Motivated by the need for larger offshore wind turbines, large diameter monopile foundations are being developed. To ensure safe design, there is a need for model testing and validation of hydrodynamic load models. Scaled model tests with a piston-type wavemaker commonly apply first order wavemaker theory for irregular waves. This approach results in the generation of second (and higher) order spurious (also known as parasitic) free waves in the tank. In this study, the effect of superharmonic spurious waves on the response of a monopile with eigenfrequency close to three times the wave peak frequency is examined experimentally. The bending moment response statistics are not found to be significantly affected by the wavemaker correction. Different wave breaking patterns are observed for individual events, but our results do not indicate any clear relation between breaking waves and the wave generation technique.

<p><span lang="en-US">The </span><span lang="en-US">thickness integrated</span><span lang="en-US"> dense flow avalanche simulation module com1DFA of the open source framework AvaFrame is used for snow avalanche simulations </span><span lang="en-US">with application in</span><span lang="en-US"> hazard mapping </span><span lang="en-US">for</span><span lang="en-US"> different mountainous areas. In order to further increase the information </span><span lang="en-US">value</span><span lang="en-US"> gained from the avalanche simulation results </span><span lang="en-US">in a global coordinate system</span><span lang="en-US">, we introduce a thalweg following coordinate system. It allows us to quantitatively compare simulation scenarios and results </span><span lang="en-US">of</span><span lang="en-US"> different</span><span lang="en-US"> modelling approaches </span><span lang="en-US">in a new way. </span><span lang="en-US">It helps to</span><span lang="en-US"> bridge the gap between the </span><span lang="en-US">modules</span><span lang="en-US"> operating in three-dimensional terrain </span><span lang="en-US">(com1DFA) </span><span lang="en-US">versus two-dimensional along the avalanche path, </span><span lang="en-US">such as the well-known alpha-beta model implemented in module com2AB</span><span lang="en-US">. </span><span lang="en-US">One </span><span lang="en-US">essential</span><span lang="en-US"> step of the analysis procedures (analysis modules in AvaFrame) is the avalanche </span><span lang="en-US">thalweg</span> <span lang="en-US">generation itself. The thalweg</span><span lang="en-US"> depends on the main flow direction, a property of the avalanche event which is </span><span lang="en-US">strongly</span><span lang="en-US"> influenced by the terrain the avalanche flow will encounter. So far, the main flow direction is usually derived from observations or avalanche simulations, and the thalweg is </span><span lang="en-US">generated</span><span lang="en-US"> manually. However, the reproducibility of this method raises an issue, and manually </span><span lang="en-US">identifying</span><span lang="en-US"> the avalanche thalweg for every slope is unnecessarily time-consuming. </span></p> <p><span lang="en-US">In this work, we use com1DFA simulations in three dimensional terrain. We automatically generate the two-dimensional avalanche thalweg by extracting the centre of mass coordinates at every time step. Projecting the simulation results into this thalweg following coordinate system, we can derive the position of the avalanche front and the local travel angles, from which scalar measures like runout length and runout angle are determined. We combine temporal and spatial information by introducing the thalweg-time and thalweg-altitude diagrams. These offer a different perspective on the simulation results and, at a glance, provide information on the evolution of spatio-temporal flow variables (thickness, velocity) along the avalanche thalweg in a single plot. Additionally, by using a numerical particle-grid method, we can evaluate simulation outputs at a particle level and relate them to the whole avalanche flow. Another advantage of the analysis tools operating in the thalweg coordinate system is the possibility to compare simulation results with field measurements. For example, we present in-flow particle sensors trajectories and corresponding velocities recorded during field experiments to evaluate com1DFA simulation results and thereby help to improve the dense flow module. For different avalanche simulations, we show how these analysis modules provide a new way to summarize the complex spatio-temporal flow variables evolution in three dimensional terrain in a more intuitive two dimensional illustration along the </span><span lang="en-US">automatically generated thalweg.</span></p>

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<p>At the core of many avalanche simulation tools, numerical kernels are utilized to solve flow model equations. Aside from trying to fit the models as best as possible to the current understanding of actual flow mechanisms, these kernels have to fulfill general mathematical requirements, such as convergence, stability and consistency. The precision of numerical solutions is limited and needs to be determined by appropriate uncertainty quantification approaches. It is also necessary to assess the impact of input variability propagating through the numerical kernel.</p><p>To allow kernel testing and uncertainty quantification, the AvaFrame framework provides a suite of test cases as well as analysis tools. This includes tests with known solutions usable to determine the kernel errors (ana1Tests) and idealized/real world topographies to estimate effects of varying simulation setups. By changing numerical settings, flow model setup or input data it is possible to show their effects on simulation results in a quantitative manner. It therefore allows us to relate input variations to the uncertainty in simulation results. Error and uncertainty quantification is done using modules for computing statistical measures (ana4Stats), indicators along an avalanche path (ana3AIMEC) and various visualization routines.</p><p>We showcase this for our com1DFA dynamical dense flow avalanche (DFA) module. The kernel of com1DFA is based on depth integrated governing equations (shallow water) and solved numerically using the smoothed particle hydrodynamics (SPH) method. Applying our analysis tools, we evaluate the convergence of the DFA kernel with regard to the numerical parameters time step, SPH kernel size and particles size. We investigate the accuracy and precision of the numerical solution using the similarity solution test, a test with a semi-analytic solution for depth integrated equations. It allows us to establish a suitable relation between time step, SPH kernel size and particles size for the com1DFA kernel.</p><p>Using the same approach for an avalanche setup, we can also vary selected input parameters like friction coefficients and/or release thickness and quantify the resulting uncertainties on simulation results, e.g. runout and peak flow variables.</p>

<p>Testing and benchmarking avalanche models is a crucial step in developing models as well as assessing their applicability. This is not only limited to the representation of physical processes within models, be it via first principles or using empirical relationships, but also concerns their computing environment, including compilers, hardware used, programming language, among others. </p><p>Test, benchmarking, and comparison strategies can aim at different issues, among others: numerics, the implementation thereof, plausibility, verification, or evaluation. However, they always require reference or expected results. References can come from observations, analytical results, comparison to other models, known physical processes or material properties that cannot be changed – e.g., “avalanches cannot fly”. The question is: which characteristics or properties do we test and how to design appropriate tests?  </p><p>To facilitate this, as part of the newly developed opensource avalanche framework - AvaFrame -, we started providing commonly accessible tools to make testing and developing easier. This ranges from tools to import data, generate input parameters to automatic analysis and plotting. Not only do we provide the infrastructure for testing, but we also provide a set of test cases complete with all necessary input data, reference results, and run script examples. These tests so far include idealized (generic) topographies, specific test cases for numerical questions, and 6 real world avalanches with distinct characteristics. </p><p>In this contribution we present this freely available set of tests and benchmarks suitable to assess various aspects and properties of a shallow water model solver for a dense flow avalanche model, one of the core computing modules of AvaFrame (com1DFA). We highlight how we utilize the entire range of tests in our continuous model development to assure the quality and applicability / validity of our development. Showing results from comparison to existing models, but also how to extend and apply our strategies to other models or research questions, we invite other researchers and developers to make full use of these tools.</p>