Comparing one and two-dimensional hydraulic modelling of flow on varying spatial scales

Abstract

In the past years, climate change has caused an increasing number of extreme weather events. In the Netherlands this is, for instance, reflected by the growing amount of extreme rainfall events. This creates big issues for water management authorities like water boards. Water boards are often responsible for local streams, that cannot handle the peak discharges caused by extreme rainfall. This raises the question whether measures have to be taken, for instance by creating additional storage areas to decrease discharge peaks. For questions like these computational model studies can be used to gain insight in the distribution of discharges and water levels.

During these model studies often one-dimensional models are used. Recent developments made two-dimensional modelling, including for instance the simulation of inundation, possible for regular users like water boards. Two-dimensional modelling is proved to be more accurate for rivers, compared to one-dimensional modelling. Water boards, however, often deal with water systems of smaller scale. This raises the question whether it is worth for authorities like water boards to invest their resources in this new modelling approach. Several physical system properties are of influence on the answer to this question. Therefore, the main question of this research is:

Which physical processes are of influence to the choice of a modelling approach, one or two dimensional, for the modelling of stream systems in particular situations?

The methodology of answering this question consists of three major parts:

1) identify possible differences in the model properties of 1D versus 2D modelling;
2) analyze the output of test models to see whether the differences in model properties actually influence the effects of physical processes; and
3) analyze a case area to see whether these processes are important in practice.

The research scope consists of the hydrodynamics of systems with a length scale of 10^3 – 10^5 m and a temporal scale of hours to a few days. This range corresponds with a range in discharges of a few cubic meters per second up to a few thousands of cubic meters per second. The choice for this range has been made to be able to analyze the effects between the scales of streams and rivers, as until now mostly rivers have been modelled using 2D modelling approaches.

The starting point of this research has been the analysis of differences in model properties. The used flow equations, numerical methods, computational grids and bathymetry implementation are analyzed and the differences are discussed. Concluding, it can be stated that there are differences, which may be of influence to the model output. The main differences are the number of dimensions on which the flow equations are calculated and the way the bathymetry is schematized by the computational grid.

Using these differences, physical parameters have been specified that were varied in a range of test models. These are mainly the parameters that cause 2D effects, like meandering and varying roughness coefficients. The modelling of flood waves could also cause differences due to the fact that the 1D model is not able to model storage with the used default settings. Lastly, the way the bathymetry is used in the simulations is of great importance, due to the way the bathymetry is discretized in 2D models. The goal of varying these physical properties is to analyze whether these variations would influence the quantity of the effects the differences in model properties are causing. Comparing the output of both a 1D and 2D model, it appeared that there are significant differences in the observed water levels. Generally speaking, the following observations were made:

1. The smaller the simulated spatial scale, the larger the 1D-2D differences are
2. The higher the meandering intensity, the larger the 1D-2D differences are
3. The lower the summer bed roughness, the larger the 1D-2D differences are
4. The larger the 2D grid cell size, the larger the 1D-2D differences are
5. The smaller the flood wave duration, the larger the 1D-2D differences are

The underlying physical processes have been analyzed to see how their influence varies in different situations and for different spatial scales. In the end, six processes were found to be influencing the 1D-2D differences:

1. The effects of grid size on bathymetry discretization
2. The water level and velocity difference in cross-sectional direction for varying roughness
3. The water level and velocity difference in cross-sectional direction for varying meandering intensities
4. The interaction between summer bed and floodplains
5. The Boussinesq approach and consequences for the summer bed – floodplain flow area ratio
6. The effects of storage

When combining the findings of the test models and the analysis of a small scale stream system, it was found that the above processes are of the most influence on the following situations:

1. In situations with a complex bathymetry the process of grid discretization is having the most influence.
2. In situations with a high meandering intensity two physical processes are playing a role: high water level and velocity gradients in lateral direction, and a high summer bed – floodplain interaction.
3. In situations with a very low roughness compared to the surrounding area two physical processes are playing a role: high water level and velocity gradients in lateral direction, and a high summer bed – floodplain interaction.
4. In situations with a lot of elevation changes and open water bodies, a lot of potential storage is present.

In these four situations a 2D approach is preferred, as the physical processes that are present in these situations are all processes that are poorly implemented or represented by a 1D model. Of course, there are also some more practical considerations to be made about the modelling choice. The most important one is the research goal; whether inundation modelling is desired and what the required model output is. Another important consideration is the available time for running the simulations; 2D models have a significantly longer simulation time compared to 1D models.

All things considered, this research provides an overview of the differences in model properties between 1D and 2D modelling approaches, an analysis of the important physical processes that determine the choice of a modelling approach and some recommendations about practical issues one could encounter when performing a modelling study.