Quantifying the Drivers of the Clear Sky Greenhouse Effect, 2000–2016

The clear sky greenhouse effect (G) is defined as the trapping of infrared radiation by the atmosphere in the absence of clouds. The magnitude and variability of G is an important element in the understanding of Earth's energy balance; yet the quantification of the governing factors of G is poor. The global mean G averaged over 2000 to 2016 is 130–133 W m−2 across data sets. We use satellite observations from Clouds and the Earth's Radiant Energy System Energy Balance and Filled (CERES EBAF) to calculate the monthly anomalies in the clear sky greenhouse effect (ΔG). We quantify the contributions to ΔG due to changes in surface temperature, atmospheric temperature, and water vapor by performing partial radiation perturbation experiments using ERA‐Interim and Geophysical Fluid Dynamics Laboratory's Atmospheric Model 4.0 climatological data. Water vapor in the middle troposphere and upper troposphere is found to contribute equally to the global mean and tropical mean ΔG. Holding relative humidity (RH) fixed in the radiative transfer calculations captures the temporal variability of global mean ΔG while variations in RH control the regional ΔG signal. The variations in RH are found to help generate the clear sky super greenhouse effect (SGE). Thirty‐six percent of Earth's area exhibits SGE, and this disproportionately contributes to 70% of the globally averaged magnitude of ΔG. In the global mean, G's sensitivity to surface temperature is 3.1–4.0 W m−2 K−1, and the clear sky longwave feedback parameter is 1.5–2.0 W m−2 K−1. Observations from CERES EBAF lie at the more sensitive ends of these ranges and the spread arises from its cloud removal treatment, suggesting that it is difficult to constrain clear sky feedbacks.


Introduction
The clear sky greenhouse effect (G) is known to maintain Earth's temperature at habitable levels but has been perturbed by natural variability and anthropogenic influences over the past century with significant implications for the climate system. It can be measured by the difference between the surface upwelling flux (E) and the clear sky outgoing longwave radiation (OLR) at the top of the atmosphere, Since March 2000, there has been a continuous time series of G from the Clouds and the Earth's Radiant Energy System Energy Balance and Filled (CERES EBAF) observational data set. The goal of this study is to use this observational data set to characterize how G varied during this time period and breakdown the factors responsible for G's temporal anomalies by carrying out partial radiation perturbation experiments.
Previous studies that aimed to explain the physics of the greenhouse effect used only a few discontinuous months of Earth's Radiation Budget Experiment (ERBE) (Raval & Ramanathan, 1989) data, ship data and radiosondes. Moreover, they correlated G and SST for all points around the Earth and obtained linear fits that were not representative of the physics of a given region (Hallberg & Inamdar, 1993;Inamdar & Ramanathan, 1994;1998;Soden & Fu, 1995;Raval & Ramanathan, 1989). Studies which carried out sensitivity analyses of G only used one month of data and relied on fixed perturbations (Huang et al., 2007 and which are not representative of observed anomalies, i.e., deviations from a climatology. A breakdown with only one month does not allow us to deduce what factors are responsible for the transition from negative to positive anomalies for any given location. Studies that had a longer time series did not attempt to explain the drivers of the anomalies and only showed a comparison between observations and general circulation models (Soden, 1997 andRadley et al., 2014).

10.1029/2019JD031017
Key Points: • Global mean clear sky greenhouse effect (G) over 2000-2016 is 130-133 W m −2 and its sensitivity to surface temperature is 3.1-4.0 W m −2 K −1 • Middle and upper tropospheric water vapor contribute equally to anomalies in global G, while regionally midtroposphere dominates • Variations in relative humidity are crucial in explaining regional anomalies in G and help generate the clear sky super greenhouse effect Supporting Information: • Supporting Information S1 • Figure S1  The time series spanning 16.5 years allows us to characterize the frequently occurring super greenhouse effect (SGE), the phenomenon in which the rate of change of G with surface temperature exceeds the surface emission's rate (Hallberg & Inamdar, 1993;Stephens et al., 2016;Valero et al., 1997). Hallberg and Inamdar (1993) focused on surface temperatures above 298 K, where G was found to nonlinearly increase. Recently, Koll and Cronin (2018) showed a nonlinear decrease in clear sky OLR at high temperatures, which can also be characterized as SGE. Past work on SGE has been based on idealized models that used a single global mean column and did not account for RH variations (Dewey & Goldblatt, 2018). It also did not focus on questions such as what percentage of Earth's area experiences SGE, how often does it occur across the globe, and what factors make a particular location transition from a regular greenhouse state to a super greenhouse state from 1 month to the next (Huang & Ramaswamy, 2008;Kahn et al., 2016;Stephens et al., 2016). Our paper seeks to address these outstanding questions about SGE in the current climate.
