Sampling the Ocean Using Fleets of Gliders in the Presence of Non-Maneuverable Assets

Using fleets of underwater gliders to sample the ocean has been proved to be an appealing alternative to more expensive solutions like those based on vessels. Because of the long endurance of the mission of a fleet of gliders (order of months), when compared to the endurance of the mission of AUVs (order of days), gliders are nowadays routinely involved in ocean sampling campaigns. However, where to send the vehicles (the so called “adaptive sampling” problem) in order to maximize the content of information gathered is still an active research topic. The underlying philosophy of many adaptive sampling algorithms is the following. First, the knowledge of the a-priori covariance matrix of the field of interest (temperature, salinity, etc.) is assumed to be available (either provided by a forecasting model or estimated from forecasts/analyses/reanalyses) for the region of interest. Then an assimilation algorithm is used to estimate the posterior covariance matrix, once the list of way points is generated by an adaptive sampling algorithm. We will refer to this class of algorithms as covariance-based adaptive samplers with assimilation. However in some cases the a-priori covariance matrix cannot be used, because it is not available at all or it is available but judged not enough reliable (sometimes this can be due to the fact that simply it has not been validated yet). In such cases a viable alternative (although less powerful) is represented by the use of the variance of the field, instead of its covariance. The schemes based on the variance may use or not an assimilation phase. Of course, in case the assimilation is present, it will involve the variance only, in order to estimate the posterior variance. We will call these approaches as variance-based adaptive samplers with/ without assimilation. In this work we present a new adaptive sampling algorithm, specifically designed for the sampling missions where: i) the covariance matrix is not available/not reliable/not validated, and ii) non-maneuverable sampling assets are present (like fixed buoys, drifters, and floating buoys), other than maneuverable ones (gliders, AUVs, etc.). In this scenario, since the a-priori covariance matrix is unknown, it is not possible to assimilate the measurements of the fixed buoys before planning the mission of the gliders. Instead, we have to decide where to send the gliders (i.e., to generate their lists of way-points), exploiting the presence of fixed buoys. The algorithm extends an earlier version presented in [1], which was based on the idea of deriving a distribution of points from the a-priori variance (by using an adaptive meshing algorithm) and then use a clustering algorithm to find the location of the centroids, where such locations were used as next way-points for the gliders. However, that method assumed all-maneuverable assets (and thus a number of centroids equal to the number of gliders). In this study we extend it by exploiting the existence of non-maneuverable assets like fixed buoys (a situation that frequently occurs in real scenarios). The first essential idea is to consider the positions of fixed buoys as part of the centroids to obtain from the clustering algorithm: the remaining centroids to be computed will be considered as the next positions where to send each glider. By using the clustering algorithm described in [2], called “Partially Provided Centroids Fuzzy C-Means” (PPC-FCM), we have been able to exploit the presence of fixed buoys by sending the gliders in regions not already covered by the buoys/floats. This allows a better distribution (lower overlapping) of the sensing assets, with respect to the direct use of the standard Fuzzy C-Means, uninformed of the presence of the buoys. An interesting advantage of the proposed algorithm over covariance-based schemes with assimilation, is that it can be used in surveillance applications too, where a time variant risk map (generated by other tools, like [3-5]) is assumed to be available, together with the presence of some fixed observing stations (harbor control towers, coast guard station, etc.).