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<br />the total fields is recovered by adding the mesoscale field to the <br />macroscale field analyses. Shortwave noise is controlled by selecting <br />the appropriate weight function for the phenomena of interest. <br /> <br />The analysis system provides a two-step iteration. Where the first <br />estimate of gridded values for some parameter, f is given by: <br /> <br />N N <br />fo (i,j) ="Ewn fn (x,y)/'Lwn <br />1 1 <br /> <br />(1) <br /> <br />where the weight function, Wn' is: <br /> <br />Wn = exp (-dn2/4C) <br /> <br />(2) <br /> <br />The weight function constant, c is chosen to fit a particular grid <br />scale and phenomena of interest. The distance from a grid point (i,j) <br />to the location of the observed data, fn(x,y) is denoted by dn and N <br />is the number of observations that influence a computed grid point <br />value. The second correction pass uses a reduced value of the weight <br />function, so that the final low-pass grid point values are given by: <br /> <br />N N <br />f(itj) = fo(i,j) +L:WlnDn(LW'n <br />1 1 <br /> <br />(3) <br /> <br />where the modified weight function, Win' is: <br /> <br />Win = exp (-dn2/49C), 0 < g < 1 <br /> <br />(4) <br /> <br />Dn = fn (x,y) - fo (x,y) <br /> <br />(5) <br /> <br />40 <br />