The analysis is based on clear-sky OLR spectral fluxes which are derived from radiance measurements acquired by two different sounders: the AIRS and IASI instruments.

The first is a grating array spectrometer which measures spectrally resolved radiances across three different bands, 650–1136, 1216–1613, 2170–2674 cm⁻¹ . The corresponding fluxes have been derived by for both clear and all-sky observations of the instrument flying on board the Aqua satellite from November 2002 to present days. Simulated radiances have been used to fill the spectral gaps and extend the original spectral range below 650 cm⁻¹, down to 15 cm⁻¹. The final product consists of monthly mean spectral fluxes computed at 10 cm⁻¹ from 15 to 1995 cm⁻¹, with a horizontal resolution of 2° latitude by 2° longitude. Two separate flux products are provided for the two AIRS overpass times at the equator, 01:30 and 13:30 LT. In this study, we use the average of these two overpasses.

IASI is a Fourier transform spectrometer which measures radiances across the range from 645 to 2760 cm⁻¹, with a spectral resolution of 0.25 cm⁻¹ . We use the dataset of clear-sky spectral fluxes derived from measurements acquired by IASI on board the MetOp-A (October 2007–December 2021), as described in . The dataset consists of monthly mean spectral fluxes for the period from January 2008 to October 2021. Spectral fluxes are provided over a 2° longitude by 2° latitude grid and span the wavenumber range from 645 to 2300 cm⁻¹, with a spectral resolution of 0.25 cm⁻¹. Two products are provided for night-time (21:30 LT at the equator) and daytime (09:30 LT at the equator) observations, respectively. As was as done for AIRS, these overpasses have been averaged. The same product is also available for data collected on board the MetOp-B (2013–today) and C (2017–today), however, for this study, the MetOp-A ensures the greatest temporal overlap with the AIRS and CERES datasets. It should be noted that the MetOp-A platform began drifting from its nominal orbit in autumn 2017, resulting in an earlier local time of the ascending node.

In addition to AIRS and IASI spectral fluxes, we used broadband OLR values derived from CERES measurements. CERES is a broadband radiometer with three channels that measure radiances across the whole spectrum (50–3000 cm⁻¹), the shortwave (2000–3000 cm⁻¹) and the atmospheric window (830–1250 cm⁻¹) regions, respectively . We use the CERES Energy Balanced and Filled (EBAF) Edition 4.1 data product , which gathers data collected by different CERES instruments on board Terra and Aqua platforms since 2000. Two clear-sky products are available, one that only considers cloud-free observations and another that additionally applies a correction factor for a better comparison with climate models output, for which clear-sky fluxes are artificially produced by removing clouds from the flux calculation. The first product has been selected for consistency with IASI and AIRS observations. CERES-EBAF 4.1 provides monthly mean TOA OLR fluxes with an horizontal resolution of 1° per 1° and a temporal coverage from January 2000 to March 2022.

The main features of the three datasets are resumed in Table .

Radiative kernels (or Jacobians) represent the partial derivative of the spectral flux or radiance with respect to specific climate variables, evaluated across the atmospheric levels. They can be used to estimate the OLR perturbation at the TOA resulting from changes in atmospheric and surface climate variables .

For this study we use a set of clear-sky spectral kernels developed by . The kernels have been computed using the RTTOV model (Radiative Transfer model for the TIROS-N Operational Vertical Sounder) and monthly mean profiles from the European Center for Medium-Range Weather Forecast (ECMWF) Reanalysis v5 (ERA5) dataset as the input for meteorological fields. The derivatives have been computed for three different years 2008, 2009, and 2010, and then averaged to obtain representative monthly kernels of surface and atmospheric temperature, water vapor and ozone. Furthermore, in order to obtain the derivatives of the spectral flux (W (m² cm⁻¹)⁻¹), radiance derivatives (W (m² cm¹ sr)⁻¹) were computed at three distinct viewing angles (24.29, 53.80, 77.74°). The resulting values were then integrated using Gaussian quadrature, which has been shown to yield accurate results for clear-sky radiative transfer calculations . More details regarding the construction of the spectral kernels can be found in .

