[This is an important essay, so I’m going to make it a top post at WUWT for a day. New stories will appear below this one. -Anthony]

Guest Post by Bob Tisdale

OVERVIEW

I recently presented the modeled energy imbalance at the top of the atmosphere (TOA) in the post No Consensus: Earth’s Top of Atmosphere Energy Imbalance in CMIP5-Archived (IPCC AR5) Climate Models. As you’ll recall, there was a very wide spread in the individual model simulations of the TOA energy imbalance. (See Figure 13 from that post.) I’ve shortened the timeframe to 1955-2014 in Figure 1, which is the period for which ocean heat content data are available from the NODC.

Figure 1

Ponder that graph for a moment. The average TOA energy imbalance (red curve) in recent years is in the expected range…the range we’ve been told by the climate science community. Example: According to Trenberth et al. (2014) Earth’s Energy Imbalance:

All estimates (OHC and TOA) show that over the past decade the energy imbalance ranges between about 0.5 and 1 Wm-2.

Trenberth et al. (2014) must not have been referring to the individual climate models, because they show a much larger range. In fact, some of the models show relatively high positive TOA energy imbalances, in the neighborhood of +2 to +3 watts/m^2, while others show negative energy imbalances, roughly -3 to -2 watts/m^2.

The simulated oceans in the models with the high positive TOA energy imbalances have to be accumulating heat at relatively fast rates. On the other hand, the simulated oceans in the models with the negative TOA energy imbalances have to be losing heat very quickly. Yes, losing heat.

In this first look, we’re going to calculate and illustrate the ocean heat accumulation from 1955 to 2014 based on the climate-model-simulated TOA energy imbalances for all of the models included in the earlier energy imbalance post. We’ll start with the full oceans compared to data for the top 2000 meters, and we’ll then compare models and data for the top 700 meters.

INTRODUCTION

Because the oceans to depth have a tremendous capacity to store heat, they are supposed to be storing about 93% of the excess heat created by the emissions of manmade greenhouse gases. See Figure 2.

Figure 2

The pie chart in Figure 2 is based on the Earth’s total energy change inventory from Box 3.1 of Chapter 3 – Observations: Oceans of the IPCC’s 5th Assessment Report. There they write:

Ocean warming dominates the total energy change inventory, accounting for roughly 93% on average from 1971 to 2010 (high confidence). The upper ocean (0-700 m) accounts for about 64% of the total energy change inventory. Melting ice (including Arctic sea ice, ice sheets and glaciers) accounts for 3% of the total, and warming of the continents 3%. Warming of the atmosphere makes up the remaining 1%.

WE CAN USE THE MODELED ENERGY IMBALANCE AT THE TOP OF THE ATMOSPHERE TO DETERMINE HOW MUCH HEAT THE OCEANS SHOULD BE ACCUMULATING, ACCORDING TO THE MODELS

The ocean heat content outputs of the climate models stored in the Climate Model Intercomparison Project Phase 5 (CMIP5) archive are not available in easy-to-use form at the KNMI Climate Explorer. In fact, I know of no place where ocean heat content outputs are easy to access for any of the CMIP5-based models.

Fortunately, the components of the modeled Energy Imbalance at the Top of the Atmosphere (TOA) are available. So we can determine the energy imbalance, and, in turn, how much heat the oceans should be storing, according to the models.

As you’ll recall from No Consensus: Earth’s Top of Atmosphere Energy Imbalance in CMIP5-Archived (IPCC AR5) Climate Models, the energy imbalance at the top of the atmosphere is made up of 3 components (nomenclature and acronym used at the KNMI Climate Explorer are shown in parentheses):

the amount of sunlight reaching the top of the atmosphere (TOA Incident Shortwave Radiation, rsdt), the sunlight being relected back to space primarily by clouds and volcanic aerosols (TOA Outgoing Shortwave Radiation, rsut), and the infrared radiation being emitted by Earth relative to the top of the atmosphere (TOA Outgoing Longwave Radiation, rlut).

The top of the atmosphere energy imbalance is calculated by subtracting the Outgoing Shortwave and Longwave Radiation from Incident Shortwave Radiation.

Figure 3 presents the average TOA energy imbalance of the climate models stored in the CMIP5 archive, specifically the multi-model mean of the models using historic and RCP6.0 forcings. We’re discussing the multi-model mean now for simplicity sake…for those new to the topic. The 1955 to 2014 timeframe relates to the NODC’s ocean heat content data for the depths 0-2000 meters (about 6600 feet or about 1.25 miles).

Figure 3

The large dips and rebounds are caused by the aerosols emitted into the stratosphere by explosive volcanic eruptions.

Each year that the energy imbalance is positive, the oceans gain heat, and each year the TOA energy imbalance is negative, the oceans lose heat. The energy imbalance is positive most of the time, so the modeled oceans should be warming to depth, according to the model mean.

