Notes about offline ’Holmlike’ calibration diagnostics with UKV NMClike data
The following procedure is followed, with each of two options that we call “Anal” and “Fc”.

Define a population of pairs of states, x_{1} and x_{2} (for total RH).

For option “Anal”:

x_{1} is an analysis, x_{a}, and

x_{2} is a 3hour forecast, x_{f3}, valid at the same time as the analysis.

For option “Fc”:

x_{1} is a 3hour forecast, x_{f3}, and

x_{2} is a 6hour forecast, x_{f6}, valid at the same time as x_{f3}.

Construct a histogram of the joint distribution.

For option “Anal”, see joint distribution here.

For option “Fc”, see joint distribution here.

Calculate difference fields, Δx = (x_{2} − x_{1}) ⁄ √(2).

Construct the following conditional PDFs for each level: P(Δxx_{1}), P(Δxx_{2}) and P(Δxx), where x = (x_{1} + x_{2}) ⁄ 2.

For option “Anal”:

For P(Δxx_{1}) = P((x_{f3} − x_{a}) ⁄ √(2) x_{a}) averaged over four layers of the atmosphere, see PDFs here.

For P(Δxx_{2}) = P((x_{f3} − x_{a}) ⁄ √(2) x_{f3}) averaged over four layers of the atmosphere, see PDFs here.

For P(Δxx) = P((x_{f3} − x_{a}) ⁄ √(2)( x_{a} + x_{f3}) ⁄ 2) averaged over four layers of the atmosphere, see PDFs here.

For option “Fc”:

For P(Δxx_{1}) = P((x_{f6} − x_{f3}) ⁄ √(2) x_{f3}) averaged over four layers of the atmosphere, see PDFs here.

For P(Δxx_{2}) = P((x_{f6} − x_{f3}) ⁄ √(2) x_{f6}) averaged over four layers of the atmosphere, see PDFs here.

For P(Δxx) = P((x_{f6} − x_{f3}) ⁄ √(2)( x_{f3} + x_{f6}) ⁄ 2) averaged over four layers of the atmosphere, see PDFs here.

The mean, standard deviation and skewness are computed from the conditional PDFs (and the relative frequency of x_{1}, x_{2} or x is also shown), each a function of x_{1}, x_{2} or x, and vertical level.

For option “Anal”:

For P(Δxx_{1}) = P((x_{f3} − x_{a}) ⁄ √(2) x_{a}), see mean, stddev here.

For P(Δxx_{2}) = P((x_{f3} − x_{a}) ⁄ √(2) x_{f3}), see mean, stddev here.

For P(Δxx) = P((x_{f3} − x_{a}) ⁄ √(2)( x_{a} + x_{f3}) ⁄ 2), see mean, stddev here.

For option “Fc”:

For P(Δxx_{1}) = P((x_{f6} − x_{f3}) ⁄ √(2) x_{f3}), see mean, stddev here.

For P(Δxx_{2}) = P((x_{f6} − x_{f3}) ⁄ √(2) x_{f6}), see mean, stddev here.

For P(Δxx) = P((x_{f6} − x_{f3}) ⁄ √(2)( x_{f3} + x_{f6}) ⁄ 2), see mean, stddev here.