Scatter plots of model-predicted verses target (measured) values are used to qualitatively evaluate groundwater flow model calibration error. Often a 45° line representing complete agreement between model-predicted and target values is drawn on the plot for reference. The model is considered calibrated when, based on visual observation, the data points composing the scatter plot are all clustered tightly around the 45° line representing complete model agreement. Because model calibration error is assessed visually, the degree to which the model is calibrated is purely subjective.
The mirror figure of merit (MFM), a number between minus one and one, was developed to quantify how close measured verses model-predicted values are to a 45° line when plotted. To calculate the MFM, the data constituting the scatter plot are mirrored around the 45° line. A best-fit regression line is determined for the mirrored scatter plot. The best-fit regression line is then mirrored around the 45° line. The ratio of the slopes of the best-fit regression and mirrored lines yields the MFM value. For the ideal case, where the measured and model-predicted values are identical and fall on the 45° line, the MFM will equal one. For all other cases, the MFM will be less than one. For very poorly calibrated models, the MFM can be negative, but typically is a positive value.
Calibration of a number of groundwater flow models have been evaluated using the MFM. Because the MFM is scaled between minus one and one, when correctly applied, it is a convenient calibration parameter for comparing model calibration errors associated with individual model layers, for comparing model calibration errors associated with individual time steps, and for comparing both of these types of errors to the overall model calibration error. The MFM is not a panacea for detecting all problems of model calibration and is best used in conjunction with other measures of model calibration.