c173c273_lec5_w11[1]

# c173c273_lec5_w11[1] - University of California Los Angeles...

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University of California, Los Angeles Department of Statistics Statistics C173/C273 Instructor: Nicolas Christou More on the variogram Variogram model parameters: The various parameters of the variogram model are: 1. Nugget Efffect ( c 0 ): If we stand by the assumption that sample values are measured precisely and accurately then the semi-variogram model must have a value of zero at zero distance. It is like calculating the difference of Z ( s ) with itself. That is, γ (0) = 0 The term nugget effect (or nugget variance) was introduced on the basis of the interpre- tation of gold mineralization. It was suggested by Matheron (1962) and it is believed that microscale variation (small nuggets) is causing a discontinuity at the origin. 2. Range ( α ): As the separation distance increases the value of the variogram increases as well. How- ever, after a certain distance the variogram reaches a plateau. The distance at which the variogram reaches a plateau is the range. We generally interpret the range of influence as that distance beyond which pairs of sample values are unrrelated. Beyond the range the variogram remains essentially constant. 3. Sill ( c 0 + c 1 ): It is the variogram value for separation distances h α . Outline of spatial continuity analysis: 1. We begin usually with the calculation of an omnidirectional variogram. With all possi- ble directions combine in a single variogram only the separation distance is important. The omnidirectional variogram can be thought as the average variogram of all direc- tions. Strictly speaking is not the average because in one direction we may have more pairs than other directions. 2. The second step is to explore anisotropy by calculating the directional variograms for different directions (one at a time). In many spatial data the direction of anisotropy may be determined by the nature of the problem. For example, if we analyze airborne pollutants, the wind direction may be an important factor in the calculation of the variogram.

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