Section 2 describes the data and climate models we use and the methods we apply. It discusses several innovations in how low-cloud regions are identified and in how models are weighted to obtain a posterior ECS, which together contribute to more robust results than those obtained in previous studies. Section 3 analyzes the covariation of TLC reflection with temperature on time scales ranging from seasonal to interannual, both in observations and in historical simulations with climate models. It also presents the posterior ECS estimate obtained by weighting current climate models. Section 4 discusses the robustness of our results by examining, additionally, how TLC reflection covaries with the strength of the trade inversion, an environmental factor considered in several previous studies (e.g., Qu et al. 2014 , 2015b ; Myers and Norris 2015 ). Finally, section 5 summarizes our conclusions and their implications.

Here we show how space-based observations can be used to robustly and quantitatively constrain likely ECS. We first use space-based observations to show how TLC reflection over oceans covaries with the underlying sea surface temperature (SST). We then demonstrate that the covariance of TLC reflection with SST in historical climate simulations correlates strongly with the models’ TLC feedback and ECS. This suggests that TLC reflection and its covariance with the underlying SST are controlled by similar physical processes, both as they vary temporally in the present climate and as they change under global warming. Therefore, the covariance of TLC reflection with SST provides an “emergent constraint”—an empirical relation between past variations and future trends in models, with a plausible physical basis for generalizations ( Collins et al. 2012 ; Klein and Hall 2015 ). This emergent constraint can be used to constrain ECS. We obtain an observationally constrained posterior ECS estimate given current climate models through an information-theoretic weighting of the models according to how well they reproduce the observed covariance of TLC reflection with SST. The posterior ECS estimate shifts the most likely ECS upward and renders ECS at the low end unlikely, but a wide range of ECS remain consistent with the observations.

2. Data, models, and methods Section: Choose Top of page Abstract 1.Introduction 2.Data, models, and metho... << 3.Results 4.Influence of inversion ... 5.Conclusions REFERENCES CITING ARTICLES

a. Observational data We use monthly shortwave fluxes and insolation at the top of the atmosphere from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) dataset, version Ed2.8, for all 183 currently available months from March 2000 through May 2015 (Loeb et al. 2009). We obtain the concurrent monthly SST from the Extended Reconstructed Sea Surface Temperature (ERSST) dataset (Smith and Reynolds 2003). As described below, we identify TLC regions on the basis of the midtropospheric (500 hPa) relative humidity from the ERA-Interim atmospheric reanalysis (Dee et al. 2011). We interpolate all data (simulated and observed) to an equal-area grid with 240 × 121 cells globally. A fixed land mask is used for models and observations to identify ocean areas, defined as grid cells with less than 10% land.

b. Climate simulations We use simulation results from 29 climate models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) of the World Climate Research Programme. The models are listed in Table 1. Table 1. Climate models, dependence of TLC reflection on SST, and model weights. For each model, the table lists the ECS, δα c /δ〈T〉 for global warming (GW) and present-day deseasonalized variability (DV), and the weight w i ∝ exp(−Δ i ) assigned to each model in the calculation of the posterior ECS given the DV δα c /δ〈T〉. ECSs are primarily from Forster et al. (2013), Sherwood et al. (2014), and Meehl et al. (2013). Global-warming δα c /δ〈T〉 is calculated from TLC reflection and temperature differences between years 130–149 and years 2–11 of an abrupt CO 2 quadrupling simulation. Models are numbered in order of increasing ECS. Models numbered 1–14 have lower sensitivity, and models numbered 15–29 have higher sensitivity. (Acronym expansions are available online at http://www.ametsoc.org/PubsAcronymList.) Image of typeset table For comparison of the models with the observational data, we create simulated datasets of the same length as the observational data by using 183-month periods of the historical CMIP5 simulations of the present climate. For each model, we use three nonoverlapping 183-month periods between the simulated years 1959 and 2005. (The simulations do not cover the exact period for which observations are available.) We analyze each of the three simulated periods like the observational data and pool the results to quantify the statistics of interest and their uncertainties reliably. For computation of TLC feedbacks under global warming, we use the CMIP5 simulations in which CO 2 concentrations were abruptly quadrupled from preindustrial levels. We calculate TLC reflection and temperature changes from the differences between years 130–149 and years 2–11 of the CO 2 quadrupling simulations. (The results are insensitive to the length of the averaging periods.) Excluding the first year from the analysis removes the rapid cloud adjustments that occur in response to carbon dioxide concentration changes, which can be viewed as a forcing rather than a feedback (Gregory and Webb 2008; Webb et al. 2013; Zelinka et al. 2013). We subdivide the climate models into two groups according to their ECS. The median ECS of 3.45 K separates the 14 lower-sensitivity (LS) models from the 15 higher-sensitivity (HS) models (Table 1).