Note: You’ll notice in the title block of Figure 3 that I excluded three models: CESM-CAM5 and two IPSL models. There were shifts at 2006 in the TOA Outgoing Longwave Radiation outputs of all three runs of the CESM-CAM5 model (one with a monstrous shift), which skewed the multi-model mean of that metric for that scenario. (I notified KNMI of that problem, and NCAR has since corrected them. I’ve continued to exclude them so that the models in this post are the same in the TOA energy imbalance post.) I also excluded the two IPSL models because their TOA Incident Shortwave Radiation contains a volcanic aerosol component, while all other models do not. (The other models address volcanic aerosols with the Outgoing Shortwave Radiation.)

That leaves 21 models, including BCC-CSM1-1, BCC-CSM1-1-M, CCSM4 (6 runs), CSIRO-MK3-6-0 (10 runs), FIO-ESM (3 runs), GFDL-CM3, GFDL-ESM2G, GISS-E2-H p1, GISS-E2-H p2, GISS-E2-H p3, GISS-E2-R p1, GISS-E2-R p2, GISS-E2-R p3, HadGEM2-AO, HadGEM2-ES (3 runs), MIROC5 (3 runs), MIROC-ESM, MIROC-ESM-CHEM, MRI-CGCM3, NorESM1-M, and NorESM1-ME.

For those models with multiple runs, the ensemble members are averaged before being included in the multi-model mean.

[End note.]

CONVERTING FROM WATTS/M^2 TO JOULES*10^22/YEAR

We’ll need to convert the units of the modeled TOA energy imbalance (watts/m^2) to those used for ocean heat content to the depths of 2000 meters (Joules * 10^22). Gavin Schmidt presented two conversion factors (the one he originally used in his model-data comparisons at RealClimate and the corrected one) in his post OHC Model/Obs Comparison Errata.

My error was in assuming that the model output (which were in units W yr/m2) were scaled for the ocean area only, when in fact they were scaled for the entire global surface area (see fig. 2 in Hansen et al, 2005). Therefore, in converting to units of 1022 Joules for the absolute ocean heat content change, I had used a factor of 1.1 (0.7 x 5.1 x 365 x 3600 x 24 x 10-8), instead of the correct value of 1.61 (5.1 x 365 x 3600 x 24 x 10-8).

Unfortunately, Gavin didn’t present the units for those factors.

So we’ll turn to the always very helpful Willis Eschenbach, who replied to me in an email, after presenting how the conversion factor is derived:

1 watt/m2 = 1.14E22 joules/ocean/year Or to put it another way, for the ocean we can say: 1 W/m2 = 1.14E+22 joules/year added to the ocean

The 1.14*10^22 Joules/year per watt/m^2 factor is the roughly same as the 1.1 presented by Gavin Schmidt.

[Note: It turns out I didn’t need to bother Willis for the units. They were identified in Gavin’s reference: Hansen et al. (2005).]

When I first prepared the spreadsheets for this post, I used the higher of the two scaling factors used by Gavin Schmidt (1.61*10^22 Joules/year per watt/m^2) because the TOA imbalance refers to Earth’s total surface area. But then it became obvious to me that if I used the smaller scaling factor (1.14*10^22 Joules/year per watt/m^2) the trends of the model means of all of the models would align almost perfectly with the data. So on this first pass, I decided to give the models the benefit of the doubt and use the smaller of the two factors, which helps the models. But am I making the same mistake that Gavin Schmidt initially made in his model-data comparisons?

We’ll make one more adjustment to the conversion factor. We’ll assume the oceans are accumulating 93% of the TOA energy imbalance, which lowers the conversion factor to 1.06*10^22 Joules/year per watt/m^2.

MODELED ANNUAL OCEAN HEAT UPTAKE AND ACCUMULATION BASED ON THE MODEL MEAN (FULL OCEAN)

Based on that conversion factor, the annual modeled ocean heat uptake (absolute) for the full oceans that was derived from the simulated TOA energy imbalance are shown in Figure 4…again using the model mean to simplify these early discussions. Basically, Figure 4 illustrates the average of the modeled TOA energy imbalance but in terms used for ocean heat content. Every year the value is positive, the oceans gain heat, and each year the value is negative, the oceans lose heat. The difference between an annual value and zero indicates how much heat the oceans gain or lose in a given year. In other words, the graph shows the annual ocean warming and cooling rates for the global oceans.

Figure 4

But that still doesn’t allow us to directly compare the models to the data. The (much-adjusted) global ocean heat content data from the NODC for the depths of 0-2000 meters are presenting how much heat the oceans are accumulating in the top 2000 meters. To determine the modeled ocean heat accumulation, we simply take a running total (cumulative sum) of the annual heat uptake…like the balance in a bank account. See Figure 5.

