## 1. Introduction

^{−2}, OLR = 235 W m

^{−2}, and ISR = 342 W m

^{−2}were closely balanced to NET = 0 (Kiehl and Trenberth 1997). However the global balance is not static: 1) the ISR varies seasonally due to the eccentricity of Earth’s orbit, 2) the RSW changes due to changes in cloud cover and surface albedo; and 3) the OLR is influenced by the presence of clouds. The increase in the greenhouse gases creates long-term changes in the OLR and possibly in the RSW. The question of how the earth climate system responds to these long-term changes initiated an extensive research effort that included numerical modeling and analyses of observational data [see Bony et al. (2006) for a comprehensive review]. Here, we focus on the observational part of the problem and evaluate a global-mean NET sensitivity usingin units of watts per meter per kelvin, where

*T*is the surface temperature. If the earth were a 255-K blackbody, that is, the influence of its atmosphere and any shortwave reflected component were ignored, its NET sensitivity would be the derivative of the Planck function,

_{s}*λ*

_{Planck}= −3.6 W m

^{−2}K

^{−1}. A negative NET sensitivity, that is, when the NET decreases as the surface temperature increases, implies a stable system. The OLR and the RSW are influenced by the presence of clouds. The paper by Schneider (1972) was among the earliest publications pointing out the effect of clouds on the NET. Clouds and their effects were discussed in terms of the “thermostat hypothesis” (Ramanathan and Collins 1991), “self-regulation” (Waliser and Graham 1993), the “iris hypothesis” (Lindzen et al. 2001; Hartmann and Michelsen 2002; Lindzen and Choi 2009; Dessler 2010; Murphy 2010; Dessler 2011, and references therein). However, clouds are still identified as a key uncertainty in climate models (Solomon et al. 2007).

Here, we define the cloud effect as the sensitivity of the NET radiation with clouds minus the NET sensitivity if the clouds are removed without otherwise changing the state of the atmosphere or the surface, that is, we replace (RSW + OLR) with [(RSW − ClearRSW) + (OLR − ClearOLR)]. This approach is known as the “cloud forcing” analysis, which was introduced by Cess et al. (1990), who defined the cloud forcing as the difference between the all-sky and clear-sky radiation at TOA. The advantage of this approach is that the cloud forcing is directly observable and hence it may be used for validating climate models. The weakness of this approach is that the changes in the cloud forcing cannot be directly interpreted as being caused solely by the clouds or caused by changes in the other variables (temperature, lapse rate, water vapor, and albedo) that occur under the transformation from clear to cloudy conditions (Bony et al. 2006). To infer the feedbacks produced by each variable, one needs to calculate the radiative kernels (partial derivative of the radiation relative to a specific variable) and the change of each variable relative to the surface temperature (Soden et al. 2008). However, the assumptions of linearity and separability of the different feedbacks used in these calculations have been the subject of debate (Aires and Rossow 2003), and the results are sensitive to compensating errors. The changes in different variables are calculated in model runs with some prescribed forcing, usually due to the doubling of CO_{2}. The effect of clouds in the model runs can in principle be inferred from evaluating the NET by calculating the OLR and RSW without clouds, or by backing the effect of the clouds out of the NET sensitivity by subtracting the sum of the model sensitivities calculated with kernels, as done by Soden and Held (2006) and Dessler (2010).

Up to now the observational evaluation NET sensitivity has been limited to the analysis of the seasonal and interannual variability of the OLR and RSW from Earth Radiation Budget Experiment (ERBE) and Clouds and the Earth’s Radiant Energy System (CERES) data. Tsushima and Manabe (2001) and Tsushima et al. (2005) used the seasonal variability of *T _{s}*. Murphy et al. (2009) analyzed the interannual variability of the NET and found a sensitivity of −1.25 ± 0.5 W m

^{−2}K

^{−1}based on the analysis of ERBE and CERES data between 1985 and 2004. Chung et al. (2010a, hereafter CSS2010) used ERBE data from 1985 through 1999, and Dessler (2010) deduced a cloud effect based on the interannual variability of 2000–10 CERES data. Here, we use data from the Atmospheric Infrared Sounder (AIRS; Aumann et al. 2003) to determine RSW and OLR, and their clear counterparts to evaluate the NET sensitivity defined by Eq. (1).

