Using Climate Model Simulations to Constrain Observations
Benjamin D. Santer,a Stephen Po-Chedley,a Carl Mears,b John C. Fyfe,c Nathan Gillett,c Qiang Fu,d
Jeffrey F. Painter,a Susan Solomon,e Andrea K. Steiner,f Frank J. Wentz,b Mark D. Zelinka,a
and Cheng-Zhi Zoug
a Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Livermore, California
b Remote Sensing Systems, Santa Rosa, California
c Canadian Centre for Climate Modelling and Analysis, Environment and Climate Change Canada,
Victoria, British Columbia, Canada
d Department of Atmospheric Sciences, University of Washington, Seattle, Washington
e Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
f Wegener Center for Climate and Global Change, University of Graz, Graz, Austria
g Center for Satellite Applications and Research, NOAA/NESDIS, Camp Springs, Maryland
(Manuscript received 5 October 2020, in final form 29 March 2021)
ABSTRACT: We compare atmospheric temperature changes in satellite data and in model ensembles performed under phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). In the lower stratosphere, multidecadal stratospheric cooling during the period of strong ozone depletion is smaller in newer CMIP6 simulations than in CMIP5 or satellite data. In the troposphere, however, despite forcing and climate sensitivity differences between the two CMIP ensembles, their ensemble-average global warming over 1979–2019 is very similar. We also examine four properties of tropical behavior governed by basic physical processes. The first three are ratios between trends in water vapor (WV) and trends in sea surface temperature (SST), lower-tropospheric temperature (TLT), and mid- to upper-tropospheric temperature (TMT). The fourth property is the ratio between TMT and SST trends. All four ratios are tightly constrained in CMIP simulations but diverge markedly in observations. Model trend ratios between WV and temperature are closest to observed ratios when the latter are calculated with datasets exhibiting larger tropical warming of the ocean surface and troposphere. For the TMT/SST ratio, model–data consistency depends on the combination of observations used to estimate TMT and SST trends. If model expectations of these four covariance relationships are realistic, our findings reflect either a systematic low bias in satellite tropospheric temperature trends or an overestimate of the observed atmospheric moistening signal. It is currently difficult to determine which interpretation is more credible. Nevertheless, our analysis reveals anomalous covariance behavior in several observational datasets and illustrates the diagnostic power of simultaneously considering multiple complementary variables.
KEYWORDS: Climate change; Satellite observations; Climate models; Ensembles; Model evaluation/performance

DOI: 10.1175/JCLI-D-20-0768.1
^ 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

