by Roger A. Pielke Sr., Richard T. McNider, and John Christy
The thing we’ve all forgotten is the heat storage of the ocean – it’s a thousand times greater than the atmosphere and the surface. - James Lovelock
This aspect of the climate system is why it has been proposed to use the changes in the ocean heat content to diagnose the global radiative imbalance, as summarized in Pielke (2003, 2008). In this weblog post, we take advantage of this natural space and time integrator of global warming and cooling.
We present this alternate tool to assess the magnitude of global warming based on assessing the magnitudes of the annual global average radiative imbalance, and the annual global average radiative forcing and feedbacks. Among our findings is the difficulty of reconciling the three terms.
As summarized in NRC (2005) “the concept of radiative forcing is based on the hypothesis that the change in global annual mean surface temperature is proportional to the imposed global annual mean forcing, independent of the nature of the applied forcing. The fundamental assumption underlying the radiative forcing concept is that the surface and the troposphere are strongly coupled by convective heat transfer processes; that is, the earth-troposphere system is in a state of radiative-convective equilibrium.”
According to the radiative-convective equilibrium concept, the equation for determining global average surface temperature is
ΔQ = ΔF – ΔT/ λ (1)
where ΔQ is the radiative imbalance, ΔF is the radiative forcing, and ΔT is the change in temperature over the same time period. The quantity λ is referred to as the radiative feedback parameter which has been used to relate temperature response to a change in radiative forcing (Gregory et al. 2002, NRC 2005). As such, it has been used as the primary global metric for assessing global warming due to anthropogenic changes in radiative forcing. The quantity ΔT is typically defined as the near-surface global average surface air temperature.
While perhaps conceptually useful, the actual implementation of the equation can be difficult. First, the measurement of ΔT has been shown to have issues with its accurate quantification. In the equation, ΔT is meant to represent both the radiative temperature of the Earth system and the accumulation of heat through the temperature change that would occur as a radiative imbalance occurs. However, changes in temperature at the surface can occur due to a vertical redistribution of heat not necessarily due to an accumulation of heat (McNider et al. 2012), site location issues (Pielke et al. 2007; Fall et al. 2011), as well as due to regional changes in surface temperatures from land-use change, aerosol deposition, and atmospheric aerosols (e.g., Christy et al. 2006, 2009; Strack et al. 2007; Mahmood et al. 2013). Even more importantly, as shown in recent studies (Levitus et al. 2012), a significant fraction of the heat added to the climate system is at depth in the oceans, and thus cannot be sampled completely by ΔT (Spencer and Braswell 2013).
Computing the radiative imbalance ΔQ as a residual from large positive and negative values in the radiative flux budget introduces a large uncertainty. Stephens et al. (2012) reports a value of the global average radiative imbalance (which Stephens et al. calls the “surface imbalance”) as 0.70 Watts per meter squared, but with the uncertainty of 17 W m-2!
We propose an alternate approach based on the analysis of the accumulation rate of heat in the Earth system in Joules per time. We believe the radiative imbalance can much more accurately be diagnosed by the ocean heat update since the ocean, because of the ocean’s density, area, and depth (i.e., its mass and heat capacity), is by far the dominate reservoir of climate system heat changes ( Pielke, 2003, 2005; Levitus et al. 2012; Trenberth and Fasullo 2013). Thus, the difference in ocean heat content at two different time periods largely accounts for the global average radiative imbalance over that time (within the uncertainty of the ocean heat measurements). Once the annual global annual average radiative imbalance is defined by the ocean accumulation of heat (adjusted for the smaller added heating from our parts of the climate system), we can form an equation that drives this imbalance as
Global annual average radiative imbalance [GAARI] = Global annual average radiative forcing [GAARF] + Global annual average radiative feedbacks [GAARFB] (2)
where the units are in Joules per time period (and can be expressed as Watts per area).
Levitus et al. (2012) reported that since 1955, the layer from the surface to 2000 m depth had a warming rate of 0.39 W m-2 ± 0.031 W m-2 per unit area of the Earth’s surface which accounts for approximately 90% of the warming of the climate system. Thus, if we add the 10%, the 1955-2010 GAARI= 0.43 W m-2 ± 0.031 W m-2.
The radiative forcing can be obtained from the 2013 IPCC SPM WG1 report (unfortunately, they do not give the values for specific time periods but give a difference from 1750 to 1950, 1980 and 2011). Presumably, some of this forcing has been accommodated by warming over the time period, but the IPCC does not address this.
