by Roger A. Pielke Sr., Richard T. McNider, and John Christy
Original link: http://judithcurry.com/2014/04/28/an-alternative-metric-to-assess-global-warming/
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.
Introduction
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.