## 2. Data

AIRS is a hyperspectral infrared sounder aboard the Earth Observing System (EOS) *Aqua* spacecraft, which was launched into a polar sun-synchronous orbit at 705-km altitude in May 2002. The ascending node of the orbit has been maintained within a minute of 1330 UTC. AIRS generates 4 million spectra each day by scanning ±49° cross track with 1.1° (13.5 km at nadir) diameter field of view (FOV). Of these data about 10%, 300 000 spectra each day, are within 3° of nadir. About 2% of the near-nadir spectra, typically 6500, are selected randomly each day. To make the sample “area representative,” the random nadir data from the high-latitude areas are thinned to eliminate the high-latitude spatial overcoverage from the EOS *Aqua* polar orbit. Typically 50 000 spectra are identified each day as “clear,” based on a number of spatial and spectral tests (Aumann et al. 2006). The daily collection of random nadir spectra, clear spectra, data from deep convective clouds (DCC), and data from a number of special sites used for monitoring the calibration are saved in the AIRS Calibration Data Subset (ACDS). The AIRS data are exceptionally well calibrated and extremely stable (Aumann et al. 2006). Half of the daily samples come from the 0130 LT overpasses, referred to as “night,” and the other half of samples comes from the 1330 overpasses, referred to as “day.” Each spectrum saved in the ACDS is associated with the surface temperature, a land fraction, an infrared clear flag, and reflected light measurements. The surface temperature is obtained from the National Oceanic and Atmospheric Administration (NOAA) Global Forecast System (Iredell and Caplan 1997). The surface temperatures from the 3-, 6-, and 9-h forecast, made daily at 0000, 6000, 1200, 1800 UTC, respectively, on a ½° grid, are interpolated in space and time to match the AIRS sample times and positions. AIRS also measures the reflected shortwave radiation in three channels in the 8 × 9 pixel array associated with each IR FOV (Gautier et al. 2003): channel 1 (0.40–0.44 *μ*m), channel 2 (0.58–0.68 *μ*m), and channel 3 (0.75–0.95 *μ*m). The mean of the 8 × 9 pixel array associated with each IR FOV is saved in the ACDS. Since our data are selected from within 3° of nadir, we can ignore slant path effects and glint contamination. Significant surface glinting in the reflected light channels is first apparent at more than 10° off nadir. The random nadir data are used to calculate the “all sky” RSW, OLR, and their “clear sky” counterparts associated with each FOV.

### a. RSW and ClearRSW

Unlike CERES (Wielicki et al. 1996), which measures the RSW in a broadband 0.1–5-*μ*m channel, AIRS measures the shortwave reflected flux density in the three much narrower channels between 0.4 and 1.1 *μ*m described above. These measurements have to be converted to a spectrally integrated RSW. For this purpose we regressed the AIRS data against the CERES *Aqua* RSW global 1° × 1°^{2} gridded product from September 2002. Referring to the individual measurements of AIRS reflected light channel 2 as vis2, we have to first order RSW = *A*vis2, where *A* = 1.04 ± 0.02 *μ*m is an effective bandwidth. CERES measures the reflected shortwave radiation under clear conditions using a cloud mask. The AIRS ClearRSW can be inferred from the vis2 associated with footprints identified each day as cloud free. The conversion from vis2 to ClearRSW uses *A* = 1.04 ± 0.04 *μ*m. Details on the regression training are given in Appendix A.

### b. OLR and ClearOLR

The OLR and ClearOLR are available from the AIRS level 2 (L2) standard products (Susskind et al. 2003), where a high-quality temperature and water vapor profile, surface emissivity, and surface temperature retrieval are available. The OLR and the ClearOLR for each footprint are derived here directly from AIRS L1b spectral radiances using regression trained on L2 version 6 (V6) OLR and ClearOLR. This provides an OLR and the ClearOLR even under extremely cloudy conditions. Details on the regression training are given in Appendix B. The uncertainty in the derivation of ClearOLR and the OLR are accounted for in the error analysis.

