GISS OHC Model Trends: One Question Answered, Another Uncovered

OVERVIEW

The RealClimate Ocean Heat Content hindcast/projection trend for the GISS Model-E ensemble mean is different than the value that Roger Pielke Sr. has provided based, assumedly, on the same GISS Model ensemble mean. Why?

There is another curiosity to do with the GISS Model-E ensemble mean for Ocean Heat Content. For those readers with graph digitization software or other means of reproducing data from a graph, you may wish to help confirm which model RealClimate has presented for Ocean Heat Content in their Model-Data posts. An example is shown in Figure 1. They identify the coupled model as Model-ER, but is it?

Figure 1

First let’s look at the question with an answer. Then we’ll move onto attempting to determine which Model-E (Model-ER or Model-EH) RealClimate has been presenting for Ocean Heat Content in their annual Model-Data comparison posts.

THE INCONSISTENCY

In their Updates to model-data comparisons and 2010 updates to model-data comparisons, RealClimate presented the ensemble member data and the ensemble mean of the GISS coupled Model-ER for a Global Ocean Heat Content hindcast. RealClimate then determined the linear trend of the OHC ensemble mean from 1993-2002 and projected that through 2010. Figure 2 shows the OHC model-data comparison from the January 2011 post, with some notes added by me. The trend from 1993 through 2010 is approximately 0.7*10^22 Joules per year. Figure 2 in this post is Figure 5 in On Tamino’s Post “Favorite Denier Tricks Or How To Hide The Incline”, with a new title.

Figure 2

But that RealClimate model trend of does not equal the OHC model trend Roger Pielke Sr. presented in his post Update On A Comparison Of Upper Ocean Heat Content Changes With The GISS Model Predictions. Roger Pielke Sr’s GISS Model E projection was 0.98*10^22 Joules per year and was based on the response by James Hansen, in which Hansen refers to Hansen et al (2005). [Hansen et al (2005) “Earth’s energy imbalance: Confirmation and implications”. PDF] The difference between the RealClimate trend and Hansen/Pielke Sr. trend is significant. Why is there a difference?

The trend presented in Hansen et al (2005) was 0.6 Watt years/m^2 per year. Let’s convert it to Joules per year. A quick check of Google reveals a conversion factor of 3.16*10^7 Joules per Watt year. The surface area of the global oceans is 3.61*10^8 km^2 according to Wikipedia. And, of course, there are one million square meters per square kilometer.

GISS Model-E trend in Joules =

(0.6 Watt years/m^2/year) * (3.16*10^7 Joules/Watt years) * (3.61*10^8 km^2 Global Ocean Surface Area) * (1*10^6 m^2/km^2) Or 0.68*10^22 Joules/year.

The 0.68*10^22 Joules/year trend is in line with the RealClimate value used in their Model-Data updates.

I wrote to Roger Pielke Sr. He confirmed the error and published a post within a day correcting it: 2011 Update Of The Comparison Of Upper Ocean Heat Content Changes With The GISS Model Predictions.

Since I’ve used that 0.98*10^22 Joules per year trend in a number of posts, I will go back and note the error in an update and include a link to this post.

THE SECOND QUESTION

While searching for Model-ER OHC ensemble member data online, I discovered that there is a second coupled GISS model that had been used to hindcast and project global OHC, the Model-EH, where the “H” stands for HYCOM ocean. It has a lower trend than the Model-ER, where the “R” stands for Russell ocean. Refer to Figure 3. That graph is from a 2008 presentation by Gavin Schmidt of GISS. (See page 8 of GISS ModelE: MAP Objectives and Results.) The graph also shows OHC observations from an olderversion of the NODC/Levitus et al OHC data, to which a few years of observations have been added. Notice how, with the base years of 1955-1970, the OHC data from the models bracket the older version of the NODC’s OHC data. In fact, Gavin Schmidt even notes that on the slide.

Figure 3

But the currentversion of the NODC OHC data, the version without the 1970s to early 1980s hump, runs lower than the earlier version, as shown in Figure 4. So with the base years of 1955-1970, the Model-EH ensemble mean would be more in line with the current data and the Model-ER ensemble mean would remain well above the observations after the 1980s. That doesn’t appear to agree with Figures 1 and 2, even if we were to account for the different base years.

Figure 4

I believe the OHC model presented in the annual RealClimate Model-Data posts is the Model-EH. The OHC model data in the RealClimate posts may simply have been mislabeled–a typo or a clerical error–an error that could be easily repaired at the RealClimate post by changing the title block. But if I’m correct, the GISS Model-ER and Model-EH ensemble means no longer bracket the updated version of the NODC OHC data, because of the recent flattening in OHC observations.

Readers of my posts often duplicate my graphs to assure themselves that what I’ve presented is correct. I welcome those checks. That’s why I provide links to the sources of the data. But the data presented at other blogs is not always available online in an easy-to-use format. Example: As far as I know, the GISS Model-E ensemble member data for Ocean Heat Content that RealClimate has used in its annual how-are-the-models-doing posts are not available. So if we see an inconsistency in those graphs, we can ask for the source of the data on the RealClimate thread, which I did and received no reply, or we can write an email to the author noting the inconsistency and requesting copies of the data, which I did and received no reply. When those attempts fail, we’re left to our own devices.

Many readers/bloggers have graph digitization software or they have other means to manually approximate the data illustrated in a graph. If what I’ve presented in this post interests you, please run through the process of determining whether the data presented by RealClimate is Model-EH or Model-ER data.

YOUR MISSION…

…should you decide to accept it. [My apologies to the creators of Mission: Impossible]

Step 1: Using your graph digitization software or a manual method, replicate the GISS Model-ER Ensemble Mean for Ocean Heat Content from the 2009 RealClimate post Updates to model-data comparisons. It’s the graph I’ve included as Figure 1 in this post. It runs from 1955 through 2010.

