# What Does A Global Average 2 Degrees C Increase Mean With Respect To Upper Ocean Heat Content Change? Part II

As was discussed in Part I (see), there are major biases and uncertainties with using a global average surface temperature, T’, to monitor and predict global warming.  This weblog explores ways to relate upper ocean heat content change to a temperature trend.

We could, perhaps, obtain T’ from the upper ocean heat data reported by Jim Hansen (see), where he wrote

“The Willis et al. measured heat storage of 0.62 W/m2 refers to the decadal mean for the upper 750 m of the ocean. Our simulated 1993-2003 heat storage rate was 0.6 W/m2 in the upper 750 m of the ocean. The decadal mean planetary energy imbalance, 0.75 W/m2, includes heat storage in the deeper ocean and energy used to melt ice and warm the air and land. 0.85 W/m2 is the imbalance at the end of the decade.”

The 0.62 W/m2 corresponds to 1.01 x 10**23 Joules per decade.  This rate is close to that seen in the analysis of Levitus et al (2009) [see]. As discussed on my weblog (see), this rate has not persisted since 2003, however, the value of 1.01 x 10**23 Joules per decade can be used to estimate how long different depths of the upper ocean would require at this rate to warm to a uniform temperature of 2C. While, the upper ocean does not warm uniformly in the vertical, a uniform value provides an estimate for the time required a layer of the ocean to warm to 2C at this rate [which is about 200 years].

In order to examine this issue, I contacted Josh Willis, and he graciously interacted via e-mail on this subject (I summarized my e-mails into a set questions). Below are his comments (presented with his permission):

Topic 1: What if the 2C warming was specified to be uniform to 700m (which is the depth Jim Hansen refers to in the above comment)?  [according to Josh, to warm the upper 700m of the ocean uniformly to 2C would require 2.036**24 Joules]

“The problem I see [this] calculation is that it assumes that there is a uniform 2C warming over the entire upper 700 m of the water column.  This does not happen.  Rather, in the global average the heat mixes downward slowly from the surface over time.  As a result, the surface usually warms much faster than at depth.  So a 2C warming at the surface is unlikely to happen at the same time as a 2C warming at 700m.  Furthermore, the decrease of temperature with depth is unlikely to be linear.  Levitus has noted in past papers that most of the heat content increase is actually contained in the upper 300 m, for instance.

Using the most recent analysis from Levitus, the highest rate of ocean warming over the past 50 years occurse near the surface and is about 0.4C. During this time, upper ocean heat content rose by about 1 x 10**23 J. Assuming the relationship between surface warming and ocean heat content holds over longer time scales (i.e., that the ocean continues to mix heat down at a similar rate as it has in the past), then it would take only 5 x 10^23 J of ocean heat content increase to get 2C warming at the surface”

Topc 2: What is the depth we should use to estimate an upper ocean T’? Should this be the layer down to the thermocline? Clearly, it should not just be the sea surface value of T’, since the layers of the ocean that are close to the surface interact at short time scales with the atmopshere through latent and sensible turbulent heat fluxes

“Understanding the vertical distribution of heat is still a bit tricky, I guess.  The global mean temperature of the ocean drops from about 18C at the surface to 4C at 1000 m.  By 200m, it is about 12C, by 300 m, it is about 10C and by 500 m, it is close to 7C.  So in the globally averaged sense, the thermocline is not all that sharp.  Of course, the depth of the  varies strongly with latitude as well.

In one sense, the 300m depth might work best because we actually have good historical measurements of this layer and it does seem to include most of the signal for the upper kilometer or so of ocean heat content changes on multi-decadal time scales.

Another volume of climatic relevance, however, would be the depth of the mixed layer, something like 60 m in the global average.

My Conclusion

The use of Joules by itself is all that is needed to quantify global warming and cooling. However, if the policymakers insist on the use of a T’, this temperature can be improved over what is used now.

By determining the layer of the ocean that interacts with the atmosphere on relatively short time periods (e.g. several years), than the T’ of this layer could be used to communicate the magnitude of global warming to policymakers. The oceanographic community should recommend the depth of the ocean to compute the most appropriate value of T’, as well as compute this value of T’, and disseminate this information to the climate science community, policymakers and the public.

Since such a value of T’ is a mass weighted average, it is a more robust method than using just a T” diagnosed from the surface temperature of the ocean. The oceanographic community should propose a method to do this, and the climate modeling community should adopt it as one of their metrics.

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