1.		Introduction
Since publication of the first assessment report of the Intergovernmental Panel on Climate Change (IPCC) in 1990, there have been major improvements in our ability to model the climate system (Randall et al. 2007; Trenberth et al. 2007; Flato et al. 2013; Hartmann et al. 2013). Thirty years ago, the climate science community performed single simulations with a small number of pioneering atmosphere–ocean models. Today, more complex Earth system models (ESMs) are used to generate large multimodel and single-model ensembles of simulations (Kay et al. 2015; Fyfe et al. 2017; Eyring et al. 2019; Deser et al. 2020). Over the last several decades, standard
Denotes content that is immediately available upon publication as open access.
Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-20- 0768.s1.
Corresponding author: Benjamin D. Santer, santer1@llnl.gov benchmark simulations have exposed and in some cases reduced systematic errors in model representation of many different aspects of Earth’s climate (Gates et al. 1999; Randall et al. 2007; Flato et al. 2013; Sperber et al. 2013; Bellenger et al. 2014).
In tandem with advances in modeling, there have been improvements in the forcings used in model simulations of historical climate change (Solomon et al. 2011; Fyfe et al. 2013; Schmidt et al. 2014; Checa-Garcia et al. 2018). Observations have also improved with advances in the ability of scientists to identify and adjust for residual inhomogeneities in the data (Wentz and Schabel 1998; Mears et al. 2003; Mears and Wentz 2005; Fu and Johanson 2005; Karl et al. 2006, 2015; Po-Chedley et al. 2015; Hausfather et al. 2017; see section 6). This evolution of models, forcings, and observations is ongoing.
The Fifth IPCC Assessment Report, published in 2013, relied on CMIP5 simulations performed with roughly four dozen models (Taylor et al. 2012). The upcoming sixth IPCC assessment will evaluate output from a larger collection of CMIP6 models and an expanded set of experiments (Eyring et al. 2016, 2019). Our interest here is in comparing atmospheric temperature changes in CMIP5, CMIP6, the latest satellite data (Mears and Wentz 2017; Zou and Wang 2011; Spencer et al. 2017), and a state-of-the-art reanalysis of weather observations with a weather forecast model (Simmons et al. 2020). We seek to determine 1) whether there are important differences between atmospheric temperature changes in CMIP5 and CMIP6 and 2) whether models and observations show consistency in well- understood physical constraints on tropical behavior: the amplification of tropical warming with increasing height, and the ratios between trends in tropical water vapor and trends in temperature at different levels. We show that the combination of these constraints provides new information on model–data consistency.
There are several reasons for our focus on atmospheric temperature. First, discrepancies between modeled and observed atmospheric temperature changes have received scientific and political attention for over 20 years (National Research Council 2000; Karl et al. 2006; Thorne et al. 2011; Fu et al. 2011; Po- Chedley and Fu 2012; U.S. Senate 2015; Santer et al. 2017a,b; McKitrick and Christy 2020; Po-Chedley et al. 2021). Determining the causes of these differences remains a priority. Second, estimates of atmospheric temperature from satellites have recently undergone important revision, primarily due to improved understanding of the effects of drifts in satellite orbits and instrument calibration (Po-Chedley et al. 2015; Mears and Wentz 2016, 2017; Zou and Qian 2016; Zou et al. 2018; Spencer et al. 2017). Reanalysis models and data assimilation systems have also evolved (Hersbach et al. 2020; Simmons et al. 2020). Our goal is to reassess model–data consistency in the light of these improvements to observations, models, and external forcings.
The structure of our paper is as follows. Sections 2 and 3 introduce the observational and model data analyzed in our study. Section 4 discusses basic features of atmospheric temperature time series and trends. Trend comparisons are over the full satellite era (1979–2019), a period of stratospheric ozone depletion (1979–2000), and a period of ozone recovery (2001–2019). Section 5 examines the relative magnitudes of forced and unforced temperature changes on different time scales, and considers whether observed changes are consistent with results from the forced simulations. The statistical methodology in section 5 follows Santer et al. (2011) and is provided in the online supplemental material (SM) with only minor modifications. Section 6 focuses on the covariability of different aspects of tropical climate change. We examine ratios between tropical trends in column-integrated water vapor (WV) and sea surface temperature (SST), WV and the temperature of the lower troposphere (TLT), WV and the temperature of the mid- to upper troposphere (TMT), and between TMT and SST. These four ratios are compared in observations and multimodel and single-model ensembles. Prospects for using such covariability information to constrain divergent observations are considered in section 7. Appendixes A and B provide information regarding the calculation of synthetic satellite temperatures and the adjustment of tropospheric layer-average temperature for stratospheric influence.
2.		Observational data
a.		Satellite temperature data
Since late 1978, NOAA polar-orbiting satellites have monitored the microwave emissions from oxygen molecules using the Microwave Sounding Unit (MSU) and the Advanced Microwave Sounding Unit (AMSU; Mears and Wentz 2017; Spencer et al. 2017; Zou et al. 2018). Microwave emissions are proportional to the temperature of broad atmospheric layers. By measuring at different microwave frequencies, MSU and AMSU provide estimates of temperatures at different heights. Here, we analyze TLT, TMT, and the temperature of the lower stratosphere (TLS).
We rely on TLS and TMT datasets produced by Remote Sensing Systems (RSS; Mears and Wentz 2016), NOAA’s Center for Satellite Applications and Research (STAR; Zou and Qian 2016), and the University of Alabama in Huntsville (UAH; Spencer et al. 2017). Only RSS and UAH supply TLT measurements. We use the most recent dataset versions: RSS 4.0, STAR 4.1, and UAH 6.0. The University of Washington (UW) also produces a TMT dataset, but this is available for the tropics only (Po-Chedley et al. 2015). We did not use UW TMT data for the present study.
We consider three different versions of the RSS atmospheric temperature data. As noted in Mears and Wentz (2017), ‘‘a total of nine MSU instruments cover the period from 1978 to 2005, followed by a series of AMSU instruments that began in mid-1998 and continue to the present’’ (p. 7695). MSU and AMSU do not measure at the same microwave frequencies; different plausible choices can be made in merging their estimated brightness temperatures.
Mears and Wentz (2016) employed three approaches to merge MSU and AMSU data:
1)		MSU and AMSU measurements were used during the merge period from mid-1998 to 2003.
2)		Only AMSU data were used after 1999. MSU data were excluded after 1999.
3)		MSU data were used after 1999. AMSU data were excluded before 2003.
These approaches are referred to subsequently as ‘‘baseline,’’ ‘‘AMSU merge,’’ and ‘‘MSU merge,’’ respectively, and are described in more detail in the SM. In sections 5 and 6,we address the question of whether these three RSS datasets yield different statistical inferences regarding the correspondence between simulated and observed measures of climate change.
All satellite temperature datasets analyzed here are in the form of monthly means on the same 2.583 2.58 latitude– longitude grid. Near-global averages of TLS, TMT, and TLT were calculated over areas of common coverage in the RSS, UAH, and STAR datasets (82.58N–82.58S for TLS and TMT, and 82.58N–708S for TLT). At the time this analysis was performed, satellite temperature data for full 12-month years were available for the 492-month period from January 1979 to December 2019.
b.		SST data
Section 6 considers two ratio statistics involving SST. The first is R{WV/SST}, the ratio between tropical trends in WV and SST (Wentz and Schabel 2000; Held and Soden 2006; Mears et al. 2007; Mears and Wentz 2016). The second is R{TMT/SST}, the ratio of tropical TMT and SST trends (Wentz and Schabel 2000; Santer et al. 2005; Po-Chedley et al. 2015). We seek to 
determine whether simulated and observed values of these ratio statistics are consistent, and how model–data agreement is affected by structural uncertainty in observed SST data. This uncertainty arises from differences in raw data, the methods used to adjust raw data for known inhomogeneities, treatment of sea ice, and the decisions made in merging information from ship-based measurements, buoys, floats, and satellites (Karl et al. 2006, 2015; Morice et al. 2012; Hausfather et al. 2017). We quantify structural uncertainty in SST data by calculating R{WV/SST} and R{TMT/SST} with four commonly used observational records:
1)		Version 2 of the Centennial In Situ Observation-Based Estimates of the Variability of SST and Marine Meteorological Variables (COBE; Hirahara et al. 2014).
2)		Version 5 of the NOAA Extended Reconstructed SST dataset (ERSST; Huang et al. 2017).
3)		Version 1 of the Hadley Center Sea Ice and SST dataset (HadISST; Rayner et al. 2003).
4)		Version 4 of the Hadley Center SST dataset (HadSST; Kennedy et al. 2019).
All datasets except HadSST are spatially complete over the ocean domain of interest (208N–208S).
c.		Satellite water vapor data
The satellite WV data used here were produced by RSS and are from 11 different satellite-based microwave radiometers (Wentz 2013). The procedures for intercalibrating and merging information from these instruments and for estimating uncertainties in satellite WV trends are described in detail elsewhere (Mears et al. 2018). The WV retrievals are based on measurements of microwave emissions from the 22-GHz water vapor absorption line. The distinctive shape of this line provides robust retrievals. The signal-to-noise ratio (S/N) for detecting moistening in the lower troposphere by a measurement of water vapor is several times larger than for MSU-based measurements of air temperature (Wentz and Schabel 2000). Relative to WV information from radiosondes and early reanalysis products, the RSS WV dataset was judged by Trenberth et al. (2005) to provide the most credible estimate of means, variability, and trends over oceans.
While alternative satellite WV datasets exist, they span substantially shorter time intervals than the RSS WV data (Jiang et al. 2019). At the time our analysis was performed, RSS WV data were available for the 384 months from January 1988 to December 2019. Since our primary interest is in mul- tidecadal changes in WV, we focus here on the RSS product. Due to the high emissivity of the land surface, the RSS WV retrievals are provided over oceans only. We analyze WV trends spatially averaged over tropical oceans (208N–208S), where there is well-understood covariability between temperature and atmospheric moisture (Wentz and Schabel 2000; Held and Soden 2006; Mears et al. 2007; O’Gorman and Muller 2010).
Because of changes in satellite capabilities, footprint size, and rain and land masking, the spatial coverage of the RSS WV data changes over time. This results in the systematic addition of grid cells with WV data in the western Pacific and near the Maritime Continent. To avoid the introduction of trend biases arising from coverage changes, we imposed a ‘‘fixed coverage’’ mask; that is, our analysis of the satellite WV data was restricted to the subset of grid points with continuous coverage over the 384-month analysis period. After regridding model WV data to the observational grid, the same fixed coverage mask was applied to all model simulations of historical climate change.
d.		Reanalysis data
Reanalyses employ an atmospheric numerical weather forecast model with no changes over time in the model itself (Bengtsson and Shukla 1988; Kalnay et al. 1996). They provide a well-tested framework for blending and constraining assimilated weather information from different sources; each source is typically characterized by different accuracy and different temporal and spatial coverage.
The ERA5 product of the European Centre for MediumRange Weather Forecasts (ECMWF) recently superseded the ERA-Interim. ERA5 was generated with a high-resolution version (;31-km horizontal resolution, 137 vertical levels) of the ECMWF operational forecast model and a 4D variational data assimilation system (Hersbach et al. 2020). According to Simmons et al. (2020), ERA5 exhibited ‘‘a pronounced cold bias for the years 2000–06’’ (p. 1).
ERA5.1, which spans the affected 2000–06 period, corrects this error and yields ‘‘analyses with better global-mean temperatures in the stratosphere and uppermost troposphere than provided by ERA5’’ (Simmons et al. 2020, p. 1). Inclusion of ERA5.1 results allows us to test whether blending model and observational information in a state-of-the-art reanalysis framework provides layer-average atmospheric temperature trends similar to those available from actual RSS, STAR, and UAH satellite data. We also examine WV and SST trends in ERA5.1, and we consider if the ‘‘within reanalysis’’ covariance relationships between tropical WV, SST, TLT, and TMT trends are similar to those in other observational datasets and in CMIP models.
3.		Model output
a.		CMIP5 simulations
We used model TLS, TMT, TLT, SST, and WV output from phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012). The description of the CMIP5 datasets provided in the next two paragraphs follows Santer et al. (2017a).
Our focus here is on three different types of CMIP5 numerical experiment: 1) simulations with estimated historical changes in human and natural external forcings, 2) simulations with twenty-first century changes in greenhouse gases and anthropogenic aerosols prescribed according to representative concentration pathway 8.5 (RCP8.5; Meinshausen et al. 2011), and 3) preindustrial control runs with no changes in external influences on climate.
Most CMIP5 historical simulations end in December 2005. RCP8.5 simulations were initiated from conditions of the climate system at the end of the historical run. To avoid truncating comparisons between modeled and observed climate change trends in December 2005, we spliced together output from the historical simulations and the RCP8.5 runs. We refer to these spliced simulations subsequently as ‘‘extended HIST’’ runs.
In total, we analyzed 123 individual extended HIST realizations performed with 28 different CMIP5 models. We excluded models that did not consider the scattering and absorption of radiation by stratospheric volcanic aerosols (Santer et al. 2013), and therefore lack short-term lower-stratospheric warming signals after the eruptions of El Chichón in 1982 and Pinatubo in 1991. Including these models in the calculation of multimodel average (MMA) temperature changes would bias the MMA estimate of volcanic TLS signals.
Details of the start dates, end dates, and lengths of the historical integrations and RCP8.5 runs are given in Table S1 in the online supplemental material. Table S2 provides information on the 36 CMIP5 preindustrial control runs used to calculate climate noise estimates. The control integrations allow us to determine S/N characteristics of atmospheric temperature changes (see section 5).
b.		CMIP6 simulations
We also analyze sea surface temperature and atmospheric temperature and moisture from model simulations performed under phase 6 of CMIP. These simulations rely on newer versions of CMIP5 models, often with more comprehensive representation of Earth system processes (Eyring et al. 2016), and with contributions from modeling groups that did not participate in CMIP5. Efforts were made in CMIP6 to improve the representation of external forcings with known systematic errors in CMIP5, such as volcanic and solar forcing in the early twenty-first century (Solomon et al. 2011; Kopp and Lean 2011; Ridley et al. 2014; Schmidt et al. 2014; Gillett et al. 2016).
At the time this research was performed, the CMIP6 archive was still being populated with model simulation output. For preindustrial control runs, output was available from 30 different models. For the analysis of forced simulations, the CMIP6 historical runs from 22 different models were spliced with results from scenario integrations.
Multiple Shared Socioeconomic Pathway (SSP) scenarios were available for splicing (Riahi et al. 2017). We chose the SSP5 scenario here. SSP5 most closely approximates the radiative forcing in the CMIP5 RCP8.5 simulation. The differences in radiative forcing between the five SSPs are very small over the satellite era (Riahi et al. 2017), so the choice of scenario is unlikely to affect our model-versus-data comparisons.
In the case of TMT, TLT, SST, and WV, we analyzed 166 realizations. For reasons discussed in section 3c, the sample size was smaller for TLS (116 extended HIST realizations performed with 21 models). Further details of the CMIP6 extended HIST and control simulations are provided in Tables S3 and S4, respectively.
c.		Large initial condition ensembles
Large initial condition ensembles (LEs) are valuable tools for separating forced and unforced climate change (Deser et al. 2012; Fyfe et al. 2017; Deser et al. 2020). Individual LE members are generated with the same model and external forcings, but are initialized from different conditions of the climate system. Each LE member provides a unique realization of the ‘‘noise’’ of natural internal variability superimposed on the underlying climate ‘‘signal’’ (the response to the changes in forcing). Typical LE sizes range from 30 to 100.
We used four different LEs to quantify uncertainties in temperature and WV trends arising from multidecadal internal variability. Two LEs applied CMIP5 historical forcing until 2005 and CMIP RCP8.5 forcing thereafter. The other two LEs relied on CMIP6 historical forcing until 2014 and SSP5 forcing from 2015 to 2100. The CMIP5 LEs were performed with version 1 of the Community Earth System Model (CESM1; Deser et al. 2012) and with version 2 of the Canadian Earth System Model (CanESM2; Fyfe et al. 2017; Swart et al. 2018). The CESM1 and CanESM2 LEs consist of 40 and 50 members, respectively. The two 50-member CMIP6 LEs relied on version 5 of CanESM (CanESM5; Swart et al. 2019; Fyfe et al. 2021) and on version 6 of the Model for Interdisciplinary Research on Climate (MIROC6; Tatebe et al. 2019). All four LEs used different strategies for initialization of the individual ensemble members.
The CanESM5 LE exhibits anomalous aperiodic 1–2-month lower-stratospheric warming events in certain ensemble members, an issue that is actively under investigation. These warming events are sufficiently large to influence decadal-time scale TLS trends but have minimal impact on decadal variability in tropospheric temperature (or on the regression-based removal of stratospheric influence on TMT; see appendix B). We therefore excluded the CanESM5 LE from the multimodel analysis of CMIP6 TLS trends, but used CanESM5 TLS data to remove stratospheric influence from CanESM5 TMT data, and included CanESM5 LE results in the multimodel analysis of TMT, TLT, WV, and SST.
4.		Temperature time series and trends
a.		Lower stratosphere
Figure 1a shows time series of near-global averages of TLS. The lower stratosphere cools over the full satellite era in all