Step 2: Download the Older version of the NODC’s Global OHC data. It’s column 2 “WO” [World Ocean] in the following link:

ftp://ftp.nodc.noaa.gov/pub/data.nodc/woa/DATA_ANALYSIS/DATA/temp/basin/hc1yr-w0-700m.dat

That version of the NODC OHC data is based on Levitus et al (2005) “Warming of the world ocean, 1955–2003” (Manuscript). Refer also to NODC WARMING OF THE WORLD OCEAN: 1955-2003  webpage.

Step 3: Change the base years of both datasets (the older NODC OHC data and the GISS Model-ER ensemble mean data you’ve created) to 1955-1970.

Step 4: Plot the replicated GISS ensemble mean and the older NODC OHC data with the base years of 1955-1970. The graph should look like the Observations data and one of the Model Ensemble Mean curves in Figure 3.

You can then use an image hosting site such as TinyPic to create a link to your graph so that you can post it in a comment.

MY RESULTS

Using the x-y coordinates feature of MS Paint, I’ve approximated the annual long-term (1955-2010) ocean heat content ensemble mean from the 2009 RealClimate post. Refer to Figure 5. If you were to crosscheck between Figure 5 and Figure 1, you’d find that Figure 5 is a reasonable approximation of the ensemble mean from Figure 1.

Figure 5

We can then compare the older NODC/Levitus Global OHC data to my approximation of the Model-ER ensemble mean from the 2009 RealClimate model-data comparison, Figure 6. I’ve used the base years of 1955-1970 that Gavin Schmidt had used in his 2008 presentation. The Model-ER ensemble mean from the 2009 RealClimate post appears to mimic the Model-EH data in the Schmidt presentation, not the Model-ER data. Refer back to Figure 3.

Figure 6

APPROXIMATED MODEL-ER AND MODEL-EH DATA

I carried the analysis further and followed the same procedure to approximate the Model-ER and Model-EH data from the 2008 Gavin Schmidt presentation. Since that data is presented in Watt Years per square meter, it has to be put into terms of 10^22 Joules to agree with the NODC OHC data. I scaled the Model-EH data from the 2008 Schmidt presentation so that it coincided with the (appears-to-be-mislabeled) Model-ER data from the 2009 RealClimate post. Then I used the same scaling factor for the Model-ER data in the Schmidt presentation. And again, the base years for all of the data are 1955-1970. The results are shown in Figure 7. They mimic the model-data comparison graph from the 2008 Schmidt presentation, Figure 3.

Figure 7

BUT THAT GRAPH USES THE OLDER OBSERVATIONS

So let’s add the most currentversion of the NODC OHC data to the graph, Figure 8. I’ve used the same base years of 1955-1970 for it as well. The current OHC data is well below the Model-ER approximation from the 2008 presentation and is starting to extend below the lower Model-ER approximation from the 2009 RealClimate post. In other words, the models may no longer bracket the observations.

Figure 8

The base years used by Gavin Schmidt in the 2008 presentation are different than the base years used in the 2009 model-data comparison post at RealClimate, which are also different from the 2010 RealClimate model-data comparison. That is, every presentation of the model-data comparison so far has had different base years. Varying the base years of the models and the observations changes the appearance of how well the models match the observations. If I were to set the base years to 1993-2010, for example, the ensemble mean data would match the observations very well during that period. To prevent accusations of my having cherry picked the base years for the anomalies, I’ll use the entire term of the data (1955-2010) as the base years for the final graphs.

Figure 9 uses the base years of 1955-2010 and illustrates the ensemble means from the two versions of the GISS Model-ER and the current NODC/Levitus et al observations. As expected, the models no longer bracket the observations.

Figure 9

Let’s look at the data and trends during the ARGO era. In Figure 10, I’ve deleted all of the data from Figure 9 prior to 2003 to be consistent with past ARGO-era posts. The trend of the (blue) approximation of the Model-ER data from the RealClimate updates (0.66*10^22 Joules per year) is very close to the 0.68*10^22 Joules per year trend discussed in Hansen et al (2005). Hansen et al (2005) refer to at least one GISS paper regarding the modeling of OHC. It is Sun and Hansen (2003), “Climate simulations for 1951-2050 with a coupled atmosphere-ocean model.” (PDF) Sun and Hansen (2003) identifies HYCOM (used in the Model-EH) as one of the ocean models, but does not refer to the Russell ocean model by name, though a number of Russell papers are referenced. Referring again to Figure 10, the trend of the approximated Model-ER from the 2008 Gavin Schmidt presentation (0.83*10^22 Joules per year) is well above the trend presented by Hansen et al (2005).

Figure 10

CLOSING COMMENTS

Much of the model data presented in IPCC AR4 is available through the Monthly scenario runswebpage at the KNMI Climate Explorer. Unfortunately, Ocean Heat Content is not included. The Model-EH and Model-ER data should be available through the Program for Climate Model Diagnosis and Intercomparison (PCMDI) website, but that data is not in a format that’s easy to use.

The GISS Model-EH ensemble members and ensemble mean, not the Model-ER data, appears to be the model used in the RealClimate model-data comparisons. Is it? Without the actual model data, I don’t know.

Not discussed earlier, to add more complexity and uncertainty to the model-data comparisons, Ocean Heat Content observation data is presented for the depths of 0 to 700 meters, while the GISS models are based on depths of 0 to 750 meters.

Regardless, the Hansen et al (2005) trend of 0.6 Watt Years per year equals a trend of 0.68*10^22 Joules per year. I’ll now use that value in my ARGO-era OHC comparisons to illustrate that the flattening of the observations is causing them to diverge from the GISS model mean.