Using a sand wave model for optimal monitoring of navigation depth

In the Euro Channel to Rotterdam Harbor, sand waves reduce the navigable depth to an unacceptable level. To avoid the risk of grounding, the navigation depth is monitored and sand waves that reduce the navigation depth unacceptably are dredged. After the dredging, the sand waves slowly regain their original height. To reduce the high costs of surveying and dredging, the North Sea Service of the Department of Transport, PublicWorks andWater Management, is implementing a Decision Support System to reduce the required amount of surveys and provide optimal information on the necessity to dredge. Currently, the system predicts the growth of sand waves using a linear trend. The trend is determined from observations using a Kalman-filter including geo-statistical components to incorporate spatial dependencies. This works well for sand waves that are close to their maximum height. After dredging however, the sand wave height is far from its equilibrium and the growth rate is much higher, making the linear prediction worthless. Here we show that replacing the linear trend with a landau equation improves the predictions of the regeneration. Comparison shows that the landau equation predicts the crest evolution better than the linear equation for both undisturbed sand waves and dredged sand waves, with an root mean square error that is 25% less.