petersen omwg 140116 - University Corporation for Atmospheric … · 2014. 2. 5. · Slide 2 The MPAS-Ocean Vertical Coordinate Z-Level: Fixed coordinate.POP, MOM, MIT-GCM, NEMO Z-star:

U N C L A S S I F I E D

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Slide 1

The MPAS-Ocean Vertical Coordinate

Mark Petersen

and the MPAS-Ocean development team

Los Alamos National Laboratory

Slide 2

The MPAS-Ocean Vertical Coordinate

Z-Level: Fixed coordinate. POP, MOM, MIT-GCM, NEMO

Z-star: Layers expand with SSH. MOM, recently POP, others

sigma: terrain-following. ROMS, NEMO

isopycnal: MyCOM, GOLD

hybrid isopycnal: HyCOM

partial bottom cells (in addition to others)

z-tilde: frequency-filtered coordinate (in addition to others)

Slide 3

The MPAS-Ocean Vertical Coordinate

n  Z-Level

n  Z-star

n  sigma: only tested in idealized cases so far

n  isopycnal: idealized only, no zero thickness layers

n  hybrid isopycnal: under development

n  partial bottom cells

n  z-tilde: frequency-filtered coordinate

Arbitrary Lagrangian-Eulerian (ALE) Vertical Coordinate

Thickness equation:

wtop is transport through interface

z-level , except layer 1 ∂hk∂t

= 0

isopycnal (for adiabatic, idealized studies) w=0

x, y

z

z-star Layer thickness changes in proportion to SSH

∂hk∂t

=ckck

k∑

∂η∂t

Slide 5

Test Problems (Ilicak et al. 2012)

n  Lock exchange

n  Baroclinic eddies

n  Overflow

n  Internal gravity wave

n  Sub Ice-Shelf

x, km

dept

h, m

10 20 30 40 50 60

5

10

15

20 5

10

15

20

25

30

x, km

y, k

m

50 100 150

50

100

150

200

250

300

350

400

450

500

50 100 150 200

0

50

100

150

200

250

300

350

400

450

500

x, km

dept

h, m

11

12

13

14

15

16

17

18

19

Lock Exchange Test Case

Slide 6

n  Zero tracer diffusion n  Vary horizontal viscosity n  Linear equation of state n  Simplest test of mixing

MPAS-O

Ilicak et al. (2012)

n  Ilicak et al. (2012) compares ROMS, MITgcm, MOM, GOLD

n  Theoretical wave propagation speed is

uf =1 2 gH δρ ρ0( )

Resting Potential Energy (RPE): a measure of mixing

Slide 7

n  Definition (Ilicak et al. 2012):

n  is the sorted density state, with heaviest on the bottom.

RPE = g ρ*zdV∫∫∫ρ*

1020

1020

1030

1030

ρ(x, z)

z = 2

z = 6

ρ*(z)

z =1

z = 7 1020 1020 1030 1030

z = 5z = 3

RPE = g ρi

*ziVi

i

∑

RPE =16360gVcell

1025

1020

1030

1025 z = 2

z = 6

z =1

z = 7 1020 1025 1025 1030

z = 5z = 3

RPE =16370gVcell

1025

1025

1025

1025 z = 2

z = 6

z =1

z = 7 1025 1025 1025 1025

z = 5z = 3

RPE =16400gVcell

Example 1: No mixing

Example 2: some mixing

Example 3: fully mixed

0 5 10 15

0

2

4

6

8x 10−5

time, hours

(RPE

−RPE

(0))/

RPE

(0)

νh=0.01νh=0.1νh=1νh=10νh=100νh=200

Resting Potential Energy (RPE): Lock Exchange

Slide 8

n  RPE increases with time as fluid is mixed n  RPE depends on horizontal viscosity as follows:

low horizontal viscosity high Reyolds number high RPE, more mixing

high horizontal viscosity low Reyolds number low RPE, less mixing

data from Ilicak et al. (2012)

RPE(t)− RPE(0)RPE(0)

