Get A Practical Guide to Geostatistical Mapping of Environmental PDF

By Hengl, Tomislav

ISBN-10: 9279069047

ISBN-13: 9789279069048

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Extra info for A Practical Guide to Geostatistical Mapping of Environmental Variables

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Fig. 5 (range in minor direction is two times shorter). 10) where δ (h) is the Kronecker delta, Kv is the modified Bessel function, Γ is the gamma function and v is the smoothness parameter. The advantage of this model is that it can be used universally to model both short and long distance variation. In reality, variogram models with more parameters are more difficult to fit automatically because the iterative algorithms might get stuck in local minima (Minasny and McBratney, 2005). To avoid such problems, we will rely in ➜4 on more simple variogram models such as the Exponential model.

One way to account for this problem is to take the distance between the points into account during the estimation of the regression coefficients. , 2002). 21) 2 is the level of variation of the error terms, d(s , s ) is the Euclidian distance where σE i j between a sampled point pair and is known as the bandwidth, which determines the degree of locality — small values of suggest that correlation only occurs between very close point pairs and large values suggest that such effects exist even on a larger spatial scale.

Qp (s1 ) ··· qp (sn ) 1 .. q1 (s1 ) .. ···  qp (s1 ) ..   . 1 q1 (sn ) · · · qp (sn ) 0 0 ··· 0 0 0 ··· 0 .. 0 . 2), except the covariance matrix/vector are extended with values of auxiliary predictors. , 2007b). Start from KED where the predictions are T made as in ordinary kriging using zˆKED (s0 ) = λT KED · z. 15) where φ is a vector of Lagrange multipliers. 18) where the identity qT · λKED = q0 has been used. Substituting φ back into Eq. 19) Let us now turn to RK. 19), which proves that KED will give the same predictions as RK if same inputs are used.

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A Practical Guide to Geostatistical Mapping of Environmental Variables by Hengl, Tomislav

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