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# DSD-INT 2019 Using Multilevel Monte Carlo Methods to assess erosion-flood risk in the coastal zone - Clare

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Presentation by Mariana Clare, Imperial College London, UK, at the Delft3D and XBeach User Day: Coastal morphodynamics, during Delft Software Days - Edition 2019. Wednesday, 13 November 2019, Delft.

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### DSD-INT 2019 Using Multilevel Monte Carlo Methods to assess erosion-flood risk in the coastal zone - Clare

1. 1. Mariana Clare1 Delft3D and XBeach User Day: Coastal morphodynamics Supervisors: Prof Matthew Piggott1,Dr.Colin Cotter1 and Dr.CatherineVillaret2 1Imperial College London 2East Point Geo Consulting Using Multilevel Monte Carlo Methods to assess erosion/flood risk in the coastal zone 13th November 2019 m.clare17@imperial.ac.uk
2. 2. February 2014 in Dawlish, Devon 2 This cost £35 million to fix and is estimated to have cost the Cornish economy £1.2 billion
3. 3. 3 Assessing Risk Problem: Two main sources of uncertainty which propagate into prediction values: 1. Model Uncertainty 2. Uncertainty in Input Data Possible Solution: Use Monte Carlo simulation varying parameters e.g. Callaghan et al. (2013) Problem with Monte Carlo: XBeach is computationally expensive: Callaghan et al. (2013) estimate to use Monte Carlo with XBeach with their problem would take 4.5 millennia
4. 4. POSSIBLE SOLUTION 2: MULTILEVEL MONTE CARLO METHODS 4
5. 5. 5 RECAP: Monte Carlo Simulation Repeated random sampling of a variable from a distribution which are then run through a model to produce a range of outcomes Monte Carlo estimator for N sample points e.g. ෣𝑋𝐵𝑒𝑎𝑐ℎ(𝑤) = 1 𝑁 σ𝑖=1 𝑁 𝑋𝐵𝑒𝑎𝑐ℎ(𝑤𝑖)
6. 6. RECAP: Multilevel Grid FINER grid scales MORE Computationally expensive l = 0 l = 1 l = 2 l = 3 l = 4 6
7. 7. Multilevel Monte Carlo (MLMC) FINER grid scale l = 0 l = 1 l = 2 l = 3 l = 4 7 we see Using same random number used to generate Pi l and Pi l-1 Nl independent difference estimators
8. 8. Some MLMC Theory 8 where 𝑉𝑙 is the variance of the sample (𝑃𝑙 (𝑖) − 𝑃𝑙 𝑖−1 ) and 𝑁𝑙 the number of samples at each level Variance is main source of error: independent events compared to O(Nl -1/2) for Monte Carlo
9. 9. 9
10. 10. 10 UNCERTAINTY IN BEACH BEDSLOPE ANGLE Question: what is the maximum expected distance along the x-axis the water reaches up the beach? Angle Range 𝛼 ∈ [0, tan−1(0.5)]
11. 11. 11 Does MLMC work with XBeach? 1D
12. 12. 12 Does MLMC give a speed-up with XBeach? Maximum expected surge distance: 873 m 1D Convergence Rate
13. 13. 13 Distribution 1D
14. 14. 14 Maximum expected surge distance: 869m Runtime: 30 mins on 13 cores 2D Convergence Rate
15. 15. 15 Distribution 2D
16. 16. 16 UNCERTAINTY INWAVEHEIGHT Jonswap spectrum for H0=2.5m, fp = 0.08s-1, 𝝲 = 3.3 and fynq = 0.3s-1 Waveheight Range 𝐻0 ∈ 1, 6 𝑚
17. 17. 17 Wave Runup Height Source: Manual, EurOtop. "Wave Overtopping of Sea Defences and Related Structures–Assessment Manual." UK: NWH Allsop, T. Pullen, T. Bruce. NL: JW van der Meer. DE: H. Schüttrumpf, A. Kortenhaus. www. overtopping-manual. com (2007).
18. 18. 18 Expected 𝑅 𝑢2%: 0.108m Does MLMC work with XBeach?
19. 19. 19
20. 20. 20 Source: Gent, Marcel & Vroeg, J. (2008). Dune Erosion Prediction Method Based on Large-Scale Model Tests. Erosion Volume Use standard Delta Flume XBeach test case Waveheight Range 𝐻0 ∈ 1, 6 𝑚
21. 21. 21 Expected erosion volume: 0.0138 Does MLMC work with XBeach?
22. 22. 22 • Introduce more complex wave profiles and coastal regions with more complex shapes • Investigate the effect of uncertainty in more than one parameter for each test case simulation and for more than one quantity • Investigate more parameters and more test cases – any ideas? FURTHERWORK
23. 23. 23
24. 24. ▪ Giles, M. B. (2015). Multilevel Monte Carlo methods, Acta Numerica, 24:259-328. ▪ Callaghan, D. P., Ranasinghe, R., and Roelvink, D. (2013).Probabilistic estimation of storm erosion using analytical, semi-empirical, and process based storm erosion models. Coastal Engineering, 82:64-75. ▪ Cliffe, K. A., Giles, M. B., Scheichl, R., and Teckentrup, A. L. (2011). Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients. Computing and Visualization in Science, 14(1):3-15. ▪ Roelvink, D.,Van Dongeren, A., McCall, R., Hoonhout, B.,Van Rooijen, A.,Van Geer, P., De Vet, L., Nederhoff, K., and Quataert, E. (2015). XBeach technical reference: Kingsday release. Delft, The Netherlands: Deltares,Technical report. 24