Why would El Niño affect atmospheric CO2 measurements? Starting with this article in Gizmodo: 
El Niño Has Pushed Our Planet Past a Major Climate Milestone and then to this commentary in Nature Climate Change El Niño and a record CO2 rise there seems to be some connection.
I'm pretty sure that El Niño does not directly produce CO2! Can someone help me understand the discussion of the relationship from a physics perspective? Did El Niño affect the measured values of atmospheric CO2? Did it result in CO2 redistribution, or aid CO2 production in some way? My understanding is that El Niño is an unusual change in temperature distribution and wind direction.
I'm not looking for individual opinions or theories, I'd like an explanation of the concepts presented in those two links, from a physics perspective. Thanks!
Images from NOAA via the Gizmodo article:


 A: The article and comment you refer to are not talking about physics. They are talking about the interpretation of CO2 etc measurements according to a belief in the model of "global warming is caused by CO2".
After retirement, I spent  two years researching the subject and looking into the programming assumptions. I entered interested and not doubting the premises and then, when going into the details of theory and programming I became convinced that the subject has little to do with physics, a lot to do with programming assumptions, and particularly with the belief that correlation means causation: i.e. little to do with the physics of the chaotic system that is weather and in long time climate.  I even gave lectures on this at my former institute. Then I got bored. 
Even the plot that you are showing of CO2 rising shows little effect of El Nino on the rise.  CO2 affects temperature, but also higher temperatures in the oceans releases more CO2, so there is a correlation of the CO2 plot to temperature, partially seen also in the annual fluctuations around the average
Here is the anomaly ( difference from a standard) of global temperature

In 1998 there was a big el Nino, no strong effect on the curve of CO2 is seen.
The argument that the last time CO2 had reached 400ppm  in earth history the sea levels were 80 feet higher is spurious. If there were direct causation why are the seas so low now? One should keep in mind when reading warming literature : correlation is not causation.

I'm not looking for individual opinions or theories, I'd like an explanation of the concepts presented in those two links, from a physics perspective. 

The CO2 figure itself tells us that there is little  correlation between the 1998 el Nino and little correlation to the current one as the curve follows its extrapolation in rising. It just happened to reach 400ppm when the el Nino was strong. There is no physics presented in the links.
A: As the author of the Gizmondo article you cited explains,

[...] scientists believe that emissions spiked due to a combination of warming and drying in the tropics, which can accelerate soil carbon decomposition, and large, drought-fueled fires. 

Here you can find an equivalent explanation:

The atmospheric carbon dioxide concentration is rising year-on-year due to human emissions, but this year it is getting an extra boost due to the recent El Niño event - changes in the sea-surface temperature of the tropical Pacific Ocean. This warms and dries tropical ecosystems, reducing their uptake of carbon, and exacerbating forest fires. Since human emissions are now 25 per cent greater than in the last big El Niño in 1997/98, this all adds up to a record CO2 rise this year.

Here they give the same explanation and also explain how the influence of El Niño on the increase in CO$_2$ concentration was predicted using numerical models:

[...] carbon dioxide levels have seen a surge in recent months as a result of the El Niño climate phenomenon, which has warmed and dried the
  tropics. These conditions not only limit the ability of forests to
  draw down CO2 from the atmosphere but also trigger huge fires around
  the globe that inject extra carbon into the air.
[...]The scientists used a seasonal climate model to predict sea-surface
  temperatures in the Eastern Pacific - where the El Niño shows itself
  most obviously - and then linked these to a statistical relationship
  with CO2 to generate a picture of what levels would probably look like
  across the calendar year. This gives an average for 2016 of 404.45,
  with a September low of 401.48 (again with errors of plus or minus
  0.53ppm). The team has already had success in forecasting the 2016 high, recorded in May, of 407.7ppm. The group had predicted 407.57.
  "It's important to note that this year's rise in CO2 is bigger than
  the last El Niño, in 1997/8, because human emissions have gone up by
  25% since then. So, it's the natural effect on top of the increasing
  human effect," said Prof Betts.

Basically, the role of the tropical forest is fundamental in the carbon cycle. Plants remove carbon from the atmosphere through photosyntesis and store it in the biosphere. 
El Niño causes a rise in the temperature of the eastern Pacific Ocean, thus causing a warming and drying of the tropical rainforest. This accelerates carbon decomposition and favors forest fires, decreasing the carbon-storing capacity of the tropical biosphere. The fires are particularly bad because they destroy the biosphere while at the same time producing high quantities of CO$_2$.
