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Carbon Brief posted their 2019 State of the Climate Report. https://www.carbonbrief.org/state-of-the-climate-how-the-world-warmed-in-2019

Sea ice in the SH is doing relatively well too.

I'd like to see SharpPy add some of the features that BUFKT has like momentum xfer, ptyping, etc.

Yeah. That's pretty close. That's because it is. At least post WWII it is. In fact, the anthroprogenic force has been so large during this period that it accounts for nearly 100% of the net force. The IPCC considers all agents that are modulating the climate. They have to because the energy imbalance is modulated by the net affect of all energy fluxes; not just one of them. I posted a link to IPCC AR5 WGI chapter 8 above that provides a brief summary of the agents that have contributed to the modulation of Earth's energy budget. Not always. Humans either did not exist or were not capable of influencing the climate in the distant past. But here's the cool thing about the laws of physics. They stipulate that the radiative force induced by perturbations in GHGs are invariant of the actor that modulated them. In other words, GHG molecules have the exact same radiative behavior regardless of whether they are emitted by natural agents or by human agents. That's why GHGs are crucial and essential pieces of the puzzle in solving many paleoclimate mysteries like the PETM, glacial cycles, faint young Sun problem, etc.

Yeah, pretty close. Most estimates I've seen show DWIR to be about 345 W/m^2. The EEI would then be about 0.2% of that. I'm not sure how meaningful that is by itself though. Like you said...context.

This paper is not relevant to the error for the annual OHC anomaly or annual global temperature. Nor is the quoted 0.6C figure the measurement error that can be expected from an ARGO float which is said to be approximately ±0.002C for individual measurements. The 0.6C figure is the RMS error of ARGO derived hydrographic section temperature fields. These sections are computed even in lieu of being occupied by an ARGO float at each grid cell. Using the WOA (World Ocean Atlas) dimensions we can estimated 75x30 = 2250 grid cells along the cruise line of the hydrographic section used in the paper. If you were to then answer the question...what is the error of computed mean temperature of this hydrographic section then you might expect it to be 0.6/sqrt(2250) = ±0.01C using the standard error of the mean formula. In reality I suspect the actual error to be a bit different for a variety of reasons. I'm just giving you an order of magnitude estimate based on trivial statistical principals using the RMS error of the temperature field on that single hydrographic section mentioned in the publication. Note that this hydrographic section represents but an infinitesimally small part of a much larger 3D volume containing vastly many more grid cells by which to significantly reduce the error in the global mean temperature estimate if such a method were used. I do not see anything in this publication that is inconsistent with Cheng's OHC 2σ envelope. I do see that ARGO reduces the error by a factor 2 relative to the non-ARGO era. Perhaps this is why the 2σ envelope appears to be significantly reduced in later years on Cheng's graph?

Fun with math. The ocean has a mass of about 1.4e21 kg. The specific heat capacity is about 4 kj/kg. This means it would require 5.6e24 joules of energy to increase the mean temperature of the ocean by 1.0C. This would require an EEI of +1.2 W/m^2 to persist for 300 years. A smaller +0.7 W/m^2 imbalance is causing the GMST to increase by about +0.2C/decade. I doubt the relationship would be linear but you can certainly do an order of magnitude estimate on what might happen if we added 5.6 yottajoules of energy to geosphere over a 300 year period. Hint...hothouse Earth might be something worth researching. It's a good thing then that no reputable scientific work claims that climate forcing agents are known with perfect certainty nor is it claimed that anthroprogenically modulated forcing agents are the only contributors to changes in temperature. I highly recommend reading IPCC AR5 WGI chapter 8 on radiative forcings for a brief summary of the agents in play and estimates of their magnitudes and uncertainty. ENSO, clouds, and likely a bunch of stuff that you haven't even thought of are all actively researched. I think what you'll find when looking at the academic literature is that the exact opposite of arrogance is happening in climate science.

You can see in the graph that @chubbs posted that the 2σ (95%) confidence envelope is delineated by the green error bars.

