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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2

The effect of atmospheric transmissivity on model and observational estimates of the sea ice albedo feedback

The sea-ice-albedo feedback (SIAF) is the product of the ice sensitivity (IS) – how much the surface albedo in sea-ice regions changes as the planet warms– and the radiative sensitivity (RS) – how much the top of atmosphere radiation changes as the surface albedo changes. We demonstrate that the RS calculated from radiative kernels in climate models is reproduced from calculations using the “approximate partial radiative perturbation” method that uses the climatological radiative fluxes at the top of atmosphere and the assumption that the atmosphere is isotropic to shortwave radiation. This method facilitates the comparison of RS from satellite-based estimates of climatological radiative fluxes with RS estimates across a full suite of coupled climate models and, thus, allows model evaluation of a quantity important in characterizing the climate impact of sea ice concentration changes. The satellite based RS is within the model range of RS that differs by a factor of two across climate models in both the Arctic and Southern Ocean. Observed trends in Arctic sea ice are used to estimate IS which, in conjunction with the satellite-based RS yields an SIAF of 0.16 ± 0.04 W m-2 K-1. This Arctic SIAF estimate suggests a modest amplification of future global surface temperature change by approximately 14% relative to a climate system with no SIAF. We calculate the global albedo feedback in climate models using model specific RS and IS and find a model mean feedback parameter of 0.37 W m-2 K-1 which is 40% larger than the IPCC AR5 estimate based on using RS calculated from radiative kernel calculations in a single climate model.

Arctic, Antarctic, climate change, Climate & Earth↗

A simple and fast method for computing the relativistic Compton Scattering Kernel for radiative transfer

The Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution is analytically reduced to a single integral, which can then be rapidly evaluated in a variety of ways. A particularly fast method for numerically computing this single integral is presented. This is, to the authors' knowledge, the first correct computation of the Compton scattering kernel.

Kershaw, David S.↗

Retrieve Methane from IR sounder measurements Using Machine Learning-Enhanced Physical Inversion

The sensitivity of IR sounder measurements to atmospheric CH 4 is often limited due to interferences from signals of other trace gases, insufficient thermal contrast, and cloud blockage. In order to resolve the geographical and vertical distribution of atmospheric CH 4 profiles, accurate scene-dependent a priori information is critically needed to support an optimal estimation method-based physical inversion scheme. Following the principles of indexing, representation, and retrieval, a spectral fingerprinting methodology is developed to address the needs for both accuracy and computational efficiency in sounder-based CH 4 retrieval. Within this framework, a clustering method based on machine learning is first employed to stratify and identify the a priori state within the pre-constructed database, using optimized spectral radiances as predictors. The corresponding radiative kernel is then used to establish the physical inversion scheme for finding the solution. High-quality data from CH 4 data assimilation systems like the Carbon-Tracker and the Copernicus Atmosphere Monitoring Service (CAMS) reanalysis, as well as the state-of-art sounder products are used to build the training database, including radiative kernels. We will demonstrate the results retrieved from CrIS observations and the associated validation work.

Wan Wu↗

Hyperspectral Sounder Spectral Fingerprinting: Using Machine Learning Techniques to Enhance Model-Based Physical Inversion

Different retrieval algorithms have been developed to process top-of-atmosphere (TOA) spectral radiance data provided by hyperspectral infrared sounder missions. Those algorithms are either optimal estimation method (OEM) based schemes with radiative transfer calculation involved in the retrieval process, or machine learning based methods that allow ultra-efficient data procession but lack of radiometric consistency validation based on the directly measured information. Combining both approaches leverages their respective technical advantages, leading to more accurate results. This study introduces a hyperspectral sounder fingerprinting algorithm to explore this hybrid approach. This approach involves the use of a spectral information-based classification method to identify an reference geophysical state and the corresponding radiative kernel. This enables the efficient retrieval of geophysical variables of interest through a radiative kernel-based linear inversion procedure. The fingerprinting method has been applied to analyze a decade-long hyperspectral sounder data record.

