Available with Geostatistical Analyst license.

The Densify Sampling Network tool can be used to determine the best places for adding new sampling locations to a monitoring network based on the predefined selection criterion.

Several criteria can be used to determine where to add a station, including the maximum prediction uncertainty and the highest probability that a specified threshold value is exceeded.

The tool utilizes an existing geostatistical layer, created using a kriging or cokriging model with measurements at the existing monitoring stations, to determine prediction standard error, the interquartile range, and the probability that a specified threshold is exceeded for every input location. In ArcGIS Pro, only geostatistical layers made with empirical Bayesian kriging are supported in this tool.

If maximum prediction standard error, *stderr(s)*, is used as a criterion, a new sampling location is chosen so as to minimize *stderr(s),* and the optimality criterion *O*_{0}*(s) * can be expressed as:

*O*_{0}*(s)* = maximum of *stderr(s)*

The probability of exceeding a threshold value can be used to weigh the prediction standard error or the interquartile range (the interquartile range *Z*_{0.75}*(s)* - *Z*_{0.25}*(s)* is often used instead of the prediction standard error if the prediction distribution is not symmetrical). For example, if that probability is equal to *0.5*, the optimality criterion *O _{1}(s) *is equal to the maximum of the prediction standard error:

*O*_{1}*(s)* = maximum of *stderr(s)*(1-2ยท*abs(prob*[*Z(s)*>*Z*_{threshold}]-0.5))

The criterion value decreases as the uncertainty about exceeding the threshold value decreases. Adding the locations with the largest weighted prediction standard error *O*_{0}*(s)* to the monitoring network will improve predictions near the threshold value.

It is often useful to multiply the optimization criteria by the a priori inclusion probability (input weight raster) values. For example, values equal to 1 can be assigned to the areas where new monitoring stations are allowed, and values of 0 are assigned otherwise.