Resolution sensitivity of isolated eddy evolution

with/without steep topography

24-26 April 2007 HYCOM meeting, NRL, Stennis Space Center, MS, USA

Kyung Hoon Hyun* and Patrick J. Hogan**

hyun@nrlssc.navy.mil hogan@nrlssc.navy.mil

* University of Southern Mississippi** Naval Research Laboratory

1

• Motivation• Model configuration• Resolution sensitivity on the flat bottom

– Propagation (trajectory, speed), dissipation– Resolution convergence

• Resolution sensitivity to eddy-topography interaction– Eddy driven surface/deep currents– Collision trajectory over steep topography– Cross-shelf currents, shelf break jets– Shelf-slope, slope-abyssal exchange

• Conclusions• Future works

Overview

Hurlburt & Hogan (2000, DAO) Ffield (2005, DSR)

Motivation

What is the effect of resolution on eddy propagation, eddy-topography interaction?

NBC rings-slope interaction

3

• HYCOM– Version 2.1, vertical 10 layers– Closed boundary with idealized domain– No forcing, horizontally uniform density from GDEM (Teague 1990)– Biharmonic viscosity factor visco4= 0.2– Biharmonic diffusion velocity veldf4= 0.01 m/s (momentum),

thkdf4=0.005 m/s (thickness)– Laplacian diffusion velocity temdf2= 0.005 m/s (T,S)– Linear bottom friction cbar=0.05 m/s– quadratic bottom friction cb=2x10-3

• Domain– Horizontal resolution: 1/3, 1/5, 1/10, 1/20, 1/40 degrees resolution– 2000x2000km (800x800 nodes for 1/40 resolution)– depth: 50m-3500m

• Initialization of Eddy (Herbette et al. 2003 JPO)– R=80km– PVA (t=0)= 3.0f (f=7.0 x 10-5 s-1)– Max. Speed ~50 cm/s

Model Details

1. flat bottom

15 16 17 18

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98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 -20

-15

-10

-5

0

5

10

15

20

10.0cm/s 5.0cm/s

t=005

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98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 -10

-8

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10.0cm/s 5.0cm/s

t=005

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98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 -20

-15

-10

-5

0

5

10

15

20

10.0cm/s 5.0cm/s

t=005

sensitivity to initial adjustment

1/10 1/20 1/40

surface current with SSH (t=5d)

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24

25

91 90 89 88 -20

-15

-10

-5

0

5

10

15

20

4.0cm/s 2.0cm/s

t=125

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25

91 90 89 88 -20

-15

-10

-5

0

5

10

15

20

4.0cm/s 2.0cm/s

t=125

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25

91 90 89 88 -20

-15

-10

-5

0

5

10

15

20

4.0cm/s 2.0cm/s

t=125

1/10 1/20 1/40

sensitivity to propagation

surface current with SSH (t=125d)

7

sensitivity to trajectory

• Stepwise/continuous trajectory with low/high resolution• Resolution convergence: 1/20

−95 −94 −93 −92 −91 −90 −89 −88

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21.5

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22.5

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23.5

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x (oW)

y (o N

)

1/40o

1/20o

1/10o

1/5o

1/3o

−90 −89.8 −89.6 −89.4 −89.2 −89 −88.8 −88.6 −88.4 −88.2 −8822

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23.2

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x (oW)

y (o N

)

1/40o

1/20o

1/10o

1/5o

1/3o

trajectory for 1 yr 5d interval

• Faster propagation with high resolution (1/20 is 2 times faster than 1/3)

• Resolution convergence at 1/20

sensitivity to propagation speed

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

700

day

dist

ance

(km

)

1/40o

1/20o

1/10o

1/5o

1/3o

0 5 10 15 20 25 30 35 40200

250

300

350

400

450

500

550

600

650

700

resolution (1/No)di

stan

ce (

km)

zonalmeridional

zonal (solid)meridional (dashed)

propagation distance distance for 1 yr

9

sensitivity to dissipation

• Slow dissipation with high resolution (1/20 dissipates ~20% slower than 1/10)

• Resolution convergence 1/20• Vorticity: oscillatory/continuous

dissipation with low/high resolution

0 50 100 150 200 250 300 350−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Day

ζ (1

0−5 s−

1 )

1/40o

1/20o

1/10o

1/5o

1/3o

0 50 100 150 200 250 300 350 4000

2

4

6

8

10

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Day

ssh

(cm

)

1/40o

1/20o

1/10o

1/5o

1/3o

0 50 100 150 200 250 300 350 4000

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60

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120

140

t (day)

KE

(J

m−

2 )

1/40o

1/20o

1/10o

1/5o

1/3o

0 10 20 30 40 50 600.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Day

|ζ| (

10−

5 s−1 )