Wan Wu↗

Historical Total Ozone Radiative Forcing Derived from CMIP6 Simulations

Radiative forcing (RF) time series for total ozone from 1850 up to present-day are calculated based on historical simulations of ozone from 10 climate models contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition, RF is calculated for ozone fields prepared as input for CMIP6 models without chemistry schemes and from a chemical transport model simulation. A radiative kernel for ozone is constructed and used to derive the RF. The ozone RF in 2010 (200530 -2014) relative to 1850 is 0.35 W m-2 [0.08 to 0.61] (5-95% uncertainty range) based on models with both tropospheric and stratospheric chemistry. One of these models has a negative present-day total ozone RF. Excluding this model, the present-day ozone RF increases to 0.39 W m-2 [0.27 to 0.51] (533 - 95% uncertainty range). The rest of the models have RF close to or stronger than the RF time series assessed by the Intergovernmental Panel on Climate Change in the fifth assessment report with the primary driver likely being the new precursor emissions used in CMIP6. The rapid adjustments beyond stratospheric temperature are estimated to be weak and thus the RF is a good measure of effective radiative forcing.

ozone↗

Comparison of Clouds and Cloud Feedback between AMIP5 and AMIP6

We examine the changes in clouds and cloud feedback between Phase 5 (AMIP5) and Phase 6 (AMIP6) of the Atmospheric Model Intercomparison Project. Each model is perturbed by uniformly increasing the sea surface temperature by 4 K. The simulated cloud fraction, the perturbed states and cloud radiative kernels are used to derive cloud feedback in the shortwave (SW), longwave (LW) and their sum (Net). Compared to AMIP5, the cloud fraction in AMIP6 increases by 9.1%, while the perturbation leads to a 0.25% decrease. The Net cloud feedback at the top of the atmosphere (TOA) is almost double (174%). Statistical tests support that this change is mainly due to an increase in the surface SW cloud feedback caused by optically thick, middle and low clouds. The contribution of the atmospheric Net component (12%) stems from the increase in the atmospheric LW cloud feedback, likely to play a role in weakening (strengthening) the northward (southward) meridional atmospheric energy transport, while the opposite is true for the surface LW and Net cloud feedback in the meridional oceanic energy transport. The substantial increase in cloud feedback at the TOA primarily contributes to the higher climate sensitivity. The cloud feedback spread in AMIP6 is comparable to that in AMIP5.

Clouds↗

Radiative Feedbacks Associated with the Madden-Julian Oscillation

Radiative kernels derived from CloudSat/CALIPSO measurements are used to diagnose radiative feedbacks induced by the Madden-Julian oscillation (MJO). Over the Indo-Pacific warm pool, positive cloud and water vapor feedbacks are coincident with the convective envelope of the MJO during its active phases, whereas the lapse rate feedback shows less obvious correlation to the propagating disturbance. During phase 2/3, when the convective envelope is over the Indian Ocean, water vapor exhibits a vertically coherent response, with the largest anomalies and strongest feedback in the middle troposphere. Though spatial structures of the feedbacks vary, the most prominent difference lies in the magnitude. Cloud changes induce the largest radiative perturbations associated with the MJO. We also find that for individual MJO events, cloud feedback and precipitation are highly correlated, suggesting that the strength of individual MJO events is largely dictated by the magnitude of cloud radiative heating of the atmosphere. In addition, stronger radiative heating due to water vapor and clouds helps the MJO survive the barrier effect of the Maritime Continent, leading to further eastward propagation. These results offer process-oriented metrics that could help to improve model simulations and predictions of the MJO in the future.

radiative feedbacks↗

Deriving Climate Change Signal from Hyperspectral Sounders Using Spectral Fingerprinting Method