## 3. Data analysis procedure

*T*

_{s}(

*i*), RSW(

*i*), OLR(

*i*), ClearRSW(

*i*), and ClearOLR(

*i*) from these 6500 daily samples, where the

*i*index associated with time

*t*(

*i*) runs from 1 to 3240. The global-mean ISR(

*i*) at the TOA is calculated for each day based on the known Sun–Earth distance. We then evaluate the seasonal variation for NET(

*i*) = ISR(

*i*) − RSW(

*i*) − OLR(

*i*), the ClearNET(

*i*) = ISR(

*i*) – ClearRSW(

*i*) − ClearOLR(

*i*), and the cloud effect CE(

*i*) = NET(

*i*) − ClearNET(

*i*), as well as

*T*(

_{s}*i*) by least squares (LSQ) fitting the data to a harmonic time series usingwhere

*t*(

*i*) is the sample date. Then AT

_{s}=

*T*(

_{s}*i*) −

*Y*(

_{s}*i*), ANET(

*i*) = NET(

*i*) −

*Y*

_{net}(

*i*), and AClearNET(

*i*) = ClearNET(

*i*) −

*Y*

_{clrnet}(

*i*) define the anomaly time series. The lowest frequency fitted in Eq. (2) is the annual (seasonal,

*k*= 1) mode. This assumes that the seasonal variation seen in 9 yr can be considered as the “normal” seasonal variation, that is, the anomaly represents longer-term (lower frequency) interannual effects.

## 4. Results

Figure 1 shows the daily global-mean *T _{s}*(

*i*) (solid) and NET(

*i*) (dashed), smoothed for the graphic presentation only with a 2-month sliding mean, from the 9 yr of data. It is interesting to note the dominance of the Northern Hemisphere: The seasonal variation of

*T*peaks in July, while the peak of the NET is in December. The seasonal variation seen in these data is removed in the anomalies. An overlay of the anomalies of the NET and

_{s}*T*derived from the data presented in Fig. 1 is shown in Fig. 2, also smoothed with a 2-month sliding mean. Note that the smoothing filter was applied only for plotting of the time series. All data processing uses the unfiltered daily data.

_{s}The effective NET sensitivity is derived from the analysis of the scatter diagram of the daily anomalies, AT_{s} (*i*) and ANET(*i*), as shown in Fig. 3. The correlation between the daily values of the ANET and AT_{s} is −0.19. The slope of the linear regression line, −1.43 W m^{−2} K^{−1} with a one-sigma uncertainty of 0.13 W m^{−2} K^{−1}, is determined using the linear regression. Using the same method the ClearNET sensitivity, shown in Fig. 4, is −2.0 ± 0.1 (1*σ*) W m^{−2} K^{−1}. We calculate the cloud forcing sensitivity from the scatter diagram of the (NET- ClearNET) anomaly and the surface temperature anomaly. The slope of the linear regression line yields a cloud forcing sensitivity of +0.5 ± 0.15 (1*σ*) W m^{−2} K^{−1}.

## 5. Discussion

The sensitivities and their one-sigma uncertainties quoted above are estimated from linear regression assuming Gaussian noise. There are other factors that need to be considered in assessing the total uncertainty.

