Determining representative ranges of point sensors in distributed networks

John K. Horne, Dale A. Jacques

Distributed networks of stationary instruments provide high temporal scope (i.e., range/resolution) observations but are spatially limited as a set of point measurements. Measurement similarity between points typically decays with distance, which is used to set interpolation distances. The importance of analyzing spatiotemporal data at equivalent spatial and temporal scales has been identified but no standard procedure is used to interpolate space using temporally-indexed observations. Using concurrent mobile and stationary active acoustic, fish density data from a tidal energy site in Puget Sound, WA, USA, six methods are compared to estimate the range at which stationary measurements can be spatially interpolated. Four methods estimate the representative range of the mean using autocorrelation or paired t-test and repeated measures ANOVA. Accuracy of resulting sensor density estimates was modeled as departures from interpolated linear and aerial estimates. Two methods were used to estimate representative range of the variance by comparing theoretical spectra or by determining equivalent spatial and temporal scales. Representative ranges of means extended from 30.57 to 403.9 m. Estimation error (i.e., standard deviation) ranges of linearly interpolated or aerially extrapolated values ranged from 42.5 to 82.3%. Representative ranges using variance measurements differed by a factor of approximately two (scale equivalence = 648.7 m, theoretical = 1388.1 m). A six-step decision tree is presented to guide identification of monitoring variables and choice of method to calculate representative ranges in distributed networks. This approach is applicable for networks of any size, in aquatic or terrestrial environments, and monitoring the mean or variance of any quantity.