You say:
We do have empirical evidence that all the added greenhouse gases since year 2000, have not caused any warming,
because they di not add to Earth's longwave energy imbalance, no imbalance no warming!
I don’t see where your citation says that.
Observational Assessment of Changes in Earth’s Energy Imbalance Since 2000
You say:
Added greenhouse gases would in theory reduce the OLR and add to Earth's energy imbalance in the longwave spectrum,
but that did not happen.
However, one would also think that as warming occurs OLR would increase. In simplistic terms, a heated object radiates more heat than a cold one.That also seems to be what your citation is saying and that the additional OLR is a result of the greenhouse gas effect being overwhelmed by the increase in radiative response to warming. Your citation describes it this way:
the weaker (meaning weaker than ASR but higher than before)
OLR change is associated with compensation between increasing ERF from continued emission of well-mixed greenhouse gases and increased infrared cooling to space relating to the radiative response to warming.
So greenhouse gases are decreasing OLR, but as the planet warms OLR overall is increasing because the warmer planet is radiating more heat which increases OLR more than the greenhouse gases decrease it.
In your citation, the real problem is that ASR is higher than OLR. While this has been our problem for some time now, more recently decreased cloud reflectivity has made the problem worse. This has been a concern since around 2020:
Recent climate models project that a doubling of atmospheric CO2 above pre-industrial levels could cause temperatures to soar far above previous estimates. A warming earth, researchers now say, will lead to a loss of clouds, allowing more solar energy to strike the planet.
e360.yale.edu
While the decrease in clouds may be due to the existing warming itself there are a number of theories and it’s also possible that it is a combination of factors:
Decreases to our planet’s albedo caused by fewer low-lying clouds helped push temperatures to historic highs in 2023, according to new research.
eos.org
There is no doubt that if current trends continue we are in trouble. We need to figure out what is causing the decrease in clouds because if it’s something we can mitigate, we sure want to do it.
Unfortunately, the Trump administration is trying to squash the research that would give us the answers.
The citation shows clearly that the OLR increased during a time period that we know the CO2 level increased.
The concept of the greenhouse effect, is based upon the idea that the amount of energy reduced from the OLR,
would exceed the known increase in OLR from Planck radiation.
The IPCC's forcing formula directly implies this, 5.35 X ln(CO2_new/CO2_old), in a condition where the CO2 level is
raising, it cannot produce a negative number, and already includes the increase in Planck radiation.
Why the ASR is increasing is complicated, but the added greenhouse gases cannot increase the amount
of sunlight that reaches the surface, and because there is no positive longwave energy imbalance,
they are not causing any warming to feed a feedback system.
I am not sure we can say with certainty that the current trends will continue, as we do not know the potential
increase in ASR. What we do know is that the Sun's TSI, has been slightly reducing since 1958.
Judith Curry is correct, in that it is complicated, ASR is increasing while TSI is decreasing, one would think
we will quickly run out of potential ASR increase.
I am not sure we need to worry about warming, we are near the top of the range,
But we need to be VERY careful, of attempts at cooling, as a much greater potential for disaster
lies down that path. Our potential for warming may be one or two degrees C, but out potential
for cooling could be 10C or greater.
Actually the Trump administration is cutting funding to a movement, that was not looking at the cause of warming,
as they had already decided the science was settled.