A technique for optimizing the placement of oceanographic sensors with example case studies for the New York Harbor region

Consider a small number of sensors which are distributed over an ocean region of interest, and which take local measurements, e.g. of salinity, only at their own positions. Using only the measurements from these sensors, and no other information, it is often possible to reconstruct a surprisingly accurate approximate now-cast map of the salinity (or other data) values for the whole region, simply by best fitting a curved surface of salinity values to the observed data points. Although sophisticated, physics based computational ocean models are nowadays routinely used to reliably forecast maps of these oceanographic data, the ability to independently generate approximate models using sensor data alone is important for several reasons. Firstly, "ground-truth" data derived from independent sensor measurements are necessary for validation, error analysis and parameter tuning of computational ocean models. Secondly, data derived from sensor measurements could be assimilated with data forecast from computational ocean model outputs, thus improving the accuracy of a low resolution model without the computational burden of a high resolution model. Thirdly, a small number of scattered sensors could be used to rapidly generate an approximate model for previously un-surveyed ocean regions for which a sophisticated, physics based computer model is presently unavailable. In all of these cases, sensor placement is critical. For a given number of sensors, optimal choices of sensor positions will result in far more accurate models than arbitrary or adhoc placements. Alternatively, the same accuracy can be achieved as an adhoc arrangement of many sensors, by using fewer sensors placed at optimal positions. This paper presents a new technique for optimal placement of a set of oceanographic sensors. We first demonstrate how approximate data maps, with useful accuracy, can be interpolated from the measurements of a small number of sensors. We then evaluate the effectiveness of a partic- ular choice of sensor locations in terms of the expected errors in the approximate model which they yield. We then show how numerical, non-linear optimization techniques can be used to iteratively modify a set of sensor positions until the optimal choice of sensor placements is found, which minimizes the expected error. The technique is demonstrated with a series of simulations, using various numbers of sensors to develop approximate 2D salinity maps for complex regions of the lower Hudson River near to Manhattan.