The efficient allocation of the limited energy resources of a wireless sensor network in a way that maximises the information value of the data collected is a significant research challenge. Within this context, this paper concentrates on adaptive sampling as a means of focusing a sensor?s energy consumption on obtaining the most important data. Specifically, we develop a principled information metric based upon Fisher information and Gaussian process regression that allows the information content of a sensor?s observations to be expressed. We then use this metric to derive three novel decentralised control algorithms for information-based adaptive sampling which represent a trade-off in computational cost and optimality. These algorithms are evaluated in the context of a deployed sensor network in the domain of flood monitoring. The most computationally efficient of the three is shown to increase the value of information gathered by approximately 83%, 27%, and 8% per day compared to benchmarks that sample in a naive non-adaptive manner, in a uniform non-adaptive manner, and using a state-of-the-art adaptive sampling heuristic (USAC) correspondingly. Moreover, our algorithm collects information whose total value is approximately 75% of the optimal solution (which requires an exponential, and thus impractical, amount of time to compute).