Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method

Proper estimation of model parameters is required for ensuring accurate model predictions and good model-based decisions. The generalized likelihood uncertainty estimation (GLUE) method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the closeness-of-fit of modeled and observed data. Various likelihood functions and methods of combining likelihood values have been used in previous studies. This research was conducted to determine the effects of using previously reported likelihood functions in a GLUE procedure for estimating parameters in a widely-used crop simulation model. A factorial computer experiment was conducted with synthetic measurement data to compare four likelihood functions and three methods of combining likelihood values using the CERES-Maize model of the Decision Support System for Agrotechnology Transfer (DSSAT). The procedure used an arbitrarily-selected parameter set as the known “true parameter set” and the CERES-Maize model to generate true output values. Then synthetic observations of crop variables were randomly generated (four replicates) by using the simulated true output values (dry yield, anthesis date, maturity date, leaf nitrogen concentration, soil nitrate concentration, and soil moisture) and adding a random observation error based on the variances of corresponding field measurements. The environmental conditions were obtained from a sweet corn (Zea mays L.) experiment conducted in 2005 in northern Florida. Results showed that the method of combining likelihood values had a strong influence on parameter estimates. The combination method based on the product of the likelihoods associated with each set of observations reduced the uncertainties in posterior distributions of parameter estimates most significantly. It was also found that the likelihood function based on Gaussian probability density function was the best among those tested. This combination accurately estimated the true parameter values, suggesting that it can be used when estimating CERES-Maize model parameters for real experiments.