We transform the data to T63 resolution by adding a zero coefficient for the extra mode. For fields which have significant variance at the truncation limit, such as divergences, ringing effects are introduced. When products are taken with such fields, experience shows that computational noise is present for all waves beyond about T42. For instance, for the energy divergence, wavenumber spectra typically fall off slightly in power beyond about total wave number 15 to wave 42, but then exhibit an increase which peaks at T63. Accordingly, all fields are truncated with a tapered filter at about T42 resolution before generating comparisons and analysis of variance. The filter is applied in spectral space; at T31 has a response function of 0.93, the half power point (amplitude response 0.71) is at T36, and at T42 the response function is 0.37 (1/e). The results are smoothed to T31 or T21 resoluion for plotting purposes.The tapered function (Fn_t) is given by:
Fn_t = Fn*exp(-(n*(n+1))/(no*(no+1))^r)
where Fn is the untapered field, n is the total wave number, no = n-2, and r is a power to which Fn is tapered (it is like a diffusion in time). In the case of a T42 taper, we use n = 42, no = 40, and r = 4.