- The uncertainty of the linear regression line of the scatter diagram refers to the standard deviation of the least squares linear fit. To better evaluate the uncertainty of the fit, we apply the bootstrap method (Chernick 1999). In this method the scatterplot is recreated using the original AT
_{s}(*i*) vector, but new ANET(*i*) vectors are created by randomly permuting the entries in the original ANET(*i*) array. This procedure destroys the correlation with the AT_{s}(*i*) vector. As a result, the slope of the scatter diagram varies randomly with zero mean and the standard deviation of the slope values gives an estimate of the slope uncertainty. Using 100 random permutation runs yield a bootstrap slope uncertainty of 0.2 W m^{−2}K^{−1}(1*σ*). For the (NET − ClearNET) and cloud sensitivity, the slope uncertainty is 0.15 W m^{−2}K^{−1}(1*σ*). We accepted the larger uncertainty estimates generated by the bootstrap method. - The numerical technique used to create the anomaly time series contributes to the uncertainty of the result. To evaluate this effect, we used empirical mode decomposition (EMD; Huang et al. 1998; Huang and Wu 2008). In this approach the anomaly is defined as the data time series minus the annual EMD mode. We treat the difference between the sensitivity calculated using anomaly calculated from Eq. (2) and the sensitivity calculated using the EMD-derived anomaly, 0.05 W m
^{−2}K^{−1}, as a component of the overall uncertainty. - The length of the time series used to define the “normal” seasonal variability introduces an uncertainty in the anomaly. We evaluated the magnitude of this effect by recalculating the anomaly sensitivity using the first 8 and the last 8 of the 9 yr of data. Withholding the last year or the first year changes the NET sensitivity by ±0.04 W m
^{−2}K^{−1}. - The uncertainty in the derivations of the RSW and OLR and their clear counterparts contribute to the NET sensitivity uncertainty. Since the anomaly removes the bias, bias has no effect on the NET sensitivity. These uncertainties were modeled as multiplicative errors and as the difference between the results using multivariate regression and a simple single parameter fit as discussed in the appendices. Propagated through the anomaly and sensitivity calculations, the RSW and OLR derivation uncertainties contribute less than 0.05 W m
^{−2}K^{−1}to the NET and ClearNET sensitivity slope uncertainty. The RSW and ClearRSW vary seasonally about global means of 100 and 40 W m^{−2}, respectively. As a somewhat extreme test of RSW and ClearRSW uncertainty, we assume that both are constant, that is, their anomalies are zero. Then the NET and ClearNET anomaly sensitivities, now calculated from the OLR and the ClearOLR anomalies alone, change by +0.1 W m^{−2}K^{−1}. - An uncertainty in
*T*may contribute to the_{s}*T*anomaly. The National Centers for Environmental Prediction (NCEP)_{s}*T*agrees globally with the AIRS L2 V6 surface skin temperature with a cold bias of 0.4 K, with a standard deviation of 2.3 K, where a high-quality surface solution is obtained with the AIRS L2 (about 50% of all cases in L2 V6). Assuming that the standard deviation of the difference between AIRS L2 and NCEP_{s}*T*can be used as a conservative metric of the uncertainty of the NCEP_{s}*T*, the_{s}*T*uncertainty contributes less than 0.01 W m_{s}^{−2}K^{−1}to the sensitivity uncertainty.

*λ*

_{eff}= −1.5 ± 0.25 (1

*σ*) W m

^{−2}K

^{−1}as the NET sensitivity,

*λ*

_{eff_clear}= −2.0 ± 0.2 (1

*σ*) for the ClearNET sensitivity, and +0.5 ± 0.2 (1

*σ*) for the cloud sensitivity.

A simple theoretical evaluation of Eq. (1) can be made using an OLR that assumes that the earth radiates as a blackbody, that is, ignore the influence of its atmosphere and any shortwave reflected component. Then NET = ISR − OLR. The global-mean OLR of 238 W m^{−2} (appendix B) corresponds to a blackbody at 255 K, and the derivative of the Planck function gives *λ*_{planck} = −3.6 W m^{−2} K^{−1}. A more careful evaluation in 12 Fourth Assessment Report (AR4) models (Soden and Held 2006, their Table 1) produced an average value of *λ*_{planck} = −3.2 W m^{−2} K^{−1}. Chung et al. (2010b, hereafter CYS2010), derived a global average value of +2.0 W m^{−2} K^{−1} from the response to a uniform warming and constant relative humidity (RH), but since they refer to the Planck radiative damping +3.6 W m^{−2} K^{−1}, we infer that *λ*_{constant-RH} = −2.0 W m^{−2} K^{−1}.