1/40o

1/20o

1/10o

1/5o

KE

ssh

vorticity

pv=(ζ+f)/h

2. Eddy-topography interaction

11

• Cross-slope /alongslope translation before/after collision, slope jet (qualitatively consistent for >1/10)

• 1/40 well- resolved for filament/frontal eddies

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97 96 95 94 93 -10

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-2

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10.0cm/s 5.0cm/s

t=180

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97 96 95 94 93

t=300

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97 96 95 94 93

t=420

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97 96 95 94 93 -10

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10.0cm/s 5.0cm/s

t=180

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97 96 95 94 93

t=300

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97 96 95 94 93

t=420

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97 96 95 94 93 -10

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10.0cm/s 5.0cm/s

t=180

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97 96 95 94 93

t=300

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97 96 95 94 93

t=420

1/10

1/20

1/40

sensitivity to surface currentsurface currents (180d, 300d, 420d)

12

• Stronger subsurface cyclone for> 1/20

500

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2345

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97W 96W 95W 94W

93.8W/22.4Nt=180

2345

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97W 96W 95W 94W

95.5W/22.1Nt=300

-40

-30

-20

-10

0

10

20

30

40 2345

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97W 96W 95W 94W

95.4W/21.3Nt=420

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1000

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2345

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9

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97W 96W 95W 94W

93.9W/22.3Nt=180

2345

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7

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9

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97W 96W 95W 94W

95.6W/22.1Nt=300

-40

-30

-20

-10

0

10

20

30

40 2345

6

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8

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10

97W 96W 95W 94W

95.6W/21.1Nt=420

500

1000

1500

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2345

6

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97W 96W 95W 94W

93.9W/22.2Nt=180

2345

6

7

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9

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97W 96W 95W 94W

95.5W/22.1Nt=300

-40

-30

-20

-10

0

10

20

30

40 2345

6

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9

10

97W 96W 95W 94W

95.5W/21.0Nt=420

1/10

1/20

1/40

sensitivity to subsurface currentNS currents (180d, 300d, 420d)

100

200

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600

700

2

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5

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97W 96W 95W 94W

93.8W/22.4Nt=180

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97W 96W 95W 94W

95.5W/22.1Nt=300

-40

-30

-20

-10

0

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30

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2

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97W 96W 95W 94W

95.4W/21.3Nt=420

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97W 96W 95W 94W

93.9W/22.3Nt=180

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97W 96W 95W 94W

95.6W/22.1Nt=300

-40

-30

-20

-10

0

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30

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2

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97W 96W 95W 94W

95.6W/21.1Nt=420

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97W 96W 95W 94W

93.9W/22.2Nt=180

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97W 96W 95W 94W

95.5W/22.1Nt=300

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2

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97W 96W 95W 94W

95.5W/21.0Nt=420

• Strong deep cyclonic current (1/20, 1/40)

• 1/40 resolved better than 1/20 for deep cyclone

1/10

1/40

1/20

sensitivity to subsurface currentNS currents (180d, 300d, 420d)

14

sensitivity to collision/reflection

• 1st impinging depth is shallow with high resolution: 740m (1/20, 1/40), 820m (1/10)

• Shallowest point: topographic β effect max• Offshore turning point: topographic β effect balances planetary β effect • Smooth collision trajectory with high resolution• Low resolution suppresses cross-isobaths oscillation• Frequent collision with high resolution

250 300 350 400 450−1500

−1400

−1300

−1200

−1100

−1000

−900

−800

−700

−600

−500

Day

H (

m)

1/40o (topo)

1/20o (topo)

1/10o (topo)

−92.7 −92.6 −92.5 −92.4 −92.3 −92.2 −92.1 −92 −91.9 −91.8 −91.7

20.2

20.4

20.6

20.8

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21.2

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x (oW)

y (o N

)

1/40o (topo)

1/20o (topo)

1/10o (topo)

1

23

5

4

6

1 243

5

7

6

8

87

trajectory for 240-480d total depth of eddy center

15

sensitivity to eddy swirl currents

• strong dissipation/oscillation over topography; zonal/meridional oscillation • faster dissipation with lower resolution• 1/20 resolution convergence but smoothed pattern (following the mean of 1/40)• 1/40 stronger oscillation amplitude (more realistic)

0 50 100 150 200 250 300 350 400 4500

5

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45

t (day)

u max

(cm

s−

1 )

layer 1−2

1/40o (topo)

1/20o (topo)

1/10o (topo)

0 50 100 150 200 250 300 350 400 4500

5

10

15

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25

30

35

40

45

t (day)v m

ax (

cm s

−1 )

layer 1−2

1/40o (topo)

1/20o (topo)

