Aspects of Ocean Circulation with Finite Element Modelling

This thesis deals with development and evaluation of the three dimensional, nonstationary ocean model FEOM:sub:0:/sub: (basic version of the Finite Element Ocean Model FEOM). This model is based on the Finite Element Method (FEM) which allows for the use of unstructured grids with variable resolution. The first part of the thesis introduces the governing equations, the mathematical formulation as well as the discretisation using FEM. After introducing the discrete form of the equations some details on the numerical implementation are given.The second part of the thesis contains applications of FEOM:sub:0:/sub: to different oceanographic tasks under idealised conditions. Comparisons to analytical results as well as to results of other numerical models in corresponding experiments are presented.The first application investigates the propagation of waves in a stratified ocean. The model shows nice correspondence to theoretically obtained wave properties as well as to results of the Modular Ocean Model (MOM). The second investigation considers the wind driven ocean circulation, especially the resulting vertical structure of the flow field. The influence of topography is examined, the results coincide with the predictions of linear theory. Finally an idealised overflow scenario is investigated. The flow of dense water on a slope poses a special problem for numerical ocean models. An international intercomparison study (DOME: Dynamics of Overflow Mixing and Entrainment) was conceived in order to gain insight into the capabilities of different numerical models in reproducing this process. FEOM:sub:0:/sub: is applied to the idealised DOME setup with and without interior density stratification. In case of a homogeneous interior a variability in the overflow rate of several days shows up, the model gives a reasonable path of the plume and reproduces the theoretically obtained dependence of the overflow transport on Coriolis parameter and density structure

Systematic Comparison of Tsunami Simulations on the Chilean Coast Based on Different Numerical Approaches

This article belongs to the Special Issue Modelling and Numerical Simulation of Tsunami https://www.mdpi.com/journal/geohazards/special_issues/model_tsunamiTsunami inundation estimates are of crucial importance to hazard and risk assessments. In the context of tsunami forecast, numerical simulations are becoming more feasible with the growth of computational power. Uncertainties regarding source determination within the first minutes after a tsunami generation might be a major concern in the issuing of an appropriate warning on the coast. However, it is also crucial to investigate differences emerging from the chosen algorithms for the tsunami simulations due to a dependency of the outcomes on the suitable model settings. In this study, we compare the tsunami inundation in three cities in central Chile (Coquimbo, Viña del Mar, and Valparaíso) using three different models (TsunAWI, Tsunami-HySEA, COMCOT) while varying the parameters such as bottom friction. TsunAWI operates on triangular meshes with variable resolution, whereas the other two codes use nested grids for the coastal area. As initial conditions of the experiments, three seismic sources (2010 Mw 8.8 Maule, 2015 Mw 8.3 Coquimbo, and 1730 Mw 9.1 Valparaíso) are considered for the experiments. Inundation areas are determined with high-resolution topo-bathymetric datasets based on specific wetting and drying implementations of the numerical models. We compare each model’s results and sensitivities with respect to parameters such as bottom friction and bathymetry representation in the varying mesh geometries. The outcomes show consistent estimates for the nearshore wave amplitude of the leading wave crest based on identical seismic source models within the codes. However, with respect to inundation, we show high sensitivity to Manning values where a non-linear behaviour is difficult to predict. Differences between the relative decrease in inundation areas and the Manning n-range (0.015–0.060) are high (11–65%), with a strong dependency on the characterization of the local topo-bathymery in the Coquimbo and Valparaíso areas. Since simulations carried out with such models are used to generate hazard estimates and warning products in an early tsunami warning context, it is crucial to investigate differences that emerge from the chosen algorithms for the tsunami simulations.This study is part of the tsunami component in the RIESGOS project, with a larger scope of multi-hazard assessments in the Andes region. The RIESGOS project is funded by the German Federal Ministry of Education and Research (Grant numbers 03G0876C and 03G0905C). AG acknowledges the Research Center for Integrated Disaster Risk Management (CIGIDEN), ANID/FONDAP/15110017. NZ has received funding from the Marie Skłodowska-Curie grant agreement H2020-MSCA-COFUND-2016-75443. The Servicio Hidrográfico y Oceanográfico de la Armada de Chile (SHOA) provided high-resolution bathymetry data via the CENDHOC program (Centro Nacional de Datos Hidrográficos y Oceanográficos de Chile). We thank EDANYA Group for sharing the Tsunami-HYSEA code and X. Wang for sharing the COMCOT code. We acknowledge M. Moreno, M. Shrivastava and M. Carvajal for providing the finite faults used in the three experiments. Basemaps by OpenStreetMaps contributors were used in most of the figures. Basemaps in Figure 6 and Figure 10 are taken from Google Earth. Some figures were generated with the GMT software [44]. TsunAWI code optimization was supported by the LEXIS project, funded by the EU’s Horizon 2020 Research and Innovation Programme (2014–2020) under grant agreement no. 825532. Some figures were generated with the software QGIS. We would like to deeply thank the editors and three anonymous reviewers for valuable comments that helped us improving the manuscript.Peer ReviewedPostprint (published version