Fig. 1. Time series of monthly mean near-global averages of the temperature of (a) the lower stratosphere (TLS), (b) the mid- to upper troposphere (TMT), and (c) the lower troposphere (TLT). For TLS and TMT, observations are the average of the RSS ‘‘baseline’’, STAR, and UAH satellite datasets and the ERA5.1 reanalysis. Since STAR does not produce a TLT dataset, the observational average for TLT was calculated with RSS ‘‘baseline’’, UAH, and ERA5.1 only. CMIP5 synthetic satellite temperatures were computed from 123 realizations of historical climate change (‘‘extended HIST’’) performed with 28 models. For CMIP6, 116 extended HIST realizations were used for TLS and 166 realizations for TMT and TLT (performed with 21 and 22 models, respectively). All temperature changes are defined as anomalies relative to climatological monthly means over 1979–2019. TMT is adjusted for the contribution it receives from stratospheric cooling (see appendix B). Calculation of the multimodel average (MMA) involves first averaging over realizations of an individual model, then averaging over models. observational datasets and model extended HIST simulations. The main cause of this cooling is human-induced depletion of stratospheric ozone, with a smaller contribution from anthropogenic increases in atmospheric CO2 (Solomon 1999; Ramaswamy et al. 2006; Thompson et al. 2012; Aquila et al. 2016; Maycock et al. 2018; Bandoro et al. 2018). Satellite-era decreases in TLS are punctuated by large episodic warming signals after the major eruptions of El Chichón in 1982 and Pinatubo in 1991. Warming arises from absorption of incoming solar radiation and outgoing longwave radiation by stratospheric volcanic aerosols (Robock 2000; Shine et al. 2003).
The CMIP6 multimodel average has an unrealistically small TLS signal after El Chichón (Figs. 1a and 2). Based on the MMA root-mean-square (RMS) errors between observed and simulated volcanic TLS signals, the TLS response to El Chichón is better captured in CMIP5 (Figs. 3a,c). For Pinatubo, the MMA RMS error is smaller in CMIP6 (Figs. 3b,d). These CMIP5- versus-CMIP6 differences are significant at the 5% level for the El Chichón signal, but not for the Pinatubo signal (see the online SM).
Volcanic signal differences in CMIP5 and CMIP6 arise from multiple factors. These include differences in the type and time history of information used for prescribing historical changes in volcanic aerosol loadings, the aerosol optical properties, and the implementation of these properties in calculating volcanic radiative forcing (Thomason et al. 2018). Rather than prescribing volcanic aerosol, at least one CMIP6 modeling group calculated volcanic aerosol loadings based on observed estimates of volcanically produced SO2 (Mills et al. 2016; Danabasoglu et al. 2020). Separating and quantifying the impact of these different factors on volcanic temperature signals requires systematic numerical experimentation (Rieger et al. 2020; Fyfe et al. 2021).
Recent studies suggest that the Montreal Protocol led to a partial recovery of lower-stratospheric ozone and TLS in the early twenty-first century (Solomon et al. 2016, 2017; Philipona et al. 2018; Petropavlovskikh et al. 2019; Banerjee et al. 2020). All model and observational TLS datasets analyzed here exhibit behavior consistent with ozone recovery: pronounced global-mean cooling of the lower stratosphere over the ozone depletion portion of the satellite record, defined here as the period from 1979 to 2000, followed by weaker cooling or nearzero trends over the period of ozone recovery from 2001 to 2019 (Solomon et al. 2017; Philipona et al. 2018; Steiner et al. 2020; Mitchell et al. 2020). No individual CMIP5 or CMIP6 realization has larger lower-stratospheric cooling in the ozone recovery period than in the ozone depletion period (Fig. 4). This underscores the fact that the nonlinear behavior of TLS over the satellite era is dominated by the response to ozone forcing, not by multidecadal internal variability (Solomon et al. 2017).
The multimodel average TLS trends for the ozone depletion and recovery periods are (respectively) 20.368 and 20.078C decade21 in CMIP5 and 20.268 and 20.068C decade21 in CMIP6. During the ozone depletion period, the larger multimodel average lower-stratospheric cooling in the older CMIP5 simulations is in better accord with satellite TLS trends, which range from 20.428 to 20.498C decade21. This is partly due to the larger (negative) ozone-induced stratospheric radiative forcing in CMIP5 (Checa-Garcia et al. 2018).
Other factors may also contribute to reduced lower- stratospheric cooling in CMIP6 over 1979–2000. These factors include CMIP5-versus-CMIP6 differences in forcing from tropospheric ozone (Checa-Garcia et al. 2018), volcanoes (see above) and stratospheric water vapor (Keeble et al. 2021), possible differences in the forced response of tropical upwelling (Ball et al. 2020), and whether ozone in models was

