Here’s what I think the idea is. Ocean upwelling cools the surface by placing cooler water at the surface. It then emits less warmth to the atmosphere. Lessen this upwelling and the surface is warmer, emitting more warmth to the atmosphere. Increase this flow, with La Nina conditions and the atmosphere is cooler than it otherwise would be.
Global ocean temperatures to their full depth would be warmer with increased upwelling as cool water that receives sunlight will keep more of it when compared to warmer surface water. It evaporates less. Ocean temperatures with decreased upwelling would emit more warmth from evaporation so they would be cooler if everything else is equal.
A La Nina circulation would be vertical from the ocean depths and then horizontal along the equator. It would involve some of the coolest liquid water in the best place to warm it. We know the ocean depths have sustain with their massive thermal reserves.
The oceans have warmed as has the atmosphere. So I think this line of thought cannot explain why both have occurred at generally the same time. However if upwelling was high, the oceans would warm while slowing GMST rise. There is a saying, The hydrological cycle speeds up with warming. If this is the case, change may be limited or moderated.
Let’s now apply this to the glacial/interglacial cycle. A descent into a glacial would involve oceans cooling. Less upwelling, more emission to the atmosphere. The system slows. This cools the oceans. The oceans are less efficient at warming themselves. Compare this the efficient warming during a La Nina.
An ascent to an interglacial involves oceans warming. Upwelling increases efficiency by placing the cool water in the tropics to be warmed. As the oceans cooled during the descent their loss of energy actually increased future efficiency of warming.
JCH at Climate Etc comments with an interesting study that I quote in my reply:
“… Upwelling also varies on millennial scales. During the Roman Warm Period, Medieval Warm Period and the Current Warm Period, La Nina-like conditions with stronger trade winds dominated (Salvatteci 2014) causing above average upwelling and higher productivity. During cooler periods like the Dark Ages and Little Ice Age, the Pacific was dominated by El Nino-like conditions with less upwelling and lower productivity. …”
When it’s warm, La Ninas dominate. Warming the ocean and cooling the atmosphere more than otherwise. The oceans act as if they know not to overheat the atmosphere. When it’s cold, El Ninos dominate. Cooling the oceans and warming the atmosphere. The oceans act as if they know a too cool atmosphere isn’t good.
El Nino domination has less upwelling. There is less vertical circulation from where the upwelling occurs. As lake does in Winter in Minnesota, it is more stratified that is, less goes up to the surface. This would tend to preserve energy even though the oceans are cooling. When they are warming with La Ninas, the opposite occurs. Vertical circulation increases.
The quote says, lower productivity. With warmth comes food from the ocean depths. Without it, not so much. It is stored for when the warmth comes back. Life is sensitive to warmth. Add some warmth and there’s increased life.