1

19th Annual CESM Workshop Breckenridge, CO

Assessing the Influence of Surface Wind Waves to the Global Climate by Incorporating WAVEWATCH III in CESM!

Phase I: Langmuir Mixing in KPP

Qing Li! Baylor Fox-Kemper, Todd Arbetter

Brown University !

Adrean Webb TUMST

Image: NPR.org, Deep Water Horizon Spill

u*

⟨us⟩SL

α

LC

θ u*’

⟨us⟩SL’

κ

z

Misaligned wind and waves

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7

8

La

Enha

ncem

ent F

acto

r

E =q

1 + 0.08La�4t

E =p

1 + (3.1Lat)�2 + (5.4Lat)�4

La2t =|u⇤|

|us(0)|

La

2SL,proj

=|u⇤|cos(↵)

|hus

iSL

|cos(✓ � ↵)

VR12g

MS2KVR12a

Enhancement factor to vertical velocity scale W!Aligned wind and waves

Langmuir Mixing in KPP Choosing a better parameterization

VR12hIncluding Stokes shear!Making the boundary layer even deeper

2

+|us(0)|2Rib =

d [br � b(d)]

|huri � hu(d)i|2 + U2t

McWilliams and Sullivan, 2000; Van Roekel et al., 2012

WAVEWATCH-III !Stokes drift; 4ox3.2o

POP2 !U, T, HBL; gx3v7

CORE2 Inter-Annual Forcing

LM in KPP Boundary layer deeper

Diffusivity stronger

CTRLOBS

120

0

Summer Mixed Layer Depth (JAS for NH & JFM for SH)

15.63

17.89

19.50

Global

20S-20N

South of 30S

RMSE (m)

3

No Langmuir Mixing

OBS: de Boyer Montégut et al. 2004

Shallow bias in the Southern Ocean

Setup!• WAVEWATCH-III (Stokes drift; 4ox3.2o) <-> POP2 (U, T, HBL; gx3v7) • CORE2 interannual forcing (Large and Yeager,2009) • 4 IAF cycles; average over last 50 years for climatology • Same forcing but different Langmuir Mixing parameterizations

m

CTRL

MS2K

OBS

VR12a

120

0

Summer Mixed Layer Depth (JAS for NH & JFM for SH)

15.63

17.89

19.50

16.92

22.74

15.81

30.62

43.56

20.13

Global

20S-20N

South of 30S

RMSE (m)

4

Aligned u* and us

No Langmuir Mixing

OBS: de Boyer Montégut et al. 2004

Enhanced mixing, but too much in MS2K

m

CTRL

MS2K

OBS

VR12a

VR12g VR12h

120

0

Summer Mixed Layer Depth (JAS for NH & JFM for SH)

15.63

17.89

19.50

16.92

22.74

15.81

18.11

24.97

14.59

30.62

43.56

20.13

16.36

21.36

15.85

Global

20S-20N

South of 30S

RMSE (m)

5

Aligned u* and us

Misaligned u* and us With Stokes shear

No Langmuir Mixing

OBS: de Boyer Montégut et al. 2004

m

Winter Mixed Layer Depth (JFM for NH & JAS for SH)

49.70

19.24

62.59

46.80

26.78

54.36

48.46

31.24

56.08

129.20

64.57

183.18

47.69

24.79

56.99

Global

20S-20N

South of 30S

RMSE (m)

CTRL

MS2K

OBS

VR12a

VR12g VR12h

400

0

200

100

6

Aligned u* and us

Misaligned u* and us With Stokes shear

No Langmuir Mixing

OBS: de Boyer Montégut et al. 2004

m

D’Asaro et al. 2014

Percentage change in MLD by Langmuir Mixing

The surface wind waves increase the mixed layer depth at high latitude by 20% ~ 60%

D’ASARO ET AL.: QUANTIFYING SURFACE WAVE TURBULENCE

0° 60°E 120°E 180°W 120°W 60°W 0°

60°S

45°S

30°S

15°S

0°JUN

15°N

30°N

45°N

60°N

a

DEC

0% 10% 20% 30% 40%

0 100 200 300

−60

−40

−20

0

MLD (m)

