Equifinality in calibration of the Variable Infiltration Capacity (VIC) Model Parameters

Variable Infiltration Capacity (VIC) model is a large-scale, semi-distributed hydrologic model that operates at grid cell level. An effective application of VIC model requires proper model calibration. The total set of parameters from the two models (VIC and routing model) can be quite large but out of these parameters four soil parameters namely, exponent of soil moisture capacity curve (binfil), maximum velocity of base flow that occurs from the lowest soil layer (Dm), the fraction of Dm where non-linear baseflow occurs (Ds), and fraction of maximum soil moisture where non-linear baseflow occurs (Ws) were considered as these parameters cannot be estimated based on the available soil information. The present study attempts to model the hydrology of two synthetic and one real catchment, Ashti Catchment (sub catchment of Godavari River basin in India) using the VIC two soil layer model. The model was set in water balance mode at 0.25×0.25° spatial resolution with a daily time step. The calibration was carried out using Genetic Algorithm (GA) for six objective functions, Root mean square of error (RMSE), Maximum absolute relative error (MAXARE), Mean absolute error (MAE), Maximum absolute error (MAX_AE), Nash Sutcliffe Efficiency (NSE), and Kling-Gupta Efficiency (KGE). 

Out of six objective functions, MAXARE in simulated discharge was found to be the best objective function for VIC when compared with other objective functions based on how close the generated parameter values were to the true values and the amount of computational time taken. Throughout the calibration, the GA parameters were kept as - solution per population: 32, num of parent mating: 2, mutation type: random, mutation probability: 0.09, crossover type: uniform, and crossover probability: 0.7. The overall result of calibration for both synthetic and real catchments for twenty years of discharge data (1971-1990) indicated that the simulated discharge was more sensitive to parameter binfil as compared to Dm, Ds and Ws. Individually, parameters Ds and Dm showed an insensitivity to the GA parameters up to three hundred generations. Further, out of seventeen set of initial values of binfil, Ds, Dm, and Ws, five sets provide different final parameter values after calibration but same calibration results in terms of MAXARE = 2.037%, NSE = 1.0, Coefficient of correlation = 0.999 Coefficient of determination = 0.998 and RMSE = 4.812 cumec. This indicated the presence of equifinality—where multiple parameters set produced similar model outputs. This study offers a foundation for further refining calibration approaches to address equifinality and improve model robustness.

Keywords: Hydrological modeling, VIC, Genetic algorithm, Equifinality, optimization