Using Color Coherence Vectors to Evaluate the Performance of Hydrologic Data Assimilation

Abstract An inadequate characterization of hydrogeological properties can significantly decrease the trustworthiness of subsurface flow and transport model predictions. A variety of data assimilation methods have been proposed in order to estimate hydrogeological parameters from spatially scarce data by incorporating them into the governing physical models. In order to quantify the accuracy of the estimations, several metrics have been used such as Rank Histograms, root‐mean‐square error (RMSE), and Ensemble Spread. However, these commonly used metrics do not regard the spatial correlation of the aquifer's properties. This can cause permeability fields with very different spatial structures to have similar histograms or RMSE. In this paper, we propose an approach based on color coherence vectors (CCV) for evaluating the performance of these estimation methods. CCV is a histogram‐based technique for comparing images that incorporate spatial information. We represent estimated fields as digital three‐channel images and use CCV to compare and quantify the accuracy of estimations. The appealing feature of this technique is that it considers the spatial structure embedded in the estimated fields. The sensitivity of CCV to spatial information makes it a suitable metric for assessing the performance of data assimilation techniques. Under various factors, such as numbers of measurements and structural parameters of the log conductivity field, we compare the performance of CCV with the RMSE.