## Abstract

Tsunami modelling involves the problem of forecasting the effect that a tsunami has on a coastal area, given the recordings of the water height at several buoys. This forecast has two consecutive steps: (1) estimating the initial condition from the buoy data, and (2) propagating that initial condition to forecast the effect on the coast. In order to be effective, the forecast should be completed within reasonable time. This is challenging, as the first step involves solving a high-dimensional inverse problem, at significant computational cost. Therefore, there is a need to search for methods that accelerate the solution of the inverse problem. One approach is to reduce the number of dimensions of the inverse problem through parameter reduction. This involves determining a reduced parameter basis, which enables us to approximate the model data to a high level at accuracy while reducing the dimensionality of the inverse problem. This approach introduces an 'offline' and an 'online' stage: during the offline stage, before a tsunami occurs, we allocate significant computational cost to determining the reduced basis. As soon as a tsunami occurs and buoy data arrives, we address the inverse problem, which is now lower-dimensional as a result of our efforts of determining the reduced basis in the offline stage. (Figure Presented) In this work, we consider the model tsunami problem illustrated in Figure 1, which shows how the water height evolves over time, starting from an arbitrary initial condition. The initial condition is parameterised by the input parameters p, which result in the buoy output y(p). We focus on finding a reduced basis, such that the reduced model y(Q_{k}p) is an accurate estimate of the full model y(p), with Q_{k} an orthogonal projection corresponding to the reduced basis. We use a greedy algorithm to approximate the optimal reduced basis. We add a novel element to the greedy algorithm by quantifying how well the reduced model approximation y(Q_{k}p) can recover the full model y(p) for arbitrary p. Results for up to N = 25 input parameters show that we can efficiently approximate the full model by using a reduced number of parameters. We find that the relative amount of parameters that we need for an accurate approximation decreases when the number of input parameters increases.

Original language | English |
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Title of host publication | Proceedings - 21st International Congress on Modelling and Simulation, MODSIM 2015 |

Editors | Tony Weber, Malcolm McPhee, Robert Anderssen |

Publisher | Modelling and Simulation Society of Australia and New Zealand Inc (MSSANZ) |

Pages | 112-118 |

Number of pages | 7 |

ISBN (Electronic) | 9780987214355 |

Publication status | Published - 2015 |

Event | 21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015 - Broadbeach, Australia Duration: 29 Nov 2015 → 4 Dec 2015 |

### Publication series

Name | Proceedings - 21st International Congress on Modelling and Simulation, MODSIM 2015 |
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### Conference

Conference | 21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015 |
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Country/Territory | Australia |

City | Broadbeach |

Period | 29/11/15 → 4/12/15 |