As is clearly discussed in the excellent historical compilation of Archer and Pierrehumbert (2011), as well as the essential references therein, it has been known for decades that an increase in atmospheric greenhouse gases such as CO2 can lead to global warming essentially by changing the longwave radiative fluxes of energy at the top of the atmosphere. While remarkable progress has been made over the last few decades in laboratory, theoretical, modeling, and prediction studies of the physics of climate change (e.g., Plass, 1956; Manabe and Wetherald, 1967, 1975; Hansen et al., 1984; Ramanathan, 1988; Ramaswamy et al., 2018), experimental confirmation from space of the direct effects of CO2 (independent from temperature and water vapor changes) on the Earth's outgoing longwave spectra has been elusive. The goal of the present study is to experimentally confirm that the direct effects of CO2 increase on the Earth's outgoing longwave spectra follow theoretical estimates, by developing a methodology that allows for a direct and more precise comparison between theory and observations.

Kiehl (1983) discussed the possibility of utilizing spectrally resolved satellite measurements of longwave radiation to detect and characterize the impact of climate change on the longwave spectra and simulated the changes in clear-sky spectra due to increases in CO2 and temperature. This pioneering modeling study has been followed by other modeling studies focused on the spectral signature of climate change (e.g., Mlynczak et al., 2016; Brindley and Bantges, 2016).

The fact that measurements from space of the direct effects of increased CO2 on the longwave spectra have been notoriously difficult to obtain is associated with the sparsity of high-spectral-resolution observations of longwave radiances before the early 21st century and with the challenge of disentangling the effects of CO2, temperature, and water vapor on the spectral radiances. While measurements of the spectral effects of the combined changes in CO2, temperature, water vapor, and other gases have been published (e.g., Harries et al., 2001; Brindley and Bantges, 2016; Strow and DeSouza-Machado, 2020; Whitburn et al., 2021; Huang et al., 2022; Raghuraman et al., 2023), the direct effects of CO2 alone have been difficult to depict accurately.

For example, in a pioneering study, Harries et al. (2001) calculate the spectral differences between two infrared instruments, one launched in the 1970s and the other in the 1990s. Despite the difficulties of accurately estimating spectral differences between two different instruments, Harries et al. (2001) are able to discern and potentially assign, using model simulations, some of the spectral differences to changes in greenhouse gases such as CO2. However, they do not attempt to disentangle the effects due purely to CO2 from temperature and water vapor changes in the observational data. In a recent study, De Longueville et al. (2021) illustrate the increased CO2 absorption in the Infrared Atmospheric Sounding Interferometer (IASI) spectra from 2008 to 2017, although they do not isolate it from the joint effects of temperature and water vapor.

The recent studies of Strow and DeSouza-Machado (2020) and Huang et al. (2022) investigate in detail the Atmospheric Infrared Sounder (AIRS) instrument radiance trends over the last several years and highlight the remarkable stability of the AIRS radiance record while also discussing the role of temperature, water vapor, CO2, and other gases in framing the nature of the AIRS radiances. However, they only isolate these effects using modeling/theoretical approaches. These studies do not attempt to disentangle the impact of CO2 (or other gases) from temperature and water vapor in the observational data directly.

In the present study, a new methodology is proposed for a more direct measurement of the effect of CO2 increase on longwave spectral radiances in such a way as to provide a direct and more precise comparison to theoretically derived radiances. The goal of this approach is to isolate the effects of CO2 from the effects of temperature and water vapor. This is achieved by searching for atmospheric profiles of temperature and water vapor that are as close to each other as possible (referred to as analogues) but that have CO2 concentrations that are significantly different. Measuring from space the spectral radiances that correspond to these analogues allows us to detect, given the right circumstances, the unique impact of CO2 on the radiances with enough precision and accuracy in key spectral regions. Specifically, in this work, 1000 temperature and water vapor reference profiles are selected and a search is performed for analogue profiles that are close to the reference profiles to within a specified uncertainty range.

The spectral longwave radiances are measured by the Atmospheric Infrared Sounder (AIRS), and the profiles of atmospheric temperature and water vapor, as well as cloud properties, are from retrievals that include data from the AIRS and AMSU (Advanced Microwave Sounding Unit) suite of instruments on Aqua (e.g., Aumann et al., 2003; Chahine et al., 2006) as well as other datasets (see Appendix A).

