Upscaling is the reverse procedure of downscaling, but much simpler: All of the grid points in the fine mesh to be replaced by a single coarse grid point are averaged. Their average is the new, coarse grid value. Reverting back to the familiar downscaling, this means that the same must hold as accurately as possible: The average of the a set of fine grid points must approximate the value of their corresponding coarse grid point. Their difference, average minus value, is called the bias. If upscaling and downscaling are considered statistical procedures because of numerical fluctuations, this difference merely estimates the bias.

The unprocessed variables

In addition to downscaling, the downscale algorithm also performs some processing for 4 of the 7 output variables. The processing results are not recorded. A comparison of any kind, including bias calculation, is only warranted for the unprocessed variables: gravimetric humidity QV, surface pressure PS and temperature T.

Bias anecdotes

In advance of a statistical validation, here are some anecdotes of bias calculations for the unprocessed variables:

• Bias anecdote for gravimetric humidity
• Bias anecdote for temperature
• Bias anecdote for surface pressure

MATLAB

source:sandbox/Grib/read_grib.m

Fig.: MATLAB plot of coarse ALB_RAD over the whole available area for 2008-06-01 14 UTC.

This analysis derives from MATLAB code developed for the Multiple Objective Genetic Programming algorithm (MOGP). In order to read the Grib files with the coarse data, the validation employs read_grib.m of the collection ‘NetCDF/GRIB reader’, which in turn wraps around grib2bin.pl. READ_GRIB does return a 3-dimensional array, but only the order of the 1st 2 dimensions bears meaning, namely the horizontal structure of the read field. The 3rd dimension stores the different layers in the order of their corresponding Grib messages in the file, which has no meaning. To find the correct[15] layer in this returned matrix, the wgrib output for the file may help.

Notes

• Spline-interpolation means fitting a polynomial. Polynomials vanish either on a null set or everywhere and never have a clearly circumscribed support. ASOB_S, visibile radiation, and TOT_PREC, precipitation, are only spline-interpolated. It lies in the physical nature of these fields to have a clearly circumscribed support:
  • ASOB_S is zero at night and fluctuates positively at noon. In mornings and evenings, however, a sharp line, the terminator, separates the night from the support.
  • TOT_PREC comes with clouds which are never as big as the modeled domain. Its support is a mostly coherent subset of the cloud-covered area.

• The MATLAB code cannot access sec2date.F90, which complicates the generation of the correct file names.

Footnotes

fn1^. the physically lowest layer, designated with the highest number(s), in case of this project

fn2^. ne for each coarse pixel, i.e. 160 by 160