JUN

20

40

60

−60

−40

−20

0

20

40

60b

DEC

Latit

ude

0 100 200 300

MLD (m)

DEC

JUN

c

No wave forcing

With wave forcing

SummerWinter

JUN

Percentiles25%50% (median)75%

Figure 3. Contribution of Langmuir turbulence to global mixed layer depth. (a) Percentage increase in mixed layer depthwith wave forcing relative to no wave forcing when Langmuir turbulence is parameterized [Harcourt, 2013] into a 1-Dmixed layer model (section S7) 180 days after a near-summer solstice initial profile; (b) Zonal median (thick line) mixedlayer depth and 25th and 75th percentiles (thin lines) 180 days after near-summer solstice initial profile Ð with (black) andwithout (red) wave forcing; (c) As for Figure 3b 365 days after initial profile.

[9] Buoyancy of the floats induces errors in the measure-ment of wrms [Harcourt and D’Asaro, 2010]. The resultingvertical motion of the float relative to the water (sectionS4.2.2) changes both the measured vertical velocity andcauses the mixed layer to be nonuniformly sampled. Thefloats’ buoyancy was calibrated at least daily, with somelow-wind days dedicated to calibration profiles. Direct mea-surements of float-relative velocity in Lake Washingtonimply buoyancy errors in wrms of less than 5% (sectionS4.2.3). The finite size of the float also introduces errorsby averaging smaller turbulent eddies. We correct for thisby fitting a universal spectral form to the vertical velocityspectrum (section S4.2.5) for each drift and removing thecomponent due to finite float size. This correction increaseswrms by 10–20% from the measured value and introducesuncertainties of 7% into the corrected wrms.

[10] In summary, we measured the turbulent componentof wrms averaged across the mixed layer for winds of

8–15 m s–1, mixed layer depths of 20–100 m and waves of0.05–7 m. The wide range of wave conditions for the samewind speed allows us to assess whether waves are impor-tant and ask whether Langmuir turbulence can explain themeasured effect.

3. Theory[11] Models of Langmuir turbulence predict wrms from u*,

the Stokes drift profile uS(z), the mixed layer thickness H,and the air-sea buoyancy flux B = g˛c–1

w Q, where g is theacceleration of gravity, ˛ is the thermal expansion coeffi-cient of seawater, and c–1

w is its specific heat; we ignore smallsalinity effects. For monochromatic surface waves, uS(z) =uS(0)ekz, where k is the horizontal wave number of the sur-face waves and z increases upward. Real surface waves havea broadband spectrum producing a profile uS(z) that is thesum of many such decreasing exponentials. Waves with the

105

40%

80%30%

VR12h - CTRLVR12g - CTRL

Summer (JAS for NH & JFM for SH)

Winter (JFM for NH & JAS for SH)

7

80%30%Misaligned u* and us With Stokes shear

Second-moment closure model

pCFC11 BiasSouthern !

Hemisphere

OBS CTRL

MS2K VR12a

VR12g VR12h

20.20

30.99 18.53

18.90 16.44

280

0

60

-60

RMSE

8

80S EQ 80S EQ

1500

RMSEs are reduced by 6% ~ 18%

1500

1500

Aligned u* and us

Misaligned u* and us With Stokes shear

No Langmuir Mixing

OBS: Key et al. 2004 (GLODAP)

AnomalyObservation

Langmuir Mixing enhance

ventilation and reduce low

pCFC11 biases

pCFC11 Bias

CTRL

MS2K VR12a

VR12g VR12h

15.00

14.80 13.51

14.05 12.14

280

0

40

-40

RMSE

Equatorial Region

RMSEs are reduced by 6% ~ 19%

9

20S 20N 20S 20N

800

800

800

Aligned u* and us

Misaligned u* and us With Stokes shear

No Langmuir Mixing

Anomaly

OBS

OBS: Key et al. 2004 (GLODAP)

Observation

Langmuir Mixing enhance

ventilation and reduce low

pCFC11 biases

• WAVEWATCH III as a component of CESM and coupled with POP

• Langmuir mixing • Reduces the shallow bias of mixed layer depth in the Southern Ocean (RMSE

reduction: summer 20%; winter 10%).

