Sensitivity analysis for hydrodynamic model of the North Sea

Abstract

In this thesis, sensitivity analysis is used to study the influences of parameters on specific outputs in the hydrodynamic model 3D DCSM-FM of the North Sea. The sensitivity analysis is the study of how uncertainty in the outputs of a model can be divided and allocated to different sources of uncertainty in its inputs. The software Delft3D FM is used to simulate the model, which is developed by Deltares. This thesis is supported by German pilot of the UNITED project, which studies the possibilities of combing blue mussel and sugar kelp cultivation with wind energy. The investigation is conducted at FINO3 platform, 80 km off Sylt.

In this thesis project, temperature and current velocity are selected as outputs in sensitivity analysis, which are influential factors of blue mussel and sugar kelp growth. Specific parameters in the hydrodynamic model are selected as inputs respectively. Three sensitivity methods are conducted: Morris, copula-based and variance-based method. Among them, copula-based and variance-based consider the independency information, while parameters are assumed dependent in Morris method. To generate samples, parameters are transformed into a unit hypercube in Morris method and run on the contour of the grid cell, composing paths. Between two steps within the paths, only one parameter changes at a time (OAT method). The input domain is scanned with a better strategy to separate the paths maximizing the dispersion. Each parameter’s elementary effects are calculated within paths, evaluating the changes in outputs contributed by the single parameter. Then (absolute) mean and variance of elementary effects are used as sensitivity indices. Copula-based method uses similar sampling and the same measurements, but it gathers parameters into copulas before sampling to include the dependency information. In variance-based method, the variance of the outputs’ conditional expectations is used to measure the sensitivity. Only random samples are needed in this method.

Morris and copula-based method prove the temporal and spatial similarities of parameters’ sensitivity behavior. Convective and evaporative heat flux are the most influential parameters of temperature, and they also show correlations with other parameters. Air density influences current velocity the most, while Smagorinsky factor is the most correlated parameter of current velocity. Variance-based method gives similar results about rankings of influences. Correlations are proved to exist among parameters. Uniform horizontal eddy viscosity/viscosity in definition files have no impacts, as they are overwritten. Three methods are compared. Except the differences in independency, sampling and measurement, there are some other differences. Much more samples are required in variance-based method and it is used mainly to decide the existence of significant correlations and whether a parameter can be neglected. While Morris and copula-based method ranks the influences and correlations.