An Analysis of Sampling Methods and Uncertainty Propagation for Shallow Water Modeling Público

Abstract

Numerical models depend on inputs and parameters that are often uncertain. This causes uncertainty in the output. In this work, we explore both sampling and uncertainty propagation methods. We aim to assess which sampling methods best represent uncertainties in inputs and also explore which uncertainty propagation methods best depict the uncertainty that results in the output. We assess these methods using a two-dimensional shallow water model.

Table of Contents

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . .1

2 Sampling Methodologies . . . . . . . . . . . . . . . . . . . . . . .3

2.1 Random Sampling . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Stratified Sampling Method . . . . . . . . . . . . . . . . . . . 4

2.3 Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . 6

2.4 Comparing Sampling Methods . . . . . . . . . . . . . . . . . . 8

3 Procedures Measure Propagation of Uncertainty 9

3.1 Monte Carlo Analysis . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Monte Carlo Analysis . . . . . . . . . . . . . . . . . . . 10

3.1.2 Rejection Sampling . . . . . . . . . . . . . . . . . . . . 12

3.1.3 Importance Sampling . . . . . . . . . . . . . . . . . . . 13

3.2 Differential Analysis . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Response Surface Methodology(RSM) . . . . . . . . . . . . . . 15

3.4 Fourier Amplitude Sensitivity Test(FAST) . . . . . . . . . . . 20

4 Applications 23

4.1 Shallow Water Equation in 2D . . . . . . . . . . . . . . . . . . 23

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.1 Response Surface Method and Differential Analysis . . 28

4.2.2 The Differential Analysis . . . . . . . . . . . . . . . . . 29

4.2.3 The Fourier Amplitude Sensitivity test . . . . . . . . . 30

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Palabra Clave	Propagation of Uncertainty Sampling Methods Shallow Water Model
Committee Chair / Thesis Advisor	Sue Mialon, Emory University Bree Ettinger, Emory University Talea Mayo, Emory University

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