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The strength of the tropical inversion and its response to climate change in 18 CMIP5 models


We examine the tropical inversion strength, measured by the estimated inversion strength (EIS), and its response to climate change in 18 models associated with phase 5 of the coupled model intercomparison project (CMIP5). While CMIP5 models generally capture the geographic distribution of observed EIS, they systematically underestimate it off the west coasts of continents, due to a warm bias in sea surface temperature. The negative EIS bias may contribute to the low bias in tropical low-cloud cover in the same models. Idealized perturbation experiments reveal that anthropogenic forcing leads directly to EIS increases, independent of “temperature-mediated” EIS increases associated with long-term oceanic warming. This fast EIS response to anthropogenic forcing is strongly impacted by nearly instantaneous continental warming. The temperature-mediated EIS change has contributions from both uniform and non-uniform oceanic warming. The substantial EIS increases in uniform oceanic warming simulations are due to warming with height exceeding the moist adiabatic lapse rate in tropical warm pools. EIS also increases in fully-coupled ocean–atmosphere simulations where \(\hbox {CO}_{2}\) concentration is instantaneously quadrupled, due to both fast and temperature-mediated changes. The temperature-mediated EIS change varies with tropical warming in a nonlinear fashion: The EIS change per degree tropical warming is much larger in the early stage of the simulations than in the late stage, due to delayed warming in the eastern parts of the subtropical oceans. Given the importance of EIS in regulating tropical low-cloud cover, this suggests that the tropical low-cloud feedback may also be nonlinear .

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All authors are supported by DOE’s Regional and Global Climate Modeling Program under the project “Identifying Robust Cloud Feedbacks in Observations and Model”. The work of LLNL authors was performed under the auspices of the United States Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modelling (WGCM) for their roles in making available the WCRP CMIP5 multi-model datasets. Support of these datasets is provided by the Office of Science, U.S. Department of Energy. We thank Drs. Mark Zelinka, Florent Brient, Chen Zhou and Anthony DeAngelis for many stimulating discussions on the topic. We also thank two anonymous reviewers for their constructive comments on the original manuscript. ERA-Interim data is downloaded from, NCAR/NCEP from and MERRA from

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Correspondence to Xin Qu.


Appendix 1: EIS of moist adiabats

Fig. 11

Two idealized soundings following a dry adiabat below \(LCL\) and a moist adiabat above it: One represents the present-day climate (\(T_{s}=290\), the left solid curve), and the other represents a warmer climate (\(T_{s}=294\), the right solid curve). In both cases, \(p_{s}=1{,}010\) hPa and \(RH_{s}=80\) %. The EIS values corresponding to the two soundings are calculated using Eq. (1). To illustrate EIS, in each case, we draw two dashed lines whose lapse rates are equal to \(\varGamma ^{850}_{m}\), as defined in Sect. 2. The horizontal distance between the two lines is measured by EIS. The dotted line represents the typical height of the inversion base

While the moist-adiabatic potential temperature gradient, \(\varGamma _{m}\) is function of temperature and pressure, a single value is used in defining EIS (see Sect. 2). To assess the bias associated with this assumption, we construct an idealized sounding using typical values for surface temperature (290 K), sea level pressure (1,010 hPa) and relative humidity (80 %). The lapse rate of the sounding is dry adiabatic below the \(LCL\) and moist adiabatic above it (the left solid curve, Fig. 11). While there is no inversion in this sounding, the corresponding EIS is \(-\)0.4 K. This suggests that EIS is a negatively biased estimate of inversion strength.

Fig. 12

EIS in aqua simulations. a EIS climatology in 6 aquaControl simulations. b EIS change in 6 aqua4xCO2 simulations. c EIS change in 6 aqua4K simulations. The gray lines in each diagram represent individual simulations, while the black thick line represents the ensemble-mean

To assess whether this bias is systematic, we construct another idealized sounding, in which we increase the surface temperature by 4 K, while keeping sea level pressure and relative humidity unchanged (the right solid curve, Fig. 11). We find that EIS in this sounding differs little from that in the original sounding. This suggests that the bias in EIS is systematic and similar for a reasonably large range of temperature values. Therefore, it introduces very little bias to the EIS changes examined in this study. It is worth noting that if the temperature profile follows the solid lines in both the present-day and warmer climates, the difference in 700 hPa potential temperature between the two climates is about 1.3 times the difference in surface potential temperature.