Heat is the transfer of thermal energy. For the body being warmed/cooled it requires a net positive/negative flow of energy. If I am to interpret your question in precise terms then it is equivalent to asking...of the Earth Energy Imbalance (EEI) how much does the Sun contribute? The answer is effectively nothing. The reason is because total solar irradiance is not increasing. In fact, if anything it has actually been decreasing, albeit by a small amount, over the last few decades. I'm going to estimate the RF of the Sun over this period at about -0.01 W/m^2 as compared to the EEI of +0.70 W/m^2. In order of magnitude terms you might say it is 1/100th and in the opposite direction. Now if the question were...how much energy is being added by the Sun then the answer is about 240 W/m^2. This is the effective solar ingress flux near the surface. It is about 300x the EEI. Don't forget about the near surface egress fluxes though!

There are many potential sources of error including instrument bias, station moves, station sighting changes, time-of-day of observation, urban heat island effect, human element, etc. Ocean temperature datasets like ERSST and HadSST go back well into the 1800's as well. They are used as inputs into the global mean surface temperature (GMST) datasets as well. We have reconstructions of the ENSO cycle going back hundreds of years. The ENSO phase was positive (El Nino) in 1885 and into 1886. Speaking of cities and the potential for the urban heat island effect...Berkeley Earth concluded that the UHI bias was flat to even negative since 1950 during the period in which the anthroprogenic influence is most acute. Berkeley Earth shows that the GMST increased about 1.0C since 1880. Temperature proxies like those derived from ice cores, tree ring analysis, etc. can provide insights into the GMST going back millions of years.

Certainly not as accurate as today. But here's the cool thing about math. Trivially if a thermometer has an error of say 2C and there are 1000 thermometers then the error of the mean is only 2/sqrt(1000) = 0.06C. In reality it's far more complicated than that. After it is all said done surface datasets like GISTEMP publishes an error of about 0.10C before WWII and 0.05C after for the global mean temperature. The error envelope expands the further back in the 1800's you go. Berkeley Earth actually has some in depth papers on how it works and how the uncertainty is determined. Fair warning...it's thick stuff. http://berkeleyearth.org/static/papers/Methods-GIGS-1-103.pdf http://berkeleyearth.org/static/pdf/methods-paper-supplement.pdf

Using my +0.7 W/m^2 figure above and dividing by 240 W/m^2 yields = 0.7 / 240 = 0.3% of the surface budget. However, keep in mind that +0.7 W/m^2 is just the imbalance that still needs to equilibriate. The energy imbalance from the past that has caused 1.1C of warming has already equilibriated so is not included in my +0.7 W/m^2 value. This additional energy is probably in the 1.5-2.0 W/m^2 'ish range (just guessing right now). If you include that then we're probably close to 1% of the surface budget.

So to put that in perspective the change from 1985 to 2019 is about 350e21 joules (eyeballing for now). The average uptake is thus... 350e21 (OHC-joules) / (31.56e6 (seconds in year) * 34 (years)) / 510e12 (Earth area-m^2) = 0.64 W/m^2. The ocean takes up about 90% of the imbalance so we can probably estimate the average imbalance as 0.64 / 0.9 = +0.7 W/m^2. That is a pretty large imbalance and is inline with expectations of the net radiative force from all agents subtracted off from what has already equilibriated to raise the global mean temperature. Over the last 10 years this imbalance actually works out to about +1.0 W/m^2. The implication...even if GHG emissions were to cease instantly there is still a lot of warming waiting in the pipeline that needs to equilibriate.

Here's a pretty good (and lengthy) article talking about Arctic sea ice and the odds of seeing an ice-free summer. https://interactive.carbonbrief.org/when-will-the-arctic-see-its-first-ice-free-summer/ Bottom line...around 2050 is the 50/50 point especially if carbon emissions take a more middle-of-the-road trajectory being neither abated aggressively or allowed to grow unmitigated...basecially RCP 4.5.

I'm just wondering if there isn't going to be more warm sector activity out ahead of this line than is being advertised at the moment. The area I'm most interested in is eastern TX and LA as the LLJ ramps up in the overnight hours. Like @CheeselandSkies I'm certainly not sold on that, but I'm not going to eliminate that possibility just yet either.