I used RRTM LW (the model Trenberth uses) to calculate the effects of increasing CO2 on downwelling longwave radiation, due to the greenhouse effect.
As you can see, the effect of increasing CO2 is minuscule.
Even in the mid-latitude winter, going above 400 PPM has very little effect
By contrast, the effect of water vapor is large, and accounts for almost all of the greenhouse effect.
Increasing CO2 has very little effect on the climate, as we have seen over the past 18 years. Trenberth knows this – this is the same model he uses for his weather and climate models.