The resulting product consists of radiative kernels, averaged over 10 cm⁻¹ intervals, from 100 to 2300 cm⁻¹, spanning 17 pressure levels (hPa): 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, 10, on a horizontal grid of 2.5° longitude per 2.5° latitude. As an example, Figs.  and show a comparison of the surface and air temperature kernels used in this study with the radiative kernels computed by for the month of January. For the selected scenario, the differences between the two sets of radiative kernels are small, being within the 5 % for the tropical zone. Additional validation has been made to test the accuracy of using as input monthly mean versus instantaneous profiles for the meteorological fields, as done by (not shown). It emerges that for the clear-sky case the differences between the two approaches are small (within the 1 %) and do not appear to be significant for the results of our analysis.

Finally, the change in the radiative flux associated to the change in each climate variable is obtained multiplying the respective radiative kernel by the anomaly of that variable and then, for 3D fields, summing over the pressure levels to obtain the total atmospheric response. Surface and atmospheric temperature, water vapor and ozone fields are taken from the monthly ECMWF ERA5 reanalysis . Atmospheric variables are selected on the same 17 pressure levels used for the radiative kernels computation. Anomalies of meteorological fields are computed relative to the monthly mean from January 2008 to December 2020, the period selected for the analysis.

The Niño 3.4 index has been used as a measure of ENSO phase and magnitude. It is defined as the average SST anomaly over the Niño 3.4 region (5° S–5° N, 170–120° W), smoothed with a five-month running mean . Area-averaged SSTs provided by the NOAA database have been used for its calculation (https://www.cpc.ncep.noaa.gov/data/indices/ersst5.nino.mth.91-20.ascii, last access: 15 April 2024). The resulting Niño 3.4 index is plotted in Fig.  for the years from January 2008 to December 2020. The period examined is characterized by two strong El-Niño events. The first peaked during the 2009–2010 winter and the second during the winter of 2015–2016. Two strong La-Niña events also occurred in the winter of 2007–2008 and 2010–2011.

The time relationship between OLR anomalies and ENSO activity has been investigated through a lagged regression analysis, performed over the period from January 2008 to December 2020, which is common to all the observational datasets.

All the datasets have been regridded to a common grid of 2.5° latitude per 2.5° longitude, through a bilinear interpolation. Then, the monthly OLR anomaly has been calculated by subtracting the monthly climatology, relative to the period considered, from the OLR time series. In order to better isolate the internal variability signal from the one related to the increase in GHGs concentration, we removed the linear trend of the OLR anomaly over the given period.

Lagged regressions have been calculated performing a linear regression between the radiative anomaly and the Niño 3.4 index as follow: 1y=m⋅x+q In Eq. (), y and x are the OLR anomaly and Niño 3.4 index time series, respectively, from January 2008 to December 2020; the variable x has been shifted one month at a time from -12 to +12 months, resulting in 25 regression coefficients, m, being obtained at the end of the procedure. The regression coefficients (units of W m⁻² K⁻¹) are a measure of the radiative perturbations driven by ENSO induced SST anomalies. We will refer to these as “ENSO feedback” for the rest of the paper, as done also by and . The 95 % statistical significance of the regression coefficients has been assessed with a two-tailed t-test.

The analysis focused on the tropical zone (30° S–30° N), where the radiative perturbations induced by ENSO are strongest, and on values above ocean, to avoid introducing biases in the comparison of non-simultaneous measurements, which can arise from the rapid temperature variability typical of land surfaces .