Work on the observational evaluation of Eq. (1) has heretofore been based on ERBE and CERES data. The negative value of Eq. (1), +Δ(OLR + RSW)/ΔSST, is used in some papers. Thus, CSS2010 analyzed the NET sensitivity of the tropical oceans using ERBE data from 1985 through 1997 and found *λ*_{CSS} between −2.5 and −3 W m^{−2} K^{−1} [note that their Fig. 1d shows −Δ(OLR + RSW)/ΔSST]. However, it is difficult to compare tropical ocean values to global values. Our observed global NET sensitivity *λ*_{eff} = −1.5 ± 0.25 (1*σ*) W m^{−2} K^{−1} agrees with the sensitivity of −1.25 ± 0.5 W m^{−2} K^{−1} deduced by Murphy et al. (2009) from a totally independent dataset, ERBE and CERES data between 1985 and 2004, but it is closer to the value expected for uniform global warming with constant RH, −2 W m^{−2} K^{−1} (CYS2010). The analysis of regional, seasonal, and interannual variability of 1985–88 ERBE data (CYS2010, their Fig. 2) yielded ClearOLR sensitivities between +2.2 and +2.4 W m^{−2} K^{−1}. In terms of ClearNET sensitivity, this corresponds to −2.2 to −2.4 W m^{−2} K^{−1}, consistent with our observed global ClearNET sensitivity, *λ*_{eff_clear} = −2.0 ± 0.20 (1*σ*). Our *λ*_{eff_cloud} = +0.5 ± 0.2 (1*σ*) W m^{−2} K^{−1} agrees within the error bars with +0.54 ± 0.36 (1*σ*) W m^{−2} K^{−1} deduced by Dessler (2010), who used the anomaly correlation with a totally independent dataset, 120 monthly means from 2000 to 2010 CERES *Terra* data, and a different numerical method. Our observations indicate that the cloud component of the NET sensitivity is positive with more than 2-*σ* probability.

Our sensitivities were derived from only 9 yr of data, that is, the CO_{2} forcing and changes in the water vapor were small. To make a comparison of our results with GCM results, we have to distinguish between unforced (control) runs and runs forced by doubling the CO_{2} abundance followed by model equilibrium. Our observed sensitivities should by comparable to control runs. However, the sensitivities derived from long-term forced GCM results and unforced model runs are similar. This is supported by CSS2010, their Fig. 3c, which shows the OLR+RSW sensitivities of a collection of forced runs and preindustrial control runs. The median forced run sensitivity is about +1.4 W m^{−2} K^{−1}, while the median control sensitivity is about +1.0 W m^{−2} K^{−1}, but the scatter in the two datasets overlaps. The similarity in the results of forced and unforced runs is also seen in the cloud feedback. Thus, Dessler (2010), who analyzed the cloud sensitivity for 100 yr of control runs, has found a cloud feedback range between 0.34 and 1.11 W m^{−2} K^{−1}, which is similar to the cloud sensitivity range of the forced AR4 models (Soden and Held 2006) with an average +0.69 W m^{−2} K^{−1} and a range from 0.15 to 1.18 W m^{−2} K^{−1}. The AR4 results for the Planck, the lapse rate, the water vapor, and the surface albedo sensitivities (the sum of which gives the sensitivity without clouds) and the cloud effect were summarized in Table 1 in Soden and Held (2006). The effective sensitivities in the AR4 models with clouds, which were determined with an estimated uncertainty of 0.2 (1*σ*) W m^{−2} K^{−1}, range from −0.88 to −1.64 W m^{−2} K^{−1} compared to our *λ*_{eff} = −1.5 ± 0.25 (1*σ*) W m^{−2} K^{−1}. The clear NET sensitivity in the models ranges from −2.32 to −1.73 W m^{−2} K^{−1}, compared to our observed −2.0 ± 0.2 (1*σ*) W m^{−2} K^{−1}. The cloud sensitivity in the models ranges from +0.14 to +1.18 W m^{−2} K^{−1} compared to our +0.5 ± 0.2 (1*σ*) W m^{−2} K^{−1} cloud forcing sensitivity. Hence, the observed effective NET and clear NET sensitivities are statistically consistent with the model sensitivities, considering the observational and model derivation uncertainties. However, the global-mean NET-T_{s} relationship differs across different time scales and differs between transient and equilibrium conditions. Using the sensitivities derived here from the AIRS data as a metric for the quantitative evaluation of the AR4 models is therefore not unproblematic.

