IPCC covers a wide range of possible warming of the oceans from 0 – 2000 m, but don´t provide a best estimate.
This post contains relevant figures, references to the IPCC report, step by step calculations and link to a spread sheet with easy to follow calculations of:
– The deduced amount of warming
– The observed amount of warming
For the oceans from 0 – 2000 m for the period from 2005 – 2015.
Introduction
IPCC states that 93 % of the energy – which is absorbed by the 0,01 % of CO2 added to the atmosphere by humans – has been accumulating in the oceans. Hence, to check if predictions by IPCC match the observations, we have to look for accumulation of energy in the oceans.
But first, which predictions has IPCC actually made?
IPCC are not very clear about their predictions. Therefore, I will first have to deduce necessary consequences of the theory put forward by IPCC in the fifth assessment report.
Here is a link to the spread sheet I used:
20160130 Expected vs observed ocean warming v0 public
(If you think the calculations are wrong, please tell me about the: Right assumptions, right figures or right calculations. Please also provide relevant references.)
The spread sheet should be very easy to follow. One computation in each row. With links to the source for the values I used. If you disagree with any of the choices I made, you can easily change any of the values or any of the calculations in the spread sheet.
All references to IPCC´s theory in this post refers to:
Working Group I Report “Climate Change 2013: The Physical Science Basis”.
Predictions by IPCC
Theoretical expression
This post is based on the averaged energy balance model of Schneider and Mass, referred to in the introduction to the following paper. (This was the first paper my search engine proposed. Even if the paper is about shortcomings in the average energy balance model, it seems clear that IPCC, by quantifying the feedback parameter of this kind of model, kind of endorses this kind of energy balance model.)
On the Meaning of Feedback Parameter … ( Gerhard Kramm and Ralph Dlugi 2010 )
C * dT/dt = Q – ( lambda * T )
We can rewrite this as:
dT = (( Q – ( lambda * T ) ) * dt ) / C
As IPCC use alpha rather than lambda this becomes:
dT = (( Q – ( alpha * T ) ) * dt ) / C
dT: Temperature increment over time period increment dt: ( 2005 – 2015 )
Q: Anthropogenic radiative forcing in 2011: ( 2,3 W / m2 )
alpha: deduced IPCC feedback parameter (termed alpha): ( 1,9 W / m2*K )
T surface: Surface temperature in 2011 minus temperature in 1750: ( 0,85 K )
C: Heat capacity of the material receiving the energy
As the 10 years from 2005 to 2015 is a relative short period, Q (anthropogenic radiative forcing) and T (Temperature increase since 1750), will here be assumed to be independent of time t in that period. Hence, the equation can be solved quite easily.
The next thing we have to consider is that this is an analysis of the temperature increase in the oceans from 0 – 2000 m water depth. Hence we need to know the fraction of the energy which is supposed to go into the oceans from 0 – 2000 m (R oceans 2000). And the heat capacity of the oceans from 0 – 2000 m. (C oceans 2000).
Hence, the final expression becomes:
dT = (( Q – ( alpha * T ) ) * dt ) * R oceans 2000 / C oceans 2000
R oceans 2000:
Relative amount of accumulated energy going into the oceans from 0 – 2000 m
C oceans 2000:
Heat capacity of the oceans from 0 – 2000 m
That is the expression I use to deduce from the IPCC report the amount of warming of the oceans from 0 – 2000 m in the period from 2005 to 2015.
Q W/m2 ; Anthropogenic radiative forcing;
IPCC made the following statements in the contributions from Working Group I to the Assessment Report 5 by IPCC:
Radiative Forcing and Equilibrium Radiative Forcing are used to quantify the change in the Earth’s energy balance that occurs as a result of an externally imposed change. They are expressed in watts per square metre (W m–2). … The Equilibrium Radiative Forcing concept defined in AR5 allows rapid adjustments to perturbations, for all variables except for Global Mean Surface Temperature or ocean temperature and sea ice cover.
