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It does not help that the studies use different terminology themselves.This is a better answer, but you do create a confusion in the way you speak of "net."
Observational Assessment of Changes in Earth’s Energy Imbalance Since 2000
In this study they use,
What seems to be missing is the other side of OLR.absorbed solar radiation (ASR)
outgoing longwave radiation (OLR)
net top-of-atmosphere flux (NET)
sea-surface temperature (SST)
Earth’s radiation budget (ERB)
Earth’s Energy Imbalance, or EEI)