1/10o (topo)

zonal meridional

16

• shelf break depth = 163m• stronger cross-shelf current core

speed, frequent collision with high resolution

250 300 350 400 450500

550

600

650

700

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850

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950

1000

−7

−6

−6 −6

−5

−5

−5

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−4

−4−4

−3

−3

−3

−3

−3

−3

−2

−2

−2

−2

−2−2 −2

−1

−1

−1

−1

−1

−1

−1

−1

−1

0

0

0

0

0

0

0

0

0

0

0 0

0

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00

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1

1

1 1

1

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1/20o (topo)

Day

y (k

m)

250 300 350 400 450500

550

600

650

700

750

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850

900

950

1000

−9

−9

−8

−8

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−5 −5

−5

−5

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−4

−4

−4

−4

−4

−3

−3

−3

−3

−3

−3

−2

−2

−2

−2

−2

−2

−2

−2

−2

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

−1

0

0

0

0

0

0

0

0

0

0

0

00

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0

0

00

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0

0

0

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00

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0

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0

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1 11

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1

1

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1

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2

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2

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55

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1/40o (topo)

Day

y (k

m)

250 300 350 400 450500

550

600

650

700

750

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850

900

950

1000

−3−2

−1

−1

−1

−1

−1

0

0

0

00

0

0

0

0

0

0

0

0

0

0 0 01

1

11

2

223

34

4 56

1/10o (topo)

Day

y (k

m)

sensitivity to cross-shelf current

1 32

5

4

6

1

1 2

32

4

677

5

8

ubaro along the shelf break

17

sensitivity to shelf break jet

• Stronger/frequent shelf break jet with high resolution

250 300 350 400 450500

550

600

650

700

750

800

850

900

950

1000

−8

−6−6

−6

−6

−6

−6

−4

−4

−4

−4

−4

−4

−4

−4

−4

−4

−4

−4

−2−2

−2

−2

−2

−2

−2−2

−2

−2

−2

−2

−2

−2

−2

−2

0

0

0

0

0

0

0

0

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0

00

0

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00

2

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888

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2020

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1/40o (topo)

Day

y (k

m)

250 300 350 400 450500

550

600

650

700

750

800

850

900

950

1000

−6−6

−6

−6

−6

−4

−4

−4

−4

−4 −4

−4

−4

−2

−2

−2

−2

−2 −2

−2−2

−2−2

−2

−2

00

0

0

0

0

0

0

0

0

02

22

2

2

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88

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1010

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22 2224

1/20o (topo)

Day

y (k

m)

250 300 350 400 450500

550

600

650

700

750

800

850

900

950

1000

−4

−4

−2

−2

−2

−2

−2

−2

−2

−2

0

0

0

0

0

0

0

0

2

2

2

2 2

4

44

4

4

6

6

6

8 8

8

10

1010

12

12

14

141618

1/10o (topo)

Day

y (k

m)

vbaro along the shelf break

18

• Larger on-shelf transport with higher resolution• Smaller off-slope transport with higher resolution

net shelf-slope-abyssal exchange

250 300 350 400 450

−0.05

0

0.051/40o (topo)

Day

U (

Sv)

250 300 350 400 450

−0.05

0

0.051/20o (topo)

U (

Sv)

250 300 350 400 450

−0.05

0

0.051/10o (topo)

U (

Sv)

150 200 250 300 350 400 450−2

−1

0

1

21/40o (topo)

Day

U (

Sv)

150 200 250 300 350 400 450−2

−1

0

1

21/20o (topo)

U (

Sv)

150 200 250 300 350 400 450−2

−1

0

1

21/10o (topo)

U (

Sv)

integrated ubaro along the shelf break integrated ubaro along the slope bottom(3000m)

19

• On flat bottom, stepwise propagation, oscillatory dissipation with low resolution– Qualitative agreement in propagation for >1/10– Resolution convergence at 1/20 according to propagation and

dissipation

• Eddy-topography interaction requires high resolution (>1/20)– Frequent/stronger collision, smoothed trajectory with high resolution– Low resolution suppresses cross-isobaths translation– Enhanced on-shelf, reduced off-slope transport with high resolution

Conclusions

20

Future works

27

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29

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89 88 87 86 -5

-4

-3

-2

-1

0

1

2

3

4

5

4.0cm/s 2.0cm/s

t=005

27

28

29

30

89 88 87 86

t=065

27

28

29

30

89 88 87 86

t=125

81 82 83 84 85 86 87 88 8920.5

21

21.5

22

22.5

23

23.5

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x (oW)

y (o N

)

80km

40km

20km

0 50 100 150 200 250 300 350 40040

50

60

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80

90

100

110

120

130

140

t (day)

KE

(J

m−

2 )

dragno drag

Inter-eddy interaction

Eddy size? Bottom drag?

21

Acknowledgments

• HYCOM consortium group : HYCOM model

• Dr. Wallcraft : HYCOM Utility, ARSC HPC

• SEED (Shelf to slope Energetics and Exchange Dynamics)