The OLR response to ENSO variability is presented first from a broadband perspective. Figure  shows the tropical mean broadband OLR response to ENSO as a function of the time lag obtained using fluxes from CERES, IASI and AIRS. In the case of AIRS, the spectral fluxes are integrated over two different spectral ranges: from 50–1995 cm⁻¹, to be as consistent as possible with CERES, which encompasses the range from 50 to 2000 cm⁻¹, and from 645–1995 cm⁻¹, to match the spectral range encompassed by IASI. Note that, in order to be consistent with the definition of climate feedbacks, the sign of the OLR response has been inverted. Thus, a negative ENSO feedback corresponds to an enhanced OLR emission at the TOA, conversely, a positive feedback is associated with a decrease in OLR.

The radiative response depicted in Fig.  suggests an increase in OLR emission at the TOA associated to ENSO. In more detail, the total LW ENSO feedback becomes negative starting from about five months ahead of the ENSO peak. The negative peak is reached at a lag of 2 months, and the response gradually weakens thereafter. This result agrees with , who found a similar OLR response to ENSO in clear-sky conditions, suggesting that it is likely driven by the Planck effect.

When the entire spectral region from 50 to 2000 cm⁻¹ is accounted for, the OLR peak at the 2-months lag is of -0.46 ± 0.11 W m⁻² K⁻¹ for AIRS and -0.46 ± 0.12 W m⁻² K⁻¹ for CERES, whereas it decreases to -0.31 ± 0.05 W m⁻² K⁻¹ for AIRS and -0.31 ± 0.05 W m⁻² K⁻¹ for IASI, when the 645–1995 cm⁻¹ wavenumber range is considered. These values denote that approximately 30 % of the total OLR emission during ENSO is achieved between 50 and 645 cm⁻¹, confirming the importance of the Far-Infrared (FIR) spectral region (100–600 cm⁻¹) for the TOA ERB .

Although we find an excellent agreement in the magnitude of the OLR response peak between CERES and AIRS, the AIRS signal exhibits a delay of one month, peaking at 3-months lag, and a smaller value at negative lags, compared to CERES. Instead, the agreement between AIRS and IASI is excellent, with minor differences at negative lags.

In order to examine the factors that control the magnitude and timing of the LW ENSO feedback, we have extended the analysis to the spectral dimension. Lagged regressions between the tropical mean OLR anomalies and the Niño 3.4 index have been performed at each wavenumber encompassed by IASI and AIRS spectral fluxes. To enable a direct comparison, IASI spectra have been resampled to the same resolution as the AIRS dataset (10 cm⁻¹).

Results are showed in Fig. , which reports the spectral ENSO feedback as a function of wavenumbers and time lag (panels a and b), and for a time lag of two months (panel c), where the broadband response peaks. Different responses are obtained across the spectrum. Specifically, different spectral regions are associated with a characteristic lag, as well as a particular sign and magnitude of the ENSO feedback. The wings of the carbon dioxide absorption band (∼ 600–645 and ∼ 700–800 cm⁻¹), the atmospheric windows (∼ 800–1000 and ∼ 1100–1200 cm⁻¹) and the ozone absorption band (∼ 1000–1065 cm⁻¹) are all associated with a negative ENSO feedback. Below 600 cm⁻¹, where only AIRS simulated spectral fluxes are available, a widespread negative ENSO feedback emerges. The only positive feedback comes from the center of the carbon dioxide absorption band (∼ 645–700 cm⁻¹).

The strongest response across the whole spectrum is found in correspondence with the ozone absorption band, where the OLR is sensitive mainly to surface temperature and upper tropospheric/lower stratospheric ozone. It is followed by the carbon dioxide band, wings and center, which provide information on the tropospheric and stratospheric temperature, respectively, and the atmospheric windows, where radiation is mainly sensitive to surface temperature. The negative response in the FIR is likely driven by water vapor, which exhibits strong absorption in this spectral range ().

The time lag of the ENSO feedback is also spectrally dependent. This is highlighted by thicker black dots in Fig. , which mark the lag of the response peak at each wavenumber. A lag of 2 months is observed across the atmospheric windows, while a 3-months lag characterizes the spectral regions associated with the wings of the carbon dioxide and the ozone absorption band. Finally, at the center of the carbon dioxide band the OLR response peaks at a lag of 5 months.

