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Omens of coupled model biases in the CMIP5 AMIP simulations

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Abstract

Despite decades of efforts and improvements in the representation of processes as well as in model resolution, current global climate models still suffer from a set of important, systematic biases in sea surface temperature (SST), not much different from the previous generation of climate models. Many studies have looked at errors in the wind field, cloud representation or oceanic upwelling in coupled models to explain the SST errors. In this paper we highlight the relationship between latent heat flux (LH) biases in forced atmospheric simulations and the SST biases models develop in coupled mode, at the scale of the entire intertropical domain. By analyzing 22 pairs of forced atmospheric and coupled ocean-atmosphere simulations from the CMIP5 database, we show a systematic, negative correlation between the spatial patterns of these two biases. This link between forced and coupled bias patterns is also confirmed by two sets of dedicated sensitivity experiments with the IPSL-CM5A-LR model. The analysis of the sources of the atmospheric LH bias pattern reveals that the near-surface wind speed bias dominates the zonal structure of the LH bias and that the near-surface relative humidity dominates the east–west contrasts.

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Acknowledgements

We wish to thank Jean-Louis Dufresne for the fruitful discussions in the early stages of this work which have helped shape the CMIP5 analysis. We also wish to thank Lidia Mellul and Jérôme Servonnat for providing the wind-nudged simulations used in this study. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table  1 of this paper) for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. For the access and analysis of the CMIP5 data, we have benefited from the IPSL Prodiguer-Ciclad facility, supported by CNRS, UPMC, and Labex L-IPSL which is funded by the ANR (Grant ANR-10-LABX-0018) and by the European FP7 IS-ENES2 project (Grant 312979). The research leading to these results received funding from the EU FP7/2007-2013 under grant agreement no. 603521 and benefited as well from support of the ANR project "CONVERGENCE" (N8ANR-13-MONU-0008). Finally, we are extremely grateful to Olivier Boucher for providing financial support for this work through the MACC II project.

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Authors and Affiliations

  1. Laboratoire de Météorologie Dynamique/IPSL/UPMC Univ Paris 06/Sorbone Universités/CNRS, Paris, France

    Alina Găinuşă-Bogdan, Frédéric Hourdin & Abdoul Khadre Traore

  2. Environnements et Paléoenvironnements Océaniques et Continentaux/OASU/Université de Bordeaux/CNRS, Talence, France

    Alina Găinuşă-Bogdan

  3. Laboratoire des Sciences du Climat et de l’Environnement, IPSL, unité mixte CEA-CNRS-UVSQ, Gif sur Yvette, France

    Pascale Braconnot

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  1. Alina Găinuşă-Bogdan
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  4. Pascale Braconnot
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Correspondence to Frédéric Hourdin.

Appendix: Computation of explained variance

Appendix: Computation of explained variance

In order to calculate the variance of pattern A (e.g., the CPL SST bias pattern) explained by pattern B (e.g., the AMIP LH bias pattern), we project pattern A on pattern B. We first normalise B so as to obtain a representative unit vector, perform the vector projection and then compare the variance represented by this projection to the total variance of pattern A.

In practice, this consists of considering vectors \(\mathbf {a}\) and \(\mathbf {b}\) containing the ordered sequences of grid point values corresponding to A and B, respectively. We calculate the projection of \(\mathbf {a}\) on \(\mathbf {b}\), \(\mathbf {a_b}\), as:

$$\begin{aligned} \mathbf {a_b}=(\mathbf {a}\cdot \hat{b})\hat{b}, \end{aligned}$$
(11)

where

$$\begin{aligned} \hat{b}=\frac{\mathbf {b}}{\Vert \mathbf {b}\Vert }. \end{aligned}$$
(12)

We then calculate the associated proportion of explained variance as the squared norm of the projection divided by the squared norm of \(\mathbf {a}\), i.e., \(\dfrac{\Vert \mathbf {a_b}\Vert ^2}{\Vert \mathbf {a}\Vert ^2}\).

This process is mathematically equivalent to calculating \(\dfrac{(\mathbf {a}\cdot \mathbf {b})^2}{(\mathbf {a}\cdot \mathbf {a})(\mathbf {b}\cdot \mathbf {b})}\).

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Găinuşă-Bogdan, A., Hourdin, F., Traore, A.K. et al. Omens of coupled model biases in the CMIP5 AMIP simulations. Clim Dyn 51, 2927–2941 (2018). https://doi.org/10.1007/s00382-017-4057-3

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