Table of Contents:

1. Preamble

2. Quick Summary

3. Summary

3.1 Energy balance

3.2 Evaporation

3.3 IR vs solar radiation

4. Method

4.1 Input Data

4.2 The Matching Process

5. Absorption changes from last time

Abbreviations

1. Preamble

In an earlier article, I expressed the opinion that Infra-Red radiation (IR), eg. as from Greenhouse Gases (GHGs), did not warm the ocean as effectively as the wavelengths of direct solar radiation which penetrated into the ocean (ITO): “The GHG process involves only IR, which cannot penetrate the ocean more than a fraction of a millimetre, where its energy goes mainly into evaporation. ie, the energy goes straight back into the atmosphere.” and “The ITO warms the ocean well below the surface with little direct effect on the atmosphere.”.

Some time after my last article was published, I realised that Nick Stokes’ (NS) diagram (Figure 2) provided an opportunity to test my statement. If I could reproduce the diagram from first principles – ie. reverse engineer it – then I would have the means to calculate whether IR and direct solar radiation did indeed differ in their effect, and if so by how much.

It took me a long time, but I have completed (to my satisfaction) the reverse engineering, using a notional “average” patch of ocean over one 24-hour day without upwelling. The comparisons for IR and direct solar radiation were then very simple. The results are summarised below, and then the whole process is described in more detail.

There is one important caveat. The results can only be as good as the assumptions that went into them. The ocean surface is a pretty volatile place, and everything is necessarily some kind of approximation. It is possible that changed assumptions could give significantly different results.

2. Quick Summary

· With no upwelling, nearly a third of all input radiation remains in the ocean at the end of the day. It is not all lost on the same day.

· Results do support the idea that a proportion of inward IR is immediately lost in evaporation, but the proportion comes out at about 17% rather than “mainly”.

· IR and solar radiation do differ in their ability to warm the ocean. A Watt of direct solar radiation is nearly 50% more effective at warming the ocean than a Watt of IR.

· Retained energy can build up for later upwelling, eg. with El Niño, AMO or PDO, or for transport towards the poles.

· Results suggest that from 1983-2009, cloud changes were responsible for a bit over 90% (90.6%) of global warming, man-made CO2 for less than 10% (9.4%).

My take: Changes to direct solar radiation as caused by changes in cloud cover are much more important than changes to back radiation as caused by man-made GHGs. Solar energy is always being stored in the ocean, and it is reasonable to suppose that this energy is the key to Earth’s climate, as also evidenced by the global climate (= atmospheric temperature) changes that result from warming/cooling phases of ENSO, AMO, PDO, etc. Upwelling would seem to be a (or the?) major mechanism by which the stored energy is delivered from the ocean to the atmosphere. We have to understand the ocean if we want to understand climate.

3. Summary

3.1 Energy balance

The Kiehl and Trenberth (K&T) energy balance (Figure 1) that I use for some of the input information is useful and informative, but it conceals as much information as it reveals. It shows a perfect energy balance, but it shows nothing of the different timescales involved. Looking at K&T it would be easy to suppose that the energy coming in during a day also goes out – as is shown, for example, in the diagrams that Nick Stokes presented (Figure 2).

In fact, much of the energy from solar radiation remains in the ocean at the end of the day. This is the heat which builds up and is transported poleward or is later released by an El Niño or by the AMO or PDO, etc. In the “average” patch of ocean, 168 Wm-2 of direct solar radiation and 324 Wm-2 of back radiation enter the ocean, and if there is no upwelling then 160 Wm-2 stays there – only 332 Wm-2 escapes to the atmosphere. The actual numbers may be surprising, but the concept should not be. We all know that the ocean transports heat from the tropics towards the poles, and that the ocean oscillations release heat that has built up in the ocean over a period of time. Heat cannot build up if it is not being retained in the first place. An implication is that much of the energy shown by K&T escaping from the ocean has been there for quite a long time – it does not all escape on the day it came in, it does not escape at a steady rate, and it is not released uniformly across the oceans. By implication, over short periods or even up to a few decades, atmospheric temperature may bear little or no relationship to the global temperature.

3.2 Evaporation

In the calculations, I test the possibility that some of the inward IR gets lost in evaporation by, for example, exciting water molecules at the surface so that they escape into the atmosphere. There is an obvious limit to how much can get lost in this way, because less than half of the excited molecules would go in the right direction. I don’t put any restriction on the parameterisation for this, so the reverse engineering is free to settle on any percentage.

For the balance of thermals and evaporation, I assume that the rate varies linearly with temperature. In the real world, other factors such as wind speed are important, so there is an implicit assumption that these other factors remain unchanged. Given that we are working with a notional “average” patch of ocean over a single day, that should not be an issue.

