A novel objective function DYNO for automatic multivariable calibration of 3D lake models

This study introduced a novel Dynamically Normalized Objective Function (DYNO) for multivariable (i.e., temperature and velocity) model calibration problems. DYNO combines the error metrics of multiple variables into a single objective function by dynamically normalizing each variable's error terms using information available during the search. DYNO is proposed to dynamically adjust the weight of the error of each variable hence balancing the calibration to each variable during optimization search. DYNO is applied to calibrate a tropical hydrodynamic model where temperature and velocity observation data are used for model calibration simultaneously. We also investigated the efficiency of DYNO by comparing the calibration results obtained with DYNO with the results obtained through calibrating to temperature only and with the results obtained through calibrating to velocity only. The results indicate that DYNO can balance the calibration in terms of water temperature and velocity and that calibrating to only one variable (e.g., temperature or velocity) cannot guarantee the goodness-of-fit of another variable (e.g., velocity or temperature) in our case. Our study implies that in practical application, for an accurate spatially distributed hydrodynamic quantification, including direct velocity measurements is likely to be more effective than using only temperature measurements for calibrating a 3D hydrodynamic model. Our example problems were computed with a parallel optimization method PODS, but DYNO can also be easily used in serial applications.

Automated summary

This study introduces a novel Dynamically Normalized Objective Function (DYNO) for multivariable model calibration problems. DYNO combines the error metrics of multiple variables into a single objective function by dynamically normalizing each variable's error terms. It adjusts the weight of each variable's error dynamically to balance the calibration. The results indicate that DYNO can balance the calibration of water temperature and velocity and that calibrating to only one variable cannot guarantee the goodness-of-fit of another variable. Our study suggests that including direct velocity measurements is likely to be more effective than using only temperature measurements for calibrating a 3D hydrodynamic model.