Once a neighborhood shape has been specified, you can restrict which data locations within the shape should be used. The adjustment for this directional influence is justified because you know that locations upwind from a prediction location are going to be more similar at remote distances than locations that are perpendicular to the wind but located closer to the prediction location. However, if there is a directional influence in your data, such as a prevailing wind, you may want to adjust for it by changing the shape of the search neighborhood to an ellipse with the major axis parallel with the wind.
To do so, you will define the search neighborhood as a circle. If there are no directional influences in your data, you'll want to consider points equally in all directions.
The shape of the neighborhood is influenced by the input data and the surface you are trying to create. In the following image, five measured points (neighbors) will be used when predicting a value for the location without a measurement, the yellow point. Other neighborhood parameters restrict the locations that will be used within that shape. The shape of the neighborhood restricts how far and where to look for the measured values to be used in the prediction. As a result, it is common practice to limit the number of measured values by specifying a search neighborhood. To speed calculations, you can exclude the more distant points that will have little influence on the prediction.
The search neighborhoodīecause things that are close to one another are more alike than those that are farther away, as the locations get farther away, the measured values will have little relationship to the value of the prediction location. The default value is p = 2, although there is no theoretical justification to prefer this value over others, and the effect of changing p should be investigated by previewing the output and examining the cross-validation statistics. When p = 2, the method is known as the inverse distance squared weighted interpolation. Geostatistical Analyst uses power values greater or equal to 1. Decrease of weight with distance illustration If the p value is very high, only the immediate surrounding points will influence the prediction. As p increases, the weights for distant points decrease rapidly. If p = 0, there is no decrease with distance, and because each weight λ i is the same, the prediction will be the mean of all the data values in the search neighborhood. The rate at which the weights decrease is dependent on the value of p. As a result, as the distance increases, the weights decrease rapidly. Learn more about the interpolation techniques available in ArcGIS Geostatistical Analyst The Power functionĪs mentioned above, weights are proportional to the inverse of the distance (between the data point and the prediction location) raised to the power value p. The Weights window contains the list of weights assigned to each data point that is used to generate a predicted value at the location marked by the crosshair. Weights assigned to data points are illustrated in the following example: Search Neighborhood illustration It gives greater weights to points closest to the prediction location, and the weights diminish as a function of distance, hence the name inverse distance weighted. IDW assumes that each measured point has a local influence that diminishes with distance. The measured values closest to the prediction location have more influence on the predicted value than those farther away. To predict a value for any unmeasured location, IDW uses the measured values surrounding the prediction location. Inverse distance weighted (IDW) interpolation explicitly makes the assumption that things that are close to one another are more alike than those that are farther apart. Available with Geostatistical Analyst license.