variable, and thus here to the residual variance of the Pu-FIDLER regression; hence the difference between FIDLER > 5,000 and FIDLER < 5,000 sills, An enlargement of the variogram for FIDLER > 5,000 is also shown in Figure 7. We can fit it to a spherical model with a range "a" of 600 feet (the distance at which correlations vanish): y(0) = 0 y(h) = 0.065 + 0.025 [3/2 (h/600) - 1/2 (h/600)3} (12) 0 < |h] < 600 feet y(h) = 0.09 In| < 600 feet The "apparent nugget effect" of 0.065 is the sum of the FIDLER data nugget effect aon = (1.287)2 x 0.0127 = 0.02 and the Pu data nugget effect, which by Pu variogram extrapolation is found to be 0.045 (wariogram not shown here). Thus T(x)--the true value--has no nugget effect of its own and its variogram is simply the spherical model with a sill at 0.025. Though blurred by noise, T(x) does show a structure up to a distance of 600 feet and it is worth exploiting it. The variogram of T(x) is not well determined when FIDLER < 5,000, espe~ cially at short distances, as a consequence of much sparser sampling (number of pairs typically less than 15). For simplicity, we will assume that the variogram in this case is the same as above, except for an upward shift of 0.135 = 0.225 - 0.09 (Figure 7). It is convenient to think of this shift as due to a nonsystematic uncertainty of variance 0.135, attached to correction terms when FIDLER < 5,000. Then, all data may be processed by BLUEPACK in the same manner: the uncertainty variance is just added to the appropriate diagonal terms of the kriging system matrix. COMING BACK TO ARITHMETIC SCALE We now have all the elements to carry out the estimation of Pov) --or equivalently P(v), since these are equal~~that is, of the mean concentration in the log scale. How can we come back to the arithmetic scale? An Estimate of the Geometric Mean * P (v) . One way is to simply use the inverse transform 10 to estimate the . geometric mean 10 * : P(v) By the unbiasedness property of kriging, we know that the error P (v) - P(v) has mean zero. symmetric distribution, then If moreover this error has a 384 r- :