




Sampling, Detection, and Estimation of Episodic Phenomena 
Michael B. Matthews, Dan Davis Estimating oceanographic fields from both a priori and observational information is an essential and ubiquitous problem in oceanography. This problem poses the following reciprocal questions: (1) What is the optimal sampling topology over a field? (2) What is the optimal estimate of a field over a sampling topology? This project anticipated the event detection and adaptive sampling capabilities of the MBARI Ocean Observing System (MOOS) by addressing the topic of detection and estimation of episodic events based on multiresolution statistical models. Consistent with our previous investigations, we will determine the relationship between episodic event detection probability, estimation error, and sampling topology. Our results will enable us to determine the necessary MOOS system sampling topology for optimally detecting and estimating episodic events. The MOOS sampling assets, including fixed instrumentation and transiting AUVs, realized this optimal sampling topology. Many physical processes exhibit relevant statistical variations on a number of different spatial and temporal scales. For example, in addition to underlying geographic variations, certain chemical processes in the ocean exhibit seasonal, lunar, and diurnal variations. A common problem is that of estimating the spatial and temporal components of such a process given a nonuniform sampling topology. The process is often sampled uniformly with a high temporal resolution but with a low spatial resolution. These measurements are augmented by samples taken at a high spatial resolution but with a low temporal resolution. For example, a system of buoys samples an oceanographic process at a high temporal resolution at only a few fixed locations; an autonomous underwater vehicle periodically performs synoptic highresolution spatial sampling of the same process. We approach this problem by modeling the random process using a multiresolution statistical model where the change in resolution is specified by a firstorder Markov process. The optimal estimation of random processes based on such a model consists of a hightolow resolution smoothing operation using the RauchTungStriebel algorithm followed by a lowtohigh resolution filtering operation using the Kalman filter. The smoothing operation uses regions of high sampling resolution to update the lowerresolution states of the model; the filtering operation propagates these states to higherresolution model states. We illustrate the application of such a technique for estimating primary productivity in the Monterey Bay. 