d. TLC reflection We calculate the monthly TLC reflection α c = −〈S c 〉/〈I〉 from the top-of-atmosphere shortwave cloud radiative effect (SWCRE) S c and insolation I for observations and models, with angle brackets 〈⋅〉 denoting the mean over the TLC regions. The SWCRE S c in turn is calculated from the difference between all-sky and clear-sky shortwave fluxes at the top of the atmosphere. The TLC reflection α c then gives the fraction of the incoming shortwave radiation that is reflected by clouds in the TLC regions. Ambiguities in attributing reflection to clouds may generally arise where cloud and surface reflection cannot be clearly distinguished; however, such ambiguities should be minimal over tropical oceans. Using the TLC reflection α c instead of SWCRE S c to quantify shortwave cloud effects has the advantage that the effects of insolation variations with latitude or season are normalized out. We also calculate how the low-cloud fraction (LCF) depends on SST. This calculation is based on LCF data (cllcalpso field) from the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) GCM-Oriented CALIPSO Cloud Product (GOCCP) dataset (Chepfer et al. 2010), for June 2006 through December 2014. However, because an accurate model-to-observation comparison needs simulators to represent how satellites would see model clouds (Bodas-Salcedo et al. 2011), we prefer using top-of-the-atmosphere radiation. Our method of identifying TLC regions makes using LCF optional, and we merely present the LCF results for comparison.

e. Regressions, stationary bootstrap, and confidence intervals The dependence of cloud properties on surface perturbations is calculated as the regression slope between temporal anomalies. To reduce the effect of large residuals on the estimated regression coefficients, we use robust regressions to estimate the coefficients δα c /δ〈T〉 of the regression of TLC reflection α c onto the underlying SST 〈T〉 (and analogously for the regressions including the inversion strength as a predictor in section 4). As robust regression methodology, we use iteratively reweighted least squares with a bisquare weighting function (Holland and Welsch 1977). We include an intercept term in all regression estimates. We obtain confidence intervals on regression coefficients such as δα c /δ〈T〉 through a nonparametric bootstrap procedure, which takes the autocorrelations of the time series into account (Politis and Romano 1994). The original pairs of α c and 〈T〉 time series were resampled by drawing blocks of random length L i and assembling new pairs of bootstrap time series from them, of the same total length L as the original time series (the last block to be added is simply truncated to obtain the correct total length L). The block lengths L i are a sequence of independent and identically distributed random variables, drawn from a geometric distribution so that the probability of each block to have length L i = m is p(1 − p)m−1, where p = b−1 and b is the optimal block length for the time series. The optimal block length b is chosen so as to minimize the mean squared difference between the original time series and versions with a time shift (Politis and White 2004). The block length is chosen for the α c time series; however, the resulting confidence intervals are essentially unchanged if the block length is calculated for the 〈T〉 time series or if a fixed block length is used. For each pair of observational or model time series considered, we create 200 bootstrap samples in this way. We repeat the robust regression estimation procedure for each pair of time series, thereby obtaining 200 bootstrap samples of the regression coefficients. The bootstrap samples allow us to quantify the sampling uncertainties in the regression coefficients (e.g., because of the finiteness of the time series), robustly and without assumptions about the underlying probability distributions. To quantify the uncertainties, we fit probability density functions (PDFs) to the bootstrap samples using a Gaussian kernel density estimator with bandwidth chosen to minimize the mean integrated squared error for normal data (Bowman and Azzalini 1997). From the fitted PDFs, we obtain most likely values (modes) and confidence intervals of the regression coefficients. For the estimated confidence intervals of the TLC feedback, which are based on the scatter of the feedbacks among HS and LS models, we use multiples of the standard deviation σ among HS and LS models. Estimating more detailed PDFs in this case is difficult to justify, given the small sample size (14 and 15 models) and the lack of independence among the models.

f. Spectral decomposition of temporal variations Temporal variations in TLC reflection and SST are decomposed into four frequency bands. Seasonal variations are obtained by bandpass filtering to periods between 10 and 14 months. Deseasonalized variations are obtained by removing the mean annual cycle, through removing the mean deviation from the annual mean for each month of the year. Applying 1-yr high-pass and low-pass filters to the deseasonalized variations then yields the intra-annual and interannual variations. A twelfth-order Chebyshev filter is used throughout.