14.2 Types of Kriging

For example, Simple Kriging assumes the mean of the random field, μ(s), is known;

• Simple Kriging: Assumes that the mean of the variable is known and constant across the study area.

Formula: \(Z(s_0) = \mu + \sum_{i=1}^{n} \lambda_i (Z(s_i) - \mu)\)

where \(\mu\) is the mean, \(\lambda_i\) are the weights, and \(Z(s_i)\) are the observed values.

Ordinary Kriging assumes a constant unknown mean, μ(s)=μ;

• Ordinary Kriging: Assumes that the mean of the variable is unknown and varies across the study area.

Formula: \(Z(s_0) = \sum_{i=1}^{n} \lambda_i Z(s_i)\)

where \(\lambda_i\) are the weights and \(Z(s_i)\) are the observed values.

Universal Kriging can be used for data with an unknown non-stationary mean structure.

• Universal Kriging: Assumes that the mean of the variable is unknown and varies across the study area, but can be modeled as a function of covariates.

Formula: \(Z(s_0) = \sum_{i=1}^{n} \lambda_i Z(s_i) + \beta X(s_0)\)

where \(\lambda_i\) are the weights, \(Z(s_i)\) are the observed values, \(\beta\) is the coefficient for the covariate \(X(s_0)\), and \(X(s_0)\) is the value of the covariate at the unobserved location.