In the following section we describe the data and methods that we used. In section 3 we present our results starting with section 3.1 where we compare G of GFDL's AM4 to ERA-I and CERES data sets, which Held and Soden (2000) deemed important for testing the skill of general circulation models for future climate change predictions. In section 3.2, to explain the origins of G every month, we decompose G into its contributions from surface temperature, atmospheric temperature, and water vapor. We investigate whether fixed RH controls interannual variations in G regionally and globally in section 3.3. In section 3.4, we examine how sensitive G is to changes in surface temperature. We also estimate the clear sky longwave feedback parameter across different data sets to understand how sensitive the climate is during 2000-2016.
We then show how often, where, and why the super greenhouse effect is produced in section 3.5. Finally, we conclude with a discussion about the results.

Data
Monthly mean data from CERES EBAF Ed4.1 Kato et al., 2018), ERA-Interim (Dee et al., 2011), and GFDL AM4 (Zhao et al., 2018) are used to study the temporal variability of G from March 2000 to August 2016. Within Edition 4.1 of CERES EBAF, we use the "t" version: clear sky fluxes from the total area of a region. Uncertainty in CERES EBAF Edition 4's regional monthly clear sky OLR is 4.5-5 W m −2 and in the global mean it is approximately 2 W m −2 . Regional monthly surface upwelling longwave flux (E) uncertainty is 15 W m −2 and in the global mean it is 3 W m −2 . In the case of ERA-Interim, surface temperature is used to calculate the surface upwelling flux (E = T 4 s ) with the assumption of unit emissivity (Wilber et al., 1999). Outputs from GFDL AM4 are generated using prescribed observed SSTs.
Monthly mean ozone mixing ratio, water vapor mixing ratio, atmospheric temperature, and surface temperature from ERA-I and AM4 are used as inputs for the Rapid Radiative Transfer Model (RRTM; Mlawer et al., 1997) for the partial radiative perturbation (PRP) experiments. The dimensions, units, and resolutions of the relevant quantities are listed in Table 1. For the "ERA+RRTM" PRP experiments, we regrid H 2 O, T a , andT s onto 2.25 • × 2.25 • (10 • × 10 • resolution for "AM4+RRTM") to reduce computational time (Table 1). This yields 2.25 • × 2.25 • grid box means of G covering the globe.

Definitions
The time series of G (deseasonalized anomaly) for a particular grid box is found using the following: Note. Time denoted by "t", longitude denoted by "x", latitude denoted by "y", and height denoted by "z". ERA-Interim has 37 vertical levels and GFDL AM4 has 33 vertical levels. All quantities are monthly means. "*" refers to G derived from existing data set, "**" refers to G calculated using RRTM, and "***" refers to inputs used for radiative transfer calculations in RRTM. "ERA+RRTM" and "AM4+RRTM" spatial resolutions are obtained first by taking area averages at native grid resolution.
Throughout this paper, refers to a temporal anomaly and the overbar denotes a temporal mean at a particular latitude and longitude, unless otherwise stated. For ease of notation, if a quantity ( ) is temporally averaged, we shorten (t, x, , z) to and for an anomaly, (t, x, y, z) is shortened to . When several grid boxes of a climatological quantity are averaged to a larger region such as the globe or Tropics, we will explicitly mention (x, ) with the quantity.
The Tropics are defined as 30 • S to 30 • N, the West Pacific as 15 • S to 15 • N, 90-150 • E, and the Central Pacific as 15 • S to 5 • N, 150-240 • E (rectangles in Figure 4a). The West Pacific and Central Pacific are similar in area, and each occupy ∼9% of the Tropics. El Niño and La Niña events are classified using the Oceanic Niño Index (ONI), that is, surface temperature anomalies greater than 0.5 K and less than −0.5 K, respectively, for five or more consecutive months in the Niño 3.4 region (5 • S to 5 • N, 190-240 • E) using a 3-month running mean. The troposphere is partitioned into the lower troposphere (surface-700 hPa), middle troposphere (700-400 hPa), and upper troposphere (400-150 hPa).

Partial Radiative Perturbation Experiments
In order to quantify the drivers of G, we performed nine PRP experiments. The PRP method (e.g., Becker & Stevens, 2014;Colman & McAvaney, 2011;Colman, 2015;Colman et al., 2001;Klocke et al., 2013) assumes that for small perturbations to the climate system, G can be linearly decomposed into its constituents: The PRP method substitutes each variable from the perturbed climate into the control climate one by one in an off-line radiation code (RRTM). The radiative perturbations, that is, anomalies, on the RHS of equation (3) are then calculated by subtracting off the radiation from the nonperturbed state.