A summary of the ENSO spectral feedback for the spectral regions discussed above is provided by Table . It reports the value of the ENSO feedback integrated over each wavenumber interval, along with the lag at which the OLR response peaks in each spectral region.

AIRS and IASI spectral footprints are generally in a good agreement, showing the same main features. There are some differences in the magnitude of the response peak within the atmospheric window (∼ 800–1000 cm⁻¹), where the AIRS signal is slightly higher than that of IASI, but inside the uncertainty range (Table , fifth row and Fig. a). The opposite behavior is observed within the ozone absorption band (Table , sixth row and Fig. a), where a stronger signal is obtained for IASI. One factor to consider is the different overpass time of AIRS and IASI. This could partly explain the observed bias within the atmospheric window, where radiance is more sensitive to surface temperature . However, the different clear-sky scene selection could also play a role. Specifically, AIRS clear-sky fluxes are based on the collocated CERES measurements considered as clear-sky by the scene type information provided by the Moderate Resolution Imaging Spectroradiometer (MODIS), as described in . We found that this strategy produced a more conservative cloud screening than that of IASI (not shown). This aspect will be more evident in Sect. , when we will examine the spatial pattern of the ENSO feedbacks.

The spectral fluxes of IASI and AIRS allowed us to study the total LW ENSO feedback associated with characteristic spectral regions and relate it to atmospheric and surface variables to which radiation is sensitive. Now, spectral radiative kernels are exploited to investigate the origin of the ENSO signal in more depth. Specifically, we address the individual radiative contribution associated with changes in surface and atmospheric temperature, water vapor and ozone. The corresponding surface and atmospheric Planck, water vapor and ozone ENSO feedbacks have been obtained by performing the same regression analysis that was performed on the IASI and AIRS observations. Results of the lagged regressions are plotted in Fig. .

The Planck surface ENSO feedback (Fig. a) is negative and contributes to the TOA OLR only within the atmospheric windows, where the OLR is sensitive to the surface temperature. It peaks at a lag equal to 2 months across the two spectral ranges (∼ 800–1000 and ∼ 1100–1200 cm⁻¹). A negative feedback is also associated with the Planck atmospheric effect (Fig. b) below about 600 cm⁻¹, between 700–1000 cm⁻¹ and above 1100 cm⁻¹. Instead, the positive sign of the Planck atmospheric feedback between 645–700 cm⁻¹ (Fig. b) explains the positive ENSO feedback that characterizes also IASI and AIRS observations at the center of the carbon dioxide band (Fig. ). In this spectral region the Planck atmospheric feedback peaks with a lag of 5 months, whereas over the remainder of the spectral range it peaks between 3 and 4 months lags. When the Planck atmospheric feedback is separated in a tropospheric and stratospheric contribution, with the tropical tropopause fixed at 100 hPa, it becomes evident that the positive feedback originates from the stratospheric temperature change (Fig. ) and that the strong negative feedback within the FIR spectral region comes from the troposphere (Fig. ), with the largest contribution from the upper troposphere (600–150 hPa) (Fig. ). The Planck surface and atmospheric feedbacks are both negative, enhancing the OLR emission. Water vapor changes, instead, constitute the main positive ENSO feedback, acting to dampen the OLR emission. The water vapor feedback peaks with a lag of 3 months at all wavenumbers. As for the Planck atmosphere, the strongest signal occurs in the FIR spectral region, with the majority of the contribution coming from the upper troposphere (Fig. ).

Given the strong ENSO feedback observed in correspondence of the ozone absorption band (Fig. ), we isolated the ozone contribution to assess its specific impact. A negative feedback, peaking in the stratosphere (Fig. ), is found between about 1010–1065 cm⁻¹, with a pick at 4-months lag. At the same wavenumbers and lags there is also a smaller positive feedback associated to the stratospheric temperature (Fig. ), which, opposed to ozone, acts to reduce the OLR emission.