Ref.: Box TS.2  Radiative Forcing and Effective Radiative Forcing
And:
 The total anthropogenic Radiative Forcing for 2011 relative to 1750 is
2.29 [1.13 to 3.33] W m−2Ref.: Summary for policymakers; C. Drivers of Climate Change
In this post I will use the central estimate 2,29 W/m2 for anthropogenic radiative forcing in 2011 relative to 1750.
alpha W/m2*K ; Feedback parameter
Regarding the feedback parameter the first thing to note is the following quote:
No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies.
Page 16
However (on a preliminary basis and not claimed by IPCC but deduced from the IPCC report), – the following diagram can be used to estimate a value for the climate feedback parameter which matched the central estimate for anthropogenic forcing and observed ocean warming.
TFE.4, Figure 1  The Earth’s energy budget from 1970 through 2011.
(a) The cumulative energy inflow into the Earth system from changes in wellmixed and shortlived greenhouse gases, solar forcing, tropospheric aerosol forcing, volcanic forcing and changes in surface albedo due to land use change (all relative to 1860–1879) are shown by the coloured lines; these contributions are added to give the total energy inflow (black; contributions from black carbon on snow and contrails as well as contrailinduced cirrus are included but not shown separately).
(b) The cumulative total energy inflow from (a, black) is balanced by the sum of the energy uptake of the Earth system (blue; energy absorbed in warming the ocean, the atmosphere and the land, as well as in the melting of ice) and an increase in outgoing radiation inferred from changes in the global mean surface temperature. The sum of these two terms is given for a climate feedback parameter of 2.47, 1.23 and 0.82 W m–2 °C–1, corresponding to an equilibrium climate sensitivity of 1.5°C, 3.0°C and 4.5°C, respectively; 1.5°C to 4.5°C is assessed to be the likely range of equilibrium climate sensitivity. The energy budget would be closed for a particular value of if the corresponding line coincided with the total energy inflow. For clarity, all uncertainties (shading) shown are likely ranges. {Box 12.2; Box 13.1, Figure 1}
The black line in figure B seems to match a value for the climate feedback parameter equal to 1,85 W/m2*K. I will use this value on a preliminary basis.
2,47 W / m2 * K corresponds to a equilibrium climate sensitivity of 1,5 K
1,23 W / m2 * K corresponds to a equilibrium climate sensitivity of 3,0 K
I deduce that:
1,85 W / m2 * K corresponds to a equilibrium climate sensitivity of 2,3 K
T surface K:
Surface temperature in 2011 compared to 1750:
Finally an easy one:
 The globally averaged combined land and ocean surface temperature data as calculated by a linear trend, show a warming of 0.85 [0.65 to 1.06] °C3, over the period 1880 to 2012
Page 5
Hence I will use 0,85 K as a value for the temperature increase from 1750 to 2011. I assume that for all practical purposes, 1880 can be regarded as preindustrial preindustrial just as well as 1750.
R oceans 2000:
Relative amount of energy expected to go into the oceans
The following gives a clear indication about where IPCC expects that energy to go.
Ocean warming dominates that total heating rate, with full ocean depth warming accounting for about 93% (high confidence), and warming of the upper (0 to 700 m) ocean accounting for about 64%. Melting ice (including Arctic sea ice, ice sheets and glaciers) and warming of the continents each account for 3% of the total. Warming of the atmosphere makes up the remaining 1%.
Ref.: Page 39 ; TS.2.3 Changes in Energy Budget and Heat Content
The majority of energy is supposed to go into the oceans. Hence, we have to look into the oceans to compare the predictions with observations.
Regarding the energy budget in the oceans – we find the following statements by IPCC:
Warming of the ocean between 700 and 2000 m likely contributed about 30% of the total increase in global ocean heat content (0 to 2000 m) between 1957 and 2009.
Ref.: Page 257 ; Oceans; Executive summary; Temperature and Heat Content Changes
30 % of 93% = 27,9% ; 27,9 % of the warming went into the oceans between 700 m and 2000 m.
64 % + 27,9 % = 91,9
Hence IPCC reported that 91,9 % of the energy went into the oceans between 0 m and 2000 m in the period between 1957 and 2009.
