Computational Methods for Storm Surge

Transcription

1 Computational Methods for Storm Surge Columbia University Department of Applied Physics and Applied Mathematics 1

2 Source: Jocelyn Augustino / FEMA - Storm Surge 2

3 Storm Surge Wind 3

4 Storm Surge Generation 4

5 Storm Surge Forcing Wind Bottom Friction Atmospheric Pressure b = hu gn2 h 4/3 u 2 + v 2 rp A Coriolis (2 sin ) u Short (deep) water waves 5

6 Storm Surge Model h t +(hu) x +(hv) y =0 hu (hu) t gh2 x +(huv) y = ghb x + fhv h (P A) x + 1 ( sx bx ) (hv) t +(huv) x + hv gh2 y = ghb y fhu h (P A) y + 1 ( sy by ) 6

7 Storm Representation Montage of Hurricane Ike. Image courtesy of CIMMS: 7

8 Holland Hurricane Model Holland, G. J. An Analytic Model of the Wind and Pressure Profiles in Hurricanes. Monthly Weather Review 108, (1980) 8

9 Hansen, J., R. Ruedy, M. Sato, and K. Lo, 2010: Global surface temperature change, Rev. Geophys., 48, RG4004, doi: /2010rg GISTEMP Team, 2015: GISS Surface Temperature Analysis (GISTEMP). NASA Goddard Institute for Space Studies. Dataset accessed at Questions 9

10 Geophysical Fluid Dynamics Laboratory - Climate Impact of Quadrupling CO2, Princeton, NJ, USA: NOAA GFDL, How does sea-level rise effect surge? 10

11 NASA and NHC Will dangerous storms become more frequent? 11

12 NOAA Will dangerous storms become more powerful? 12

13 NOAA - NHC Can we forecast events? 13

14 Gauge µ µ ± 2σ Water surface elevation (m) Time (s) Can we quantify uncertainty? 14

15 Donar Reiskoffer How do we protect ourselves? 15

16 Can we protect ourselves? 16

17 Needed Capabilities Climate Sea-Level Rise Change in storm frequency and intensity Forecasting Uncertainty in storm forecasts Critical Decision Making Protection Optimality Region implications Requirements Ensembles ~ 10 6 Disparate scales Bathymetry Protection Strategies Approach Adaptive Mesh Refinement H-box Methods Sub-scale Models 17

18 Things we are doing Adaptive Mesh Refinement Sub-Scale Barrier Modeling Two-Layer Shallow Water Air-Sea Interaction Jeff Schmaltz, MODIS Rapid Response Team, NASA/GSFC 18

19 Adaptive Mesh Refinement 19

20 Adaptive Discretization Level 3 Level 2 y x Level 1 20

21 GeoClaw Marsha Berger (NYU) Randy LeVeque (U. Washington) Dave George (USGS) Berger, M. J., George, D. L., LeVeque, R. J. & Mandli, K. T. The GeoClaw software for depth-averaged flows with adaptive refinement. Advances in Water Resources 34, (2011). 21

22 Chile 2010 Tsunami 22

23 Chile 2010 Tsunami 23

24 Hurricane Ike Level Refinement Factor Resolution (m) NASA 24

25 Domain and Friction 25

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27 27

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29 29 0

30 ADCIRC Comparison Hope, M. E. et al. Hindcast and validation of Hurricane Ike (2008) waves, forerunner, and storm surge. J. Geophys. Res. Oceans 118, 1 37 (2013). 30

31 Gauge Locations 31

32 Gauge Comparisons 32

33 Gauge Comparisons 33

34 Gauge Comparisons 34

35 Gauge Comparisons 35

36 Patch Statistics 36

37 Timings Package Bathymetry Computer Cores Wall Time Core Time ADCIRC Fine Stampede minutes 2333 hours GeoClaw Fine Stampede 16 2 hours 32 hours GeoClaw Coarse Laptop 4 2 hours 8 hours 37

38 Surge Protection 38

39 Surge Protection Where do we put protection? How high does it need to be? Is it regionally destructive? Is this optimal? 39

40 Flood Protection MRGO and the Intracoastal Waterway and Industrial (IHNC) Canals, Eastern New Orleans, Louisiana (New Orleans, U.S. Army Corp of Engineers) 40