Finally, we reconstructed the total observed LW response summing the individual feedbacks calculated with kernels. The feedback sum is shown in Fig. , as a function of wavenumber and lag (panel a) and wavenumber only for the 2-months lag (panel b), along with its components. The main features of the AIRS and IASI clear-sky OLR response (Fig. ) are present. The kernel regression analysis correctly reproduces the negative feedback within the two atmospheric windows and the wings of carbon dioxide absorption bands, as well as the positive feedback at the center of it. Except for the magnitude of the latter, which is overestimated by the feedback sum with respect to AIRS (Table , third row), both the amplitude and time-lag are well reproduced (Table ). The difference between IASI total LW response and the feedback sum is reported in Fig. b. The main discrepancy arises in the spectral regions below 600 and above 1300 cm⁻¹: here AIRS fluxes indicate a negative feedback that peaks 3 months after ENSO, while the kernels reconstruction indicates a contribution close to zero at that lag (Table , first row) and a positive feedback that anticipates the ENSO peak (Fig. ). A possible explanation for these two biases lies in the fact that ERA5 profiles used in the kernel reconstruction represent all-sky conditions. This leads to higher humidity content than in clear-sky profiles, causing an overestimation of the associated water vapor feedback and leading to the complete compensation between the atmospheric temperature and water vapor signal below 600 and above 1300 cm⁻¹ at positive lags.

In the next section (Sect. ), the spatial pattern of the OLR response to ENSO is examined, which will help to trace the OLR response to specific regions of the tropical Pacific Ocean.

We now examine the spatial pattern of the OLR response to ENSO across the tropics (30° S–30° N). Starting from the top of Fig. , the total OLR ENSO feedback obtained for IASI, AIRS and the kernel reconstruction is shown. The left column refers to the 900–910 cm⁻¹ interval, within the atmospheric window, where OLR is sensitive to surface temperature, but also to water vapor, that we want to assess and compare among the observed and reconstructed signal. The right column corresponds to the 1020–1030 cm⁻¹ interval, located within the ozone absorption band. Here, the OLR is mainly sensitive to surface temperature and ozone.

At 905 cm⁻¹ the response, obtained from IASI and AIRS fluxes, shows a dipole within the tropical Pacific Ocean, in phase with the SST pattern typical of El-Niño conditions. Indeed, a positive ENSO feedback characterizes the western part of the basin, while a negative value is found in the central and eastern parts of the basin. Significant negative contributions are also found over the north-east subtropical region and over the Maritime Continent. The OLR response at 1025 cm⁻¹ is characterized by a negative feedback coming from the central and eastern part of the Pacific Ocean. Its magnitude is highest within the Niño 3.4 region (marked by a black box in Fig. ), and decreases moving off the equator.

Although, there is a good agreement in the pattern obtained from IASI and AIRS data, as anticipated in Sect. , the impact of the clear-sky scene selection of AIRS observations is evident here. Specifically, AIRS shows a more scattered pattern with respect to IASI in the western and central tropical Pacific at 905 cm⁻¹.

Regarding the feedback sum, it correctly reproduces the response pattern at 905 cm⁻¹, but the magnitude of the positive feedback within the west Pacific is clearly overestimated. A similar discrepancy is also obtained for the reconstructed response at 1025 cm⁻¹, where the signal in the central and eastern regions is smaller in magnitude than observations and its peak is shifted eastward. The anomalous positive feedback can be attributed to the water vapor ENSO feedback, which shows a positive signal in the western and central parts of the Tropical Pacific Ocean at both 905 and 1025 cm⁻¹ (Fig. ). These differences consolidate our hypothesis of an overestimation of the water vapor feedback, that would also overcompensate the Planck contribution below 600 cm⁻¹ and above 1300 cm⁻¹ in the kernel reconstruction (Sect. ).