Further, IPCC did not report any warming of the oceans between 2000m and 3000m:
It is likely that the ocean warmed between 700 and 2000 m from 1957 to 2009, based on 5year averages. It is likely that the ocean warmed from 3000 m to the bottom from 1992 to 2005, while no significant trends in global average temperature were observed between 2000 and 3000 m depth during this period.
This implies that IPCC expects that:
– 93% of the energy captured by the CO2 humans have added to the atmosphere is accumulated in the oceans
– 91,9 % of the energy captured by the CO2 humans have added to the atmosphere is accumulated in the oceans between 0 m and 2000 m depth.
The above gives us a pretty good idea about where to look for warming. (It should be noted however, that for future warming, the following might be a better estimate for where IPCC expects to see warming.
For RCP4.5 by the end of the 21st century, half of the energy taken up by the ocean is in the uppermost 700 m, and 85% is in the uppermost 2000 m.
Page 93; TS.5.5.6 Projected Longterm Changes in the Ocean
Anyhow, from the statements above, I deduce that IPCC expects that roughly 91,9 % of the energy, captured by the 0,01 % CO2 humans have added to the atmosphere, was accumulated in the oceans between 0 m and 2000 m, in the period between 2005 and 2015.
C oceans 2000 J/kg*K
Heat capacity of the oceans from 0 – 2000m
In addition to the figures presented above, we also need the volume fractions of the ocean layers for 0 – 2000 m. Fortunately I found the relevant information in a post by Bob Tisdale at Watts Up With That:
Then on the last page of the NOAA presentation here, under the heading of “ARGO Future Possibilities”, they have the bullet point:
52% of ocean volume below 2000 m
That obviously means that about 48% of the ocean volume is above 2000 meters.
Estimate by Bob Tisdale; Rough Estimate of the Annual Changes in Ocean Temperatures from 700 to 2000 Meters Based on NODC Data
Now I know almost everything I need, to deduce necessary consequences of the theory put forward by IPCC. The rest of the values are found quite easily. See links in the table below.
Deduced amount of warming 0 – 2000 m
Based on statements by IPCC, the information above and additional information linked to in the table below, I can now calculate the expected amount of warming of the oceans from 0 – 2000 m:
02000 m 

Units 
Deduced central estimate 

IPCC estimate of total anthropogenic Radiative forcing in 2011 relative to 1750.
Ref. IPCC Summary for policy makers C. Drivers of Climate Change. «The total anthropogenic RF for 2011 relative to 1750 is 2.29 [1.13 to 3.33] W m−2» 
W / m2 
2,3E+00 
Feed back parameter
Deduced from TFE.4, Figure 1  The Earth’s energy budget from 1970 through 2011 
W / m2*K 
1,9E+00 
Temperature increase since 1750
Ref IPCC AR5; WGI; Page 5 
K 
9,0E−01 
Outgoing radiation  W / m2 
1,7E+00 
IPCC – Current system heat uptake rate  W / m2 
6,3E−01 
Global surface area 510,072,200 km^{2}  m2 
5,1E+14 
Deduced IPCC estimate of total anthropogenic radiative forcing  W 
3,2E+14 
Fraction of energy going into the relevant part of the oceans
«Ocean warming dominates the global energy change inventory. Warming of the ocean accounts for about 93% of the increase in the Earth’s energy inventory between 1971 and 2010 (high confidence), with warming of the upper (0 to 700 m) ocean accounting for about 64% of the total. Warming of the ocean between 700 and 2000 m likely contributed about 30% of the total increase in global ocean heat content (0 to 2000 m) between 1957 and 2009.» Ref. IPCC; WG1;AR5; Oceans; executive summary; Temperature and Heat Content Changes 
Fraction 
9,2E−01 
Deduced IPCC estimate of amount of energy going into the relevant part of the oceans  W 
2,9E+14 
Deduced IPCC estimate of amount of energy going into the relevant part of the oceans per second  J / s 
2,9E+14 
Number of seconds per year  s 
3,2E+07 
Deduced IPCC estimated for amount of energy going into the relevant part of the oceans  J / 1year 
9,2E+21 
Deduced IPCC estimate for amount of energy going into the relevant part of the oceans  J / 10year 
9,2E+22 
Mass of all the oceans 1,4 E18 metric tons  kg 
1,4E+21 
Relevant part / all oceans
52% of ocean volume below 2000 m That obviously means that about 48% of the ocean volume is above 2000 meters. 
