# The double ITCZ bias in CMIP5 models: interaction between SST, large-scale circulation and precipitation

## Abstract

The double intertropical convergence zone (ITCZ) bias still affects all the models that participate to CMIP5 (Coupled Model Intercomparison Project, phase 5). As an ensemble, general circulation models have improved little between CMIP3 and CMIP5 as far as the double ITCZ is concerned. The present study proposes a new process-oriented metrics that provides a robust statistical relationship between atmospheric processes and the double ITCZ bias, additionally to the existing relationship between the sea surface temperature (SST) and the double ITCZ bias. The SST contribution is examined using the THR-MLT index (Bellucci et al. in J Clim 5:1127–1145, 2010), which combines biases on the representation of local SSTs and the SST threshold leading to the onset of ascent in the double ITCZ region. As a metrics of a model’s bias in simulating the interaction between circulation and precipitation, we propose to use the Combined Precipitation Circulation Error (CPCE). It is computed as the quadratic error on the contribution of each vertical regime to the total precipitation over the tropical oceans. CPCE is a global measure of the circulation-precipitation coupling that characterizes the model physical parameterizations rather than the regional characteristics of the eastern Pacific. A linear regression analysis shows that most of the double ITCZ spread among CMIP5 coupled ocean–atmosphere models is attributed to SST biases, and that the precipitation large-scale dynamics relationship explains a significant fraction of the bias in these models, as well as in the atmosphere-only models.

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1. 1.

The coefficient of determination $$R^{2}$$ is the proportion of variability in a data set that is accounted for by the statistical model. It is defined as: $$R^{2}=\frac{\sum _{i}(\hat{SI}_{i}-\bar{SI}_{i})^{2}}{\sum _{i}(SI_{i}-\bar{SI}_{i})^{2}}=1-\frac{\sum _{i}(SI_{i}-\hat{SI}_{i})^{2}}{\sum _{i}(SI_{i}-\bar{SI}_{i})^{2}}$$, where $$SI$$ is the observed value, $$\hat{SI}$$ is the predicted value by the regression model and $$\bar{SI}=\frac{1}{n}\sum _{i}{SI}_{i}$$. $$\overline{R^{2}}$$ is the proportion of variability in a data set that is accounted for by the statistical model, that accounts for the number of explanatory variables in the model. It is defined as: $$\overline{R^{2}}=1-\frac{n-1}{n-p}\frac{\sum _{i}(SI_{i}-\hat{SI}_{i})^{2}}{\sum _{i}(SI_{i}-\bar{SI}_{i})^{2}}$$.

2. 2.

LOESS denotes a method that is also known as locally weighted polynomial regression. At each point in the data set a low-degree polynomial is fitted to a subset of the data, with explanatory variable values near the point whose response is being estimated. The polynomial is fitted using weighted least squares, giving more weight to points near the point whose response is being estimated and less weight to points further away.

## References

1. Adler RF, Huffman GF, Chang A, Ferraro R, Xie P, Janowiak J, Rudolf B, Schneider U, Curtis S, Bolvin D, Gruber A, Susskind J, Arkin P, Nelkin E (2003) The version 2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979-present). J Hydrometeorol 4:1147–1167

2. Arakawa A, Schubert WH (1974) Interaction of a cumulus cloud ensemble with the large-scale environment, part I. J Atmos Sci 31:674–701

3. Back L, Bretherthon C (2008) On the relationship between sst gradients, boundary layer winds and convergence over the tropical oceans. J Clim 22:4182–4196

4. Bacmeister JT, Suarez MJ, Robertson FR (2006) Rain reevaporation, boundary layerconvection interactions, and pacific rainfall patterns in an AGCM. J Atmos Sci 63:3383–3403

5. Bellon G, Gastineau G, Ribes A, Le Treut H (2010) Analysis of the tropical climate variability in a two-column framework. Clim Dyn 37:73–81

6. Bellucci A, Gualdi S, Navarra A (2010) The double-ITCZ syndrome in coupled general circulation models: the role of large-scale vertical circulation regimes. J Clim 5:1127–1145

7. Betts AK (1986) A new convective adjustment scheme. Part I: observational and theoretical basis. Quart J R Meteorol Soc 112:677–691

8. Bony S, Dufresne JL, Le Treut H, Morcrette JJ, Senior C (2004) On dynamic and thermodynamic components of cloud changes. Clim Dyn 22:71–86

9. Bougeault P (1985) A simple parametrisation of the large scale effects of cumulus convection. Mon Weather Rev 4:469–485

10. Charney JG (1971) Tropical cyclogenesis and the formation of the ITCZ. In: Reid WH (ed) Mathematical problems of geophysical fluid dynamics. American Mathematical Society, Providence, pp 355–368

11. Chikira M (2010) A cumulus parameterization with state-dependent entrainment rate. part II: impact on climatology in a general circulation model. J Atmos Sci 67:2194–2211

