This study addresses the subsea search performance of an autonomous underwater vehicle equipped with a search sensor and an environment characterization sensor. The performance of the search sensor is assumed to be dependent on characteristics of the local environment, and thus sensor performance in some locations can be different than in other locations. For the case that the agent is able to occasionally characterize the environment, and therefore estimate the performance of its search sensor, we describe a method for selecting when and where to characterize the environment and when and where to search in order to maximize overall search effectiveness. Our work accounts for false positives, false negatives and uncertainty in the performance of the search sensor that varies geographically. We show that effort applied to characterizing the environment, and therefore the performance of the search sensor, can improve search performance. We derive a utility function that is used to compute the best path and when to switch between the tasks of search and environmental characterization. The objective of the subsea search mission is to maximize the probability of attaining a desired level of risk reduction, and we terminate the search mission as soon as it is found that the desired risk reduction cannot be attained. To the best of our knowledge, this is the first study that addresses the problem of attaining a desired level of risk and stopping the mission when the desired risk is found to be unachievable. Through numerical illustrations, we show realistic scenarios where the findings of this study can be useful to improve search effectiveness and attain the desired level of risk where the standard exhaustive search techniques will fail to achieve.