• Reduces low biases in zonal mean pCFC11 both in the Southern Ocean and Equatorial region (RMSE reduction: ~18%).

• Equatorial region, depend on the MLD definition. • LM enhances ventilation; Mean MLD might not be a good indicator there.

!

• More tests: • Fully coupling with active atmosphere and sea ice model.

• Considerations in the Equatorial region.

• CVMix.

• An efficient but accurate data wave model.

Summary and Future Work (by Jan, 2015)

10

• WAVEWATCH III v3.14 • 3rd generation wave model • Solves the spectral action density balance equation • Res: WW3a (4ox3.2o)

• CESM1.2; Ocean-Wave only • Compset: CIAF_WAV Res: gx3v7 • CORE2 Interannual forcing; 4 IAF cycles (62 years); average over the last

50 years for climatology • CFC active starting near the end of the 3rd cycle (model year 170,

corresponding to data year1931) and through the 4th cycle • CFC11 comparison: annual mean of model year 233 (corresponding to

data year 1994) • Mixed layer depth definition

• OBS: MLD in density with a variable threshold criterion (equivalent to a 0.2°C decrease)

• CESM: Shallowest depth where the local, interpolated buoyancy gradient matches the maximum buoyancy gradient between the surface and any discrete depth within that water column

11

Model Setup

• At the surface !

!!

• Surface layer mean

12

Stokes Drift

us(0) = 2

Z 2⇡

0

Z 1

0(cos✓, sin✓, 0)

!

3

g

S(!, ✓)d!d✓

husiSL =1

HSL

Z 2⇡

0

Z 1

0(cos✓, sin✓, 0)(1� e�

2!2HSLg )!S(!, ✓)d!d✓

• Turbulent Langmuir Number

!• Vertical velocity scale

!• Enhancement factor (MS2K)

!• Diffusivity

!• Shape function

!• The boundary layer depth is determined from

!!

• Enhancement factor (VR12a)

13E =

p1 + (3.1Lat)�2 + (5.4Lat)�4

E =q

1 + 0.08La�4t

W =kU⇤�

E

v = WHBLG(�)

G(�) = �(1� �)2 � =d

HBL

κ

z

Rib =HBL [br � b(HBL)]

|huri � hu(HBL)i|2 + U2t

⇡ 0.3

La2t =|u⇤|

|us(0)|

Langmuir Mixing in KPP Aligned Wind and Waves

• Surface layer averaged, projected Langmuir Number

!!

• Angle between Langmuir cell and wind

!!

• Enhancement factor (VR12g, VR12h)

!!

• The boundary layer depth (VR12h) is determined from

14

Langmuir Mixing in KPP Misaligned Wind and Waves

La

2SL,proj

=|u⇤|cos(↵)

|hus

iSL

|cos(✓ � ↵)

↵ ⇡ tan

�1

"sin (✓)

u⇤us(0)

ln (|HBL/z1|) + cos (✓)

#

u*

⟨us⟩SL

α

LC

θ u*’

⟨us⟩SL’

E = |cos↵|q

1 + (1.5LaSL,proj

)�2 + (5.4LaSL,proj

)�4

Rib =HBL [br � b(HBL)]

|huri � hu(HBL)i|2 + U2t + |us(0)|2

⇡ 0.3

CTRL

MS2K

OBS

VR12a

VR12g VR12h

120

0

Summer Mixed Layer Depth (JAS for NH & JFM for SH)

13.36

6.39

22.16

11.37

7.58

17.90

9.75

8.69

13.65

13.57

16.22

14.64

11.38

7.11

18.71

Global

20S-20N

South of 30S

RMSE (m)

15

Aligned u* and us

Misaligned u* and us With Stokes shear

No Langmuir Mixing

OBS: de Boyer Montégut et al. 2004

0.03 kg/m3 density criterion