Dear All,
I intend to fit spatial covariance structure model to geostatistical data with yield as attribute component and longitude and latitude as spatial component. I plotted the point locations using projected coordinates easting and northing after conversion into UTM. It is hard for me to visualize the pattern due to large number of observations. Do I assume the presence of trend by regressing the yield as function of easting and northing to remove the trend? Must we always remove the trend for any geostatistical data?
Thanks
Hi Moshood
Yes, it´s necessary to eliminate the trend of the data to ensure the principle of stationarity (mean and variance known and constant). One technique is to offer a regression model, no longer than 3 polinomial grade. Another technique is median polish
http://mmc2.geofisica.unam.mx/cursos/gest/Articulos/Geostatistics/Modified%20Median%20Polish%20Kriging%20and%20its%20Application%20to%20the%20Wolfcamp-Aquifer%20Data.pdf
Other link
http://www.wright.edu/~thaddeus.tarpey/es714spatial.pdf
A key question is how you plan to fit a spatial covariance model to the data. For example if you were to use a sample (empirical) variogram then non-stationarity in the mean of the random function will result in the sample variogram estimating the variogram PLUS a quadratic term (quadratic in length of the separation vector. I.e., the plot of the sample variogram will appear to increase at a rate that is quadratic or greater. However there are no variogram models with this growth rate. Because non-stationarity is a characteristic of the random function and not of the data there is no theoretical best way to deal with the problem.It is common to fit the data to a trend surface, subtract the trend surface and fit the variogram to the residuals, this is an ad-hoc,, practical solution. Most geostatistical software packages include this option. After fitting the variogram to the residuals use the original data in "universal kriging" If you use ordinary kriging with the residuals you will not obtain the kriging variances correctly.
You might want to look at the book on "model Based geostatistics", however they assume a multivariate Gaussian distribution.
You mention using latitude and longitude, this should be done with caution since these do not work correctly with the usual distance formula. I.e., the actual distance corresponding to a minute of latitude is constant irrespective of latitude but the same is not true for longitude. A GIS package would likely handle longitude and latitude correctly but most geostatistics software packages would not.
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