Stochastic modeling of mesoscale eddies

HAL Id: hal-03221416

https://hal.archives-ouvertes.fr/hal-03221416

Submitted on 10 May 2021

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Stochastic modeling of mesoscale eddies

Long Li, Bruno Deremble, Noé Lahaye, Etienne Mémin

To cite this version:

Long Li, Bruno Deremble, Noé Lahaye, Etienne Mémin. Stochastic modeling of mesoscale eddies. EGU General Assembly 2021, Apr 2021, Vienne, Austria. �hal-03221416�

Stochastic modeling of mesoscale eddies

Long Li

1

, Bruno Deremble

2

, No´e Lahaye

1

and Etienne M´emin

1

1 _{Inria Rennes Bretagne Atlantique, France} 2 _{Institut des G´eosciences de l’Environnement, France}

Dq

Dt

=

@q

@t

+ (u + ˙⌘)

·r q

1

2

r· r·(aq)

Stochastic material derivative

QG kinematic relations

f

0

(q

y) =

r

2

p

f

0

2

Ap, f

0

u =

r

?

p

Noise and variance

˙⌘(x, t) = ⌘(x) +

X

k

k

(x, t)⇠

k

, a = t

X

k

k

T

k

⇠ N (0, 1)

Stochastic evolution of layered PV

LU formalism

Barotropic mode of p 1st Baroclinic mode of p

Long-term mean

40 80 120 0 500 1000 1500 2000 10-6 10-5 101 102 103

Energy budget

Benefits: reproduction of jet and recirculation, energy

backscattering and internal variability

Reference: Li 2021, Stochastic modeling and numerical simulation of ocean dynamics, Chap. 8, https://hal.archives-ouvertes.fr/tel-03207741

k

? r(Ap)

LU–POD–P:

⌘,

_{

_k

_}

LU–POD:

learned from data

Parameterizations

Dq