12. Chikira M, Sugiyama M (2010) A cumulus parameterization with state-dependent entrainment rate. Part I: description and sensitivity to temperature and humidity profiles. J Atmos Sci 67:2171–2193

13. Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman and Hall, New York

14. Dai AG (2006) Precipitation characteristics in eighteen coupled climate models. J Clim 9:4605–4630

15. De Szoeke SP, Xie SP (2008) The tropical eastern pacific seasonal cycle: assessment of errors and mechanisms in IPCC AR4 coupled ocean–atmosphere general circulation models. J Clim 21:2573–2590

16. Del Genio AD, Yao MS (1993) Efficient cumulus parameterization for long-term climate studies: the GISS scheme. American Meteorological Society, Providence, pp 181–184

17. Derbyshire SH, Maidens AV, Milton SF, Stratton RA, Willett MR (2011) Adaptive detrainment in a convective parametrization. Quart J R Meteorol Soc 137:1856–1871

18. Emanuel KA (1991) A scheme for representing cumulus convection in large-scale models. J Atmos Sci 48:2313–2329

19. Emanuel KA (1994) Atmospheric convection. Oxford University Press, Oxford

20. Fox J (2002) Nonparametric regression: appendix to an r and s-plus companion to applied regression. Sage Publications, Thousand Oaks, CA

21. Geoffroy O, Saint-Martin D, Olivié DJL, Voldoire A, Bellon G, Tytéca S (2012) Transient climate response in a two-box 1 energy-balance model. part I: analytical solution and parameter calibration using CMIP5 AOGCM experiments. J Clim 26:1841–1857

22. Gill AE (1980) Some simple solutions for heat-induced tropical circulation. Quart J R Meteorol Soc 106:447–462

23. Graham NE, Barnet TP (1987) Sea surface temperature, surface wind divergence, and convection over tropical ocean. Science 238:657–659

24. Grandpeix JY, Lafore JP (2010) A density current parameterization coupled with emanuel’s convection scheme. Part I: the models. J Atmos Sci 67(4):881–897

25. Grandpeix JY, Lafore JP, Cheruy F (2010) A density current parameterization coupled with emanuel’s convection scheme. Part II: 1d simulations. J Atmos Sci 67(4):898–922

26. Gregory D, Rowntree PR (1990) A mass flux convection scheme with representation of cloud ensemble characteristics and stability dependent closure. Mon Weather Rev 118:1483–1506

27. Gutzler DS, Wood TM (1990) Structure of large-scale convective anomalies over the tropical oceans. J Clim 3:483–496

28. Hess PG, Battisti DS, Rasch PJ (1993) Maintenance of the inter-tropical convergence zones and the tropical circulation on a water-covered earth. J Atmos Sci 50:691–713

29. Hirota N, Takayabu YN, Watanabe M, Kimoto M (2011) Preciptation reproducibility over tropical oceans and tis relationship to the double ITCZ problem in CMIP3 and MIROC5 climate models. J Clim 24:4859–4873

30. Holton JR, Wallace JM, Young JA (1971) On boundary layer dynamics and the ITCZ. J Atmos Sci 28:275–280

31. Hubert LF, Krueger AF, Winston JS (1969) The double intertropical convergence zone-fact or fiction? J Atmos Sci 26:771–773

32. Hwang YT, Frierson DMW (2013) Link between the double-intertropical convergence zone problem and cloud biases over the southern ocean. Proc Natl Acad Sci. doi:10.1073/pnas.1213302110

33. Lau KM, Wu HT, Bony S (1997) The role of large scale atmospheric circulation in the relationship between tropical convection and sea surface temperature. J Clim 10:381–392

34. Lin JL (2007) The double-ITCZ problem in IPCC AR4 coupled GCMs: ocean–atmosphere feedback analysis. J Clim 18:4497–4525

35. Lindzen RS (1974) Wave-CISK in the tropics. J Atmos Sci 31:156–179

36. Lindzen RS, Nigam S (1987) On the role of the sea surface temperature gradients in forcing the low-level winds and convergence in the tropics. J Atmos Sci 44:2418–2436

37. Liu H, Lin P, Yu Y, Zhang X (2012) The baseline evaluation of LASG/IAP climate system ocean model (LICOM) version 2. Acta Meteor Sinica 26:318–329

38. Liu Y, Guo L, Wu G, Wang Z (2010) Sensitivity of the ITCZ configuration to cumulus convective parametrizations on an aquaplanet. Clim Dyn 34:223–240

39. Mechoso CR, Robertson AW, Barth N, Davey MK, Delecluse P, Gent PR, Ineson S, Kirtman B, Latif M, Le Treut H, Nagai T, Neelin JD, Philander SGH, Polcher J, Schopf PS, Stockdale T, Suarez MJ, Terray L, Thual O, Tribbia JJ (1995) The seasonal cycle over the tropical pacific in coupled ocean–atmosphere general circulation models. Mon Weather Rev 123:2825–2838

