The Dutch Ministry of Transport, Public Works and Water Management continuously inspects and improves the protection that sea dikes, river dikes and dunes - shortly dikes - offer us against large-scale floodings. The total length of all inspected dikes is approximately 3600 km and the yearly expenses amount to nearly one billion euros.

Following the great flooding of 1953, David van Dantzig of the Mathematical Centre in Amsterdam (the current CWI), proposed a mathematical model, that describes how much a dike should be heightened to obtain a prescribed safety. Van Dantzig's model still forms the basis of present-day safety norms for dikes. It considers a control problem in which an optimum is found between, on the one hand cost for dike-height increase now, and on the other hand damage cost due to flooding.

Over the years, Van Dantzig's model has been improved by Carel Eijgenraam of the Netherlands Bureau for Economic Policy Analysis (CPB). Under the authority of the Directorate-General for Public Works and Water Management (Rijkswaterstaat, RWS) and the later Deltares, the model has been worked out in a computer program. Recently, this computer program has been used for a cost-benefit analysis of all major dikes in the Netherlands. The software combines RWS-concepts like water levels and dike heights, with concepts as monetary values of goods, vegetation, animals and even human beings. (In the program, the life of a single person is valued at 2.2 million euro.)

Future model

At present, at Tilburg University (UvT), under the authority of Deltares and in co-operation with CPB, research is carried out which is directed towards an extended version of the current model. In the extended model of Tilburg University, a dike ring can be segmented. And at CWI, since the beginning of 2009, a project is running, also in cooperation with Deltares and CPB, in which a more dynamical mathematical model for dike-height control is being developed. An important role in the CWI model is played by a partial differential equation, the Hamilton-Jacobi-Bellman (HJB) equation. The HJB-equation for the dike-height-control problem can not be solved exactly with pencil and paper; it has to be solved numerically. At CWI, a numerical method is being developed for this purpose. In contrast to the UvT model, in the CWI model, the discount rate is determined endogenously. The discount rate from the CWI model will be worked out in the UvT model in 2010. The resulting model will be used to determine economically optimal safety levels for all major dikes in the Netherlands.

Barry Koren (CWI), 2009

Workshop Dike-Height Control, CWI, December 9, 2009
Programme

• Jarl Kind (Deltares): Dutch policy context - role of CBA in determining optimal flood protection standards
• Joris Bierkens (CWI): Optimal control of dike levels under risk aversion
• Michelle Woodward (HR Wallingford and Exeter University): Real options, optimisation methods and flood risk management
• Rob Aalbers (CPB): Discounting investments in mitigation and adaptation (including dikes)
• Mohammed Chahim (Tilburg University): An impulse control approach for dike height optimization
• Sander van der Pijl (CWI): Control of dike levels in continuous time: numerical aspects
  

• Carel Eijgenraam (CPB): Optimal safety standards for dike-ring areas
• Pia Kempker (VU/CWI): Optimal control for dike levels
• Sander van der Pijl (CWI): Control of dike levels in continuous time
• Kees Roos (TU Delft): Mathematical analysis of the homogeneous dike height optimization problem
• Ruud Brekelmans (UvT): A mixed integer nonlinear programming approach for the non-homogeneous dike height optimization problem