100 10510−4

10−3

grid Reynolds number

dRPE

/dt,

W/m

2

MPAS−O: z−levelMPAS−O: z−starMITGCM

dRPE(t)dt

less mixing

Baroclinic Eddies Test Case

100 101 102 103

10−4

10−3

grid Reynolds number

dRPE

/dt,

W/m

2

MPAS−Ocean z−levelMPAS−Ocean z−starPOP z−levelPOP z−starMITGCMMOM

dRPE(t)dt

10km resolution

Slide 9

n  Idealized ACC: periodic channel, f-plane

n  Compare to POP z-level and POP z-star

less mixing

Overflow Test Case

n  Zero tracer diffusion

n  vary hor. viscosity

n  Test z-level, z-star, partial bottom cells, and sigma coordinate

100 102 104 106

100

101

grid Reynolds number

dRPE

/dt,

W/m

2

MPAS−O, z*−full cellMPAS−O, z*−pbcMPAS−O, σ

dRPE(t) / dt

100 101 102 103

10−4

10−3

grid Reynolds number

dRPE

/dt,

W/m

2

MPAS−Ocean z−levelMPAS−Ocean z−starPOP z−levelPOP z−starMITGCMMOM

Internal Wave Test Case

Slide 11 100 101 102 103 104 105

10−4

10−3

grid Reynolds number

dRPE

/dt,

W/m

2

MPAS−O z−levelMPAS−O z−starMITGCMMOM

dRPE(t) / dt

Frequency-filtered thickness: z-tilde (Leclair & Madec 2011)

Slide 12

n  Motivation: We would like internal gravity waves to not cause mixing.

n  Here lines show grid cells, for z-star vertical grid:

n  What if we allow layer thickness to oscillate with internal waves?

n  This can be done with a low-pass filter on the divergence

Frequency-filtered thickness: z-tilde (Leclair & Madec 2011)

Slide 13

n  A low-pass filter on the baroclinic divergence:

Dk = D+ !Dk = D+Dklf +Dk

hfDivergence:

hor. divergence

low frequency baroclinic div.

high frequency baroclinic div. barotropic

baroclinic

τ Dlf

Low-pass filter:

n  is the filter time scale, typically five days.

n  It controls the time scales included in the low frequency divergence.

∂Dklf

∂t= −

2π

τ DlfDk

lf − ′Dk

τ Dlf

short time, high frequency oscillations change layer thickness

long time, low frequency oscillations do not change layer thickness

Dk =∇⋅ hkuk( )

Frequency-filtered thickness: z-tilde (Leclair & Madec 2011)

Slide 14

n  A low-pass filter on the baroclinic divergence:

∂Dklf

∂t= −

2π

τ DlfDk

lf − ′Dk Low-pass filter:

∂hkhf

∂t= −Dk

hf−2π

τ hhfhkhf+∇⋅ κhhf∇hk

hf( )

∂hk

∂t=∂hk

ext

∂t+∂hk

hf

∂t

High-frequency thickness equation:

Revised thickness equation:

Two new prognostic equations

z-star part

z-tilde part

forcing restoring diffusion

Dk = D+ !Dk = D+Dklf +Dk

hfDivergence:

low frequency baroclinic div.

high frequency baroclinic div. barotropic

baroclinic

hor. divergence

Frequency-filtered thickness: Internal Wave Test Case

Slide 15

n  It works!

n  Here lines show grid cells, for z-tilde vertical grid:

Frequency-filtered thickness: Internal Wave Test Case

Slide 16

n  Similar results for global simulations

τ Dlf

short time, high frequency oscillations change layer thickness

long time, low frequency oscillations do not change layer thickness

grid Reynolds number

stronger z-tilde

less vertical transport

less mixing

grid Reynolds number

vertical transport through layer interface dRPE(t)

dt

Slide 17

MPAS-Ocean: Ice Shelf Above Ocean Surface

n  For coupled ocean-ice shelf modeling, we need to depress the ocean surface with the weight of the ice shelf.

image from Joughin ea. Science, 2012

image from Jenkins ea. Science, 2010

Observations: Pine Island Glacier

Slide 18

MPAS-Ocean: Ice Shelf Above Ocean Surface

n  For coupled ocean-ice shelf modeling, we need to depress the ocean surface with the weight of the ice shelf.

140 km 30 km

A: 100 m (varies)

500 m

500 m (varies)

linear stratification in salinity, constant temperature

Stop=34.5

Sbot=34.7

B: 15 km (varies)

y

z

MPAS-Ocean model 22 layers, 50 m each

30 km

ice shelf, imposed by surface pressure

Test 2: Driven Cavity

surface wind stress of 0.1 N/m2

cavity, S=34.3 throughout

fixed slope

varying slope

250 m

Slide 19

MPAS-Ocean: Ice Shelf Above Ocean Surface

n  For coupled ocean-ice shelf modeling, we need to depress the ocean surface with the weight of the ice shelf.

n  Ocean layers were compressed to 5 cm thickness with no negative effects.

n  Sheer cliff face may be used at ice shelf edge.

n  Tests used linear EOS. For nonlinear EOS, must account for sigma-coordinate correction.

Initial salinity

salinity, day 20

Slide 20

The MPAS-Ocean Vertical Coordinate

n  Z-Level

n  Z-star

n  sigma: only tested in idealized cases so far

n  isopycnal: idealized only, no zero thickness layers

n  hybrid isopycnal: under development

n  partial bottom cells

n  z-tilde: frequency-filtered coordinate