Figure SPM.5 in IPCC (2013) [reproduced below] yields the net radiative forcing = 2.29 (1.13 to 3.33) W m-2 for the net change in the annual average global radiative forcing from 1750 to 2011. The report on the change of radiative heating from 1750 to 1950 is 0.57 (0.29 to 0.85) W m-2. If we assume that all of the radiative forcing up to 1950 has already resulted in feedbacks which remove this net positive forcing, the remaining mean estimate for the current GAARF is 1.72 W m-2.
For GAARFB, Wielicki et al. (2013; their figure 1; reproduced below) has radiative feedbacks = -4.2 W m-2 K-1 (from temperature increases) + water vapor feedback (1.9 W m-2 K-1) + the albedo feedback (0.30 W m-2 K-1) + the cloud feedback (0.79 W m-2 K-1) = -1.21 W m-2 K-1.
It needs to be recognized that deep ocean heating is an unappreciated effective negative temperature feedback, at least in terms of how this heat can significantly influence other parts of the climate system on multi-decadal time scales. Nonetheless, we have retained this heating in our analysis.
Over the time period 1955 to 2010, the global surface temperatures supposedly increased by about 0.6 K (Figure SPM1 from IPCC, 2013 and reproduced below).
Thus, GAARFB = -1.21 W m-2 K-1 x 0.6K = -0.73 W m-2.
Using the IPCC GAARF of 1.72 W m-2 and the GAARFB of -0.73 W m-2 in equation (2) yields
GAARF + GAARFB = 1.72– 0.73 = 0.99 W m-2 = GAARI
This, however, is more than twice as large as the ocean diagnosed GAARI of 0.43 W m-2 ± 0.031 based on Levitus et al. (2012).
Even the IPCC agrees that the radiative imbalance is relatively smaller than the 0.99 W m-2 calculated above. They report that the global average radiative imbalance is 0.59 W m-2 for 1971-2010 while for 1993-2010 it is 0.71 W m-2. Trenberth and Fasullo (2013) state that the imbalance is 0.5–1W m−2 over the 2000s.
Rather, than using the IPCC (Wielicki, 2013) GAARFB, we can use equation (2) to solve for the radiative feedbacks with the ocean heat data as a real world constraint, i.e.
GAARFB = GAARI – GAARF (3)
Inserting the heat changes in the ocean to diagnose GAARI and the IPCC GAARF in (3)
0.43 W m-2 ± 0.031 W m-2 [GAARI] – 1.72 [-1.13 to -3.33] W m-2 [GAARF]
then results in the estimate of GAARFB of - 1.29 W m-2 with an uncertainty range from the IPCC and Levitus (2012) yielding -1.10 to -3.36 W m-2.
Thus, even assuming that the fraction of the global average radiative forcing change from 1750 to 1955 has already equilibrated through increasing surface temperatures, the global average radiative imbalance, GAARI, is significantly less than the sum of the global average radiative forcings and feedbacks – GAARF + GAARFB (the use of 1950 and 1955 as a time period should not introduce much added uncertainty).
Also, since there has been little if any temperature increase for a decade or more (nor, apparently little if any recent water vapor increase; Vonder Haar et al. 2012), the disparity between the imbalance and the forcings and feedbacks is even more stark. While including the uncertainty around each of the best estimates of the radiative forcings and feedbacks, and of the radiative imbalance, could still result in a claim that they are not out of agreement, the lack of proper closure of equation (1) in terms of the mean values that are available needs further explanation.
Thus as the next step, the uncertainties in each of the estimates needs to be defined for each of the values in equation (2). The estimates need to be made for the current time (2014). The recognition and explanation for this apparent discrepancy between observed global warming and the radiative forcings and feedbacks needs a higher level of attention than was given in the 2013 IPCC report.
In order to aid in the analyses of equation (2), the combined effects of the radiative forcings and feedbacks over specified time periods (e.g., decades) could be estimated by running the climate models with a set of realizations with and without specific radiative forcings (e.g., CO2). One could also do assessments of each vertical profile in a global model at snapshots in time with the added forcings since the last snapshot to estimate the radiative forcing change.
JC note: This post was submitted to me via email. I also refer you to my recent post Ocean heat content uncertainties. As with all guest posts, please keep your comments relevant and civil.