A set of 1000 temperature and water vapor reference profiles from July 2003 are randomly selected, albeit obeying the following constraints: these profiles are over the tropical/subtropical oceans (30° S to 30° N), with cloud cover less than 10 % and within a sea surface temperature (SST) range of 298 to 302 K.

For each of these 1000 reference profiles, a search is performed to find analogue profiles that are within absolute value thresholds of 1.4 K for temperature and 1.4 g kg-1 for water vapor at any vertical level (with respect to the corresponding reference profiles). The search spans a period from 2003 to 2012 but only includes June–July–August (JJA) for each year. These analogue profiles are also over the tropical/subtropical oceans and in (almost) clear sky (cloud cover less than 10 %), and the analogue SST differences are also within 1.4 K. For each of these analogue profiles, the corresponding cloud-cleared (e.g., Susskind et al., 2003) AIRS spectral radiances are selected.

To estimate the impact of CO2 increase on the observed spectral radiances, the differences between the radiances observed at the location and time of each analogue and the radiances observed at the location and time of the corresponding reference profile are calculated. These differences (which correspond to different reference profiles and different years from 2003 to 2012) are aggregated to provide an estimate of the overall annual mean difference. These differences between the spectral radiances – which are measured at different years and as such reflect different amounts of CO2 – are compared with theoretical estimates of the radiance impact of CO2. A key assumption (which is discussed below) is that the annual mean spectral radiance differences corresponding to each reference state are (to first order) not sensitive to the reference state itself for these selected reference profiles.

To estimate the theoretical values, the spectral radiances corresponding to the reference temperature and water vapor profiles are simulated with different values of CO2 concentration that reflect its mean increase from 2003 to 2012 as measured by the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa station (see Appendix A). The kCARTA forward model (Strow et al., 1998; DeSouza-Machado et al., 2020) is used to simulate the spectral radiances and is convolved with the AIRS spectral response functions to obtain theoretical AIRS radiances.

To investigate the uncertainties associated with the temperature and water vapor thresholds used to search for analogues, a preliminary theoretical study of these uncertainties is performed: using one pair (temperature and water vapor) of reference profiles, 1000 synthetic temperature and water vapor analogues are created by drawing from a normal distribution defined by a zero mean and standard deviations of 0.5 K and 0.5 g kg-1 (which are close to the values estimated based on the observed temperature and water vapor analogues corresponding to the 1000 observed reference profiles) with the constraint that the absolute difference values at any level cannot be larger than the thresholds of 1.4 K and 1.4 g kg-1. Theoretical spectral radiances are calculated for each of these 1000 synthetic analogue pairs of profiles, and these theoretical values are used to estimate the impact of the temperature and water vapor thresholds on the spectral radiances.

Figure 1 compares the theoretical spectral radiance differences due to the annual mean increase in CO2 (for that reference profile) during this period with the mean spectral differences between the 1000 (synthetic) analogues and the reference profile. Three specific lines are shown in this context: one that includes all the 1000 synthetic spectral radiances and two additional ones in which radiance difference outliers which are larger than 0.5 or 1 mW m-2 sr-1 (cm-1)-1 are filtered out. The figure is focused on the 680-to-780 cm-1 spectral range where the CO2 effect is more prominent (see below).

In the spectral region between 680 and 720 cm-1, the spectral radiance differences due to temperature and water vapor uncertainties are much smaller than the spectral radiance differences due solely to CO2 increase, for all the analogue difference lines. Between 720 and around 750 cm-1, although the analogue lines are starting to diverge among themselves in certain regions, their values are still smaller than the CO2 differences. For values above around 750 cm-1 where the CO2 impact is reduced while the impact of water vapor becomes dominant, the analogue difference lines are of the same order of magnitude as the CO2 difference lines – although the analogue difference values that are calculated using the filter value of 0.5 mW m-2 sr-1 (cm-1)-1 are in certain spectral regions clearly smaller than the CO2 differences. Given the apparent small impact of these temperature and water vapor uncertainties on the spectral radiances in certain key spectral regions, these results provide a degree of confidence in the methodology.

