Choosing between Universal and Ordinary Kriging for Interpolation in Earth Science

Interpolation is a common technique used in Earth science to estimate values of a variable at unsampled locations. Interpolation can be used to create continuous surfaces of various parameters such as temperature, precipitation, or soil moisture. Among the various interpolation methods available, kriging is one of the most widely used, especially in geostatistical analysis. Kriging is a spatial interpolation method that uses statistical analysis of spatial autocorrelation to estimate values at unsampled locations.

There are two main types of kriging: Ordinary Kriging and Universal Kriging. Both methods have their advantages and limitations, and the choice of method depends on the specific geoscience application. In this article, we will discuss the differences between Ordinary Kriging and Universal Kriging and provide guidance on how to choose the best method for your particular application.

Ordinary Kriging

Ordinary Kriging assumes that the variable to be interpolated has a constant mean and a spatially varying covariance. It is a popular method because it is relatively simple and requires only a few parameters to be estimated. Ordinary Kriging is particularly useful when the data are spatially correlated and the spatial autocorrelation structure is stationary.
One of the main limitations of ordinary kriging is that it assumes that the underlying spatial autocorrelation structure is isotropic, i.e., independent of direction. This assumption may not hold when the spatial autocorrelation structure varies with direction, such as in areas with complex terrain or when dealing with anisotropic variables. In such cases, Universal Kriging may be a better option.

Universal Kriging

Universal Kriging, also known as Kriging with a Trend, is a more flexible interpolation method that allows for the inclusion of a deterministic trend in addition to spatial autocorrelation. The trend can be a function of one or more covariates, such as elevation, slope, or aspect, and can be used to capture the spatial variation in the interpolated variable that cannot be explained by the spatial autocorrelation structure alone.

Universal Kriging is particularly useful when dealing with non-stationary spatial autocorrelation structures or when the variable being interpolated has a clear trend. However, Universal Kriging requires the estimation of more parameters than Ordinary Kriging, including the parameters of the trend function, which can be challenging when dealing with large data sets.

Choosing the Best Method for Your Application

The choice of interpolation method depends on the specific geoscience application. In general, Ordinary Kriging is a good option when dealing with spatially correlated data with a stationary spatial autocorrelation structure and when a deterministic trend is not expected. On the other hand, Universal Kriging is more appropriate when there is a clear trend in the data or when dealing with non-stationary spatial autocorrelation structures.

It is important to note that both methods assume that the underlying spatial autocorrelation structure is known and can be estimated from the available data. However, this assumption may not hold in some cases, especially when dealing with complex spatial patterns or limited data. In such cases, other interpolation methods, such as inverse distance weighting or radial basis functions, may be more appropriate.

Conclusion

Interpolation is an important tool in geoscience for estimating values at unsampled locations. Kriging is a popular interpolation method that uses statistical analysis of spatial autocorrelation to estimate values. Ordinary kriging and universal kriging are two main types of kriging, each with its advantages and limitations. The choice of method depends on the specific geoscience application and the underlying spatial autocorrelation structure of the data. By understanding the differences between Ordinary Kriging and Universal Kriging, researchers can choose the best interpolation method for their particular application and improve the accuracy of their estimates.

FAQs

What is the main difference between Ordinary Kriging and Universal Kriging?

The main difference between Ordinary Kriging and Universal Kriging is that the latter allows for the incorporation of a deterministic trend in addition to the spatial autocorrelation, while the former assumes that the variable being interpolated has a constant mean and a spatially varying covariance.

When is Ordinary Kriging a good option?

Ordinary Kriging is a good option when dealing with spatially correlated data with a stationary spatial autocorrelation structure and when a deterministic trend is not expected.

When is Universal Kriging more appropriate?

Universal Kriging is more appropriate when there is a clear trend in the data or when dealing with non-stationary spatial autocorrelation structures.

What is the main limitation of Ordinary Kriging?

One of the main limitations of Ordinary Kriging is that it assumes that the underlying spatial autocorrelation structure is isotropic, meaning that it is independent of direction. This assumption may not hold if the spatial autocorrelation structure varies with direction, such as in areas with complex terrain or when dealing with anisotropic variables.

What are the advantages of Universal Kriging?

Universal Kriging is a more flexible interpolation method that allows for the incorporation of a deterministic trend in addition to the spatial autocorrelation. This makes it particularly useful when dealing with non-stationary spatial autocorrelation structures or when the variable being interpolated exhibits a clear trend.

What are some other interpolation methods that can be used in Earth science?

Other interpolation methods that can be used in Earth science include Inverse Distance Weighting and Radial Basis Functions.

What factors should be considered when choosing an interpolation method for a specific application?

The choice of interpolation method depends on the specific application in Earth science and the underlying spatial autocorrelation structure of the data. Factors that should be considered include the stationarity of the spatial autocorrelation structure, the presence of a deterministic trend, and the size and complexity of the dataset.