Hyperspectral observations from satellite-based sensors provide high information content for the Earth’s atmospheric temperature, water vapor and trace gas vertical profiles. We have developed a radiometrically consistent spectral fingerprinting method to derive climate change signals from Aqua AIRS/AMSU and S-NPP CrIS/ATMS data. The climate variables include temperature and water vapor profiles, cloud, trace gases, and surface skin temperature. The radiative kernels obtained via a single field of view physical retrieval algorithm under all-sky conditions. A key component to this work is a Principal Component-based Radiative Transfer Model (PCRTM). It is 4 orders of magnitude faster than a line-by-line radiative transfer model while keeping a similar accuracy (0.03 K RMS errors with close to zero bias). The PCRTM includes multiple scattering of clouds and non-thermodynamics equilibrium of CO2 in the RT calculations. Instead of quantifying the radiometric differences between AIRS/AMSU and CrIS/ATMS measurements directly using Simultaneous Nadir Overpass (SNO) or Double Difference Technique (DDT), we use the radiometric consistent fingerprinting scheme to derive two sets of space-time averaged anomalies from the Level 1 data of AIRS/AMSU and CrIS/ATMS. The derived anomalies in geophysical space will form a long-term, stable, and continuous climate data record. We can further infer the causes of any offset or drift by studying the differences between two overlapping data sets. For example, the offset in surface skin temperature anomaly time series will most likely caused by the Blackbody temperature calibration errors of the sounder instruments.

climate↗

Evaluation of ACCMIP Outgoing Longwave Radiation from Tropospheric Ozone Using TES Satellite Observations.

We use simultaneous observations of tropospheric ozone and outgoing longwave radiation (OLR) sensitivity to tropospheric ozone from the Tropospheric Emission Spectrometer (TES) to evaluate model tropospheric ozone and its effect on OLR simulated by a suite of chemistry-climate models that participated in the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP). The ensemble mean of ACCMIP models show a persistent but modest tropospheric ozone low bias (5-20 ppb) in the Southern Hemisphere (SH) and modest high bias (5-10 ppb) in the Northern Hemisphere (NH) relative to TES ozone for 2005-2010. These ozone biases have a significant impact on the OLR. Using TES instantaneous radiative kernels (IRK), we show that the ACCMIP ensemble mean tropospheric ozone low bias leads up to 120mW/ sq. m OLR high bias locally but zonally compensating errors reduce the global OLR high bias to 39+/- 41mW/ sq. m relative to TES data. We show that there is a correlation (Sq. R = 0.59) between the magnitude of the ACCMIP OLR bias and the deviation of the ACCMIP preindustrial to present day (1750-2010) ozone radiative forcing (RF) from the ensemble ozone RF mean. However, this correlation is driven primarily by models whose absolute OLR bias from tropospheric ozone exceeds 100mW/ sq. m. Removing these models leads to a mean ozone radiative forcing of 394+/- 42mW/ sq. m. The mean is about the same and the standard deviation is about 30% lower than an ensemble ozone RF of 384 +/- 60mW/ sq. m derived from 14 of the 16 ACCMIP models reported in a companion ACCMIP study. These results point towards a profitable direction of combining satellite observations and chemistry-climate model simulations to reduce uncertainty in ozone radiative forcing.

troposphere↗

A new method for diagnosing effective radiative forcing from aerosol–cloud interactions in climate models

