Key features of the IPSL ocean atmosphere model and its sensitivity to atmospheric resolution

Abstract

This paper presents the major characteristics of the Institut Pierre Simon Laplace (IPSL) coupled ocean–atmosphere general circulation model. The model components and the coupling methodology are described, as well as the main characteristics of the climatology and interannual variability. The model results of the standard version used for IPCC climate projections, and for intercomparison projects like the Paleoclimate Modeling Intercomparison Project (PMIP 2) are compared to those with a higher resolution in the atmosphere. A focus on the North Atlantic and on the tropics is used to address the impact of the atmosphere resolution on processes and feedbacks. In the North Atlantic, the resolution change leads to an improved representation of the storm-tracks and the North Atlantic oscillation. The better representation of the wind structure increases the northward salt transports, the deep-water formation and the Atlantic meridional overturning circulation. In the tropics, the ocean–atmosphere dynamical coupling, or Bjerknes feedback, improves with the resolution. The amplitude of ENSO (El Niño-Southern oscillation) consequently increases, as the damping processes are left unchanged.

Appendix 1: Interface for coupling the turbulent fluxes

A first standard interface for the coupling between the surface and the atmosphere was proposed by the PILPS project (Polcher et al. 1998, 2005). A drawback of the proposed approach is that the separation between the solving of the turbulent fluxes in the boundary layer and the solving of the temperature by the surface model is not complete. Indeed, the time evolution of the first atmospheric level variables (Polcher et al. 1998) is a function of the surface flux, but also of some surface coefficients. We overcome this difficulty by rewriting the discretized form of the vertical diffusion equation of the first atmospheric level and by considering explicitly the flux $F_{X,1 /2}^{t + \delta t}$between layer 1 and the surface:

$$ \begin{gathered} {\frac{{X_{1}^{t} - X_{1}^{t + \delta t} }}{\delta t}} = \hfill \\ {\frac{1}{{\delta z_{1} }}}\left( {K_{{X,{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} {\frac{{X_{2}^{t + \delta t} - X_{1}^{t - \delta t} }}{{\delta z_{{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} }}} - F_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}^{t + \delta t} } \right) \hfill \\ \end{gathered} $$

(1)

and

$$ F_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}^{t + \delta t} = K_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}} {\frac{{X_{1}^{t + \delta t} - X_{0}^{t + \delta t} }}{{\delta z_{1/2} }}} $$

(2)

Variables X stands for the dry static energy, the specific humidity or the wind speed, F _X,k−1/2 is the flux of X at interface k − 1/2 (between level k and k − 1), K _X,k−1/2 is the vertical diffusion coefficient for variable X at this level; δz _k is the thickness of layer k and δz _k+1 is the distance between the centres of layers k and k − 1.

1.1 1.1 In the boundary layer

To solve the vertical diffusion equation in the boundary layer, each variable of level k is written as a function of the variable of the level below k − 1, for all levels except level 1:

$$ X_{k}^{t + \delta t} = A_{X,k} X_{X,k - 1}^{t + \delta t} + B_{X,k} {\text{ for }}k \ge 2 $$

(3)

For level 1, $X_{2}^{t + \delta t}$ may be suppressed from Eq. 1, using:

$$ A_{X,1} = - {\frac{\delta t}{{\delta z_{1} C_{X,1} }}} $$

(4)

and

$$ X_{1}^{t + \delta t} = A_{X,1} F_{X,1/2}^{t + \delta t} + B_{X,1} $$

(5)

$$ A_{X,1} = - {\frac{\delta t}{{\delta z_{1} C_{X,1} }}} $$

(6)

$$ B_{X,1} = \left( {X_{1}^{t} + {\frac{{\delta tK_{{X,{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} }}{{\delta z_{1} \delta z_{{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} }}}} \right){\frac{1}{{C_{X,1} }}} $$

(7)

and

$$ C_{X,1} = 1 + {\frac{{\delta tK_{{X,{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} }}{{\delta z_{1} \delta z_{{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}} }}}\left( {1 - A_{X,2} } \right) $$

(8)

One may verify that Eqs. 5–8 make only use of the flux with surface $F_{X,1/2}^{t + \delta t}$ and of atmospheric variables above layer 1. There is no use of surface variable or surface coefficient. For each variable X, variables X _X,1, A _X,1 and B _X,1 are transmitted by the boundary layer model to the surface model.

1.1.1 1.1.1 In the surface model

The surface model has to compute the surface flux $F_{X,1/2}^{t + \delta t}$ for each variable X. For the temperature and the humidity at the surface, the new values $X_{1}^{t + \delta t}$ are computed (if required) through the energy and water budget of the surface. The coupling between atmosphere and surface being implicit, a relationship between $F_{X,1/2}^{t + \delta t}$ and $X_{0}^{t + \delta t}$ is required. This is obtained by combining Eqs. 2–5:

$$ F_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}^{t + \delta t} = {\frac{{K_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}} }}{{\delta z_{1/2} - K_{{X,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}} A_{X,1} }}}\left( {B_{X,1} - X_{0}^{t + \delta t} } \right) $$

(9)

1.2 1.2 Decomposition of the oceanic heat transport

The oceanic heat transport across a latitude λ due to advection is computed as:

$$ F = \int\limits_{z = 0}^{\text{bottom}} {\int\limits_{{}}^{{}} {\rho C_{\text{p}} Tvr_{\text{a}} { \cos }(\lambda )d\varphi dz} } $$

(10)

c mass, C _p the heat capacity per mass unit, T the temperature, v the northward velocity, r _a the Earth radius, φ the longitude and z the depth. T and z the depth. T, a and v are separated in $T = \overline{T} + T^\prime$ and $v = \overline{v} + v^\prime$, where the overline denotes the latitudinal average, and prime the latitudinal anomaly. The transport can be decomposed (2001) as:

$$ \begin{gathered} F = \iint {\rho C_{\text{p}} }\overline{T} \overline{v} r_{\text{a}} \,{ \cos }\left( \lambda \right)d\varphi dz \hfill \\ \,\,\,\,\,\,\, + \iint {\rho C_{\text{p}} }T^{\prime}v^{\prime}r_{\text{a}} \,{ \cos }\left( \lambda \right)d\varphi dz \hfill \\ \end{gathered} $$

(11)

The first term is the overturning transport and the second one the gyre transport.

1.3 1.3 Time filtering of snow accumulation on land ice

On land–ice surface, the local snow mass is limited to 3,000 kg m⁻². At each time-step, the snow mass over this limit C(t) is computed. The calving C ^* send to ocean is computed as a filtered snow mass C(t) = (∆t/τ)C(t) + (1 − ∆t/τ).C × (t − 1), where ∆t is the model time-step and τ is a characteristic time, set to 10 years in all experiments.