## 6. Summary and conclusions

The sensitivity of the reflected shortwave and outgoing longwave radiation under clear and cloudy conditions to a change in the global-mean surface temperature is evaluated from 9 yr of AIRS data using the anomaly correlation technique. The observed global-mean temperature sensitivity of the NET, including the effects of clouds, is −1.5 ± 0.25 (1*σ*) W m^{−2} K^{−1} compared to −2 W m^{−2} K^{−1} expected from the uniform warming with a constant RH. The cloud forcing effect, +0.5 ± 0.2 (1*σ*) W m^{−2} K^{−1}, is a positive component of the NET sensitivity, consistent with previous work using ERBE and CERES data. The similarity of the NET sensitivities derived for forced and unforced models makes the comparison between our observation and AR4 models illuminating. The effective NET and clear NET sensitivities derived from the AIRS data are statistically consistent with the model sensitivities. However, because the global-mean NET-*T _{s}* relationship differs across different time scales and differs between transient and equilibrium conditions, the use of the sensitivities derived here from the AIRS data as a metric for the quantitative evaluation of the AR4 models requires some caution.

## Acknowledgments

The research described in this paper was carried out at the Jet Propulsion Laboratory at the California Institute of Technology under a contract with the National Aeronautics and Space Administration. We are grateful for the long-term support of Dr. Ramesh Kakar, *Aqua* Program Scientist at NASA HQ. We acknowledge the discussions with Dr. Joao Teixeira at JPL and the helpful comments by two anonymous reviewers.

## APPENDIX A

### Derivation of the All-Sky and Clear-Sky RSW from AIRS Data

AIRS measures the reflected shortwave radiation in three channels using a 8 × 9 pixel array associated with each 13.5 IR FOV (Gautier et al. 2003): channel 1 (0.40–0.44 *μ*m), channel 2 (0.58–0.68 *μ*m), and channel 3 (0.75–0.95 *μ*m). The mean of the 72 pixels associated with each AIRS FOV is saved in the ACDS as vis1–vis3, respectively. The three channels exhibit small decreases in signal with time. For the vis2 and vis3 channels, this requires a linear correction of +0.40 ± 0.01% yr^{−1} related to differential scan mirror contamination. For presently unknown reasons, the vis1 channel requires a nonlinear correction. These corrections were worked using the observations of DCC (Aumann et al. 2007), with the assumption that DCC act as nearly perfect diffusers of sunlight.

We used the CERES_SSF1deg-Month-lite-Aqua_Ed2.5 SW_all to derive an approximation to the all sky RSW (CERES SW) using AIRS data. The CERES product is available as monthly averages on a global 360 × 180 grid. We converted AIRS vis2 measurements from September 2002, March 2003, and September 2009 into 3 monthly 360 × 180 gridded maps, each of which was then collapsed into (90) 1°-wide latitude bands. We used monthly-mean CERES data to create the equivalent 1°-wide latitude bands for the same month. Figure A1 is an overlay of the AIRS vis2 and CERES SW latitude dependence for the month of September 2002, which was used as the regression training set. Figure A1 shows that the AIRS vis2 and the CERES SW are highly correlated (*r* = 0.98). Note the left-to-right latitude asymmetry and the spike at 5°N latitude, which is apparently caused by the ITCZ. For the September 2002 training set, RSW = 1.045vis2 with zero bias relative to CERES by definition. The overlay of CERES and AIRS from the two independent 1-month datasets (March 2003 and September 2009) looks almost identical to Fig. A1, but it shows a bias of +2 and −2 W m^{−2} relative to the training set. The 9-yr global-mean RSW of 100 W m^{−2} is consistent with the global-mean RSW quoted for CERES in CERES (2011). We also evaluated the RSW based on multivariate regression with vis1–vis3 in support of the sensitivity uncertainty analysis. To avoid the uncertainty introduced by a nonlinear vis1 trend correction, we used RSW = (1.04 ± 0.02)vis2 for the analysis presented in this paper. The 9-yr global-mean RSW is 100 with a 14 W m^{−2} peak-to-peak seasonal variation. During the past 9 yr, the RSW has changed by less than 0.07% yr^{−1} (2-*σ* upper limit).

We also used the vis2 data to create the time series of clear-sky RSW. The ACDS data include a “clear” flag, which is based on a number of infrared tests. The combination of the clear flag, the land fraction, and *T _{s}* allowed us to generate three daily average clear-sky RSW time series, for nonfrozen ocean clear, nonfrozen land clear, and frozen clear. The boundary between frozen and nonfrozen is set at

*T*= 273 K. The three time series are combined by weighting the daily mean values from the three components by their area fractions, 0.64, 0.23 and 0.13, respectively. This approximates an area representative clear-sky RSW dataset. During the past 9 yr, the global-mean clear RSW has changed by less than 0.16% yr

_{s}^{−1}(2-

*σ*upper limit) in the mean of 40 W m

^{−2}.

