring program.