In our study, the control climate refers to the monthly climatology of each variable. Experiment 1 calculates G and experiments 2-4 decompose G into its constituents as shown in equation (4). Similarly, in experiments 5-8, contributions by water vapor (ΔG H 2 O ) to G are further decomposed into contributions from lower, middle, and upper tropospheric water vapor (equations (5b)-(5d)) and water vapor arising from fixed and varying RH (equations (6c)-(6d)). Lastly, experiment 9 computes the contributions from varying carbon dioxide, methane, and nitrous oxide (section 3.1 and Figure 1). Note. ERBE's time period was over April 1985 to January 1986. CE 4.1 "c" and CE 4.1 "t" denote CERES EBAF Edition 4.1 observations using cloud-free areas of a region and the total area of a region, respectively. Units of G are in W m −2 . Uncertainties in G are the 95% confidence intervals.

Testing the Sensitivity of Experiments
Conducting the PRP experiments in different orders did not make a quantitative difference in our results. We tested the influence of spatial resolution on the results by comparing finer spatial resolution (2.25 • × 2.25 • ) to coarser spatial resolution (10 • × 10 • ) in the ERA+RRTM PRP experiments. We found that the coarser resolution G explained over 99% of the variance in the finer resolution G time series. We tested the sensitivity of our results to radiative computational accuracy by using a line-by-line (LBL) radiative transfer model (Dudhia, 2017) as opposed to a band model (RRTM) for a 10 • × 10 • grid box in the Central Pacific. Near-perfect agreement (r 2 = 0.98) between the LBL calculated and the RRTM calculated G time series was found. The agreement between LBL models and band models has been found in past literature too (Briegleb, 1992). Lastly, we show in Figure S1 in the supporting information that the use of monthly mean profiles with RRTM (AM4+RRTM) is accurate (r 2 = 0.99) relative to radiative fluxes calculated from instantaneous profiles and then averaged up to monthly fluxes (AM4 output).

G and G in CERES Era
In Table 2, we compare the globally averaged and time-averaged values of G, that is, G(t, x, ) between data sets. We find that the reanalysis data set, ERA-Interim, and the general circulation model, GFDL AM4, agree to within 1 W m −2 of CERES EBAF 4.1 version "t" values. Values from CERES EBAF 4.1 version "c" are lower than version "t" because version "c" outputs clear sky fluxes from cloud free areas of a region, which are generally less moist than the grid point's cloudy columns. Version "t" contains an adjustment that ignores clouds in the atmospheric column, which makes version "t" more consistent with how general circulation models calculate clear sky fluxes (Potter et al., 1992 andLoeb et al., 2018). Values of global mean G obtained and derived from other studies such as 135.4 W m −2 and 131 W m −2 from Huang (2013) and Wild et al. (2018), respectively, are also consistent with Table 2's values.
Note that, over oceans, G(t, x, ) from ERBE (Raval & Ramanathan, 1989) is higher than the G from each of the modern data sets. This discrepancy is most likely due to the fact that ERBE was not energy balanced like CERES EBAF. Radley et al. (2014) also summarized differences between ERBE and CERES by noting that the satellites had different orbits, data processing techniques, and calibrations, which yielded different OLR values. Detailed explanations regarding the differences between ERBE and the modern data sets is outside the scope of this paper (see Wielicki et al., 2002;Raschke et al., 2012). Figure 1a shows the seasonal cycle of G. The variability of G from CERES EBAF (red) is captured by ERA+RRTM (black) and ERA+RRTM_gg (green). In the ERA+RRTM_gg case, varying monthly concentrations of CO 2 , CH 4 , and N 2 O are used. However, in the ERA+RRTM case (black), CO 2 , CH 4 , and N 2 O monthly values are held fixed at 2015's values. The peak of G is during Northern Hemispheric (NH) summer and its trough is during NH winter. This is consistent with the NH summer (winter) being hotter (colder) than the Southern Hemisphere's summer (winter), and the fact that G is driven by the surface temperature and its accompanying changes in atmospheric temperature and water vapor (section 3.2).
Although G has a large seasonal cycle, we are interested in how anomalous G is for a given month, so we calculate G using equation (2). In Figure 1b we plot the time series of globally averaged G. This reveals that G's variability from CERES EBAF is reproduced by ERA+RRTM_gg (r 2 = 0.84) and ERA+RRTM (r 2 = 0.77). The fact that G from ERA+RRTM_gg and G from ERA+RRTM are in agreement (r 2 = 0.93) implies that greenhouse gas variations do not impact interannual variability in G. ERA+RRTM_gg is important for explaining trends. The trend in CERES EBAF Ed4.1 "t" of 1.07 ± 0.07 W m −2 ·decade −1 is ERA+RRTM_gg G is calculated from RRTM using ERA-Interim's climatological data with CO 2 , CH 4 , and N 2 O varying (green), ERA+RRTM G is calculated from RRTM using ERA-Interim's climatological data with CO 2 , CH 4 , and N 2 O fixed at 2015's values (black), and satellite observed G is from CERES EBAF Edition 4.1 "t" (red). Light red and blue shadings indicate El Niño and La Niña events, respectively. Dotted lines indicate trends.
better explained by the 0.76 ± 0.07 W m −2 ·decade −1 trend in G with varying greenhouse gas concentration (ERA+RRTM_gg) rather than the 0.49 ± 0.07 W m −2 ·decade −1 trend in G with fixed greenhouse gas concentration (ERA+RRTM). However, since we are interested in the month-to-month and interannual changes, we use ERA+RRTM and not ERA+RRTM_gg for the rest of the paper so as to isolate the effects of changes in surface temperature, atmospheric temperature, and water vapor on G. We repeated the above calculations for G with "AM4+RRTM_gg" and "AM4+RRTM" and found poorer correlations with CERES EBAF (r 2 = 0.62 and r 2 = 0.52, respectively).
