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The sensitivity of the climate system to an imposed radiative imbalance remains the largest source of uncertainty in projections of future anthropogenic climate change. Here we present further evidence that this uncertainty from an observational perspective is largely due to the masking of the radiative feedback signal by internal radiative forcing, probably due to natural cloud variations. That these internal radiative forcings exist and likely corrupt feedback diagnosis is demonstrated with lag regression analysis of satellite and coupled climate model data, interpreted with a simple forcing-feedback model. While the satellite-based metrics for the period 2000–2010 depart substantially in the direction of lower climate sensitivity from those similarly computed from coupled climate models, we find that, with traditional methods, it is not possible to accurately quantify this discrepancy in terms of the feedbacks which determine climate sensitivity. It is concluded that atmospheric feedback diagnosis of the climate system remains an unsolved problem, due primarily to the inability to distinguish between radiative forcing and radiative feedback in satellite radiative budget observations.

The magnitude of the surface temperature response of the climate system to an imposed radiative energy imbalance remains just as uncertain today as it was decades ago [

From a modeling standpoint, this lack of progress is evidence of the complexity of the myriad atmospheric processes that combine to determine the sign and magnitude of feedbacks. It is also due to our inability to quantify feedbacks in the real climate system, a contentious issue with a wide range of published feedback diagnoses [

Spencer and Braswell ([

In simple terms, radiative changes

Much can be learned about the interaction between radiative forcing and feedback through a simple time dependent forcing-feedback model of temperature variations away from a state of energy equilibrium,
_{p} d

Equation (1) states that time-varying sources of non-radiative forcing _{p}_{p}_{p}

Radiative forcings (

Although not usually considered a feedback ^{−2} K^{−1} in the global average [

The larger the net feedback parameter ^{−2} K^{−1}, all of the IPCC models therefore exhibit net positive feedbacks. Also, since all climate models have net feedback parameters greater than zero, none of the climate models are inherently unstable to perturbations.

It is worth reiterating that satellite radiative budget instruments measure the combined effect of the radiative terms on the RHS of Equation (1), that is, the radiative forcing term _{p}

Simple forcing-feedback model demonstration that satellite radiative budget instrument measurements of Net radiative flux (forcing + feedback) are very different from what is needed to diagnose the net feedback parameter (feedback only).

In response to radiative forcing, the model ocean warms, which in turn causes a net radiative feedback response. Significant to our goal of diagnosing feedback, the net feedback response to a temperature change is always smaller than the radiative forcing which caused it, owing to the heat capacity of the system, until radiative equilibrium is once again restored. At that point the radiative feedback equals the radiative forcing.

Unfortunately, in the real climate system radiative forcings are continually changing, which means the feedback response will in general be smaller than the radiative forcing. The presence of this radiative forcing tends to confound the accurate determination of feedback. If the only source of radiative variability was feedback, then regression of the time series (−^{−2} K^{−1}. But the presence of time varying radiative forcing in

As shown by SB10, the presence of any time-varying radiative forcing decorrelates the co-variations between radiative flux and temperature. Low correlations lead to regression-diagnosed feedback parameters biased toward zero, which corresponds to a borderline unstable climate system. We believe that the low correlations associated with previous feedback diagnoses with satellite data are themselves

In the real climate system, it is likely there is almost always a time-varying radiative forcing present, as various internally-generated changes in clouds and water vapor oscillate between positive and negative values faster than the resulting temperature changes can restore the system to radiative equilibrium. This means that feedback diagnosis will, in general, be contaminated by an unknown amount of time-varying internal radiative forcing

Central to the difficulty of feedback diagnosis is the very different time-dependent relationships which exist between forcing and temperature, ^{−2} K^{−1}), and the relatively rapid convective coupling of the surface to the atmosphere, which causes surface temperature-dependent changes in water vapor, clouds, and the vertical profile of temperature.

While SB10 provided evidence that such radiatively-induced temperature changes do exist, and in general lead to an underestimate of the net feedback parameter, this view has been challenged ([

Here we will provide evidence that those temperature changes instead had a strong component of radiative forcing, with radiative accumulation preceding, and radiative loss following temperature maxima. While SB10 used phase space analysis to demonstrate the presence of radiative forcing, here we will use lag regression analysis. By examining regression coefficients between temperature and radiative flux at a variety of leads and lags, rather than at just zero time lag, we can identify behaviors of the climate system that otherwise cannot be discerned.

First we will demonstrate what these lag relationships look like in the satellite observations and in the coupled climate models. Then, we will explore with a simple forcing-feedback model of the climate system what the relationships mean in terms of forcing and feedback.