40. Moorthi S, Suarez MJ (1992) The relaxed Arakawa-Schubert. A parametrization of moist convection for general circulation models. Mon Weather Rev 120:978–1002

41. Neale RB, Richter JH, Jochum M (2008) The impact of convection on ENSO: from a delayed oscillator to a series of events. J Clim 21:5904–5924

42. Nordeng TE (1994) Extended versions of the convection parametrization scheme at ECMWF and their impact upon the mean climate and transient activity of the model in the tropics. ECMWF Tech Memo No 206

43. Numaguti A (1993) Dynamics and energy balance of the Hadley circulation and the tropical precipitation zones: significance of the distribution of evaporation. J Atmos Sci 50:1874–1887

44. Oueslati B, Bellon G (2013a) Tropical precipitation regimes and mechanisms of regime transitions: contrasting two aquaplanet general circulation models. Clim Dyn 40:2345–2358

45. Oueslati B, Bellon G (2013b) Convective entrainment and large-scale organization of tropical precipitation: sensitivity of the CNRM-CM5 hierarchy of models. J Clim 26:2931–2946

46. Pan DM, Randall DA (1998) A cumulus parametrization with a pronostic closure. Quart J R Meteorol Soc 124:949–981

47. Rayner NA, Parker DE, Horton EB, Folland CK, Alexander LV, Rowell DP, Kent EC, Kaplan A (2003) Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J Geophys Res Atmos 108:4407

48. Richter JH, Rasch PJ (2008) Effects of convective momentum transport on the atmospheric circulation in the community atmosphere model, version 3. J Clim 21:1487–1499

49. Song XL, Zhang GJ (2009) Convection parameterization, tropical pacific double ITCZ, and upper-ocean biases in the NCAR CCSM3. Part I: Climatology and atmospheric feedback. J Clim 22:4299–4315

50. Xie S, Hume T, Jakob C, Klein SA, MacCoy RB, Zhang M (2010) Observed large-scale structures and diabatic heating and drying profiles during TWP-ice. J Clim 23:57–79

51. Zhang C (2001) Double ITCZs. J Geophys Res Atmos 106(11):11,785–11,792

52. Zhang GJ, McFarlane NA (1995) Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Center general circulation model. Atmos Ocean 33:407–446

53. Zhang GJ, Mu M (2005) Effects of modifications to the zhang-mcfarlane convection parameterization on the simulation of thetropical precipitation in the national center for atmospheric research community climate model, version 3. J Geophys Res Atmos 110(D09):109

## Acknowledgments

We would like to thank Aurélien Ribes for helpful discussions. We also 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.

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Correspondence to Boutheina Oueslati.

## Appendix

### Evaluating the results of a linear regression

To validate the results of a linear regression, it is important to examine the residuals ($$\epsilon$$) from the regression and identify extreme data points (leverage), that can potentially exercise a great influence on the regression line. The residuals are normalized (i.e., divided by the standard deviation of the residuals) in order to make the analysis on a standard scale.

The leverage is based on how the observed values differ from the values predicted by the regression model: $$\hat{SI}=H \ SI$$, where $$SI$$ is the vector of observed values, $$\hat{SI}$$ is the vector of values predicted by the regression model and $$H$$ is the hat matrix. The leverage of the i-th value is the i-th diagonal element ($$h_{ii}$$) of the hat matrix $$H$$.

Combining both residuals and leverage, we obtain a measure of the actual influence each point has on the slope of the regression line, namely the Cook’s distance. Cook’s distance is a measure of the effect of deleting a given observation on the regression analysis (Cook and Weisberg 1982).

Cook’s distance is calculated as: $$D_{i}= \frac{\sum _{j=1}^{n}(\hat{SI}_{j}-\hat{SI}_{j(i)})^{2}}{p \ MSE}$$, where $$\hat{SI}_{j}$$ is the prediction from the full regression model for observation j, $$\hat{SI}_{j(i)}$$ is the prediction for observation j from a refitted regression model in which observation i has been omitted, $$MSE$$ is the mean square error of the regression model and p is the number of parameters in the model. Cook’s distance can be expressed as a function of both residuals and leverage: $$D_{i}= \frac{\epsilon _{i}^{2}}{p \ MSE} [\frac{h_{ii}}{(1-h_{ii})^2} ]$$, where $$\epsilon _{i}$$ is the residual of the regression. Data points with large residuals and/or high leverage may alter the result of the regression.

Smaller Cook’s distances means that removing the observation has little effect on the regression results. Distances larger than 1 are suspicious and suggest the presence of a possible outlier or a poor model.

Figure 17 shows the standardised residuals versus leverage plot of the regression model, described by Eq. (3), performed with AGCMs, with and without INMCM4. The relationship between residuals and leverage is highlighted through a LOESS curve (LOcal regrESSion,Footnote 2 Fox 2002). Superimposed on the plot are contour lines for the Cooks distance.