Fig. 2. Time series of monthly mean anomalies of the temperature of the lower stratosphere (TLS) in CMIP6 extended HIST simulations. Results are for 21 individual CMIP6 models (in gray) and for the RSS ‘‘baseline’’ satellite data (in red). (bottom right) The CMIP6 multimodel average. All anomalies are spatially averaged over 82.58N–82.58S and are defined relative to climatological monthly means over 1979–2019. The number of extended HIST realizations is indicated in parentheses. Vertical lines denote the times of maximum lower-stratospheric warming in the RSS ‘‘baseline’’ data after the eruptions of El Chichón and Pinatubo.

prescribed or calculated with interactive ozone chemistry (Lin and Ming 2021).
The zonal-mean structure of TLS trends may provide some diagnostic clues. Over the ozone depletion period, the smaller global-mean lower-stratospheric cooling in the CMIP6 MMA (relative to the CMIP5 MMA) arises primarily from the tropics (Fig. 5a). During the ozone recovery period, the multimodel
average TLS trends from the two CMIP phases are more similar in their zonal-mean structure, except at high latitudes in the SH (Fig. 5b). More detailed analyses and more systematic numerical experimentation will be required to quantify the relative contributions of forcing, response, chemistry, and dynamics to differences between CMIP5 and CMIP6 TLS trends (Solomon et al. 2017; Checa-Garcia et al. 2018; Fyfe et al. 2021).

Fig. 3. Root-mean-square (RMS) differences between simulated and observed volcanic signals in lower- stratospheric temperature in (a),(b) CMIP5 and (c),(d) CMIP6 models. RMS differences were calculated for 24-month periods after (a),(c) the 1982 eruption of El Chichón and (b),(d) the 1991 Pinatubo eruption. The observational target is the RSS ‘‘baseline’’ TLS time series, spatially averaged over 82.58N–82.58S. Blue dots denote RMS values from individual realizations of the CMIP5 and CMIP6 extended HIST runs. Horizontal bars are average RMS differences for individual models. The dashed vertical lines are the multimodel average RMS differences, calculated by first averaging RMS values over a model’s individual realizations, and then averaging over models.

b.		Troposphere
Multidecadal warming of the global troposphere is a ubiquitous feature of the observations and all CMIP5 and CMIP6 forced simulations (Figs. 1b,c). Over the full satellite era, the MMA tropospheric warming rate is very similar in CMIP5 and CMIP6 (0.288 and 0.298C decade21, respectively). This holds both for TMT and TLT (Fig. 6a). The similarity of the CMIP5 and CMIP6 results is noteworthy given that CMIP6 has a larger number of models with higher transient climate response (TCR) and higher effective climate sensitivity (ECS) (Zelinka et al. 2020; Flynn and Mauritsen 2020; Meehl et al. 2020). An independent analysis of surface temperature supports our finding: despite higher average TCR and ECS in CMIP6, the MMA historical surface warming rate is comparable in older and newer generations of CMIP models, possibly due to a larger response to anthropogenic aerosol forcing in CMIP6 (Flynn and Mauritsen 2020; Fyfe et al. 2021).
In the four single-model large ensembles, the spread of TMT and TLT trends arising from internal variability is substantial, spanning 31%–47% of the trend spread in the CMIP5 and CMIP6 multimodel ensembles (Fig. 6a). These results are consistent with other recent comparisons of LE spread to

Fig. 4. Least squares linear trends in near-global average lower- stratospheric temperature over ozone depletion and ozone recovery periods (1979–2000 and 2001–19, respectively). Model results are from 123 and 116 extended HIST simulations performed with 28 different CMIP5 and 21 different CMIP6 models, respectively. CMIP5 trends include results from the 40-member CESM1 and 50-member CanESM2 large ensembles (LEs). CMIP6 trends incorporate the 50-member MIROC6 LE. Observed estimates of TLS trends rely on satellite data (RSS, STAR, and UAH) and the ERA5.1 reanalysis. Three different versions of the RSS data are shown. The 1:1 line (with trends of equal size over the ozone depletion and ozone recovery periods) is marked in purple. The shaded ellipses are the 2s confidence intervals for each of the three LEs. For information on spatial averaging and calculation of multimodel averages, refer to Fig. 1.
multimodel ensemble spread (Mitchell et al. 2020; Po-Chedley et al. 2021).
Observed trends in global-mean tropospheric temperature range from 0.138 to 0.198C decade21 for TMT and from 0.138 to 0.218C decade21 for TLT (Fig. 6a). For TLT, over 84% of the total number of CMIP5 and CMIP6 extended HIST realizations analyzed here have trends exceeding the largest observational result; the corresponding figure is 91% for corrected TMT trends. Related work suggests that the smaller observed warming is partly due to an unusual manifestation of natural internal variability. Model realizations with phasing and amplitude of internal variability similar to the observations yield global-mean and tropical tropospheric temperature trends that are closer to satellite results (Po-Chedley et al. 2021).
In all individual extended HIST realizations, the ratio R{TMT/TLT} between global-mean trends in TMT and TLT is close to unity (Fig. 6b). This narrow range occurs despite differences in external forcings, ECS, and internal variability in the multimodel and single-model ensembles, and despite differences in the patterns of warming in TMT and TLT (Santer et al. 2019). The 5th–95th percentile ranges of the CMIP5 and CMIP6 R{TMT/TLT} sampling distributions encompass the UAH-derived ratio, but all other observational datasets have R{TMT/TLT} values significantly less than one. The decisions made by RSS in merging MSU and AMSU have limited impact on TLT trends and substantial impact on TMT trends (Fig. 6a), thereby introducing large spread in the three RSS-derived R{TMT/TLT} values. The RSS ‘‘MSU merge’’ dataset, which has the largest global-mean TMT trend, is closest of the three to the model expectations of R{TMT/TLT} (Fig. 6b).
It is now recognized that there were systematic deficiencies in the early twenty-first century solar and volcanic forcing used in CMIP5 (Kopp and Lean 2011; Solomon et al. 2011; Flato et al. 2013; Schmidt et al. 2014). Efforts were made to improve representation of both forcings in CMIP6 (Eyring et al. 2016; Gillett et al. 2016; Thomason et al. 2018; Rieger et al. 2020). We find, however, that CMIP5 and CMIP6 multimodel average trends in TMT are virtually identical over 2001–19 (Fig. 7). Since other external forcings also changed between these two generations of models (Checa-Garcia et al. 2018; Fasullo et al. 2021, manuscript submitted to Nat. Climate Change), isolating the climate impact of improvements in volcanic or solar forcing is challenging. Such diagnosis will benefit from simulations in which the same physical climate model is run with different versions of individual forcings (Fyfe et al. 2021; Fasullo et al. 2021, manuscript submitted to Nat. Climate Change).
Tropospheric trends in ERA5.1 exhibit several notable differences relative to the satellite datasets (Hersbach et al. 2020). Reanalysis TMT trends are smaller than in all satellite datasets over 1979–2000 and larger than in all satellite datasets over 2001–19 (Fig. 7). Over the 2002–18 period covered by Global Positioning Satellite (GPS) radio occultation measurements, both GPS data and radiosondes yield trends in the middle troposphere that are in reasonable accord with the ERA5.1 results (Steiner et al. 2020).
While the satellite data analyzed here are derived from measurements of microwave emissions alone, ERA5.1 uses a state-of-the-art 4D-variational data assimilation system to constrain a weather forecast model with a wide range of multivariable measurements from satellites, radiosondes, and surface stations (Hersbach et al. 2020; Simmons et al. 2020). Detailed observing system experiments can help to understand the impact of different features of the assimilation system and assimilated data (Bormann et al. 2019). Such studies will be useful in reconciling the trend differences found here and elsewhere (Steiner et al. 2020) between microwave sounders and ERA5.1.
5.		Signal-to-noise properties and model–data signal differences
In previous statistical comparisons of modeled and observed temperature changes, discussion often focused on the appropriateness of different comparison periods (Santer et al. 2011). This can be uninformative if attention is restricted to a short segment of the overall temperature record. Here we analyze atmospheric temperature changes over all NL maximally overlapping L-year periods (see the SM). We consider four different values of L: 10, 20, 30, and 40 years. For each value of L, sampling variability is reduced by averaging over all NL individual measures of temperature change. As we show