The CERES (Clouds and the Earth’s Radiant Energy System) [

We will use the same SSF Edition 2.5 monthly gridpoint radiative flux dataset used by D10, updated through June 2010, from which D10 claimed evidence for positive cloud feedback. The SSF dataset also includes a calculation of the ‘Net’ flux, which additionally accounts for the effect of small variations in the solar constant during 2000–2010,

We computed monthly global area averages from the monthly gridpoint Net radiative fluxes in the 10+ year SSF Edition 2.5 dataset. From the resulting time series of monthly averages we then computed monthly anomalies, where each month’s anomaly is the departure from the ten-year (or eleven-year) average for that calendar month. This allows us to examine year-to-year variations in the climate system.

Global monthly anomalies in surface temperature were similarly computed from the HadCRUT3 surface temperature dataset [

Global monthly anomalies in LW and SW fluxes, as well as in surface temperature, were also computed from the 20th Century runs of the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset archived at PCMDI, for the years 1900 through 1999. Because of the significant trends in the 20th Century simulations, the 100-year trend was removed from each anomaly time series in order to better isolate the interannual variability that will be compared to the relatively short (10 year) period of satellite data. While we computed results for 14 of the models archived, here will only present results for the three most sensitive models (MIROC3.2-hires; IPSL-CM4; MIROC3.2-medres), and the 3 least sensitive models (FGOALS; NCAR PCM1; GISS-ER), where their sensitivity to transient carbon dioxide forcing was estimated by [

The time series of observed monthly global HadCRUT3 surface temperature anomalies from March 2000 through June 2010 is shown in

Times series of monthly global average anomalies in

Lagged regressions were performed between the surface temperature and the Net radiative flux time series shown in

Lead and lag regression coefficients between monthly surface temperature anomalies and Net radiative flux anomalies in observations

One of the most obvious conclusions from

Also, note the change in sign of the radiative imbalances in

The effect of radiative (^{−2} K^{−1}; and an ocean mixed layer depth of 25 m, a choice which requires some discussion.

We found that the assumed mixed layer depth of 25 m is consistent with the average behavior of both the IPCC AR4 coupled climate models and the satellite observations on interannual time scales. Using Equation (1), we estimated _{p}_{p} as the regression coefficient. The resulting C_{p} values from 14 IPCC AR4 models ranged from 11 m to 50 m, with a 14-model average of 27 m, while a similar regression on the 10+ years of satellite data revealed an equivalent mixing depth of 26 m, which supports our use of 25 m. (Note that, since about 30% of Earth is land having comparatively negligible heat capacity, the equivalent mixing depth of 25 m implies an average ocean mixing depth of about (25/0.7=) 35 m for the interannual time scales addressed here. Also, if most of the interannual temperature variability originates in the tropics, our diagnosed mixed layer depth will be biased toward tropical values, which are typically much shallower than at high latitudes.)

For the radiative forcing

The lag regression results from the simple model are shown in

If the temperature variations are radiatively forced, the lag regression relationships are very different (dashed line in

Lag regression coefficients between temperature and radiative flux from the simple forcing-feedback model run for three forcing cases: pure non-radiative forcing (dotted line); pure radiative forcing (dashed line); and a 70% radiative/30% non-radiative forcing mixture. A feedback parameter of 3 W m^{−2} K^{−1} and ocean mixing depth of 25 m were specified for all three simulations, which each ran for 500 years of simulated time.

Finally, a mixture of 70% radiative and 30% non-radiative forcing (solid line in

Thus, we must conclude that time-varying radiative forcing exists in the satellite observations, as evidenced by the radiative gain/loss couplet patterns seen in

Determination of whether regression coefficients at various non-zero time lags might provide a more accurate estimate of feedback has been recently explored by [

We have shown clear evidence from the CERES instrument that global temperature variations during 2000–2010 were largely radiatively forced. Lag regression analysis supports the interpretation that net radiative gain (loss) precedes, and radiative loss (gain) follows temperature maxima (minima). This behavior is also seen in the IPCC AR4 climate models.

A simple forcing-feedback model shows that this is the behavior expected from radiatively forced temperature changes, and it is consistent with energy conservation considerations. In such cases it is difficult to estimate a feedback parameter through current regression techniques.

In contrast, predominately non-radiatively forced temperature changes would allow a relatively accurate diagnosis of the feedback parameter at zero time lag using regression since most radiative variability would be due to feedback. Unfortunately, this appears not to be the situation in either the satellite observations or the coupled climate models.

Yet, as seen in

Finally, since much of the temperature variability during 2000–2010 was due to ENSO [

What this might (or might not) imply regarding the ultimate causes of the El Niño and La Niña phenomena is not relevant to our central point, though: that the presence of time varying radiative forcing in satellite radiative flux measurements corrupts the diagnosis of radiative feedback.

We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modeling (WGCM) for their roles in making available the WCRP CMIP3 multi-model dataset. Support of this dataset is provided by the Office of Science, US Department of Energy. This research was sponsored by DOE contract DE-SC0005330 and NOAA contract NA09NES4400017.