Recent developments in NEMO within the Albatross project

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Recent developments in NEMO within the Albatross project

Florian Lemarié, Guillaume Samson, Xavier Couvelard, Gurvan Madec, Romain Bourdallé-Badie

To cite this version:

Florian Lemarié, Guillaume Samson, Xavier Couvelard, Gurvan Madec, Romain Bourdallé-Badie.

Recent developments in NEMO within the Albatross project. DRAKKAR 2019 - Drakkar annual

workshop, Jan 2019, Grenoble, France. �hal-02418218�

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Recent developments in NEMO within the Albatross project

F. Lemari ´e¹, G. Samson², X. Couvelard³, G. Madec^1,4, R. Bourdall ´e-Badie²

1Inria (Airsea Team), Univ. Grenoble-Alpes, LJK, France

2Mercator Oc ´ean International, Toulouse, France

3Laboratoire d’Oc ´eanographie Physique et Spatiale (LOPS), Brest, France

4Sorbonne Universit ´es-CNRS-IRD-MNHN, LOCEAN Laboratory, Paris, France

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Context: Albatross project funded by CMEMS

→ Representation of ocean/waves/atmosphere interactions in global eddying operational systems

- Focus on the characteristic scales of the oceanic mesoscale (a few kilometers and from a few days to a few weeks)

. Demonstrate the contribution of ocean/waves coupling . Account for eddy-scale wind-SST and wind-currents effects

1. Implementation of a 2-way ocean/waves coupling (more conventional) 2. Explore the possibility to dynamically downscale atmospheric data to the

oceanic resolution via a simplified model (more exploratory)

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F. Lemari ´e – Recent developments in NEMO within Albatross 3

Inclusion of wave-induced terms in NEMO & coupling 1

infrastructure

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Inclusion of wave-induced terms in the PE models

Mathematical derivation

• McWilliams et al. (2004)

- Eulerian frame

- Asymptotic expansion of the wave effects to some order in wave steepness

• Ardhuin et al. (2008)

- Hybrid Lagrangian-Eulerian frame (Generalized Lagrangian Mean)

- Effects of vertical shear are ignored

→ nearly equivalent wave-current equations at leading orders(Ardhuin et al., 2017)

→ the wave effects on the current momentum expressed in the form of the vortex force

. Examples of practical implementations in PE models:

Uchiyama et al. (2010);Bennis et al. (2011)

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Curl form of NEMO equations with generalized vert. coordinate (e3=∂kz)

∂tu = +(f+ζ)(v+v^s)−∂_xku_hk²

2 −(ω+ω^s)

e₃ ∂_ku−∂_x(p_s+p^J)

ρ₀ −

∂_x(p_h+

ep) z ρ₀ +F^u

∂tv = −(f+ζ)(u+u^s)−∂yku_hk² 2

−(ω+ω^s) e3

∂_kv−∂y(ps+p^J) ρ0

−

∂_y(p_h+

pe) z ρ0

+F^v

∂_kp_h = −ρge₃−∂_kpe+ρ0

u^s∂_ku+v^s∂_kv

“wavy hydrostatic” balance

∂t(e3θ) = −∂_x(e3θ(u+u^s)−∂y(e3θ(v+v^s))−∂_k(θ(ω+ω^s)) +F^θ

∂_te₃ = −∂_x(e₃(u+u^s))−∂y(e₃(v+v^s))−∂_k(ω+ω^s) ρ = ρeos

• (u^s, v^s, ω^s): Stokes drift velocity (assumed to be non-divergent)

• p^J: depth-uniform wave-induced kinematic pressure term

•

pe: shear-induced 3D pressure term associated with vertical component of VF

W_St−Cor=



 fv^s

−fu^s 0



, W_VF=







ζv^s−^ωs_e 3∂_ku

−ζu^s−^ωs e3∂_kv us

e3∂_ku+^vs_e 3∂_kv







, W_Prs=



 p^J+ep p^J+ep

pe





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Curl form of NEMO equations with generalized vert. coordinate (e3=∂kz)

∂_tu = +(f+ζ)(v+v^s)−∂xku_hk² 2

−(ω+ω^s) e3

∂_ku−∂x(ps+p^J) ρ0

−

∂x(p_h+ep) z ρ0

+F^u

∂_tv = −(f+ζ)(u+u^s)−∂yku_hk²

2 −(ω+ω^s)

e₃ ∂_kv−∂y(ps+p^J)

ρ₀ −

∂y(p_h+pe) z ρ₀ +F^v

∂_kp_h = −ρge₃−∂kep+ρ0(u^s∂ku+v^s∂kv) “wavy hydrostatic” balance

∂t(e3θ) = −∂_x(e3θ(u+u^s)−∂y(e3θ(v+v^s))−∂_k(θ(ω+ω^s)) +F^θ

∂te₃ = −∂_x(e₃(u+u^s))−∂y(e₃(v+v^s))−∂_k(ω+ω^s) ρ = ρeos

. Small vertical shear limit (Bennis et al., 2011)→hydrostatic relation is unchanged . Neglect wave-induced non-conservative forces (wave dissipation, rollers, etc) . Adjustments in the barotropic mode due to the convergence of the Stokes drift . No need to explicitly computeω^s

