A Stochastic Approach for Crop Growth Simulations: A Case Study for Sugarcane.

Crop models are increasingly being used for different purposes including evaluation of climate change impacts on crop yields and opportunities for adapting management to future conditions. However, past uses of these models have been criticized in part due to a failure of researchers to quantify uncertainties of crop yield prediction. This paper describes a simple stochastic sugarcane model that includes an approach for quantifying uncertainty in crop model predictions for regions where it has been parameterized. The data were collected in five field experiments at four locations around Brazil where crops received adequate nutrients and good weed control. Two of the experiments addressed the irrigation effects on the crop, and 3 of them were conducted under rainfed conditions. All of them studied of an important cultivar in Brazil. To validate our model, we show that observed correlations between simulated plant variables are consistent with experimental data. A Bayesian Monte Carlo approach (Generalized Likelihood Uncertainty Estimation - GLUE) was used to estimate model parameters and correlations among them using experimental data. These mean parameter values and the parameter covariance matrix are inputs in this approach, which includes a Toeplitz-Cholesky factorization to generate correlated random variable samples to simulate means and variances of stalk dry mass and sucrose content among other variables. The correlated random variable approach based on the Toeplitz-Cholesky factorization showed an interesting reduction on the uncertainty of simulations compared with a typical stochastic Monte Carlo simulation. The possibility to assure the physiological parameter relationships being respected through this approach is another issue that seems interesting for stochastic crop growth simulations.