Fig. 5. Zonal-mean trends in monthly mean lower-stratospheric temperature over the (a) ozone depletion and (b) ozone recovery periods. For information regarding the numbers of CMIP5 and CMIP6 models and extended HIST realizations, calculation of multimodel averages, spatial averaging, and observational data, refer to Fig. 1.

below, examining behavior averaged over a particular time scale can have diagnostic value.
Figure 8 shows two different types of statistic: trends and regression coefficients. Results are from individual observational datasets and from distributions of statistics in forced and unforced simulations.
Consider the trend results first. Rows 1–3 of Fig. 8 display trends in TLS, TMT, and TLT, respectively, for our four selected values of the time scale L. With increasing L, the amplitude of internally generated trends decreases. As a result, the standard deviations of the forced and unforced trend distributions decrease. For all three atmospheric layers, forced and unforced trend distributions are completely separated at L 5 40 years (Figs. 8d,h,l). This is a simple visual illustration of the dependence of signal and noise on time scale, and of the difficulty in their separation on shorter, noisier time scales of 1– 2 decades (Santer et al. 2011).
Despite the evolution in model complexity and resolution between CMIP5 and CMIP6, the sampling distributions of unforced atmospheric temperature trends are remarkably similar in the two generations of coupled models. The same is true for the sampling distributions of forced trends on 10- and 20-year time scales. On longer 30- and 40-year time scales, however, small differences are apparent in the distributions of forced tropospheric temperature trends in CMIP5 and CMIP6. These may arise because CMIP5 and CMIP6 do not have identical multidecadal evolution of certain external forcings (Checa- Garcia et al. 2018; Fyfe et al. 2021).
Figure 8 also provides information on the consistency between global-mean temperature trends in observations and the extended HIST simulations. On shorter 10- and 20-year time scales, all observed TLS, TMT, and TLT trends are contained within the respective CMIP5 and CMIP6 distributions of forced trends. The same is true for observed TLS trends on longer 30- and 40-year time scales (Figs. 8c,d). For TMT and TLT, however, only observed datasets with larger tropospheric warming rates are within the model 30- and 40-year distributions of forced trends. The UAH-inferred warming on these time scales is invariably smaller than model expectations (Figs. 8g,h,k,l).
Amplification of warming with increasing height is a well- known and well-understood property of the tropical atmosphere (Stone and Carlson 1979; Santer et al. 2005; Held and Soden 2006). Figures 8m–p display one measure of tropical amplification behavior—the regression coefficient b{TMT:TLT} between time series of tropical ocean averages of TMT and TLT. All model and observational values of b{TMT:TLT} are greater than 1, indicating that temperature changes in the midto upper troposphere exceed those in the lower troposphere. The means and widths of the CMIP5 and CMIP6 sampling distributions of b{TMT:TLT} are relatively insensitive to increases in L, and show substantial overlap for the forced and unforced runs. The model results imply that b{TMT:TLT} is both invariant to time scale and insensitive to forcing, and that it may impose a robust, physically based constraint on observations (Santer et al. 2005; Held and Soden 2006).
Observational values of b{TMT:TLT} show a number of interesting features. First, the ERA5.1 and RSS ‘‘MSU merge’’ results are well within the range of model expectations on all four time scales considered here. In terms of this tropical amplification metric, therefore, there is no fundamental discrepancy between simulations and all observations.
Second, as in the model simulations, b{TMT:TLT} is invariant to time scale for UAH, ERA5.1, and the RSS ‘‘MSU merge’’ case. While the three RSS sensitivity tests have almost identical

Fig. 6. (a) Scatterplot of linear trends in near global-mean lower-tropospheric temperature (TLT) and mid- to upper-tropospheric temperature (TMT) and (b) histograms of the TMT/ TLT trend ratio. All trends are over 1979–2019. TMT is corrected for lower-stratospheric cooling. The multimodel averages include information from the 50- and 40-member CanESM2 and CESM1 LEs (for CMIP5) and from the 50-member CanESM5 and MIROC6 LEs (for CMIP6). The shaded ellipses in (a) are the 2s confidence intervals for each LE. Because TLT is not produced by STAR, the STAR TMT trend is plotted as a horizontal line in (a). Selected isopleths of equal values of the TMT/TLT trend ratio are denoted by dashed gray lines in (a). For further details of CMIP5 and CMIP6 realizations and models, calculation of multimodel averages, spatial averaging, observational data sources, and fits to histograms, refer to caption of Fig. 1 and the online supplemental material (SM).

b{TMT:TLT} values for L 5 10 years (Fig. 8m), the RSS baseline and ‘‘AMSU correct’’ datasets yield regression coefficients that decrease in size as L increases, and are generally outside the range of model results for 30- and 40-year time scales (Figs. 8o–p). On these longer time scales, the maximally overlapping L-year windows always sample the 1998–2003 transition between earlier and more advanced microwave sounders, and thus are more likely to reflect the impact of different merging choices on amplification behavior (see section 2a).
Third, the UAH b{TMT:TLT} value is ;1.1 on all four time scales and is smaller than almost all model results. The anomalous UAH value is due to a change in the method used by the UAH group to estimate TLT (Spencer et al. 2017). The impact of this change was to increase the height of the effective weighting function for TLT, thus decreasing the vertical separation between the TLT and corrected TMT weighting functions. This