In Figure 1b we observe that the dominant mode of interannual variability in the climate system, the El Niño-Southern Oscillation (ENSO; Trenberth, 1997), shows its imprints on the global G. During a La Niña, such as the 2007-2008 event, Earth becomes colder and consequently G decreases by 1.5 W m −2 . Conversely, during an El Niño, such as the 2015-2016 event, Earth becomes warmer and consequently G increases by 1.8 W m −2 . In the next section, we discuss how these changes in G arise by decomposing G into its constituents, in particular during ENSO events.

Breakdown of G
The time series of G is broken down into contributions from surface temperature (purple), atmospheric temperature (gray), and water vapor (orange; Figure 2a) using the ERA+RRTM experiments (equation (4)). ΔG T s can be interpreted as the "passive" atmosphere contribution-the atmosphere absorbs upwelling photons associated with surface temperature changes while the atmospheric state stays fixed. The maximum ΔG T s can be E = T 4 s . In turn, ΔG T a loses photons to space, which acts to balance ΔG T s . To the first order, this balance determines the greenhouse effect-the atmospheric temperature is colder than the surface temperature, leading to radiation being trapped in the atmosphere. In addition, ΔG H 2 O acts to increase the radiation trapped by the atmosphere.
As seen in Figure 2a, all three components are important in contributing to the overall anomaly in G each month. This is further seen in Table 3, which decomposes G into its components during ENSO events.
Here, we took a spatial average of each quantity and then did a temporal average only during ENSO events.  Note. Lower troposphere (surface-700 hPa) denoted by "LT", middle troposphere (700-400 hPa) denoted by "MT", and upper troposphere (400-150 hPa) denoted by "UT". Units of G are in W m −2 . Uncertainties are 95% confidence intervals.
The ΔG T s and ΔG H 2 O components are of the same sign (barring the West Pacific) and are offset partially by the ΔG T a component of the opposite sign. The magnitude of the offset varies in location and ENSO events. These results are largely consistent with "AM4+RRTM" (supporting information's Figure S2 and Table S1).
We have quantitatively shown that the radiative contribution by water vapor is important for explaining the greenhouse effect anomaly (Figure 2a and Table 3). To understand the reasons for water vapor's radiative contributions, we break down ΔG H 2 O into contributions from water vapor in the lower troposphere (LT), middle troposphere (MT), and upper troposphere (UT) using the PRP method (equation (5) and section 2.3).
In Figure 2b We obtain the saturation vapor pressure from the Claussius-Clapeyron equation (equation (6a)). To obtain the "fixed RH," that is, the monthly climatology RH, we find the ratio of the monthly climatology of water vapor (H 2 O) and the monthly climatology of the saturation vapor pressure (e sat (T)). Equation (6b) Figure 3a shows that the fixed RH approximation is especially accurate during ENSO events (La Niñas in 2000-2001and 2007El Niños in 2009-2010and 2015. During El Niño, the global ΔG H 2 O is dominated by the fixed RH contributions (Table 5).
Although assuming fixed RH for each grid box yielded a globally averaged ΔG H 2 O FRH ≈ ΔG H 2 O , smaller regions are known to exhibit large shifts in RH . For smaller regions, the variability in radiative contributions by water vapor can be explained by the contributions from water vapor arising from varying RH and not by fixed RH. For example, in Figure 3b's West Pacific case, ΔG H 2 O VRH explains 92% of ΔG H 2 O 's variance (r 2 = 0.92). In the last two rows of Table 5 we further see that varying RH plays a much bigger role locally, with 60-70% of ΔG H 2 O coming from ΔG H 2 O VRH . Spatial maps of G (Figures 4a and 4b), (Figures 4c and 4d), and ΔG H 2 O FRH (Figures 4d and 4e) demonstrate this result further. Readers interested in the spatial patterns of G's breakdown into ΔG H 2 O , ΔG T a , and ΔG T s can view Figure S5 in the supporting information.
