Dear authors,

Please include the changes suggested by the reviewer.

Best regards
V. Grewe

Dear authors,

I think all remarks from the reviewer are taken well into account. However, there is still my request from the initial submission phase, to take special care on the mathematical formulations. To my understanding PDF is the abbreviation of probability density function. Please correct that. In addition it is call density, because the percentage on the y-axis is always relative to the unit of the x-axis. E.g. Fig. 3 %/degC, and the integral over the whole range should be 100%=1. In Fig. 3a it is around 260%, if the unit for the y-axis were %/degC.

As far as I see this does not have implications on the paper, b ut I still recommend this definition of PDF. If you have other mathematical sources for PDFs you rely on, please let me know.

Best regards,
Volker Grewe

Dear authors,

Thanks for the changes. However, the main issue has not been resolved.
Please have a look at http://planetmath.org/probabilitydistributionfunction for the definitiion of PDFs.

Please change the units on the y axis to:
3a) %/°C
3b) %/%
3c) %/(ms^-1)
3d) %/mm
and Figure 5 accordingly.

Please also change the numbers on the y-axis so that the integral over the whole range is 1. E.g. in Figure 3a) the integal can be approximated by a triangular with the points (-5°C,0%); (12°C,14%); (30°C,0%). The integral equals the area and hence the integral equals = 0.5 * 35 * 14 % = 245 %, but should be 100%. (That is that the temperature is between -infinity and +infinity is 100%)

Best regards,
V. Grewe