Fig. 7. As in Fig. 4, but for linear trends in global average mid- to upper-tropospheric temperature (TMT) over 1979–2000 (x axis) and over 2001–19 (y axis). TMT is corrected for the influence of lower-stratospheric cooling. While Fig. 4 excluded TLS results from the 50-member CanESM5 LE because of anomalous TLS variability, TMT trends from the CanESM5 LE are minimally affected by this anomalous variability and are included here. The 1:1 line (with TMT trends of equal size over the two periods) is marked in purple. Simulated TMT trends are larger in the second analysis period in approximately 90% of the realizations. In satellite data, trends in the two periods are of roughly equivalent size.
leads to a smaller amplification ratio. To maintain continuity with previous tropical amplification studies (Santer et al. 2017b) and to increase the amplification signal, the model, RSS, and ERA5.1 results shown here do not use the new UAH approach for calculating TLT.
6.		Covariability of different aspects of tropical climate change
Properties of the climate system that are controlled by well- understood physical mechanisms and are tightly constrained in model simulations may be useful for reducing large uncertainties in observed temperature trends (Santer et al. 2005). We consider four such properties here. The first three properties are ratios between tropical WV trends and trends in tropical SST, TLT, and corrected TMT.8 We refer to these ratios as R{WV/SST}, R{WV/TLT}, and R{WV/TMT}, respectively. The relationship between temperature and saturation vapor pressure changes is governed by the Clausius–Clapeyron (C-C) equation (Iribarne and Godson 1981). If relative humidity remains approximately constant as temperature increases, C-C predicts the increase in columnar content of WV (Wentz and Schabel 2000; Held and Soden 2006; Mears et al. 2007; O’Gorman and Muller 2010).
The fourth property we examine, the trend ratio R{TMT/SST}, is a measure of the amplification of tropical SST changes in the tropical troposphere. Its behavior is governed by moist thermodynamics (Stone and Carlson 1979; Held and Soden 2006). The ratio R{TMT/SST} provides information that differs from that of b{TMT:TLT}, the regression-based amplification metric considered in section 5.9
In a climate model, these four ratios are internally and physically consistent. The observed covariability of tropical WV, tropospheric temperature, and SST should also exhibit internal and physical consistency. As we show below, however, observed R{WV/SST}, R{WV/TLT}, R{WV/TMT}, and R{TMT/SST} values can be inconsistent for certain combinations of observed datasets, and may depart noticeably from model expectations.
Such departures can have at least three explanations. First, WV, tropospheric temperature, and SST are measured independently by different instruments on different satellites and/ or measurement platforms. Each variable has different measurement accuracy and errors. These measurement differences can affect the estimated covariability between multidecadal trends in WV, tropospheric temperature, and SST.
Second, the tropospheric temperature and SST datasets analyzed here were generated by multiple research groups. In the case of TMT and TLT, each research group uses different procedures to adjust for drifts in satellite orbits and instrument calibration, to merge measurements from multiple satellites, and to merge brightness temperatures estimated from earlier and more recent types of microwave sounders. For SST, groups use different methods to blend information from ships, buoys, drifting floats, and satellites, to adjust for changes over time in how SST measurements were made, and to infill SSTs in datasparse regions. The decisions made in adjusting tropospheric temperature and SST for these known nonclimatic influences can affect trends (Karl et al. 2006, 2015; Hausfather et al. 2017; Mears et al. 2011; Mears and Wentz 2016, 2017; Zou and Qian 2016; Zou et al. 2018; Spencer et al. 2017; Po-Chedley et al. 2015), and can therefore influence the estimated covariability between real-world temperature and WV changes (or between observed trends in SST and TMT). Trends in satellite WV data

Fig. 8. Trends and regression coefficients in CMIP5, CMIP6, and observations. Maximally overlapping L-year trends were calculated from time series of monthly-mean, near-global spatial averages of (a)–(d) TLS, (e)–(h) TMT, and (i)–(l) TLT. (m)–(p) The regression coefficient b{TMT:TLT}, a measure of amplification of warming in the tropical troposphere, was computed with maximally overlapping L- year time series of monthly mean TMT and TLT, spatially averaged over ocean areas between 208N and 208S. The four selected time scales shown here are (left to right) 10, 20, 30, and 40 years, respectively. Histograms of these L-year trends and regression coefficients are shown for CMIP5 and CMIP6 extended HIST simulations and for preindustrial control runs. Histograms are weighted to account for model differences in the number of extended HIST simulations or in control run length. For each histogram, results are normalized by the total number of trend or regression coefficient samples. Fits to the model trend and b{TMT:TLT} distributions were performed with kernel density estimation (see the SM). The vertical lines for the observed trends and regression coefficients are the averages across the maximally overlapping L-year analysis periods. For trends in TMT, the RSS ‘‘MSU merge’’ and STAR results are almost identical.

are also sensitive to dataset construction choices (Mears et al. 2018), but we currently have uncertainty estimates from RSS only.
Third, models may have incomplete or inaccurate representation of the basic physics driving observed tropical covariability relationships on multidecadal time scales. This seems unlikely (Held and Soden 2006), particularly given the fact that on interannual time scales, observed tropical covariability relationships between surface and tropospheric temperature (Santer et al. 2005) and between temperature and WV (Mears et al. 2007) are well captured by models (see section 7).
Figure 9 shows scatterplots of the individual trend components of the four ratio statistics. For each statistic, model results are tightly constrained in the CMIP5 and CMIP6 multimodel ensembles. At least 96% of the variance in simulated WV trends (plotted on the y axis in Figs. 9a–c) and in simulated TMT trends (plotted on the y axis of Fig. 9d) is explained by simulated trends in the independent (x axis) variable. This indicates that the four covariance relationships of interest here are relatively insensitive to model differences in the applied historical forcings, the temperature and WV responses to these forcings, and the properties of simulated multidecadal internal variability. A related inference is that even though most of the mass of atmospheric water vapor resides in the lower troposphere, simulated tropical SST, TLT, and TMT trends impose

Fig. 9. Scatterplot of tropical trends in (a) WV and SST, (b) WV and TLT, (c) WV and corrected TMT, and (d) corrected TMT and SST. Trends are over 1988–2019, the period of availability of observed WV data from seven different microwave radiometers (Mears et al. 2018), and were calculated with WV, TLT, TMT, and SST data averaged over tropical oceans (208N–208S). For ERA5.1, the location of the purple pentagonal symbols is based on reanalysis data only (i.e., the ERA5.1 WV trend in (a) is plotted against the ERA5.1 SST trend). All other observational symbols provide information on the joint variability between trends in different climate variables estimated by different research groups. In (a), for example, the satellite WV trend (which is available from RSS only) is plotted against observed SST trends from ERSST, HadISST, COBE, and HadSST. In (b) and (c), the RSS WV trend is plotted against TLT and TMT trends from five and six different satellite datasets, respectively. In (d), there are four different observed SST trends and five different satellite TMT trends, yielding 4 3 5 combinations of SST and TMT trends (plus the symbol denoting the relationship between the ERA5.1 TMT and SST trends). The x axis position of observational symbols in (d) reflects the observed SST trend; they axis position depends on the observed TMT trend. The regression fits and slopes were estimated with orthogonal distance regression and are given separately for CMIP5 and CMIP6 results (see the SM). The ERSST and HadSST trends are almost identical; this is why the solid blue diamond and red star symbols overlap in (a) and (d).

similar constraints on simulated tropical WV trends—that is, there is no evidence that (on multidecadal time scales) SST or TLT explains noticeably more of the WV variance than TMT.
The regression fits to the CMIP5 and CMIP6 trends are 8.5% and 8.7% 8C21 for WV and SST, 6.3% and 6.4% 8C21 for WV and TLT, and 5.3% and 5.5% 8C21 for WV and TMT (Figs. 9a–c, respectively). The decrease in regression slope in the progression from Figs. 9a to 9c reflects the fact that tropical temperature changes closely follow a moist adiabatic lapse rate (Stone and Carlson 1979). As the magnitude of warming amplifies with increasing height, the slope of the regression between temperature trends and moisture trends decreases. The regression slope for simulated tropical SST and TMT trends (1.6 for both CMIP5 and CMIP6; see Fig. 9d) is also consistent with moist adiabatic lapse rate (MALR) expectations (Fu et al. 2004).
Unlike the model covariance relationships in Fig. 9, all four sets of observed covariance relationships show substantial spread. The tight clustering of model expectations and the large observational uncertainty are clearer if we directly compare

