Model validation and calibration based on component functions of model output

The target in this work is to validate the component functions of model output between physical observation and computational model with the area metric. Based on the theory of high dimensional model representations (HDMR) of independent input variables, conditional expectations are component functions of model output, and the conditional expectations reflect partial information of model output. Therefore, the model validation of conditional expectations tells the discrepancy between the partial information of the computational model output and that of the observations. Then a calibration of the conditional expectations is carried out to reduce the value of model validation metric. After that, a recalculation of the model validation metric of model output is taken with the calibrated model parameters, and the result shows that a reduction of the discrepancy in the conditional expectations can help decrease the difference in model output. At last, several examples are employed to demonstrate the rationality and necessity of the methodology in case of both single validation site and multiple validation sites.