During ENSO events, the spatial pattern of ΔG H 2 O VRH matches that of G, because, locally, varying RH contributions dominate ΔG H 2 O , which in turn is a significant contributor to G. The spatial pattern of ΔG H 2 O FRH does not resemble that of ΔG H 2 O VRH and G (the latter two quantities match the canonical ENSO SST pattern ; Trenberth, 1997), signaling that, locally, ΔG H 2 O FRH is a poor assumption at each grid box. This implies that changes in the temperature will not be a good indicator of how G will change. To accurately know how G will change locally, information on variations in RH are needed. Results from AM4+RRTM in supporting information Figures S3 and S4 and In the next section, we will see that the fixed RH approximation for global ΔG H 2 O extends to its sensitivity to surface temperature. In section 3.5 we will demonstrate that the radiative contributions from varying RH are crucial for generating the super greenhouse effect.

Sensitivity of G and G to Surface Temperature
In this section, we apply two methods to determine the sensitivity of G and G to surface temperature (T s ) and also breakdown G' s sensitivity to T s into its components. Raval and Ramanathan (1989) calculated the sensitivity of all sky G to surface temperature by obtaining the slope from a linear least squares regression between G (4-month mean from 1985-1986) and SST over all spatial points. We replicate this method and regress clear sky G and T s across all latitudes and longitudes (land and ocean) to obtain dG(t,x, )  for this data set. We apply this method to multiple data sets in Table 6, which yields similar values in the range of 2.4-2.5 W m −2 K −1 . The surface temperatures used for regression in ERA-I, ERA+RRTM, AM4, and AM4+RRTM are directly from skin temperatures in the ERA-I and AM4 data sets, respectively. We find that G is a nonlinear function of T s and hence using a linear fit does not capture the extremes of the curve (Figure 5a). The method by Raval and Ramanathan (1989) correlates unrelated spatial regions, which masks important differences in underlying physics. For example, parts of the West Pacific warm pool and the Sahara Desert have similar surface temperatures (≈ 300 K), but they have wildly different values for G due to different humidity conditions (≈ 210 W m −2 over West Pacific and ≈ 150 W m −2 over Sahara Desert). Thus, the slope obtained from regressing across such different regions together misrepresents the sensitivity of G to T s for Earth.
To be consistent with how radiative sensitivities to surface temperature are calculated (Andrews et al., 2012;Otto et al., 2013), we regress the time series of the globally averaged ΔG(t, x, ) against ΔT s (t, x, ) to obtain dΔG(t,x, ) dΔT s (t,x, ) (Figure 5b). This method weights different spatial points appropriately and yields a representative "global column." This method yields an observed sensitivity of 3.96 W m −2 K −1 when using CERES EBAF 4.1 "t" data. This sensitivity is 0.42 W m −2 K −1 higher than the sensitivity of CERES EBAF 4.1 "c," demonstrating that the method used to obtain clear sky fluxes, either from ignoring clouds in the atmospheric column or sampling cloud free regions, impacts the sensitivity of global mean G to global mean surface temperature. The standard error associated with these gradients increases as the number of data points decreases (O(10 4 ) for dG(t,x, ) dT s (t,x, ) and O(10 2 ) for dΔG(t,x, ) dΔT s (t,x, ) ). When variations in greenhouse gases are included, the ERA+RRTM sensitivity (Table 6) increases from 3.13 to 3.47 W m −2 K −1 . Similarly, the AM4+RRTM sensitivity increases from 3.10 to 3.33 W m −2 K −1 and the sensitivity from AM4's output increases from 3.17 to 3.40 W m −2 K −1 . The sensitivities with greenhouse gas variations included (3.33-3.47 W m −2 K −1 ), are closer to CERES EBAF's estimates, implying that the greenhouse gas forcing from 2000 to 2016 is important in explaining the observed sensitivity of the global clear sky greenhouse effect to surface temperature. As mentioned earlier, CERES EBAF 4.1 version "t" is consistent with how general circulation models compute clear sky fluxes, so it is intriguing that the estimate of sensitivity from version "t" is further from models and reanalysis estimates as compared to the estimate from version "c". ERA-I's output produces an abnormally low sensitivity of 1.1 W m −2 K −1 . This discrepancy arises due to abruptly occurring large anomalies in ERA-I's time series of G ( Figure S6). This results in a larger spread and thus a lower sensitivity.
An application of the linear sensitivities obtained in Table 6 is that we can estimate G using the sensitivity and surface temperature change. The monthly values of G calculated using the linear sensitivity and surface temperature change captures the variability of G obtained by full radiative transfer calculations (r 2 = 0.8). For example, for an increase of 0.5 K in surface temperature during El Niño 2015-2016, we expect the anomalous total greenhouse trapping to rise by 3.13 W m −2 K −1 × 0.5 K = 1.57 W m −2 . This increase is precisely recorded in early 2016 for G (Figure 1b).
Next, we decompose dΔG(t,x, ) dΔT s (t,x, ) into its contributions from water vapor, atmospheric temperature, and surface temperature with ERA+RRTM. To obtain these sensitivities, we regress G's monthly means for each The standard errors for each term in equation (7b) (7b)).