Figure 2 shows the annual mean differences in terms of spectral radiances due to CO2 increase for the AIRS observations and the theoretical values, together with the standard deviation of the observations. This figure is focused on the 680-to-780 cm-1 spectral range, which represents the R branch of the 15 µm CO2 band and is a spectral region where the CO2 signal is particularly significant. In this spectral region, the enhanced absorption within the troposphere, where temperature decreases with height, leads to a reduction in the outgoing radiation. From a broader climate perspective, the reduction in outgoing radiation is behind the increase in global surface temperature that is necessary for the overall climate system to re-establish energy balance at the top of the atmosphere, and as such it is a critical component of global warming. During this period, the measured monthly mean CO2 mole fraction at Mauna Loa increased on average by approximately 2 ppm yr-1 (see Appendix A).

The theoretical annual mean differences and associated standard deviations are calculated based on the 1000 reference profiles. These standard deviations are not shown because they are so small that they would be almost imperceptible in the figure. This apparent lack of theoretical sensitivity to the reference states supports the key assumption mentioned above that the annual mean spectral radiance differences corresponding to each reference state are (to first order) not particularly sensitive to the reference state within this specific set of reference profiles.

Figure 2 illustrates that the new methodology leads to observed radiance differences that are close to the theory. Despite some noise and a small negative bias in some spectral regions, there is good agreement between theory and observations, with the observations following closely the theoretical impact of increased CO2. It is noticeable that even in the 750–780 cm-1 spectral region, where water vapor plays a large role and larger uncertainties are expected based on Fig. 1 and the standard deviations, the observations in Fig. 2 match the theory to a good level of accuracy.

The sensitivity of the observations to different aspects has been analyzed. In particular, the observations shown in Fig. 2 correspond to observed scan angles between -5 and 5° from nadir (see Appendix A), and the theoretical radiances are estimated at nadir. To remove outliers and to select analogues that are as close as possible to the reference states, analogues that have absolute radiance differences, as compared to the reference states, that are larger than 0.5 mW m-2 sr-1 (cm-1)-1 are filtered out. Overall, the observed spectral radiances shown in Fig. 2 correspond to about 250 analogues. Results obtained with scan angles between -10 and 10° and with outlier filter values of 1 mW m-2 sr-1 (cm-1)-1 show no meaningful differences, highlighting the robustness of the methodology.

Given the spatial and temporal variability in CO2, the lack of accurate knowledge of the CO2 values for each specific reference state and corresponding analogues leads to uncertainties in the theoretical radiance estimates. A preliminary analysis of this uncertainty (not shown) appears to indicate that the observations, in some regions where there are biases, could still be within the theoretical standard deviation range if the CO2 uncertainties were to be considered explicitly. In fact, using data from the Orbiting Carbon Observatory-2 (Crisp et al., 2004), this analysis leads to theoretical standard deviations of the order of 0.025 mW m-2 sr-1 (cm-1)-1 in several channels in the region between 700 and 740 cm-1. This suggests that some of the observational biases could be, at least partly, related to CO2 uncertainties. Small biases of the radiative transfer model could also potentially be behind some of the differences. A more detailed uncertainty study focused on these two critical aspects would be a natural follow-up to this work.

We present a direct measurement of the impact of increased atmospheric CO2 on the spectra of the Earth's longwave radiation obtained from space. The approach involves a new methodology to disentangle the impact of CO2 on the observed longwave spectral radiances from the effects of temperature and water vapor in such a way as to provide a direct and more precise comparison with theoretical estimates of the radiance impact of CO2. The observations obtained using this methodology compare well with theoretical estimates of the direct CO2 radiative impact on the Earth's longwave spectra.

In the future, variants of this methodology could be used to isolate the observational radiative impact of different physical and chemical properties of the climate system and as such provide a better observational depiction of the Earth's radiative forcing (e.g., Huang et al., 2016; Ramaswamy et al., 2018) and of climate feedbacks.

The stability of the AIRS instrument has been determined to be about 1 order of magnitude smaller (better) than the climate temporal signal for this spectral region (Strow and DeSouza-Machado, 2020), providing a high level of confidence in the results presented. This work also illustrates the unique and critical role of accurate and stable hyperspectral infrared observations from space in addressing fundamental climate physics questions.

This new methodology can undoubtedly be refined and its uncertainties better characterized and understood to establish its accuracy and precision more clearly. But as far as the authors are aware, this study represents the first attempt to establish a more precise experimental confirmation from space of the direct effects of CO2 on longwave spectral radiances. The results (solely based on observations) confirm that the effects of the recent atmospheric CO2 increase on longwave spectral radiances follow theoretical estimates. As such, these results confirm a critical foundation of the science of global warming.