Some additions to the text could be written better.

Section 3.1: where is the verb in the first part of this sentence?
“The cooling documented by satellite measurements from the microwave sounding unit (MSU) of -0.3 K between June 1991 and December 1995 after ENSO removal and reached a peak cooling of -0.5 K (Soden et al., 2002).”

Section 4.2:
I could not find a Santer (2003) in the references.
“Santer (2003) discuss a global warming of the lower stratosphere caused by the eruption of Mt Pinatubo. “

Grammar:
“The warming in the time frame of the Mt Pinatubo eruption as measured by MSU amountS to 0.75-1.5 K. “

Angell (1997) reportS the stratospheric warming due the eruption of Mt. Pinatubo based on radiosonde data. The warmest seasonal anomaly in the 100-50 hPa layer at the equator REACHED (2.0±0.8) K, where we find an ensemble mean of 1.8 K for the 5 Tg S and 5.2 K for the 10 Tg S scenario in OND 1991. The corresponding SWV increase at background levels of 4.5-5 ppmv WAS ESTIMATED TO BE 1.13-1.3 ppmv, WHICH IS CONSISTENT with our findings (Figure 7).”

L378-383
A bit too convoluted. make 2 sentences.
“The slightly higher values reported for early 1990 fall into the era of the Mt. Pinatubo eruption, however, and may be increased compared to the multi- year mean due to an amplification of the seasonal signal by the presence of the aerosol layer, an effect leading to maximum deviations of up to +/- 1.6 ppmv in the 10 Tg S scenario of the EVAens simulations.”

Section 3.6:
Please, give the error is absolute term, i.e. in K, instead of % of T
“The associated errors in average cold point temperature lie below one percent of the respective cold point temperature.”

Grammar: why this ‘found’? remove “the” before “those”. Replace “form” by “WV dependency”
““In the inner tropics the found specific humidity values agree nicely with the those from the Clausius Clapeyron equation and its approximated form of a 12 % per Kelvin. “