Figure 5

I’ve included the NODC ocean heat content reconstruction for the top 2000 meters (zeroed at 1957) in pentadal form as a reference for the (much-adjusted) observations. (Data here.) The data have been shifted so that the 1957 value is zero. That was done solely to ease the visual comparisons. Keep in mind, before the early 2000s when the ARGO floats were deployed, the NODC ocean heat content data for the top 2000 meters are based on very few temperature and salinity measurements. Phrased differently, before the ARGO era, the NODC ocean heat content data to depths of 2000 meters are basically make-believe data.

For the sake of discussion, we’ll assume there is no heat gain below 2000 meters. It’s commonly done. That is, we’ll assume all of the excess heat is being absorbed only in the top 2000 meters. That’s consistent with the findings of Liang et al. (2015) Vertical Redistribution of Oceanic Heat Content. (See the preprint copy here.) In fact, Liang et al. found (1) the oceans below 2000 meters had cooled from 1992 to 2012 and (2) part of the heat above 2000 meters was from the redistribution of heat upwards from the depths below 2000 meters. By assuming all of the observed heat gain is in the top 2000 meters, we can then compare the data to the model outputs, the latter of which are for the full ocean, from surface to floor.

With those things considered, it might be misleadingly said that the models, as represented by the model mean, do a good job of simulating the observed warming rate of the oceans. Why misleadingly? As we’ve already shown (Figure 1), there is no agreement among the models on the energy imbalance at the top of the atmosphere, and that means there is no agreement among the models on how much heat the oceans are accumulating…if they are in fact accumulating and not losing heat in their modeled oceans.

MODELED ANNUAL OCEAN HEAT UPTAKE AND ACCUMULATION FOR ALL MODELS (FULL OCEAN)

Using the conversion factor presented earlier (1.06*10^22 Joules/year per watt/m^2), the annual heat uptake and losses (absolute) in modeled ocean heat content, for the full oceans, based on the simulated TOA energy imbalance from 1955 to 2014, are shown in Figure 6…this time for the model mean (in red) and the individual models stored in the CMIP5 archive using the historic and RCP6.0 forcings. Again, in other words, Figure 6 illustrates the modeled energy imbalance of the individual models but in the terms used for ocean heat content, which is why it looks so similar to Figure 1.

Figure 6

The simulated oceans in the models with higher absolute positive values are gaining heat faster than those whose energy imbalances are closer to zero. And the oceans in the models with the negative imbalances from 1955 to 2014 are not accumulating heat; they’re losing it.

The models with the high positive imbalances and with the negative imbalances are obvious outliers. They create incredible (but not in a good way) ocean heat content curves that should probably be considered implausible. See Figure 7. Yet they are among the models used by the IPCC for their 5th Assessment Report. Then again, if we were to eliminate models because they didn’t simulate some metric properly, there would be no climate models left in the CMIP archives.

Figure 7

Obviously, based on the energy imbalances in the climate models used by the IPCC for their 5th Assessment Report, there is no agreement on how much heat the oceans should be accumulating, or even if the oceans are accumulating heat. And the differences in the simulated ocean heat accumulation are so great that using the model mean to represent the models is very misleading, because the model mean gives the impression of a consensus when there is none.

LET’S ELIMINATE THE OUTLIERS (FULL OCEAN)

Three of the 21 models in Figure 7 are showing way too much heat accumulation, and 5 of the models show the oceans losing heat because of their negative TOA energy imbalances. They are so far from the much-adjusted observations, I’ve excluded them in Figure 8.

Figure 8

But eliminating the outliers creates other problems for the models. With the obvious outliers removed, only two of the remaining 13 models have an ocean heat content trend that’s lower than the observed trend. In other words, the vast majority of the models are showing too much warming. And that means, for most the remaining models, the climate sensitivities to CO 2 are too high.

WHAT ABOUT THE GISS MODEL E2 SIMULATIONS FROM THE CMIP5 ARCHIVE (FULL OCEAN)?

For a number of years, Gavin Schmidt (now the director of GISS) presented model-data comparisons at RealClimate that included simulated and observed ocean heat content for different depths. Gavin compared models and data for the depths of 0-700 meters in the posts that appeared in December 2009, May 2010, January 2011 and February 2012. It was only in the last post that Gavin presented the comparison for the modeled full ocean and data for 0-2000 meters. We’ll illustrate the model-data comparison for the top 700 meters in a moment, but let’s first stick with the data for the top 2000 meters and the modeled ocean heat accumulation for the full oceans.

You’ll note that the ocean heat content graphs in those RealClimate posts have been corrected per Gavin’s May 2012 post OHC Model/Obs Comparison Errata. The ocean heat content comparisons in them used the GISS models from the earlier CMIP3 archive. Gavin Schmidt closed his errata post with:

Analyses of the CMIP5 models will provide some insight here since the historical simulations have been extended to 2012 (including the last solar minimum), and have updated aerosol emissions. Watch this space.