The method used to obtain dΔG(t,x, ) dΔT s (t,x, ) (Figure 5b) can also be used to obtain the sensitivity of global mean OLR to surface temperature changes, dΔOLR(t,x, ) dΔT s (t,x, ) ( Table 6). A positive sensitivity for OLR implies that the system loses energy with warming according to the sign notation used in our paper, where upward radiation denotes positive values. The CERES EBAF sensitivities include the radiative forcing due to changes in greenhouse gases and the response of the Earth system to these changes from 2000 to 2016. We estimate the radiative forcing by differencing dΔOLR(t,x, ) dΔT s (t,x, ) from ERA+RRTM and ERA+RRTM_gg. This suggests that the trend in greenhouse gas forcing from 2000 to 2016 can yield a 0.34 W m −2 K −1 radiative forcing sensitivity. Applying this correction to the two values from CERES EBAF 4.1 versions "c" and "t" gives an estimate of the clear sky longwave (LW) feedback of 1.84 and 1.49 W m −2 K −1 , respectively. The dΔOLR(t,x, ) dΔT s (t,x, ) sensitivities of AM4, ERA+RRTM, and AM4+RRTM are estimates of the clear sky LW feedback since forcing is fixed (Table 6). Thus, the range of estimates of the clear sky LW feedback parameter we obtain is 1.49-2.02 W m −2 K −1 . Much of this spread arises from CERES EBAF's cloud clearing mechanism in Edition 4.1 version "t," suggesting that it is difficult to constrain the clear sky LW feedback. The observed value from CERES EBAF Ed 4.1 "t" is much more sensitive than the reanalysis and model estimates. The clear sky LW feedback inferred from Dessler (2013), which used observations over 2000-2013, is 1.91 W m −2 K −1 . This estimate lies at the "less" (more OLR escaping with our sign convention) sensitive end of our range.
The ERA+RRTM sensitivity is broken down into contributions from water vapor (  Koll and Cronin (2018) used an idealized atmospheric column and showed that there was a near-perfect cancelation between the contributions from water vapor and atmospheric temperature to the feedback parameter, and only surface temperature contributes. However, in our ERA+RRTM calculations with real atmospheric conditions for columns across Earth, we show that this cancelation is imperfect with a 37% ( 2.70−1.95 2.02 ) contribution from atmospheric temperature to the total feedback parameter. This implies that while changes in surface temperature are still the dominant contributor to changes in OLR ( 1.27 2.02 = 63%) as posited by Koll and Cronin (2018), atmospheric temperature plays an important role by outweighing water vapor's contributions. In the next section, we will see that locally, water vapor's radiative contributions overwhelm atmospheric temperature's contributions, which in turn helps generate the super greenhouse effect.

Super Greenhouse Effect
As mentioned in section 1, the clear sky SGE is defined as an event in which the rate of increase of G with surface temperature (T s ) exceeds the surface emission's rate or, equivalently, when OLR and T s are anticorrelated (Hallberg & Inamdar, 1993;Stephens et al., 2016;Valero et al., 1997).
Here, we apply a definition of anomalous SGE, that does not depend on SST thresholds or gradients of SST, to investigate how often it occurs, how much of Earth's area experiences it, and how much the areas that exhibit SGE contribute to G. We do not define SGE as a rate, but instead define SGE in terms of anomalies, that is, when OLR and T s are of opposite signs to each other for a particular month and location.
Thus, when SGE occurs with T s > 0 and OLR < 0, excess infrared radiation is trapped in the column and the atmosphere loses its ability to cool efficiently. On the other hand, when SGE occurs with T s < 0 and OLR > 0, the atmosphere cools more efficiently.
We investigate the percentage of Earth's area that is observed to experience SGE from March 2000 to August 2016 using observations from CERES EBAF 4.1 "t" data. For each month we calculate how many grid points satisfy equation (7b) and obtain the percentage of Earth's area that exhibits SGE. Next, we calculate the average percentage of area over the time series, tabulated under A SGE in Table 7. We find that on average for any month during this time period, 36% of Earth's area experiences SGE. We also calculate the percentage of area exhibiting SGE, while restricting our domains to Tropics, West Pacific, and Central Pacific (Table 7). We find that nearly half (46%) of the tropics is in a SGE state.