Results suggest that about 17% of the energy from inward radiation that does not get past the top 10µm goes straight into evaporation (see parameter ‘v’ in worksheet parms). This evaporation is not temperature dependent. Results also indicate that my earlier assertion that IR’s energy “goes mainly into evaporation” is incorrect : partly, yes, but “mainly”, no (Roy Spencer will be pleased, I think).

3.3 IR vs solar radiation

IR and solar radiation do indeed differ in their ability to warm the ocean. Looked at in isolation, a Watt of direct solar radiation is nearly 50% more effective at warming the ocean than a Watt of IR.

I had expected a difference, but I had thought that the ratio would be higher. The result also shows the reason for the lower ratio: the mechanism is not what I had expected. The major factor is the temperature gradient near the ocean surface – IR isn’t fully effective at slowing the flow of energy from the ocean to the atmosphere.

In the previous article, I estimated that man-made CO2 contributed only 9% or less of the global warming over the 1983-2009 period. There were some errors in that article, addressed below. The corrected figures for the 19983-2009 period are +0.65 Wm-2 for man-made CO2, and +4.5 Wm-2 for direct solar radiation (all direct solar radiation, not just ITO). The CO2 figure is much higher than before, as explained below, and the direct solar figure is a bit lower. With the results from the NS reverse engineering, the man-made CO2 contribution to 1983-2009 global warming came out at about 9.4%, but the calculation has changed as described below.

If Dr. Antero Ollila is correct, then the figure for CO2 1983-2009 would be +0.38 Wm-2, not +0.65 Wm-2, giving a lower contribution (only 5.7%) from CO2.

3.4. Energy Accumulation

The results for different SSTs (see worksheet parms in spreadsheet OceanDiurnal.xlsx) are so similar, that the notion that absorbed solar energy at depth can build up over a long period is supported. [NB. Just ‘supported’, not proven. In interpretation of the figures, be aware of how they were calculated.]. The fact that ocean temperature just below the surface is higher than at depth means that the only way that energy at depth can escape to the atmosphere is by convection, ie. by mixing or by upwelling.

The ~118 Wm-2 retained from 10m to 100m depth is enough to warm that ocean band by nearly 10 deg C in a year (see the Heat content calculator in worksheet FluxDescr in spreadsheet OceanDiurnal.xlsx). Obviously the heat wouldn’t necessarily be retained for a whole year, but this shows that significant heat build-up is possible.

Note: After writing everything up, I have noticed that the ‘Thermals and evapotranspiration’, at 104 Wm-2, is higher than K&T’s 102 Wm-2. It should if anything be a bit lower, which suggests that I should have used a slightly higher SST. Maybe 19 deg C instead of the 18 deg C that I used. The results would change slightly, but the overall pattern and conclusions would remain unchanged. Percentage of inward IR lost to immediate evaporation would come down from 18% to 17%. I have changed the text above to use the lower number.

4. Method

The aim was to reproduce the Day & Night temperature profiles in the NS diagrams using the K&T energy budget figures, and using solar and absorption data as presented in the previous article.

The spreadsheet, OceanDiurnal.xlsx, models the upper ocean bands of a notional “average” patch of ocean in 20-second steps over one 24-hour day. Data for all inputs of energy is used unchanged, but data for outputs is used as a guide only with variable parameters. The parameters were then optimised to find the combination of inputs and outputs, together with the energy flows within the ocean, which matched both the Day and the Night NS temperature profiles in a single daily cycle.

It is all explained in spreadsheet OceanDiurnal.xlsx, worksheet FluxDescr, so I won’t repeat the details here. You can play with the figures in the spreadsheet, of course, but to run new optimisations you will need an external optimiser. You can verify that the result is correctly optimised by changing the ‘optimised’ parameters in worksheet parms.

4.1 Input Data

K&T data is taken from:

Figure 1. Global annual average energy budget, from here).

The data that the reverse engineering is trying to match is taken from the NS diagram:

Figure 2. The diurnal (day-night) cycle in the top few metres of the ocean. From Nick Stokes’ blog Moyhu. NB. The two panels have different scales on the x-axes (that’s not an issue at all, just be careful to see the panels correctly).

The part of the NS diagrams that I am trying to match is the top part, ie. below 1m. If you look closely at the diagrams you will see that the vertical axis is vague (“5-10m”), and that it is not accurately to scale. On a true log scale, using 10m for the last point, it looks like this:

Figure 3. Data from the NS ‘Day’ diagram. Y axis is ocean band number. “-1” is surface, 0 is to 1µm, 1 is to 10µm, then increase by a factor of 10 per band to: band 7 is to 10m. Bands 8 to 100m and 9 >100m are not covered in the NS diagrams. In the spreadsheet, band 1 is surface to 10µm.