Operational tsunami modelling with TsunAWI – recent developments and applications

In this article, the tsunami model TsunAWI (Alfred Wegener Institute) and its application for hindcasts, inundation studies, and the operation of the tsunami scenario repository for the Indonesian tsunami early warning system are presented. TsunAWI was developed in the framework of the German-Indonesian Tsunami Early Warning System (GITEWS) and simulates all stages of a tsunami from the origin and the propagation in the ocean to the arrival at the coast and the inundation on land. It solves the non-linear shallow water equations on an unstructured finite element grid that allows to change the resolution seamlessly between a coarse grid in the deep ocean and a fine representation of coastal structures. During the GITEWS project and the following maintenance phase, TsunAWI and a framework of pre- and postprocessing routines was developed step by step to provide fast computation of enhanced model physics and to deliver high quality results

Current status of TsunAWI contributions to the Indonesia Tsunami Early Warning System (InaTEWS) with a comparison of warning products from near-realtime easyWave and precomputed TsunAWI simulations

Abstract: The Indonesia Tsunami Early Warning System delivers simulated tsunami forecasts in two different ways: either matching scenario(s) from a pre-computed database or running on-the-fly tsunami simulation. Recently, the database has been extended considerably taking into account additional source regions not covered in earlier stages of the system. In this contribution, we present the current status of the data base coverage as well as a study investigating the warning products obtained by the two modeling approaches. The pre-computed tsunami scenarios are based on the finite element model TsunAWI that employs a triangular mesh with resolution ranging from 20km in deep ocean to 300m in coastal areas and to as much as 50m in some highly resolved areas. TsunAWI solves the nonlinear shallow water equations and contains a wetting-drying inundation scheme. The on-the-fly propagation model easyWave solves the linear shallow water equations on a regular finite-difference grid with a resolution of about 1 km and utilizes several simple options to estimate coastal impact. This model is used for forecasting after a tsunami has been generated in an area not covered by the database or after a moment tensor solution shows an earthquake focal mechanism not present in the database. Since warning products like estimated wave height (EWH) and estimated time of arrival (ETA) along the coast are based on modeling results, it is crucial to compare the resulting forecasted warning levels obtained by the two approaches. Resolutions and numerical settings of both models are quite different, therefore variations in the resulting outputs are to be expected; nevertheless, the extent of differences in warning levels should not be too large for identical sources. In the present study, we systematically investigate differences in resulting warning products along InaTEWS forecast points facing the Sunda arc.  Whereas the finite-element mesh of TsunAWI covers the coast up to a terrain height of 50m and warning products have been pre-calculated directly in the forecast points, easyWave offers several options for their approximation including projections from offshore grid points or vertical wall. Differences and potential reasons for variations of warning products like the role of bathymetry resolution as well as the general approach for the assessment of EWH and ETA for different modeling frameworks are discussed

Tsunami-Simulation für das indonesische Tsunami-Frühwarnsystem

Nach dem verheerenden Tsunami im Indischen Ozean 2004 wurde das internationale Kooperationsprojekt ''German-Indonesian Tsunami Early Warning System'' ins Leben gerufen und das Frühwarnzentrum am Amt für Meteorologie, Klimatologie und Geophysik in Jakarta aufgebaut. Auf deutscher Seite wurde das Projekt vom Helholtz-Zentrum Potsdam, Deutsches Geoforschungszentrum geleitet. Die Warnung nach einem starken Erdbeben basiert auf einer Datenbank möglicher Tsunamiszenarien, so dass schnell die Gefährdung der Küsten abgeschätzt werden kann. Im Vorfeld dienen detailiierte Überflutungsrechnungen als Basis für Evakuierungspläne. Der Vortrag stellt den Aufbau des Warnsystems mit einem Schwerpunkt auf der Rolle der Tsunami-Simulation vor. Insbesondere werden die physikalischen und numerischen Grundlagen des Simulationsmodells TsunAWI beleuchtet und am Beispiel einiger Modellrechnungen Möglichkeiten und Grenzen der Simulation aufgezeigt

