Modeling global trends

A surface may be made up of two main components: a fixed global trend and random short-range variation. The global trend is sometimes referred to as the fixed mean structure. Random short-range variation (sometimes referred to as random error) can be modeled in two parts: spatial autocorrelation and the nugget effect.

If you decide a global trend exists in your data, you must decide how to model it. Whether you use a deterministic method or a geostatistical method to create a surface usually depends on your objective. If you want to model just the global trend and create a smooth surface, you may use a global or local polynomial interpolation method to create a final surface. However, you may want to incorporate the trend in a geostatistical method (for instance, remove the trend and model the remaining component as random short-range variation). The main reason to remove a trend in geostatistics is to satisfy stationarity assumptions. Trends should only be removed if there is justification for doing so.

Learn more about removing trends from data

If you remove the global trend in a geostatistical method, you will be modeling the random short-range variation in the residuals. However, before making an actual prediction, the trend will be automatically added back so that you obtain reasonable results.

If you deconstruct your data into a global trend plus short-range variation, you are assuming that the trend is fixed and the short-range variation is random. Here, random does not mean unpredictable, but rather that it is governed by rules of probability that include dependence on neighboring values called autocorrelation. The final surface is the sum of the fixed and random surfaces. That is, think of adding two layers, one that never changes and another that changes randomly. For example, suppose you are studying biomass. If you were to go back in time 1,000 years and start over to the present day, the global trend of the biomass surface would be unchanged. However, the short-range variation of the biomass surface would change. The unchanging global trend could be due to fixed effects such as topography. Short-range variation could be caused by less permanent features that could not be observed through time, such as precipitation, so it is assumed it is random and likely to be autocorrelated.

If you can identify and quantify the trend, you will gain a deeper understanding of your data and make better decisions. If you remove the trend, you will be able to more accurately model the random short-range variation, because the global trend will not be influencing kriging assumption about data stationarity.