The parameter used to divide clear frozen and nonfrozen surfaces introduces an uncertainty. If *T _{s}* = 271 K, more appropriate for the transition between sea ice and frozen ocean, then the global-area fractions would be 0.65, 0.23, and 0.12, respectively, and the mean clear RSW would decrease by 3%. This redefinition of the frozen surface changes the ClearNET sensitivity by less than 0.001 W m

^{−2}K

^{−1}. We use ClearRSW = (1.04 ± 0.04)vis2 for the analysis presented in this paper.

## APPENDIX B

### Derivation of the OLR and ClearOLR from AIRS Data

The OLR and the ClearOLR are standard L2 products (Susskind et al. 2003). The OLR, with and without clouds, is calculated from the retrieved *T*_{surf}, *ε*_{surf}, *T*(*p*), *q*(*p*), and cloud height and fraction. For the AIRS L2 V6, this calculation uses a radiative transfer algorithm provided by Iacono et al. (2008). This calculation is accurate only if the retrieval is of high quality. In the soon-to-be-released L2 V6, globally about 50% of retrievals produce a Clear OLR identified as high quality; 84% produce a high-quality OLR. Since we need the OLR and Clear OLR at every footprint, we derive them directly from AIRS L1b data (calibrated radiances), which are available for every footprint independent of the state of cloudiness. The derivation uses regression with global data from 15 days, randomly selected from 9 yr of AIRS data, which were specially processed as part of the L2 V6 OLR and ClearOLR validation. The regression coefficients were derived from 4 days; the uncertainty was derived from the remaining 11 (independent) days.

#### a. OLR

Figure B1 shows the scatter diagram of all near-nadir L2 V6 OLR points from the training days as function of bt790, where bt790 is the observed brightness temperature at 790 cm^{−1}. This channel is at the longwave end of the 11-*μ*m atmospheric window area, but it has considerable water vapor absorption. The quadratic regression line (shown superimposed in Fig. B1) has a correlation of 0.99 with the AIRS L2 OLR and fits with 7 W m^{−2} standard deviation, corresponding to 3% of the mean. Since a single parameter, bt790, may not capture the full variability of the OLR, we used bt790, bt723 (a midtroposphere CO_{2} sensitive channel at 723 cm^{−1}), and bt1419 (an upper-tropospheric water-sensitive channel at 1419 cm^{−1}) to fit the OLR. This improves the standard deviation of the regression fit to 5.0 W m^{−2}. The fit of the independent set has 5.1 W m^{−2} standard deviation, and the rms bias for the 11 independent days is 0.15 W m^{−2}. The 9-yr trend in the daily global-mean OLR calculated in this fashion is less than 0.03 W m^{−2} yr^{−1} (2*σ*) in the mean of 241 W m^{−2}. The mean agrees within the nominal uncertainty, with the global mean of 238 W m^{−2} quoted for CERES in CERES (2011). We carried the effect of the OLR uncertainty through the NET sensitivity calculations in two ways: 1) as a multiplicative 1% and 2) by comparing the results using the multivariate regression with a quadratic least squares fit using only bt790.

#### b. Clear OLR

Figure B2 shows the scatter diagram of the all AIRS L2 V6 ClearOLR points in the training set as function of *T _{s}* from NCEP. The dependence of ClearOLR on

*T*is almost linear, with a correlation of 0.95. The multivariate regression using

_{s}*T*, bt723, and bt1419 fits the ClearOLR with a standard deviation of 10 W m

_{s}^{−2}(in the mean of 270 W m

^{−2}). The rms bias for the 11 independent days was 0.3 W m

^{−2}. We carried the effect of the ClearOLR uncertainty through the ClearNET sensitivity calculations two ways: 1) as a multiplicative 1% error and 2) by comparing the results using the multivariate regression with a linear least squares fit using only

*T*.

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