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<br />The value, Dn is the difference between the observed data value <br />and its first estimate value at the same point. A simple biquadratic <br />interpolation between the values of fo(i,j) at the four nearest grid <br />points is used to estimate fo(x,y). Barnes has shown that the final <br /> <br />response is a function of wavelength ~, is: <br /> <br />R = R (1 + Rg-l_R g) <br />000 <br /> <br />(6) <br /> <br />where: <br /> <br />Ro = exp (_~24c/\2) <br /> <br />(7) <br /> <br />The same procedure is followed using a second low-pass filter to <br />determine the band-pass field, which is the difference between the two <br />low-pass analyses. The band-pass analysis is performed using weight <br />function constants, such that the filter response (BR) is peaked at a <br />specific wavelength of interest shown in Fig. 3.1. The band-pass field <br />defines the mesoscale features which occur at the wavelength of interest. <br />The total field is then computed as the sum of the macroscale (first <br />low-pass) field and the mesoscale (band-pass) field. This analysis <br /> <br />system is fast, economical, and enables the meteorologist to specify a <br />response on the appropriate scale of the mesoscale triggering phenomena <br /> <br />and density of observations. <br /> <br />The response curves for the filters used in the following examples <br />are shown in Fig. 3.1. The low-pass responses Rl and R2 used to define <br />the mesoscale band-pass BR response are shown. Note the peak at maximum <br /> <br />of 500 km. The total field response (TR) is the sum of the BR and R2 <br /> <br />response curves. Appendix A provides an example of the families of <br /> <br />41 <br />