Fraction 
4,8E−01 
Specific heat capacity for water  J / kg*K 
4,0E+03 
Heat capacity for the relevant part of the oceans  J / K 
2,7E+24 
Deduced IPCC estimate for average warming of the relevant part of the oceans.  K / year 
3,5E−03 
Deduced IPCC estimate for average warming of the relevant part of the oceans.  K / 10year 
3,5E−02 
By the premises, deductions and calculations presented above the upper 2000m of the oceans should have warmed by 0,035 K the 10 years from 2005 to 2015, in accordance with the climate theory by IPCC.
Note: 20160208
It turns out that my estimate (0.63 W/m² ) for Current system heat uptake rate, which I based on IPCC figures, is corroborated by an estimate I just found in Wikipedia:
Earth’s energy budget
“Earth’s energy imbalance
If the incoming energy flux is not equal to the outgoing thermal radiation, the result is an energy imbalance, resulting in net heat added to or lost by the planet (if the incoming flux is larger or smaller than the outgoing). Earth’s energy imbalance measurements provided by Argo floats detected accumulation of ocean heat content (OHC). The estimated imbalance was measured during a deep solar minimum of 20052010 at 0.58 ± 0.15 W/m².[11] Later research estimated the surface energy imbalance to be 0.60 ± 0.17 W/m².[12] ”
This seems to support the method I used to estimate the current (2011) “energy imbalance” (However, there might still be correlated errors between these estimates, like e.g. from reported ocean temperatures).
Observed warming of the oceans
One place to find historical records over ocean temperature is in the KNMI climate explorer – where time series for “ocean mean temperatures” can be found.
(I will, for now, disregard the adjustments of the ocean records. I will also have to disregard uncertainty estimates – as decent uncertainty estimates, in accordance with the international standards for expression of uncertainty, are hard to get by.)
Please note that the only reason why I focus on the last 10 years in this post, is that the ARGO buoys have only provided temperature measurements of the oceans down to 2000 m depth in the oceans for about so long. Thats the most reliable historical record we have for the oceans.
The following curve is generated by the KNMI climate explorer by selecting: Ocean mean temperature; 02000 m; 2005 – 2015 and 12 months low pass filter:
For 0 – 2000m I find the following:
(Click the figure to enlarge)
From that figure we can simply take the difference between the first point in the time series and last point in the time series.
I would say the observed warming 0 – 2000 m is pretty close to 0, 045 K.
Comparison of expected temperature with observed observed temperature.
Now the exiting part begins. It is time to compare the predictions with observations.
In terms of temperature:
For 0 – 2000 m ocean depth, from 2005 – 2015;
The temperature increase deduced from the theory put forward by IPCC is: 0,035 K;
(for the central estimate for radiative forcing in 2011: 2,3 W / m2,
an temperature increase in 2011 compared to preindustrial times of: 0,85 K,
and a (deduced) central estimate for the feedback parameter: 1,9 W / m2*K,
corresponding to an equilibrium climate sensitivity of: 2,3 K,
for a doubling of the CO2 content in the atmosphere
(From a preindustrial level of 280 ppm to 560 ppm, the level in 2011 was about 390 ppm))
A temperature increase of 0,045 K is reported for the period from 2005 – 2015.
I would say that the estimate is spot on.
Maybe we should leave it at that then – conclude that the climate theory put forward by IPCC is spot on! Don´t we now have all the evidence we need to concluded that the climate theory put forward by IPCC has been proven right? What more could we possibly want from a theory? The reported observations fits perfectly with the theory thats it isn´t it?
When the reported observations fits perfectly with the theory, the theory must be right and proven don´t you think? How can anyone reasonably doubt that IPCC has provided a theory now proven to be right – a theory corroborated by observations?
I am sorry to be skeptic once again, in particular since I was dead wrong in my previous post, where I tried to compare reported observations of ocean warming with the theory.
Anyhow, before I conclude that the theory put forward by IPCC has been proven right, before I conclude that the theory has been corroborated by reported ocean warming, I would like to check a few more things.