Evaluation and Application of Newly Designed Finite Volume Coastal Model FESOM-C, Effect of Variable Resolution in the Southeastern North Sea

A newly developed coastal model, FESOM-C, based on three-dimensional unstructured meshes and finite volume, is applied to simulate the dynamics of the southeastern North Sea. Variable horizontal resolution enables coarse meshes in the open sea with refined meshes in shallow areas including the Wadden Sea and estuaries to resolve important small-scale processes such as wetting and drying, sub-mesoscale eddies, and the dynamics of steep coastal fronts. Model results for a simulation of the period from January 2010 to December 2014 agree reasonably well with data from numerous regional autonomous observation stations with high temporal and spatial resolutions, as well as with data from FerryBoxes and glider expeditions. Analyzing numerical solution convergence on meshes of different horizontal resolutions allows us to identify areas where high mesh resolution (wetting and drying zones and shallow areas) and low mesh resolution (open boundary, open sea, and deep regions) are optimal for numerical simulations

Designing variable ocean model resolution based on the observed ocean variability

If unstructured meshes are refined to locally represent eddy dynamics in ocean circulation models, a practical question arises on how to vary the resolution and where to deploy the refinement. We propose to use the observed sea surface height variability as the refinement criterion. We explore the utility of this method (i) in a suite of idealized experiments simulating a wind-driven double gyre flow in a stratified circular basin and (ii) in simulations of global ocean circulation performed with FESOM. Two practical approaches of mesh refinement are compared. In the first approach the uniform refinement is confined within the areas where the observed variability exceeds a given threshold. In the second one the refinement varies linearly following the observed variability. The resolution is fixed in time. For the double gyre case it is shown that the variability obtained in a high-resolution reference run can be well captured on variable-resolution meshes if they are refined where the variability is high and additionally upstream the jet separation point. The second approach of mesh refinement proves to be more beneficial in terms of improvement downstream the midlatitude jet. Similarly, in global ocean simulations the mesh refinement based on the observed variability helps the model to simulate high variability at correct locations. The refinement also leads to a reduced bias in the upper-ocean temperatur

Comparison of modeling approaches and the resulting warning products in the framework of the Indonesia Tsunami Early Warning System (InaTEWS)

The Indonesia Tsunami Early Warning System delivers simulated tsunami forecasts in two different ways: either matching scenario(s) from a pre-computed database or running on-the-fly tsunami simulation. The pre-computed tsunami scenarios are based on the finite element model TsunAWI that employs a triangular mesh with resolution ranging from 20km in deep ocean to 300m in coastal areas and to as much as 50m in some highly resolved areas. TsunAWI solves the nonlinear shallow water equations and contains a wetting-drying inundation scheme. The on-the-fly propagation model easyWave solves the linear shallow water equations on a regular finite-difference grid with a resolution of about 1 km and utilizes several simple options to estimate coastal impact. This model is used for forecasting after a tsunami has been generated in an area not covered by the database or after a moment tensor solution shows an earthquake focal mechanism not present in the database. Since warning products like estimated wave height (EWH) and estimated time of arrival (ETA) along the coast are based on modeling results, it is crucial to compare the resulting forecasted warning levels obtained by the two approaches. Resolutions and numerical settings of both models are quite different, therefore variations in the resulting outputs are to be expected; nevertheless, the extent of differences in warning levels should not be too large for identical sources. In the present study, we systematically investigate differences in resulting warning products along InaTEWS forecast points facing the Sunda arc. Whereas the finite-element mesh of TsunAWI covers the coast up to a terrain height of 50m and warning products have been pre-calculated directly in the forecast points, easyWave offers several options for their approximation including projections from offshore grid points or vertical wall. Differences and potential reasons for variations of warning products like the role of bathymetry resolution as well as the general approach for the assessment of EWH and ETA for different modeling frameworks are discussed in this contribution