Aerosol–cloud interactions (ACIs) are a leading source of uncertainty in estimates of the historical effective radiative forcing (ERF). One reason for this uncertainty is the difficulty in estimating the ERF from aerosol–cloud interactions (ERFaci) in climate models, which typically requires multiple calls to the radiation code. Most commonly used methods also cannot disentangle the contributions from different processes to ERFaci. Here, we develop a new, computationally efficient method for estimating the shortwave (SW) ERFaci from liquid clouds using histograms of monthly averaged cloud fraction partitioned by cloud droplet effective radius (r e ) and liquid water path (LWP). Multiplying the histograms with SW cloud radiative kernels gives the total SW ERFaci from liquid clouds, which can be decomposed into contributions from the Twomey effect, LWP adjustments, and cloud fraction (CF) adjustments. We test the method with data from five CMIP6-era models, using the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument simulator to generate the histograms. Our method gives similar total SW ERFaci estimates to other established methods in regions of prevalent liquid cloud and indicates that the Twomey effect, LWP adjustments, and CF adjustments have contributed -0.34 ± 0.23, -0.22 ± 0.13, and -0.09 ± 0.11 W m -2 , respectively, to the effective radiative forcing of the climate since 1850 in the ensemble mean (95 % confidence). These results demonstrate that widespread adoption of a MODIS r e –LWP joint histogram diagnostic would allow the SW ERFaci and its components to be quickly and accurately diagnosed from climate model outputs, a crucial step for reducing uncertainty in the historical ERF.

54 ENVIRONMENTAL SCIENCES↗

Attribution of Chemistry-Climate Model Initiative (CCMI) Ozone Radiative Flux Bias from Satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6-μm ozone band is a fundamental quantity for understanding chemistry-climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6-μm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Inter-comparison Project (ACCMIP) simulations. The principal culprits are tropical mid and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mWm-2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mWm-2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mWm-2). We found that AM3 and CMAM have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to difference processes. Overall, the multi-model ensemble mean bias is –133±98 mWm-2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation.

Aura Tropospheric Emission Spectrometer (TES) meas↗

Historical total ozone radiative forcing derived from CMIP6 simulations

Radiative forcing (RF) time series for total ozone from 1850 up to the present day are calculated based on historical simulations of ozone from 10 climate models contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition, RF is calculated for ozone fields prepared as an input for CMIP6 models without chemistry schemes and from a chemical transport model simulation. A radiative kernel for ozone is constructed and used to derive the RF. The ozone RF in 2010 (2005–2014) relative to 1850 is 0.35 W m -2 [0.08–0.61] (5–95% uncertainty range) based on models with both tropospheric and stratospheric chemistry. One of these models has a negative present-day total ozone RF. Excluding this model, the present-day ozone RF increases to 0.39 W m -2 [0.27–0.51] (5–95% uncertainty range). The rest of the models have RF close to or stronger than the RF time series assessed by the Intergovernmental Panel on Climate Change in the fifth assessment report with the primary driver likely being the new precursor emissions used in CMIP6. The rapid adjustments beyond stratospheric temperature are estimated to be weak and thus the RF is a good measure of effective radiative forcing.

54 ENVIRONMENTAL SCIENCES↗

Tropical High Cloud Feedback Relationships to Climate Sensitivity

Clouds constitute a large portion of uncertainty in predictions of equilibrium climate sensitivity (ECS). While low cloud feedbacks have been the focus of intermodel studies due to their high variability among global climate models, tropical high cloud feedbacks also exhibit considerable uncertainty. Here, we apply the cloud radiative kernel technique of Zelinka et al. to 22 models across the CMIP5 and CMIP6 ensembles to survey tropical high cloud feedbacks and analyze their relationship to ECS. We find that the net high cloud feedback and its altitude and optical depth feedback components are significantly positively correlated with ECS in the tropical mean. On the other hand, the tropical mean high cloud amount feedback is not correlated with ECS. These relationships are most pronounced outside of areas of strong climatological ascent, suggesting the importance of thin cirrus feedbacks. Finally, we explore connections between high cloud feedbacks, climate sensitivity, and mean state high cloud properties. In general, high ECS models are cloudier in the upper troposphere but have a thinner high cloud population. Furthermore, we find that having more thin cirrus in the mean state relates to more positive high cloud altitude and optical depth feedbacks, and it either amplifies or dampens the high cloud amount feedback depending on the large-scale dynamical regime (amplifying in descent and dampening in ascent). In summary, our analysis highlights the importance of tropical high cloud feedbacks for driving intermodel spread in ECS and suggests that mean state high cloud characteristics might provide a unique opportunity for observationally constraining high cloud feedbacks.

