1. ANUGA Workshop, 16 September 2008 How fine is fine enough? Convergence study of an ANUGA inundation model Leharne Fountain ANUGA – Present Applications and Future Potential Geoscience Australia, 16-17 September 2008

2. ANUGA Workshop, 16 September 2008 Research questions: a tale in three parts Is ANUGA really scaleable? (We hope so!) Does ANUGA really converge? (We hope so!) At what spatial mesh resolution/s will ANUGA perform optimally? (Good question!)

3. ANUGA Workshop, 16 September 2008 Part I: Is ANUGA scaleable?

4. ANUGA Workshop, 16 September 2008 Transform the Okushiri model to true-scale and verify –Elevation model –Domain & polygons –Input wave Compare model output with that from original model Methodology

5. ANUGA Workshop, 16 September 2008 Time-series comparisons

6. ANUGA Workshop, 16 September 2008 Time-series comparisons

7. ANUGA Workshop, 16 September 2008 Time-series comparisons

8. ANUGA Workshop, 16 September 2008 Part II: Does ANUGA converge?

9. ANUGA Workshop, 16 September 2008 Methodology Define model –Use contour-based interior polygons Vary mesh resolution –Alter max triangle area by factor of 2 Measure convergence –Time-series comparison  order of convergence –Spatial comparison

10. ANUGA Workshop, 16 September 2008 Depth Elevation Stage Stage = Depth - Elevation Offshore: Stage = Depth + Elevation Onshore: Stage Elevation Depth MSL Terminology

11. ANUGA Workshop, 16 September 2008 Elevation

12. ANUGA Workshop, 16 September 2008 Contour-based interior polygons -25 m -10 m -5 m 1m r = 1600R 2000m 2 – 1,024,000m 2 r = 80R 100m 2 – 51,200m 2 r = 8R 10m 2 – 5120m 2 r = 3.2R 4m 2 – 2048m 2 r = R 1.25m 2 – 640m 2

13. ANUGA Workshop, 16 September 2008 R = 640

14. ANUGA Workshop, 16 September 2008 R = 1.25

15. ANUGA Workshop, 16 September 2008 Input wave

16. ANUGA Workshop, 16 September 2008 Model statistics Resolution (max tr. area) Approx tr. side length No. of triangles Computation time (hh:mm:ss) 1.251.58474,31219:20:26 2.52.24238,8976:05:54 53.16120,8082:17:46 104.4762,0700:41:14 206.3232,9130:14:49 408.9418,4880:07:14 8012.6511,4690:04:18 16017.888,3010:03:16 32025.306,9090:02:49 64035.786,3730:02:44

17. ANUGA Workshop, 16 September 2008

18. Results: Time domain

19. ANUGA Workshop, 16 September 2008 Polygons and gauges Ch 9 Ch 7 Ch 5 a b c d e 12 3 4 5

20. ANUGA Workshop, 16 September 2008

23. Order of convergence = 1

24. ANUGA Workshop, 16 September 2008 Results: Spatial domain

25. ANUGA Workshop, 16 September 2008 Spatial mesh performance Maximum depth over whole simulation Depth at constant times Each of the 9 models subtracted from highest resolution model (R=1.25)

26. ANUGA Workshop, 16 September 2008 Maximum depth

27. ANUGA Workshop, 16 September 2008 2.5

28. ANUGA Workshop, 16 September 2008 5

29. 10

30. ANUGA Workshop, 16 September 2008 20

31. ANUGA Workshop, 16 September 2008 40

32. ANUGA Workshop, 16 September 2008 80

33. ANUGA Workshop, 16 September 2008 160

34. ANUGA Workshop, 16 September 2008 320

35. ANUGA Workshop, 16 September 2008 640

36. ANUGA Workshop, 16 September 2008 Depth at constant times

37. ANUGA Workshop, 16 September 2008 t = 200 s

38. ANUGA Workshop, 16 September 2008 t = 200 s

39. ANUGA Workshop, 16 September 2008 t = 250 s

40. ANUGA Workshop, 16 September 2008 t = 250 s

41. ANUGA Workshop, 16 September 2008 t = 300 s

42. ANUGA Workshop, 16 September 2008 t = 300 s

43. ANUGA Workshop, 16 September 2008 t = 350 s

44. ANUGA Workshop, 16 September 2008 t = 350 s

45. ANUGA Workshop, 16 September 2008 t = 400 s

46. ANUGA Workshop, 16 September 2008 t = 400 s

47. ANUGA Workshop, 16 September 2008 t = 450 s

48. ANUGA Workshop, 16 September 2008 t = 450 s

49. ANUGA Workshop, 16 September 2008 640

50. ANUGA Workshop, 16 September 2008 Difference in maximum depth Difference in depth at t = constant t

51. ANUGA Workshop, 16 September 2008 Part III: How fine is fine enough?

52. ANUGA Workshop, 16 September 2008 How fine is fine enough? What is the purpose of our model? –Determine risk –Make decisions in response to risk How does the mesh resolution affect these decisions? Balance computational expense and accuracy

53. ANUGA Workshop, 16 September 2008 Determining risk Maximum extent of inundation Offshore wave height Maximum flow speeds

54. ANUGA Workshop, 16 September 2008 Max extent of inundation R = 1.25 Max extent of inundation R = 640 Coastline (elevation = 0) Maximum extent of inundation

55. ANUGA Workshop, 16 September 2008 Summary ANUGA is scaleable ANUGA achieves first order convergence Spatial & temporal investigation of mesh resolution provides more information about mesh performance Consider purpose of model, data requirements & computational expense in selection of optimal resolution