41 Flood Protection The entrance the 168th Street subway station in New York City. Taken by Seidenstud

42 Failure is Bad 42

43 Representation of Barriers Jiao Li 43

44 Riemann Solver 44

45 Riemann Solver 45

46 Riemann Solver 46

47 Riemann Solver 47

48 Riemann Solver 48

49 Riemann Solver 49

50 Redistribution of Waves f(q k+1 ) f(q k )= M w X p=1 p k+1/2 rp M w X p=1 Z p k+1/2 Z 2 = 2 r 2 Z 3 = 3 r 3 Z 1 = 1 r 1 Z 4 = 4 r 4 50

51 Redistribution of Waves R =[r 1,r 2,r 3,r 4 ], =[ 1, 2, 3, 4 ] b =[ 1 + 1, 0, 0, ] R b = R ( 1 = (s4 s 2 ) 2 +(s 4 s 3 ) 3 s 4 s 1, 2 = (s2 s 1 ) 2 +(s 3 s 1 ) 3 s 4 s 1. Ẑ 1 =( )r 1 Ẑ 4 =( )r 4 51

52 Riemann Solver 52

53 Riemann Solver 53

54 Dry Test 54

55 Comparisons 55

56 Under Pressure g( z) 56

57 Water on the Wall Use other side of wall as ghost fluid depth Q L W = Q L k+1/2 (B W B L ) Q R W = Q R k+1/2 (B W B R ) Use averages of states Q m = QL k+1/2 + QR k+1/2 2 Q L W = Q m (B W B L ) Q R W = Q m (B W B R ) 57

58 Ghost Water 58

59 The CFL Strikes Back 59

60 H-Box 60

61 H-box: 1D 61

62 Wave-Propagation Prospective t 2 Z i 1/2 Z + Z i+3/2 Z + i+1/2 i+3/2 t 1 Z + i 1/2 Z i+1/2 62

63 Wave-Propagation Prospective Z i 1/2 Z + i+3/2 63

64 Wave-Propagation Prospective Update Solve Z i 1/2 Z + i+3/2 Q i Q i+1 64

65 Wave-Propagation Prospective Z i 1/2 Z + i+3/2 Q i Q i+1 65

66 H-Box Methods j +1 j j 1 i i +1 66

67 H-Box Methods Normal Transverse j +1 j j 1 j +1 j j 1 i i +1 i i +1 67

68 Outlook 68

69 Storm Surge Forecasting Mandli, K. T. & Dawson, C. N. Adaptive Mesh Refinement for Storm Surge. Ocean Modelling 75, (2014). 69

70 Gauge µ µ ± 2σ Water surface elevation (m) Time (s) Sraj, I., Mandli, K. T., Knio, O. M., Dawson, C. N., & Hoteit, I. Uncertainty Quantification and Inference of Manning s Friction Coefficient using DART Buoy Data during the Tohoku Tsunami. Ocean Modelling (2014). UQ and Data Assimilation 70

71 Adding Depth to the Shallow Water Equations 71

72 Two-Layer Shallow Water Mandli, K. T. A Numerical Method for the Two Layer Shallow Water Equations with Dry States. Ocean Modelling 72, (2013). 72

73 Hyperbolicity 73

74 Energy, E(f) Period 24 hr 12 hr 5 min 30 sec 1 sec 0.25 sec 0.1 sec Hs (m) Primary disturbing force Primary restoring force Sun, Moon Observed SWAN hours Moment Eqs minutes Lake Erie August 2011 Storm systems, earthquakes Coriolis force Wind Gravity Surface tension Buoy Freq-int (5.13 mins) SWAN (207 mins) Spectral models Wind-sea spectrum Swell (see Figure 3) 0 8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28 8/29 8/30 8/31 9/1 time frequency, f Colton, C. J., Mandli K.T., Kubatko, E., Fractally homogeneous, air-sea turbulence with Frequency-integrated, E. Kubatko, adapted from Munk, W. H. Origin and generation of waves. Coastal Engineering Proceedings (1950). wind-driven gravity waves. Submitted to Ocean Modelling. Air-Sea Waves 74

75 Dirty AMR Secrets 75

76 Ongoing Work Burstedde, C., Calhoun, D. A., Mandli, K. & Terrel, A. R. ForestClaw: Hybrid forest-of-octrees AMR for hyperbolic conservation laws. in ParCo

77 - DAC u integrator u DERIVATIVE DAC f (u) = 2u+1 f(u) = u 2 +u-rhs - δ integrator QUOTIENT δ f(u)/f (u) FUNCTION Analog/Digital Computing 77