Autonomous underwater vehicles (AUVs) have been extensively utilized both in civil and military applications, among which the marine environment monitoring is one of the key issue. In this paper, we focus on online informative path planning for long-term monitoring in continuous workspace. We point out that the likelihood of measurements is related to when it is acquired. Thus we first model the underwater environment based on modified Gaussian process (GP) with considering the dynamic likelihood of measurements. Then, clamped B-curve is utilized to parametrize the continuous path segments. In order to maximize the amount of received information, we propose a path replanning scheme based on cross-entropy optimization. Moreover, we introduce the numerical simulation to highlight the effectiveness of our algorithm.