Since much of Earth's area is experiencing SGE, we plot the frequency of occurrence of SGE at each grid point in Figure 6 to understand the spatial distribution of SGE. Results reveal that there is a high occurrence (up to 80% of the time period) of SGE in the tropics ( Figure 6). We observe that there is a clear land-sea contrast, which is consistent with less water vapor over land. The lower occurrence off the coast of South America is likely because of colder SSTs in upwelling regions and less convection, in comparison to the Indo-Pacific region and the Central Pacific. Since our definition of SGE (equation (7b)) uses deseasonalized anomalies, an ENSO pattern is observed in the Central Pacific. When we use nondeseasonalized anomalies in equation (7b), we observe the spatial pattern of the seasonal cycle of SGE (not shown). High frequency of occurrence is observed over the Northern and Southern Hemisphere ITCZ bands, the Bay of Bengal, and the Amazon rainforest. These areas coincide with seasonal high humidity conditions.  To understand the importance of SGE, we quantify how much SGE contributes to the total magnitude of G, that is, | G|. For each month, we calculate | G| arising from areas that exhibit SGE (Table 7). By design, taking the temporal mean of G would yield zero, so we take the mean of | G| to obtain a value that represents the full time series' variability. We find that for the entire time period, the globally averaged | G SGE | is 0.38 W m −2 and | G| is 0.54 W m −2 . This implies that just over a third of Earth's area (36%) contributes to over two-thirds ( 0.38 0.54 ≈ 70% ) of the global | G|. Thus, these SGE regions are nearly twice as powerful the non-SGE regions in contributing to greenhouse trapping. Over small regions such as the Central Pacific, 56% of the region exhibits SGE and contributes to 88% of | G|, that is, half the area is contributing to nearly all of the average | G|.
To explain why SGE occurs, we take a twofold approach in demonstrating the importance of water vapor in generating the SGE: (1) by showing how variations in RH impact A SGE and (2) how water vapor at various altitudes differentially impact the total radiative contributions. We use the ERA+RRTM methods from section 3.3 to obtain the dependence of SGE on RH changes. We calculate the total anomalous OLR with fixed RH, that is, ΔOLR FRH = OLR(H 2 O * , T a , T s ) − OLR(H 2 O, T a , T s ). This equation is identical to equation (4a) but uses water vapor with fixed RH (H 2 O * ) from equation (6b). Next, the area exhibiting SGE is calculated with OLR FRH instead of OLR in equation (7b). Table 8 shows that the area exhibiting SGE across Earth drastically reduces to 15% when using fixed RH compared to when varying RH is included (34%). Note that the value 34%, calculated using ERA+RRTM, agrees with the CERES EBAF's value of 36% (Table 7). In convective regions with large variations in RH, such as the Central Pacific, the areas exhibiting SGE with varying RH are 4 times as large as the areas with fixed RH alone.
Using equation (7b), we observe that the conditions for SGE are satisfied if G > E and T s > 0 or G < E and T s < 0. Thus, the surface emission, E, serves as a threshold for the phenomenon. In Figure 7a we plot the time series of G and E over the Central Pacific using ERA-Interim data as input for RRTM. Throughout much of the time series, SGE conditions are satisfied with G being outside the E curve. This is particularly true during ENSO events (El Niño 2003, La Niña 2008, El Niño 2010, La Niña 2011, El Niño 2015, where G significantly exceeds E ( G ≈ 2 E in 2016). We decompose G into its constituents: ΔG H 2 O , ΔG T a , and ΔG T s . ΔG T s (solid purple) is always under the threshold line (dashed purple) because it is physically impossible for variations in surface temperature alone to push a region into an SGE state. The extra push to cross E, overwhelmingly comes from the water vapor's contribution (orange), which faces only a small cancelation by ΔG T a .
Next, we break water vapor's radiative contributions into its altitude specific components over the Central Pacific (Figure 7e) as we did for the entire globe (Figure 2b). The middle tropospheric (green) water vapor traps the most radiation throughout the time series. We see that at the onset of an El Niño (e.g., 2009-2010 and 2015-2016) or a La Niña (e.g., 2007Niña (e.g., -2008Niña (e.g., and 2010Niña (e.g., -2011, the middle troposphere traps much more radiation than other parts of the atmosphere for several months until the event reaches its peak, after which the upper troposphere efficiently contributes to ΔG H 2 O due to deep convection. We explore why MT contributes the most to ΔG H 2 O (Figures 7b-7d). The amount of infrared trapping by water vapor can be broken down into two components: the sensitivity, that is, Jacobian of ΔG H 2 O to the water vapor mass anomaly ( G H 2 O in units of W kg −1 ) and the water vapor mass anomaly itself (ΔH 2 O in units of kg m −2 ), First, we calculate the sensitivity in Figure 7b where we plot ΔG H 2 O due to the lower, middle, and upper troposphere against its respective water vapor anomalies. The slope from the linear regression gives us the sensitivity of ΔG H 2 O to H 2 O. The upper troposphere (dark blue) has the largest sensitivity per a unit mass change in water vapor. It is followed by the middle troposphere (green) and then the lower troposphere (brown). Second, in Figure 7c we plot H 2 O's time series using ERA-I's input data. Although LT bears the majority of the column's mass, the anomalies in MT water vapor are of the same order of magnitude as the LT water vapor anomalies, if not slightly greater during some ENSO events. The UT anomalies in water vapor are an entire order of magnitude lower than that of LT and MT, as expected. Thus, when we multiply the sensitivity and the water vapor anomaly (Figure 7d) we obtain the water vapor greenhouse trapping due to the three parts of the troposphere. This shows that MT contributes the most to ΔG H 2 O because it sits in the "sweet spot" of intermediate sensitivity and H 2 O is the largest. Figure 7e shows that the above breakdown is identical to the ERA+RRTM anomalies. The moistening of the midtroposphere has contributed the most to the excess trapping of infrared radiation, rendering a super greenhouse effect.