Check
The first thing I would like to note is that:
Even if the little model I used seems to fit the observations perfectly, we should not forget that what I really did was to calibrate and adjust the model by adjusting the parameters of this model so that the output matched the reported warming!
Say what? I didn´t adjust anything did I?
Well – actually I did. I adjusted the parameters of a model so that it provided an output that matched the observations.
How could that possibly be?
Let me explain – First of all we have to recall the following quote from the IPCC report:
No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies.
Page 16
What does equilibrium climate climate sensitivity have to do with this at all?
Well – equilibrium climate sensitivity is closely related to the climate feedback parameter.
Let me explain. Remember what I did – when I selected “alpha” – the climate feed back parameter? Remember how I deduced the climate feedback parameter from TFE.4 Figure1:
TFE.4, Figure 1  The Earth’s energy budget from 1970 through 2011.
(b) The cumulative total energy inflow from (a, black) is balanced by the sum of the energy uptake of the Earth system (blue; energy absorbed in warming the ocean, the atmosphere and the land, as well as in the melting of ice) and an increase in outgoing radiation inferred from changes in the global mean surface temperature. The sum of these two terms is given for a climate feedback parameter of 2.47, 1.23 and 0.82 W m–2 °C–1, corresponding to an equilibrium climate sensitivity of 1.5°C, 3.0°C and 4.5°C, respectively; 1.5°C to 4.5°C is assessed to be the likely range of equilibrium climate sensitivity. The energy budget would be closed for a particular value of if the corresponding line coincided with the total energy inflow. For clarity, all uncertainties (shading) shown are likely ranges. {Box 12.2; Box 13.1, Figure 1}
To summarize what is important here!
The report states that: “No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies.” The report also states that “The energy budget would be closed for a particular value of if the corresponding line coincided with the total energy inflow”. A climate feedback parameter of 2.47, 1.23 and 0.82 W m–2 °C–1, corresponding to an equilibrium climate sensitivity of 1.5°C, 3.0°C and 4.5°C, respectively; 1.5°C to 4.5°C is assessed to be the likely range of equilibrium climate sensitivity.”
Hence, the climate feedback parameter is “likely” between 2,47 and 0,82 (W m–2 °C–1) Corresponding to an equilibrium climate sensitivity of 1.5°C and 4.5°C respectively. But no best estimate for equilibrium climate sensitivity can be given.
Another way to say this is:No best estimate for the climate feedback parameter can be given, but it is likely between 2,47 and 0,82 W m–2 °C–1.
I selected a climate feedback parameter of 1,85 W m–2 °C–1 because it closed the Earth’s energy budget from 1970 through 2011 as presented in figure TFE.4, Figure 1.
I did the calibration and adjustment by looking at the value of the curves in 2011. I noted that the black curve was right in the middle of the purple curve which was generated by using a value for the climate feedback parameter alpha equal to 2,47 and the yellow curve which was made by using a value for alpha equal to 1,23. I then selected a value for alpha equal to 1,85. By doing that I calibrated and adjusted my model to match observed ocean warming as seen in 2011. From the figures it can also be seen that the values in 2011 are dominated by the years from 2000.
Hence I calibrated and adjusted my model by using data dominated by the period I subsequently checked my model against.
I used circular reasoning – the conclusion was contained in the premises.
I couldn´t miss.
Which range of ocean warming is allowed by the theory?
Now we know that the observed ocean warming is within the range of possible outcome allowed by the theory. We also know that it is possible to calibrate and adjust the model parameters so that the model matches observed warming.
I think it would be interesting to quantify the range of possible ocean warming which would be within the range of possible outcomes allowed by the theory. It will take an uncertainty analysis to do this properly. If no fundamental flaws are revealed in this post my next post might contain this uncertainty analysis.
Let us do it the easy way first.
IPCC states that the climate feedback parameter is likely between 2,47 and 0,82 (W/m2*K) IPCC also states that no best estimate can be given.