atmosphere↗

Contributions From Cloud Morphological Changes to the Interannual Shortwave Cloud Feedback Based on MODIS and ISCCP Satellite Observations

The surface temperature-mediated change in cloud properties, referred to as the cloud feedback, continues to dominate the uncertainty in climate projections. A larger number of contemporary global climate models (GCMs) project a higher degree of warming than the previous generation of GCMs. This greater projected warming has been attributed to a less negative cloud feedback in the Southern Ocean. Here, we apply a novel “double decomposition method” that employs the “cloud radiative kernel” and “cloud regime” concepts, to two data sets of satellite observations to decompose the interannual cloud feedback into contributions arising from changes within and shifts between cloud morphologies. Our results show that contributions from the latter to the cloud feedback are large for certain regimes. We then focus on interpreting how both changes within and between cloud morphologies impact the shortwave cloud optical depth feedback over the Southern Ocean in light of additional observations. Results from the former cloud morphological changes reveal the importance of the wind response to warming increases low- and mid-level cloud optical thickness in the same region. Results from the latter cloud morphological changes reveal that a general shift from thick storm-track clouds to thinner oceanic low-level clouds contributes to a positive feedback over the Southern Ocean that is offset by shifts from thinner broken clouds to thicker mid- and low-level clouds. Our novel analysis can be applied to evaluate GCMs and potentially diagnose shortcomings pertaining to their physical parameterizations of particular cloud morphologies.

58 GEOSCIENCES↗

Sensitivity of surface temperature to oceanic forcing via q-Flux Green’s function experiments. Part III: asymmetric response to warming and cooling

Climate response is often assumed to be linear in climate sensitivity studies. However, by examining the surface temperature (TS) response to pairs of oceanic forcings of equal amplitude but opposite sign in a large set of local q-flux perturbation experiments with CAM5 coupled to a slab, we find strong asymmetry in TS responses to the heating and cooling forcings, indicating a strong nonlinearity intrinsic to the climate system examined. Regardless of where the symmetric forcing is placed, the cooling response to the negative forcing always exceeds the warming to the positive forcing, implying an intrinsic inclination towards cooling of our current climate. Thus, the ongoing global warming induced by increasing greenhouse gases may have already been alleviated by the asymmetric component of the response. The common asymmetry in TS response peaks in high latitudes, especially along sea ice edges, with notable seasonal dependence. Decomposition into different radiative feedbacks through a radiative kernel indicates that the asymmetry in the TS response is realized largely through lapse rate and albedo feedbacks. Further process interference experiments disabling the seasonal cycle and/or sea ice reveal that the asymmetry originates ultimately from the presence of the sea ice component and is further amplified by the seasonal cycle. The fact that a pair of opposite tropical q-flux forcings can excite very similar asymmetric response as a pair placed at 55°S strongly suggests the asymmetric response is a manifestation of an internal mode of the climate model system.

Liu, Fukai↗

Contributions to Polar Amplification in CMIP5 and CMIP6 Models

As a step towards understanding the fundamental drivers of polar climate change, we evaluate contributions to polar warming and its seasonal and hemispheric asymmetries in Coupled Model Intercomparison Project phase 6 (CMIP6) as compared with CMIP5. CMIP6 models broadly capture the observed pattern of surface- and winter-dominated Arctic warming that has outpaced both tropical and Antarctic warming in recent decades. For both CMIP5 and CMIP6, CO 2 quadrupling experiments reveal that the lapse-rate and surface albedo feedbacks contribute most to stronger warming in the Arctic than the tropics or Antarctic. The relative strength of the polar surface albedo feedback in comparison to the lapse-rate feedback is sensitive to the choice of radiative kernel, and the albedo feedback contributes most to intermodel spread in polar warming at both poles. By separately calculating moist and dry atmospheric heat transport, we show that increased poleward moisture transport is another important driver of Arctic amplification and the largest contributor to projected Antarctic warming. Seasonal ocean heat storage and winter-amplified temperature feedbacks contribute most to the winter peak in warming in the Arctic and a weaker winter peak in the Antarctic. In comparison with CMIP5, stronger polar warming in CMIP6 results from a larger surface albedo feedback at both poles, combined with less-negative cloud feedbacks in the Arctic and increased poleward moisture transport in the Antarctic. However, normalizing by the global-mean surface warming yields a similar degree of Arctic amplification and only slightly increased Antarctic amplification in CMIP6 compared to CMIP5.