Discussion
Our paper quantifies the origins of G's anomalies from March 2000 to August 2016, a longer time series than previous studies had used. We show that water vapor is a significant contributor to G, locally and globally. Our paper and other studies Hallberg & Inamdar, 1993;Huang & Ramaswamy, 2008;Inamdar & Ramanathan, 1994;1998) agree that water vapor in both the middle troposphere and upper troposphere is important in explaining the anomalous G in the deep tropics (Table 4). Our paper expands on this past work by demonstrating that water vapor in the middle and upper troposphere contribute nearly equally to G even in the global mean and tropical mean (Figure 2b and Table 4). We further show that in smaller regions such as the West Pacific and Central Pacific, the midtroposphere's contributions exceed those of the upper troposphere's contributions.
Our study, however, arrives at different conclusions than the conclusions in Huang et al. (2007) and Stephens et al. (2016). In the tropics, during El Niño events, the middle troposphere and upper troposphere contribute equally to G (Table 4). Focusing just on the 2015-2016 El Niño instead of looking at a composite of El Niño events, we find that the middle troposphere contributes more than the upper troposphere to G for the tropics. This is in contrast to Huang et al. 2007 finding that water vapor in the upper troposphere contributes more than water vapor in the middle troposphere to OLR, in the tropics during the 1998 El Niño. We find that in regions with high surface temperatures such as the West and Central Pacific, contributions from midtropospheric water vapor exceeds contributions from the rest of the column (Figure 7 and Table 4). This is in disagreement with Stephens et al., 2016Stephens et al., 's 2016 result that in regions of high surface temperature, upper tropospheric water vapor contributes more to OLR than the rest of the column's water vapor.
The different conclusions between our work and Huang et al. (2007) and Stephens et al. (2016) may be attributable to the following: (1) different definitions of the upper troposphere, (2) varying perturbation methods, (3) dissimilar El Niño events, and (4) the length of the time period considered. First, we define the upper troposphere as 400-150 hPa, whereas Huang et al. (2007) considers a deeper upper troposphere ranging from 400-100 hPa. Stephens et al. (2016) does not define the upper troposphere. A larger upper troposphere contains more water vapor and could contribute more to G. Second, our PRP method computes monthly anomalies using a climatology from a long time series whereas both studies assumed a fixed perturbation of +10% moistening at each layer. Fixed perturbations may not be representative of observed anomalies, that is, deviations from a climatology. Third, we analyze different El Niño events. It may be that the 1998 El Niño moistened the upper troposphere more than the 2015-2016 El Niño and this yielded a larger contribution to G. Fourth, our study considers the time period March 2000 to August 2016 whereas Huang et al. (2007) considered the 1989 La Niña and the 1998 El Niño in isolation. Stephens et al. (2016) used a climatology of the 2012 Atmospheric Infrared Sounder (AIRS) profiles. A longer time series contains more variance and results derived from it are less susceptible to noise as compared to short time periods of a single year.
Our paper shows that even in regions of low surface temperature, variations in RH can make a region exhibit the super greenhouse effect ( Figure 6). We estimate that 46% of the tropics exhibit the SGE. Intriguingly, this is in agreement with an earlier study (Valero et al., 1997) that calculated the clear sky SGE only for regions above surface temperatures of 298 K, used ERBE's shorter data set from 1985 to 1989, and used the rate of change of G (equation (7b)) instead of anomalies (equation (7b)). They found the area that experienced SGE to be 52%.
It is interesting to consider the impact of clouds on the SGE. First, we consider the longwave radiative impact of clouds. This can be calculated using all-sky OLR from CERES EBAF 4.1 "t" in equation (7b). The area that exhibits SGE increases by 8% to 44%, globally. Regions that did not exhibit SGE under clear sky conditions, do exhibit SGE when clouds are included due to their longwave trapping effect. This has also been observed by Stephens et al. (2016) and Dewey and Goldblatt (2018). Second, we consider the shortwave radiative impact of clouds in addition to the longwave radiative impact. This redefines SGE in terms of the total radiation escaping to space. This is calculated using the sum of all-sky OLR and all-sky reflected shortwave radiation in equation (7b). We find that the area exhibiting SGE further increases by 8% to 52%, globally. This implies that even though clouds have a net cooling effect in the global mean, anomalies in the cloud radiative effect enhance the SGE.