Let us see which range of ocean warming will be allowed by this range of climate feedback parameters. I will put in 2,47 and 0,82 (W/m2*K) in the model for earths globally averaged energy balance model based on Schneider and Mass. The same model I used above
For simplicity I will first use the central estimate for anthropological radiative forcing 2,3 W/m2 in 2011 provided by IPCC:
02000 m 
02000 m 

Units 
IPCC lowest estimate 
IPCC highest estimate 

IPCC estimate of total anthropogenic Radiative forcing in 2011 relative to 1750.
Ref. IPCC Summary for policy makers C. Drivers of Climate Change. «The total anthropogenic RF for 2011 relative to 1750 is 2.29 [1.13 to 3.33] W m−2» 
W / m2 
2,3E+00 
2,3E+00 
Feed back parameter
Deduced from TFE.4, Figure 1  The Earth’s energy budget from 1970 through 2011 
W / m2*K 
2,5E+00 
8,2E−01 
Deduced IPCC estimate for average warming of the relevant part of the oceans.  K / 10year 
4,3E−03 
8,7E−02 
Now we can see that: For the oceans from 0 – 2000 m. For the period from 2005 to 2015. By using only the central estimate IPCC provided for anthropological radiative forcing: 2,3 W/m2 in 2011. And, the range of climate feedback parameters from 2,5 W/m2*K to 0,82 W/m2*K provided by IPCC. The theory allows warming of the oceans anywhere in the range from 0,0043 K to 0,087 K.
Conclusion
This post is about warming of the oceans;
from 0 2000 m depth
for the period from 2005 to 2015.
The reported temperature increase based on measurements is: 0,045 K
The temperature increase deduced from the IPCC report is: 0,035 K;
based on the following figures:
central estimate for radiative forcing in 2011: 2,3 W / m2;
temperature increase in 2011 compared to preindustrial times of: 0,85 K;
deduced estimate for the feedback parameter of: 1,85 W / m2*K
which corresponds to an equilibrium climate sensitivity of: 2,3 K,
for a doubling of the CO2 content in the atmosphere
(From a preindustrial level of 280 ppm to 560 ppm)
However – the second conclusion of this post is that:
IPCC states that the climate feedback parameter is “likely” between 2,47 and 0,82 (W/m2*K). This corresponds to an equilibrium climate sensitivity of 1.5°C and 4.5°C respectively. IPCC also states that: “no best estimate for equilibrium climate sensitivity can be given because of a lack of agreement on values across assessed lines of evidence and studies”.
To deduce the range of ocean warming allowed by the theory put forward by IPCC I use the following figures:
IPCC estimate for anthropological radiative forcing:
2,3 W/m2 for 2011
And, the highest and lowest climate feedback parameters provided by IPCC:
2,5 W/m2*K and 0,82 W/m2*K
Based on these figures the theory put forward by IPCC would allow warming of the oceans anywhere in the range from 0,0043 K to 0,087 K.
As there are also other uncertainties, I will allow myself to round off the figures. The theory put forward by IPCC in the fifth assessment report would allow warming of the oceans from 0 to 2000 m between 2005 and 2015 anywhere in the range from 0 K to 0,1 K.
How can they possibly miss?
Not for nothing do we call the laws of nature ‘laws’: the more they prohibit the more they say.
Karl Popper – The logic of scientific discovery
A theory which allows everything predicts nothing.
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In this post I estimate the current system heat uptake rate based on IPCC figures to be:
IPCC – Current system heat uptake rate: W / m2 6,3E−01
It is quite amazing to observe that the cloud feedback parameter provided by IPCC is about the same magnitude as the “current system heat uptake rate.” estimated based on IPCC figures.
Figure 7.10  Cloud feedback parameters as predicted by GCMs for responses to CO2 increase including rapid adjustments. Total feedback shown at left, with centre light shaded section showing components attributable to clouds in specific height ranges (see Section 7.2.1.1), and right darkshaded panel those attributable to specific cloud property changes where available. The net feedback parameters are broken down in their longwave (LW) and shortwave (SW) components. Type attribution reported for CMIP3 does not conform exactly to the definition used in the Cloud Feedback Model Intercomparison Project (CFMIP) but is shown for comparison, with their ‘mixed’ cat egory assigned to middle cloud.
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