# How Densify Sampling Network works

Geostatistical Analyst のライセンスで利用可能。

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 O0(s) can be expressed as:

``O0(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 Z0.75(s) - Z0.25(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 O1(s) is equal to the maximum of the prediction standard error:

``O1(s) = maximum of stderr(s)(1-2·abs(prob[Z(s)>Zthreshold]-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 O0(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.