Fig. 10. Histograms of the ratios between the model trends plotted in each of the four panels of Fig. 9. Results are shown for (a) R{WV/SST}, (b) R{WV/TLT}, (c) R{WV/TMT}, and (d) R{TMT/SST}. Observational trend ratios in (a)–(c) are plotted as vertical lines. In (d), trends from each of the five satellite TMT datasets analyzed here (the three RSS versions, STAR, and UAH) can be paired with four different observed SST trends (from ERSST, HadISST, COBE, and HadSST), yielding 5 3 4 different observed values of R{TMT/SST}, plus one value for the ratio between the ERA5.1 TMT and SST trends (see Fig. 9 caption). Observed R{TMT/SST} values in (d) are plotted in six rows. There is one row for each of the five satellite TMT datasets and one row for the reanalysis. The vertical spacing and y axis location of rows is nominal; the vertical ordering of rows reflects the size of the observed tropical TMT trend over 1988–2019. The largest TMT trend (in the STAR dataset) has the largest y axis offset in (d). For details regarding fits to the model histograms and histogram weighting, refer to the SM. Because the ERSST and HadSST trends are almost identical, the ERSST-based trend ratios in (a) and (d) have been offset vertically. Other observational results with similar ratios have also been offset for the sake of clarity.

trend ratios (Fig. 10). This comparison reveals that observed SST and tropospheric temperature datasets with the largest tropical warming over 1988–2019 have R{WV/SST}, R{WV/TLT}, and R{WV/TMT} ratios closest to the model results (Figs. 10a–c).
For all three ratios involving WV trends, there is minimal overlap between simulations and observations; observed ratios generally exceed model expectations. For R{WV/SST}, only the COBE SST trend leads to a result consistent with model expectations (Fig. 10a). For both R{WV/TLT} and R{WV/TMT}, observed trend ratios are larger than almost all of the 289 model results (Figs. 10b,c). The agreement between model

