Modeling and Mapping of Interpolation Errors, by Using the Characteristics of Triangles

Interpolated data are usually used in many engineering and planning activities such as geology, climatology, natural resources and hazard management. Root Mean Squared Errors (RMSE) is the most frequently used indicator for error assessment and statement. Unfortunately, this indicator is mainly non-spatial and it does not provide the required spatial details about the local reliability of the interpolated layers. Therefore, development of more efficient and practically useful methods for spatial evaluation and visualization of interpolation errors are of prime importance.
In this research, after reviewing some of the important limitations of RMSE and interpolation methods, a practical approach based upon the triangulation, for modeling and mapping of the reliability of interpolation has been proposed. Triangles formed by application of the delauney triangulation to sample points have been used as the main spatial entities. Three characteristics of triangles including the area, shape (modeled by the ratio of perimeter to area), and variance of the values of their 3 corners have been used to model the interpolation errors in triangle levels. The reason for choosing these parameters is their important role in creation of errors, as well as simplicity of their calculation in GIS environment.
Point data of elevation from part of Tehran metropolis has been used as the case study for examination and demonstration the usefulness of the proposed approach. Modeling has been based on the least squares fitting in a multiple regression framework. The fitted model has been used for prediction of interpolation errors. Where its validity has been evaluated by the independent, well distributed test sample points with a known elevation. 
Results of the proposed approach have been encouraging, and close relationship between the actual and predicted (by model) errors have been observed. Production of the map of interpolation errors, as in the proposed approach, can be useful for efficient use of the interpolated data. Also, these maps can be used as useful guides for collection of additional samples where the improvement of the interpolated data quality is required. More close examination of the proposed approach in a wider and diverse environmental condition has been recommended.