Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

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

A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This data assimilation scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor to capture temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottom tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs velocity and height of the free surface flow based on noisy measurements of the elevation alone

Identification of shallow sea models

In this paper we consider a parameter estimation procedure for shallow sea models. The method is formulated as a minimization problem. An adjoint model is used to calculate the gradient of the criterion which is to be minimized. In order to obtain a robust estimation method, the uncertainty of the open boundary conditions can be taken into acoount by allowing random noise inputs to act on the open boundaries. This method avoids the possibility that boundary errors are interpreted by the estimation procedure as parameter fluctuations. We apply the parameter estimation method to identify a shallow sea model of the entire European continental shelf. First, a space-varying bottom friction coefficient is estimated simultaneously with the depth. The second application is the estimation of the parameterization of the wind stress coefficient as a function of the wind velocity. Finally, an uncertain open boundary condition is included. It is shown that in this case the parameter estimation procedure does become more robust and produces more realistic estimates. Furthermore, an estimate of the open boundary conditions is also obtained

A mollified Ensemble Kalman filter

It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high frequency adjustment processes in the model dynamics. Various methods have been devised to continuously spread out the analysis increments over a fixed time interval centered about analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.Comment: 16 pages, 6 figures. Minor revisions, added algorithmic summary and extended appendi

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Modeling and forecasting ocean acoustic conditions

Author Posting. © The Author, 2017. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 75 (2017): 435–457, doi:10.1357/002224017821836734.Modeling acoustic conditions in an oceanic environment is a multiple-step process. The environmental conditions (features) in the area first must be measured or estimated; relevant features include seabed geometry, seabed composition, and four-dimensionally (4D) variable sound-speed and density variations related to evolving or wave motions. Often the dynamical wave modeling depends on first obtaining correct seabed and mean stratification conditions (for example, nonlinear internal wave modeling). Next, this information must be included in sound propagation modeling. A selection of the many methods and tools available for these tasks are described, with a focus on modeling sounds of 20 to 1000 Hz propagating through water-column features that are time-dependent and variable in three dimensions (i.e., 4D variable). An example of a 3D parabolic equation acoustic calculation shows how variability caused by evolving internal tidal waves affects sound propagation. Different propagation and scattering regimes are discussed, including the theoretically delineated weak scattering and strong scattering regimes, as well as the empirically examined regime found in nonlinear internal waves. The histories and the current state of our oceanographic knowledge (the input to acoustic modeling) and of our ability to effectively model complex acoustic conditions are discussed. Example acoustic simulation applications are also discussed; these are ocean acoustic tomography, coherence prediction, and signal-to-noise ratio prediction. Types of ocean models and acoustic models and how they are interfaced are also examined. These include deterministic, statistical analytic feature models.Funding for this work was provided by the U.S. Office of Naval Research, Ocean Acoustics Program, Grants N-00014-11-1-0701 and N00014-14-1-0223