I also use absorption data as reported on last time, but with corrections (see 5. below) and with the IR wavelengths that are missing from SORCE data estimated to match the K&T data. See spreadsheet OceanDiurnal.xlsx worksheet Absorption.

4.2 The MatchingProcess

Bands 1, 2 (10µm, 0.1mm) are very thin, and a large amount of energy goes into and out of them with very small residuals, so calculating their temperature accurately is not practical. I therefore tie bands 1 and 2 to band 3 (1mm) for optimising purposes, using temperature differences from band 3 to match the NS diagram. The adjustments needed are small, averaging a lot less than 0.01 Wm-2. I then optimise for just band 3.

The resulting match looked like this:

Figure 4. The match to NS Data obtained by the reverse engineering process.

The match at band 3 is accurate, but any attempt to match the deeper bands exactly failed because the entire profile is effectively dictated by band 3. Put simply, if energy flows more between bands – conduction radiation or mixing – then band 3 cannot get up to its daytime temperature in the NS diagram. If they flow less then the heat can’t get out fast enough at night.

5. Absorption changes from last time

This para refers to assumptions and calculations in the previous post. The changes listed here were made in the absorption spreadsheet from last time. The results as used are shown in worksheet Absorption of spreadsheet OceanDiurnal.xlsx.

Changes were:

· Previously, I effectively ignored energy entering the ocean at depths beyond 10m. This energy is undoubtedly added to the system, so this time I account for it. Note that this energy cannot be released into the atmosphere by conduction or radiation because the higher ocean layers are warmer, so it is actually likely to accumulate in the system for longer than energy from other wavelengths. The ocean thermocline is typically well below 100m, so is not an issue.

· A bad arithmetic error in a RF calculation, pointed out by commenter Donald L. Klipstein was corrected. Thanks, Donald, much appreciated.

· Error corrected: Different units were used for CO2 (Wm-2 actual) and ITO (ocean Wm-2 global equivalent).

· A more subtle logical error was corrected: Last time, I left out non-ITO wavelengths when estimating the proportions of warming from CO2 and ITO, because I argued that it’s the ITO wavelengths that drive multi-decadal global temperature. But CO2 operates via non-ITO wavelengths, so I should have included those wavelengths from the sun too, for correct comparison.

· For 1983-2009, I previously used solar and cloud data averaged over all the ocean. This time, I calculated them in 5-degree latitude bands in order to get a more accurate weighted trend 1983-2009. The end result was a slightly smaller trend in cloud effect over the period.

The latest results show that IR is not as effective, Watt for Watt, as direct solar radiation at warming the ocean. This is now taken into account, too.

One of my statements (“I use SORCE data for 2003. All years are almost identical.”) was challenged by Bob Weber (“All years are not ‘almost identical’ in solar activity …”). I do agree that over extended periods all years are not ‘almost identical’, but the years covered in the SORCE data, 2003-2016, were almost identical:

Figure 5. Composition of solar radiation by wavelength, from SORCE. 14 separate curves are plotted, for the 14 years 2003-2016. They are all almost exactly the same, apart from gaps where data is missing..

Bob also asked ‘A practical question’: “how long does it take for varying solar energy deposited at depth to resurface?”. The question goes to climate’s absolute core. The results reported here show that a lot of energy is deposited. I argue that the upwelling timescale is variable. In an earlier post, I said the time taken “could be days or months (eg, it might up-well quite quickly), it could be years (eg, waiting to be scooped up in an El Nino), it could be decades (eg, accumulating until an ocean oscillation such as the AMO or PDO brings it to the surface), or it could even be many centuries (eg, taken down into the deep ocean by the THC).”.

I will try to reply to Leif Svalgaard’s comments (eg. here, here) in a later post.

Abbreviations

AMO – Atlantic Multidecadal Oscillation

C – Celsius or Centigrade

CO2 – Carbon Dioxide

GHG – GreenHouse Gas

IR – Infra-Red radiation

ITO – Into The Ocean [Band of Wavelengths approx 200nm to 1000nm]

K&T – Kiehl and Trenberth

NS – Nick Stokes

PDO – Pacific Decadal Oscillation

RF – Radiative Forcing

SORCE – Solar Radiation and Climate Experiment

SST – Sea Surface Temperature

THC – ThermoHaline Circulation

Wm-2 or W/m² – Watts per square metre

Attachments (data and code)

· The calculations reported here are in spreadsheet OceanDiurnal.xlsx. The spreadsheet also contains a guide to the calculations, see worksheet FluxDescr.

· Spreadsheet DifferenceSummary.xlsx shows the differences referenced in 3.3 below.