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Reconstruction of Stokes drift velocity profile

Inputs from wave model:u^s_h(η),kT^sk, →u^s_h(z, ke) =u^s_h(η)S(z, ke)

• ke: degree of freedom to impose thatkR

u^s_h(z, ke)dzk=kT^sk

• S(z, ke)fromBreivik et al., 2016

• Stokes drift interpreted in a FV senseu^s_h(z_k) =u^s_h(η) (e₃)_k

Z_zk+1/2 zk−1/2

S(z, k_e)dz

Computation of surface momentum flux

• In NEMO :τ^atmfrom IFS bulk formulation (Aerobulk) usingαchfrom wave model.

• In wave model :τ^atm_ww3assumes neutral stratification (wave models hyper sensitivite to stress computation).

A way to account for the momentum flux consumed by the wave field τôce=τâtm−(τâtm_ww3\−τôce_ww3)

.Pragmatic choice which breaks momentum conservation.

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Wave-enhanced mixing (1-equation TKE scheme)

Additional terms in wavy hydrostatic balance affects TKE equation u^s_h∂z

u⁰_hw⁰

= u⁰_hw⁰

∂zu^s_h+∂z u^s_h u⁰_hw⁰ .Modification of shear production term + adjustA^vevalue

∂_te= A^vm e²₃

h(∂ku)²+ (∂kv)²+ (∂ku)(∂ku^s) + (∂kv^s)(∂kv^s)i

−A^vtN²+1 e3

∂_k A^ve

e3

∂_ke

−ce^3/2 l²_ε

Surface B.C. fore:

A^ve e₃ ∂ke

z=z₁

=−ρ0gR2π 0

R∞

0 Sdsdωdθ

Surface B.C. for mixing length:lz=η=κ^(C^m_C^c⁾^1/4

m (η+z0), z0= 1.6Hs

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Wave-enhanced mixing (1-equation TKE scheme)

Additional terms in wavy hydrostatic balance affects TKE equation u^sh∂z

u⁰hw⁰

= u⁰hw⁰

∂zu^sh+∂z u^sh

u⁰hw⁰ .Modification of shear production term + adjustA^vevalue

∂te= A^vm e²₃

h(∂_ku)²+ (∂_kv)²+ (∂_ku)(∂_ku^s) + (∂_kv^s)(∂_kv^s)i

−A^vtN²+1 e3

∂_k A^ve

e3

∂_ke

−c

e^3/2 l²_ε

Langmuir cells parameterization:Axell (2002)

→ Additional source term in TKE equation∆tPLCwithPLC=w_LC³ /HLC w_LC=

(

c_LCkeu_sksin

−_H^πz_LC

, if −z≤H_LC

0, otherwise , −

Zη

−HLC

N²(z)zdz=keu_sk² 2 keusk= max{us(η)·eτ,0}intensity of LC scales withθusτ(Van Roekel et al., 2012)

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Practical implementation

• OASIS−MCTInterface shared with Croco and Mars3d

• Interface inNEMOinline with the generic interface with atmosphere

Variable description

uh(z=η) Oceanic surface currents O→W u^atm10 10 m-winds from external dataset O→W u^s_h(z=η) Sea-surface Stokes drift W→O kT^sk norm of the Stokes drift volume transport W→O Φoc TKE surface flux multiplied byρ0 W→O

αch Charnock parameter W→O

Hs Significant wave height W→O

τ^ww3_w Wave-supported stress W→O

pe^J Bernoulli head W→O

Table :Variables exchanged betweenNEMOandWW3viaOASIS−MCT.

• Examples ofORCA025numerical results in next talk

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Downscaling of atmospheric data at the oceanic resolution 2

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Objectives

SURROGATE MODEL atm

LS(x, z, t) =MAGCM(. . . , ^oce_LS(x, z=zsfc, t))

oce

HR(x, z=zsfc, t)

e^atm_HR(x, z= 10 m, t)

How to define such surrogate model ?

• Estimate∂MAGCM/∂φ^oce_sfc via sensitivity analysis and subsequent model reduction

• Build a surrogate model via learning strategies (huge computational and data requirements)

• Select feedback loops of interest and mimic the physical mechanisms

→ The newly developed computational framework allows all those possibilities to be investigated

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Air-sea interactions at the oceanic mesoscales

Wind-SST coupling (thermal coupling)

1. Modulation of PBL turbulence(e.g.

Chelton, 2013;Frenger et al., 2013) ∇×τ = F1(∇SST)

∇·τ = F2(∇SST)

2. Pressure gradient adjustment(e.g.

Minobe 2008;Lambaerts et al. 2013)

∇·τ∝ −k∇²SSTk

Current feedback (dynamical coupling)

τ =ρaCDkua−uok(ua−uo)

• Strongly reduced mesoscale activity (”eddy damping”)(e.g.Dewar & Flierl, 1987; Renault et al., 2016)

• Strongly increases vertical velocity anomalies associated to eddies(e.g.