Fig. 11. Normalized differences (Z-scores) between observed scaling ratios and the mean of model scaling ratio distributions. (a) Results for tests of R{WV/TLT} ratios based on five different satellite TLT datasets and for tests of R{WV/TMT} and R{TMT/SST} ratios based on six different satellite TMT datasets. (b) Results involving tests of R{WV/SST} and R{TMT/SST} with four different observed SST datasets. (c) Z-scores relying on tests performed with observed trend ratios computed using reanalysis data. All Z-scores were calculated using the scaling ratio data in Fig. 10. For each ratio tested, the observed ratio is subtracted from the mean of the CMIP5 or CMIP6 sampling distribution of the ratio. These differences are normalized by the CMIP5 or CMIP6 standard deviation of the ratio’s sampling distribution; CMIP5 and CMIP6 Z-scores are then averaged. For the R{TMT/SST} ratios in (a), there is an additional averaging step: each satellite TMT trend can be paired with four different observed SST trends, yielding four different Z-scores (see rows in Fig. 10d). We average these four values per TMT dataset. Likewise, each observed SST trend in (b) can be paired with 5 different satellite TMT trends, yielding five different values of R{TMT/SST} (see columns in Fig. 10d). We average these five values per SST dataset. The brown bars are average Z-scores for different types of scaling ratio. Observed ratios to the left of the dashed purple are within two standard deviations of the model trend ratio sampling distributions.
and observed R{WV/SST} values is closer, but depends on the selected combination of observed TMT and SST datasets (Fig. 10d).
We calculated Z-scores to summarize and synthesize the information in Fig. 10. For each observed ratio in Fig. 10, the Z-score is simply the difference between the observed result and the mean of the CMIP5 or CMIP6 multimodel average ratio, normalized by the CMIP5 or CMIP6 standard deviation of the sampling distribution of the ratio in question. The Z- scores in Fig. 11a are measures of the consistency between the simulated and observed values of R{WV/TLT}, R{WV/TMT}, and R{TMT/SST}. For the latter ratio, results are averaged over the individual Z-scores arising from structural uncertainty in observed SST trends. The Z-scores in Fig. 11b involve R{WV/SST} and R{TMT/SST}, with R{TMT/SST} results averaged over the individual Z-scores arising from structural uncertainty in satellite tropospheric temperature trends. The reanalysis results for all four ratios are shown in Fig. 11c.
Under the assumption that the model-generated distributions of the four ratios are realistic representations of the true (but uncertain) real-world covariance relationships, the Z-scores allow us to make certain inferences about the likelihood that individual observed SST and tropospheric temperature datasets are consistent with model expectations and with other observations. In Fig. 11a, for example, STAR and RSS ‘‘MSU merge’’—the datasets with the largest observed tropospheric warming trends—are closest to the model expectations of WV/tropospheric temperature trend ratios, and therefore have the smallest Z-scores for R{WV/TLT} and R{WV/TMT}. In contrast, the muted tropospheric warming in UAH leads to R{WV/TLT} and R{WV/TMT} values that are significantly larger than model expectations, thus leading to large UAH Z-scores for these two ratios. Based on R{WV/TLT} and R{WV/TMT} alone, therefore, we might infer that the smaller tropical tropospheric warming trend is UAH is less credible.
This inference assumes that the observed trend in tropical WV is accurate. A substantially smaller observed WV trend would decrease the UAH-derived R{WV/TLT} and R{WV/TMT} ratios, bringing them in closer agreement with model expectations. Since we do not have estimates of the observed WV trend from multiple research groups, it is difficult to assess the likelihood that the true (but uncertain) real-world WV trend is markedly smaller than the RSS WV trend estimate.
By considering the R{TMT/SST} ratio, however, we can bring in independently monitored observed SST data. This allows us to explore the constraint that observed SST trends impose on the size of observed TMT trends. All four observed SST datasets, when considered in combination with the UAH TMT trend, lead to UAH-based R{TMT/SST} ratios that are significantly smaller than climate model expectations (Fig. 10d).
In summary, the reduced tropical tropospheric warming in UAH is not supported by 1) an independent estimate of atmospheric moistening from satellite data, 2) all independent estimates of observed sea surface warming, or 3) all model expectations of R{WV/TLT}, R{WV/TMT}, and R{TMT/SST}.
The above analysis focused on comparing simulated and observed measures of tropical covariability. It is also of interest to compare modeled and observed values of the individual components of these covariability metrics. In the case of WV, 
21% of the WV trends over 1988–2019 in the 289 CMIP5 and CMIP6 extended HIST simulations are smaller than the satellite-estimated WV trend in Fig. 9a. For SST, TLT, and TMT trends over the same period, only 17%, 12%, and 12% of the model results are smaller than the largest observed trend (Figs. 9a–c, respectively).
There are multiple interpretations of this finding. One interpretation is that the higher level of consistency between simulated and observed tropical WV trends reflects a systematic low bias in observed tropical TLT and TMT trends over 1988–2019. An alternative explanation is that the satellite WV trend is overestimated. It is difficult to discriminate between these two possibilities without additional information, such as well-quantified estimates of uncertainties in observed WV trends from different research groups.
One interesting feature of Fig. 9 relates to the behavior of the ERA5.1. As noted above, the CMIP models show tight coupling between the multidecadal trends in tropical WV, SST, and tropospheric temperature. In contrast, the agreement between the CMIP expectations and reanalysis-based trend ratios is noticeably better for R{WV/SST} than for either R{WV/TLT} or R{WV/TMT} (cf. the relative distances from the regression lines of the purple pentagonal symbols in Figs. 9a–c). This closer agreement is reflected in the lower Z-score for the ERA5.1- based R{WV/SST} ratio in Fig. 11c. Our results imply that some aspect or aspects of the assimilation system or assimilated data (Hersbach et al. 2020) may be affecting the internal and physical consistency of tropical temperature and moisture trends in the reanalysis.
7.		Conclusions
Relative to CMIP5, the more recent CMIP6 models have higher resolution (on average), more complete numerical portrayal of Earth’s climate system, and nominally improved representation of external forcings (Eyring et al. 2016). These advances do not guarantee improved agreement between simulations and observations. This is apparent in at least two aspects of model performance analyzed here: lower-stratospheric cooling over the ozone depletion period and the stratospheric temperature response to the El Chichón eruption. Understanding why these features are more accurately represented in CMIP5 will require more systematic diagnostic efforts to disentangle evolutionary changes in models from evolutionary changes in model forcings (Fyfe et al. 2021).
The development of satellite temperature datasets remains a work in progress. Adjustments for known nonclimatic factors can have significant impact on observed trends in tropospheric temperature, as well as on basic physical properties related to tropospheric warming (Karl et al. 2006; Mears et al. 2011; Mears and Wentz 2016, 2017; Zou and Qian 2016; Zou et al. 2018; Spencer et al. 2017; Po-Chedley et al. 2015). Multimodel and single-model large ensembles tightly constrain four such physical properties: the ratio between tropical trends in WV and SST, WV and TLT, WV and TMT, and TMT and SST. These are denoted here by R{WV/SST}, R{WV/TLT}, R{WV/TMT}, and R{TMT/SST}, respectively. Comparing modeled and observed values of such basic covariance relationships has the advantage (relative to single-variable comparisons) that results are less sensitive to model-versus-observed differences in the phasing of internal variability (Santer et al. 2005; Po-Chedley et al. 2021).
We find significant differences between simulated and observed values of all trend ratios involving water vapor and tropospheric temperature. Observed ratios exceed model expectations in most cases (Figs. 10a–c). Observed datasets with larger warming of the tropical ocean surface and tropical troposphere yield ratios of R{WV/SST}, R{WV/TLT}, and R{WV/TMT} that are closer to model results. Ratios between moisture and temperature changes calculated with the UAH and HadISST datasets, which both have muted tropical warming over 1988–2019, are at least 10 standard deviations removed from model expectations (Fig. 11). For R{TMT/SST}, model–data consistency depends on the selected combination of observed datasets used to estimate TMT and SST trends (Fig. 10d).
One interpretation of our findings is that they are due to a systematic low bias in satellite tropospheric temperature trends; that is, the size of the observed tropical moistening signal is greater than can be explained by the independently observed warming of the tropical troposphere. Alternately, the observed atmospheric moistening signal may be overestimated. Given the large structural uncertainties in observed tropical TMT and SST trends, and because satellite WV data are available from one group only, it is difficult to determine which interpretation is more credible.
What we can say with confidence, however, is that decisions regarding how to merge MSU and AMSU TMT data have substantial impact on observed tropical TMT trends. This is evident from the three RSS sensitivity tests examined here (Mears and Wentz 2016). These sensitivity tests point toward merging decisions as a significant contributory factor to uncertainties in observed R{WV/TMT} and R{TMT/SST} trend ratios (Figs. 10c,d).
Three further points are relevant to the question of whether the model–observed differences in Figs. 10a–c are mainly due to underestimated observed tropospheric temperature trends or to an overestimated satellite WV trend. First, independent estimates of tropospheric temperature change from GPS radio occultation (RO) and radiosondes suggest that over the 2002–18 period of overlap between MSU/AMSU and GPS- RO, tropospheric warming is smaller in microwave sounders than in GPS-RO or radiosondes (Steiner et al. 2020). Second, there is some evidence that observational uncertainties may be smaller in satellite WV data than in satellite tropospheric temperature data (Wentz 2013; see section 2c). Third, when the individual trend components of our four trend ratios are examined, the agreement between models and observations is better for WV and SST trends than for TMT or TLT trends. These three lines of evidence, taken together with the results of the RSS sensitivity tests, suggest that underestimated observed tropospheric warming is plausible. This inference is predicated on the assumption that the model-based covariance constraints are realistic.
While our analysis does not definitively resolve the cause or causes of significant differences between modeled and observed tropospheric warming trends, it does illustrate the diagnostic power of simultaneously considering multiple complementary variables (Wentz and Schabel 2000). Our study also highlights the strong internal and physical consistency between the model constraints derived from multidecadal tropical trends in WV, TMT, and SST. Examining additional independently monitored constraints may be helpful in reducing the currently large uncertainties in observations of tropical climate change.
Acknowledgments. 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 for producing and making available their model output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison (PCMDI) provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. This work was performed under the auspices of the U.S. Department of Energy (DOE) by Lawrence Livermore National Laboratory under Contract DE- AC52-07NA27344. At LLNL, B.D.S., S.P.-C., M.D.Z., and J.P. were supported by the Regional and Global Model Analysis Program of the Office of Science at the DOE. S.P.-C. was also supported under LDRD 18-ERD-054. At M.I.T., S.S. was partly supported by NSF-AGS Grant 1848863. All primary satellite, reanalysis, and model temperature data sets used here are publicly available. Synthetic satellite temperatures calculated from model simulations and the ERA 5.1 are provided at https:// pcmdi.llnl.gov/research/DandA/. We thank Adrian Simmons at ECMWF for assistance with ERA 5.1 data and internal reviewers at NOAA and CCCma for helpful comments.
APPENDIX A
Calculation of Synthetic Satellite Temperatures from
Model Data
We use a local weighting function method developed at RSS to calculate synthetic satellite temperatures from CMIP5 and CMIP6 output and from the ERA5.1 reanalysis (Santer et al. 2017b). At each grid point, simulated temperature profiles were convolved with local weighting functions. The weights depend on the grid-point surface pressure, the surface type (land, ocean, or sea ice), and the selected layer-average temperature (TLS, TMT, or TLT). The local weighting function method provides more accurate estimates of synthetic satellite temperatures than use of a global-mean weighting function, particularly over high-elevation regions.
APPENDIX B
Method Used for Correcting TMT Data
Trends in TMT estimated from microwave sounders receive a substantial contribution from the cooling of the lower stratosphere (Fu et al. 2004; Fu and Johanson 2004, 2005; Johanson and Fu 2006). In Fu et al. (2004), a regression-based method was developed for removing the bulk of this stratospheric cooling component of TMT. This method has been validated with both observed and model atmospheric temperature data (Fu and Johanson 2004; Gillett et al. 2004; Kiehl et al. 2005). We calculated two different versions of corrected TMT, the first with latitudinally fixed and the second with latitudinally varying regression coefficients. We refer to these subsequently as TMT1 and TMT2, respectively. The main text discusses corrected TMT1 only, and does not use the subscript 1 to identify corrected TMT.
The regression equation applied in Fu and Johanson (2005) for calculating corrected TMT is
TMT 5 a24TMT 1 (1 2 a24)TLS.	(B1)
For TMT1, we use a24 5 1.1 at each latitude. For TMT2, a24 5 1.1 between 308N and 308S, and a24 5 1.2 poleward of 308. This is consistent with how we have calculated TMT1 and TMT2 in previous work (Santer et al. 2017b).
The advantage of TMT2 is that lower-stratospheric cooling makes a larger contribution to TMT trends at mid- to high latitudes. The latitudinally varying regression coefficients in TMT2 remove more of this extratropical cooling. We prefer to use the more conservative TMT1 here. In practice, the choice of TMT1 or TMT2 has minimal influence on the statistical significance of differences between the modeled and observed statistics of interest here (temperature trends and a regressionbased measure of the amplification of warming with increasing height in the tropical atmosphere).
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with the regression slope of ;5.4% 8C21 estimated from Fig. 9c
would require that the RSS WV trend of 1.46% decade21 was
roughly a factor of 2 smaller. Such an error is well outside the WV
trend uncertainty assessed by RSS (Mears et al. 2018). An error
by a factor of ;2 in the observed WV trend would also be required
to obtain agreement between the HadISST-derived value of R{WV/ SST} and the regression slope of ;8.6% 8C21 in Fig. 9a.