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.