Oerder et al., 2017)

WEk[m day¹] Absolute winds

Relative winds

Oerder et al., 2017

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Air-sea interactions at the oceanic mesoscales

. A good representation of those interactions requires an interactive MABL

- Under-estimation of wind-SST coupling in bulk mode

- Over-estimation of wind-current coupling in bulk mode

. The atmospheric resolution must be ”eddy-resolving”(i.e.∆xoce≈∆xatm) . Interactive MABL required for a consistent integration of surface waves

Similar initiatives :

• Advective atmospheric mixed layer model ofSeager et al., 1995

• CheapAML (Deremble et al., 2013)→dynamically passive ABL model

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Current status of the project (1/2)

1. Definition of a single-column model (ABL1d)

Integrate windsu, potential temperatureθand specific humidityq







∂tu = fk×u+∂z(Km∂zu)−

1 ρ∇p

LS

∂tθ = ∂z(Ks∂zθ) +λs(S(θ)−θLS)

∂tq = ∂z(Ks∂zq) +λs(S(q)−qLS) Blue termsare specified via large-scale data

Red termsare given by turbulent closure

. Radiative forcingis kept as it is

. Surface boundary conditionsfor Km∂zu|_z=0, Ks∂zθ|_z=0,Ks∂zq|_z=0via IFS (aerobulk) bulk formulation

. Relaxation termscales with PBL height

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Current status of the project (2/2)

2. Turbulent closure scheme: TKE-based scheme ofCuxart et al. (2000) . used operationally at Meteo-France (e.g. in Arome and Meso-NH models) . recoded from scratch to allow more flexibility and better performances 3. Development of preprocessing toolsfor

large-scale forcing

4. Implementation in NEMO surface module

- Option to split NEMO and SAS on separate nodes

- Standalone mode

- Compatible with sea-ice

Computational cost (50vertical levels, no sea-ice)

• + 12% in memory

• + 7 - 12 % en elapsed time (depending on options)

GLS ext. mode ABL1d I/O

Bulk mode 19.44% 11.3% - 0.34%

ABL mode 18.06% 10.5% 6.3% 0.64%

waves

BULK formulation Simplified Atmospheric

Boundary layer model 3D Large-scale

data Surface module

LIM sea-ice

OCEAN

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Current status of the validation strategy (1/2)

1. Standardized test-cases from ABL community (see GABLS initiative)

→ Neutral turbulent Ekman layerat45⁰N (Cuxart et al., 2000)

-1 0 1 2 3

V [m/s]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Z f / u*

nn_amxl = 1 nn_amxl = 3

Cuxart et al., 2000

MESO-NH 1D

LES

MESO-NH 1D LES

SIMBAD1D

2 4 6 8 10 12

U [m/s]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Z f / u*

nn_amxl = 1 nn_amxl = 3

→ Stably stratified boundary layer(typical situation over sea-ice)

Rodier et al., 2017

a) b)

0 2 4 6 8 10

Wind speed [m/s]

0 100 200 300 400

altitude [m]

nn_amxl = 0 nn_amxl = 1 nn_amxl = 2 nn_amxl = 3

263 264 265 266 267 268

Potential temperature [K]

0 100 200 300 400

altitude [m]

nn_amxl = 0 nn_amxl = 1 nn_amxl = 2 nn_amxl = 3

SIMBAD1D

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Current status of the validation strategy (2/2)

2. Winds across a Midlatitude SST Front (Kilpatrick et al., 2014)

ABL_1D MESO-NH LES

2D x-z (solution at equilibrium)

3. NEMO1D / ABL1D coupling at PAPA station (50.1^oN,144.9^oW)

→ Th ´eo Brivoal MSc

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Examples of numerical results

Large-scale winds over an idealized eddy

100 200 300

Relative winds (ABL)

50 100 150 200 250 300

100 200 300

Relative winds (Bulk)

8 6 4 2 0 2 4 6 1e 78

⇒Reduction by30%of wind stress curl

Bay of Biscay1/12^◦realistic simulations

Courtesy of Mercator Ocean

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Conclusions

• Implementation of a 2-way ocean-wave model including the wave-induced terms thought to be relevant at global eddying scales

• Representation of some mesoscale air-sea feedbacks with a simplified model

- ABL response qualitatively and quantitatively ok in idealized experiments

→extension to realistic cases

- Validation of implementation over sea-ice

- More advanced formulation including horizontal advection and fine-scale pressure gradient will be tested (based onKonor, 2013; Durran, 2008)

Publications to come

• Couvelard X., F. Lemari ´e, G. Samson, J.L. Redelsperger, F. Ardhuin, R. Benshila, G.

Madec,Development of a 2-way coupled ocean-wave model: assessment on a global oceanic configuration, Geosc. Mod. Dev.

• Lemari ´e F., G. Samson, J.-L. Redelsperger, H. Giordani, G. Madec, R. Bourdall ´e Badie, T. Brivoal,A simplified atmospheric boundary layer model for oceanic modeling purposes, Geosc. Mod. Dev.