54 ENVIRONMENTAL SCIENCES↗

The ENSO Effects on Tropical Clouds and Top-of-Atmosphere Cloud Radiative Effects in CMIP5 Models

The El Nino-Southern Oscillation (ENSO) effects on tropical clouds and top-of-atmosphere (TOA) cloud radiative effects (CREs) in Coupled Model Intercomparison Project Phase5 (CMIP5) models are evaluated using satellite-based observations and International Satellite Cloud Climatology Project satellite simulator output. Climatologically, most CMIP5 models produce considerably less total cloud amount with higher cloud top and notably larger reflectivity than observations in tropical Indo-Pacific (60 degrees East - 200 degrees East; 10 degrees South - 10 degrees North). During ENSO, most CMIP5 models considerably underestimate TOA CRE and cloud changes over western tropical Pacific. Over central tropical Pacific, while the multi-model mean resembles observations in TOA CRE and cloud amount anomalies, it notably overestimates cloud top pressure (CTP) decreases; there are also substantial inter-model variations. The relative effects of changes in cloud properties, temperature and humidity on TOA CRE anomalies during ENSO in the CMIP5 models are assessed using cloud radiative kernels. The CMIP5 models agree with observations in that their TOA shortwave CRE anomalies are primarily contributed by total cloud amount changes, and their TOA longwave CRE anomalies are mostly contributed by changes in both total cloud amount and CTP. The model biases in TOA CRE anomalies particularly the strong underestimations over western tropical Pacific are, however, mainly explained by model biases in CTP and cloud optical thickness (tau) changes. Despite the distinct model cloud biases particularly in tau regime, the TOA CRE anomalies from cloud amount changes are comparable between the CMIP5 models and observations, because of the strong compensations between model underestimation of TOA CRE anomalies from thin clouds and overestimation from medium and thick clouds.

Su, Wenying↗

Efficacy of Climate Forcings in PDRMIP Models

Quantifying the efficacy of different climate forcings is important for understanding the real‐world climate sensitivity. This study presents a systematic multimodel analysis of different climate driver efficacies using simulations from the Precipitation Driver and Response Model Intercomparison Project (PDRMIP). Efficacies calculated from instantaneous radiative forcing deviate considerably from unity across forcing agents and models. Effective radiative forcing (ERF) is a better predictor of global mean near‐surface air temperature (GSAT) change. Efficacies are closest to one when ERF is computed using fixed sea surface temperature experiments and adjusted for land surface temperature changes using radiative kernels. Multimodel mean efficacies based on ERF are close to one for global perturbations of methane, sulfate, black carbon, and insolation, but there is notable intermodel spread. We do not find robust evidence that the geographic location of sulfate aerosol affects its efficacy. GSAT is found to respond more slowly to aerosol forcing than CO2 in the early stages of simulations. Despite these differences, we find that there is no evidence for an efficacy effect on historical GSAT trend estimates based on simulations with an impulse response model, nor on the resulting estimates of climate sensitivity derived from the historical period. However, the considerable intermodel spread in the computed efficacies means that we cannot rule out an efficacy‐induced bias of ±0.4 K in equilibrium climate sensitivity to CO2 doubling when estimated using the historical GSAT trend.

T B Richardson↗