This validation is based on run over 1464 time steps, the 61 days of January … February 2008. In total, 2008 consists of 8784 steps.

Table of contents

• Inference of variance
• Interpretation
• A subset of 6 days

To put all variables in one plot, they are processed into relative increases c. The expectation value and variance are inferred firstly from the coarse data, yielding the reference r, and then from the downscaled data, giving f. Each 3-tuple of time step, variable and moment gets its own relative increase:

c= (f-r)/r

The reference r sometimes disappears, most commonly for solar radiation at night. The denominator then defaults to the temporal minimum of the variable excluding 0. The substitution is harmless given that the algorithm always downscales coarse fields of all 0 successfully to fine fields of all 0.

Fig. 1: The absolute value of the relative increase of the average by downscaling. Around c=1, ‘:’ symbolizes that on that time step and for that variable, there were no discernable differences in mean. R assesses its minimal discernable difference between numbers to be 2.220446e-16, given the ideal circumstances.

Fig. 2: The relative increase of the estimated variance by downscaling.

Tab. 1: The temporal range of c for the average

Tab. 2: The temporal range of c for the estimated variance

The validation codes source:plotting/verif.R and source:plotting/verif.F90 are independet of the algorithm.

Inference of variance

The 2nd inferred moment is the centralized 2nd moment. As the expectation value was also inferred and not given, the Bessel correction removes the bias from the estimator. Removing bias is also the reason not to infer the standard deviation, which could share a plot with the mean.

Interpretation

The increase in mean is insignificant. R’s minimal difference is just barely smaller for than the increase for most variables. The others are too small to impact any calculation by 3 orders of magnitude. By this standard, downscale succeeded.

The increase in variance is insignificant for solar and terrestial radiation. Downscaling in general leads to higher variance due to additional fine-scale variability. It usually stems from the spline interpolation, which generates much too smooth field compared to observations. The more advanced Schomburg rules increase the variance by a larger margin, as exhibited by pressure. Temperature appears to shift between these two groups of increases. The most opportune conjecture points to the switch in its Schomburg rule, which turns off the advanced downscaling in case of a high temperature lapse rate.

A subset of 6 days

This validation is based on run over 166 time steps, i.e. 166h, i.e. 6 days and 22h. The case can be made that this does not suffice as a sample for the entire year 2008 with its 8784 time steps.

Fig. 3: The relative increase of the estimator variance by downscaling.

Fig. 4: The absolute value of the relative increase of the expectation value by downscaling.