I suspect some of you, like me, have been patiently waiting for those CMIP5-archived GISS Model E2-based model-data comparisons for ocean heat content. Yet, for more than three years, none have been posted at RealClimate.

For those interested, Figure 9 compares the data with the TOA energy imbalance-based ocean heat content for the three GISS Model E2-R simulations…along with the mean of those 3 runs. The “R” suffix letter stands for the Russell Ocean model that’s coupled to the GISS Model E.

Figure 9

This batch of GISS climate models is showing that they are too sensitive to CO 2 by a wide amount. Keep in mind, I’m using the lower of the two scaling factors.

Looking at the legends in Figures 6, 7 and 8, you’ll note that GISS also has another group of model experiments with an “H” suffix. The “H” stands for HYCOM ocean. Figure 10 includes the model-data comparison of the GISS models with the HYCOM oceans.

Figure 10

Once again, the GISS models show they are way too sensitive to CO 2 .

I’ll let you speculate about why there have been no model-data comparisons of ocean heat content at RealClimate for 3 years.

MODEL-DATA FOR 0-700 METERS

We’ll be using the annual NODC ocean heat content data (0-700m) here in the following comparisons. For the comparisons I’ve simply shifted the data so that the 1955 value is zero.

There is better sampling at the depths of 0-700 meters than at 700-2000 meters before the ARGO era, so the NODC ocean heat content data for the depths of 0-700 meters is a better dataset. While sampling at these upper depths may be better globally, they are still very poor in the southern hemisphere. With that in mind…

For these comparisons we’ll rely on the IPCC’s statement that “The upper ocean (0-700 m) accounts for about 64% of the total energy change inventory…” from the earlier quote. That is, we’re taking the lower of the two scaling factors (1.14*10^22 Joules/year per watt/m^2) and multiplying it by 0.64 to determine the annual ocean heat content uptake for the top 700 meters of the oceans from the TOA energy imbalance. The following are the pertinent graphs without commentary, because the comments would basically be the same as those for the full oceans.

Figure 11

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Figure 12

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Figure 13

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Figure 14

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Figure 15

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Figure 16

CLOSING

Let’s start with the big question: Should I have been using the larger of the two scaling factors when converting the TOA energy imbalance to the annual change in ocean heat content? See the discussion under the heading of CONVERTING FROM WATTS/M^2 TO JOULES*10^22/YEAR. If that’s the case, then all of the model-related ocean heat content information will need to be multiplied by a factor of 1.41. It would only take a few hours for me to update this post, if it’s determined that I made the same mistake that Gavin Schmidt did with his original model-data comparisons.

It’s a shame that the modeled ocean heat content of the models store in the CMIP5 archive are not available in easy-to-use form. It would be interesting to compare the actual modeled ocean heat content for the full oceans and the top 700 meters to the respective values derived from the TOA energy imbalance.

Looking at the model-mean for all of the models, the similarities in the trends of the modeled full oceans and data for 2000 meters (Figure 5) and between the trends for the models and data for the top 700 meters (Figure 11) are striking. One might believe they’re too close…as though the data are adjusted to match the models, or the models are adjusted to match the data…or both. Then again, I may have used the wrong scaling factor and there are no similarities.

The energy imbalance at the top of the atmosphere and ocean heat accumulation are crucial elements in the hypothesis of human-induced global warming. Because there is no agreement among the climate models about the energy imbalance at the top of the atmosphere (Figure 1), there can be no agreement among the climate models about the heat accumulating in the oceans (Figures 7 and 13).

With the unlikely outliers removed, or referring to the GISS Model E2-R and GISS Model E2-H simulations, the differences between the observed and modeled ocean heat accumulation indicate the models are much too sensitive to the hypothetical impacts of CO 2 .

Many of the modeled oceans in the models used by the IPCC for their 5th Assessment Report are not storing heat close to the (much-adjusted) observed rates, so those models are not simulating global warming as it exists on Earth. But there’s really nothing new about that either. We can simply add ocean heat accumulation and TOA energy imbalance to the list of things that climate models do not simulate properly: like surface temperatures, like precipitation, like polar sea ice, like polar amplification, like El Niño and La Niña processes, like the Atlantic Multidecadal Oscillation, like the Pacific Decadal Oscillation, and so on.

Once again, climate models have shown they are good for one thing and one thing only: to display how poorly they simulate Earth’s climate.

I look forward to your feedback on the scaling factors. It would only take a few hours to update this post if needed.

THANKS

Many thanks to Willis Eschenbach and Roger Pielke, Sr. for their comments on the initial (but much different) drafts of this post.

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