Modeling ENSO with a simple coupled model


Linearized Shallow Water Equations:

∂u/∂t - β0 y v + g´ ∂h/∂x= τx/ρH
∂v/∂t + β0 y u + g´ ∂h/∂y= τy/ρH
∂h/∂t + H( ∂u/∂x + ∂v/∂y) = -A h

H = 150 m   ;    c = 2.9 m/s
Domain: 124E-80W, 30S-30N
where the atmospheric coupling comes in the τx term, making it dependent on the depth at the equator in the east, h0:
τx = (k/ε) tanh(εh0) exp(-(μ/2)y2/L2) g(x)  ;     τy = 0
where L is the equatorial length scale, L2=c/β,
and
g(x´) = 1    x´ in [x1,x2]
0    otherwise

Coupling Strength, k: Friction Parameter, A: e-8
Stress Parameters, μ: x1:   x2:
tanh Parameter, ε: