Abstract
The LMDZ4 general circulation model is the atmospheric component of the IPSL–CM4 coupled model which has been used to perform climate change simulations for the 4th IPCC assessment report. The main aspects of the model climatology (forced by observed sea surface temperature) are documented here, as well as the major improvements with respect to the previous versions, which mainly come form the parametrization of tropical convection. A methodology is proposed to help analyse the sensitivity of the tropical Hadley–Walker circulation to the parametrization of cumulus convection and clouds. The tropical circulation is characterized using scalar potentials associated with the horizontal wind and horizontal transport of geopotential (the Laplacian of which is proportional to the total vertical momentum in the atmospheric column). The effect of parametrized physics is analysed in a regime sorted framework using the vertical velocity at 500 hPa as a proxy for large scale vertical motion. Compared to Tiedtke’s convection scheme, used in previous versions, the Emanuel’s scheme improves the representation of the Hadley–Walker circulation, with a relatively stronger and deeper large scale vertical ascent over tropical continents, and suppresses the marked patterns of concentrated rainfall over oceans. Thanks to the regime sorted analyses, these differences are attributed to intrinsic differences in the vertical distribution of convective heating, and to the lack of self-inhibition by precipitating downdraughts in Tiedtke’s parametrization. Both the convection and cloud schemes are shown to control the relative importance of large scale convection over land and ocean, an important point for the behaviour of the coupled model.
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Notes
The pressure p l at level l is defined as a function of surface pressure p s as \(p_{l}=A_l p_{s} +B_l.\) The values of A l and B l are chosen in such a way that the \(A_l p_s\) part dominates near the surface (where A l reaches 1), so that the coordinate follows the surface topography, and B l dominates above several km, making the coordinate equivalent to a pressure coordinate.
A 50-layer version is also used for stratospheric studies (Lott et al. 2005).
TOGA-COARE: Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment.
In the bucket model, the soil water content is described as a single reservoir height h which evolves according to the net water budget P−E (Precipitation minus Evaporation); E = β E p , where E p is the potential evaporation (that of a free surface of water) and β = min(1,h/h p ) with h p = 75 mm. Water in excess of the maximum content (h max = 150 mm) is lost through run-off.
Note that a numerical problem in the surface scheme was identified after the realisation of the IPCC simulations. It produces occasionally very cold temperatures over one time-step in very dry continental regions in the tropics. Although a more robust and improved version of this surface model is now available, the same version as for the IPCC simulations is used here, on purpose.
The AMIP II experimental protocol requirements are all fulfilled for the simulations presented here, except that the model was not explicitly spun-up at the beginning of the AMIP period. Instead, each simulation starts from a "quasi-equilibrium" state corresponding to a previous AMIP II simulation for which there was no perceptible trend in deep soil temperature and moisture.
The difference is the same when comparing CLOUDSB with CLOUDSA or CONTROL simulations.
In the tropics, nearly all of the upward motion associated with ensemble-average ascent occurs within cumulus clouds, and gentle subsidence occurs in-between clouds. The rate of subsidence in-between clouds being strongly constrained by the clear-sky radiative cooling (which is nearly invariant), an increase of the large-scale mean ascent corresponds, to first order, to an increase of the mass flux in cumulus clouds (Emanuel et al. 1994).
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Acknowledgements
The numerical simulations presented here were performed on the NEC-SX5 of the IDRIS/CNRS computer centre. The graphics have been made with the user-friendly and public domain graphical package GrADS originally developed by Brian Dotty (COLA, support@grads.iges.org). The authors thank the anonymous referees for their constructive comments which helped us to improve the original version of the paper.
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Appendix 1: about vertically integrated velocity potential
Appendix 1: about vertically integrated velocity potential
The purpose of this appendix is: (1) to express the vertical momentum of atmospheric columns as a z-weighted integral of the Laplacian of the velocity potential; (2) to show that it is also approximately the Laplacian of a z-weighted integral of the velocity potential. Only monthly mean velocity fields are considered and the scalar velocity potential at each level is chosen so that it is zero at the poles.
1.1 Vertical momentum
The vertical momentum \(\tilde{w}\) of atmospheric columns reads:
where w and ω (≃ −ρ g w for these monthly mean fields) are the vertical velocity expressed in z and pressure coordinates, respectively, and z s is the altitude of the surface.
Vertical integration of the continuity equation (taking into account \(\vec{\nabla} \vec{V} = \nabla^2 \varphi\)) yields an expression of ω in terms of the velocity potential:
For monthly mean fields, the term \({\omega_s = {{\partial p_s}/{\partial t}}}\) is negligible. Then, substitution of (8) in (7) yields:
Let Z 0 be an altitude high enough so that \(\omega_{(Z_0)} \simeq 0.\) Then the integration may be limited to the triangle (z<Z 0, z′<z). Permuting the two integrations yields:
The Z 0 term drops out since the vertical integral of ∇2 φ is close to zero:
1.2 Expressing the vertical momentum \(\tilde{w}\) in terms of the potential of the geopotential transport
We wish to express \(\tilde{w}\) as the Laplacian of some potential. In order to do this, one has to commute the Laplacian operator in formula (10) with the z term and with the integral operator.
We shall limit ourselves to the tropical band where the geopotential altitude has weak horizontal variations. With such an approximation, the Laplacian and the z term commute.
Now we want to commute the horizontal differentials with the vertical integration. Taking into account the fact that the velocity is zero at the surface (so that \(\vec{\nabla} \varphi(p_s) = 0\)), one may write:
Adding the analog formula for the y derivative, one gets:
Over oceans, the last rhs term is zero. Over continents, it is not necessarily zero, because of orography. However, with a spatial resolution of the order of 100 km, it stays several order of magnitude smaller than the first rhs term and we shall neglect it.
Then, one may write the vertical momentum \(\tilde{w}\) as the Laplacian of a function \(\tilde{\varphi}:\)
Finally, using the same technique and the same approximations one may prove that \(\tilde{\varphi}\) is close to the saclar potential of the horizontal transport \(\vec{G}\) of geopotential:
As an illustration, Fig. 21 displays the potential \(\tilde{\varphi}\) of the annual mean geopotential transport and the mean vertical velocity. The similarity of \(\overline{\omega}\) and ω500 is obvious. However, \(\overline{\omega}\) is smoother than ω500 and might be a better indicator of dynamic regimes. Finally, the lowest pannel illustrates the strong link between large-scale ascent and precipitation.
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Hourdin, F., Musat, I., Bony, S. et al. The LMDZ4 general circulation model: climate performance and sensitivity to parametrized physics with emphasis on tropical convection. Clim Dyn 27, 787–813 (2006). https://doi.org/10.1007/s00382-006-0158-0
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DOI: https://doi.org/10.1007/s00382-006-0158-0