Fig. 13

Vertical profiles of potential temperature change (solid lines) in 6 aqua4K simulations relative to their control simulations (aquaControl) averaged over the 10S–10N latitude band. To focus on the regions with deep convection (i.e., those with large upward motion in the mid-troposphere), we weight the potential temperature change by total precipitation (including both convective and non-convective) before spatially averaging it. The corresponding profiles of potential temperature change implied by moist adiabatic lapse rate are also shown for comparison (dashed lines). To get these profiles, we first compute the potential temperature at each level in both aquaControl and aqua4K simulations using moist adiabatic lapse rate (see Appendix 1 for detail), as well as simulated sea level pressure and temperature. (Surface relative humidity is fixed at 80 %.) Then, we calculate the difference between the two potential temperatures

Appendix 2: EIS in aqua simulations

The climatological zonal-mean EIS in the 6 aquaControl simulations (gray lines) is shown in Fig. 12a. It is generally positive poleward of 15 degrees. Averaged over the six simulations, the areal coverage of the inversion in the region 30S-30N is 0.53, and the mean inversion strength is 1.33 K. Fig. 12b shows the EIS change in the 6 aqua4xCO2 simulations (gray lines). In at least 4 of the 6 models, positive EIS changes are seen at all latitudes. Averaged over the six simulations, the EIS increase is about 0.13 K and largely independent of latitude, with a large intermodel spread near 30S/N. Figure 12c shows the EIS change in the six aqua4K simulations. Broad EIS increases are also seen in these simulations, albeit with significant intermodel spread. Averaged over the six simulations, EIS change ranges from 0.3 to 0.8 K, with the tropical mean of 0.5 K.

Figure 13 shows the vertical profile of potential temperature change averaged over the 10S-10N latitude band in the six aqua4K simulations. While simulated change in potential temperature generally follows the moist adiabat (dashed lines) from the surface to 850 hPa, it is robustly more positive than the moist adiabat between 850 and 600 hPa.

Appendix 3: Role of changing \(RH_{s}\)

Fig. 14

Changes in surface relative humidity and their influence on simulated EIS change in tropical oceanic area with positive EIS values. a The \(RH_{s}\) change in various simulations including 6 amip4xCO2 (FR), 6 amip4K (UOW), 6 ampiFuture (NOW), 15 abrupt4xCO2 (abrupt), 16 RCP8.5 and 3 LGM. The \(RH_{s}\) change due to FR and UOW is with respect to the corresponding amip simulation, the change due to NOW is with respect to the corresponding amip4K simulation, the change in abrupt4xCO2 simulation is with respect to the corresponding piControl simulation and was averaged over the first 30 years of abrupt4xCO2 simulation, the change in RCP8.5 simulation is between the periods 1979–2008 and 2070–2099, and the change in LGM simulation is with respect to present-day. b Differences in simulated EIS change due to changing \(RH_{s}\). To obtain them, we first re-compute various EIS changes using simulated \(RH_{s}\) rather than 80 %. Then we quantify the difference between the new estimates of EIS changes and the original ones

Surface relative humidity assumes a constant value (80 %) in all EIS calculations done so far. However, climate simulations suggest that \(RH_{s}\) changes somewhat in climate change (Richter and Xie 2008). To assess whether these changes significantly affect estimated EIS change, we first examine the \(RH_{s}\) in the various perturbation experiments analyzed in this study (Fig. 14a). Positive \(RH_{s}\) changes are seen in all warming experiments, while negative changes are seen in LGM simulations. The ensemble-mean \(RH_{s}\) change in the warming experiments ranges from 0.2 to 1.5 %, while it is close to \(-\)1 % in LGM simulations. There is a large spread across models in the \(RH_{s}\) increase within a particular warming experiment.

Figure 14b shows the difference in simulated EIS change due to changing \(RH_{s}\). We find that the \(RH_{s}\) increase reduces simulated EIS increase in the warming experiments, while the \(RH_{s}\) decrease reduces simulated EIS decrease in LGM simulations. This is consistent with our expectation because an increase in \(RH_{s}\) tends to reduce \(LCL\) and a decrease in \(RH_{s}\) tends to increase \(LCL\) (see Eq. (1)). Note that in the case of NOW, the \(RH_{s}\) increase has no systematic effect on simulated EIS change. Averaged over models within each simulation type, the \(RH_{s}\)-induced difference in EIS change is generally less than 20 % of estimated EIS change with fixed \(RH_{s}\) (see Tables 6, 7; Figs. 8, 14b). Note that similar reductions in the EIS change also occur in the aqua4xCO2 and aqua4K simulations, which contribute up to 30 % of the additional warming at \(T_{700}\) (relative to the moist adiabat) seen in Fig. 13 (not shown).

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Qu, X., Hall, A., Klein, S.A. et al. The strength of the tropical inversion and its response to climate change in 18 CMIP5 models. Clim Dyn 45, 375–396 (2015).

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  • Tropical inversion
  • EIS
  • Fast response
  • Temperature-mediated change