The probabilistic behavior of AquaCrop parameters: a Monte-Carlo study

Crop growth models are multi-outputs and can be valuable tools for the quantification of crop Growth and production. However, these models usually require several input data, which are costly, time-consuming, and sometimes impossible to measure. These model parameters are mostly estimated by calibration and inverse solving. In this study, five output variables of the AquaCrop model, including soil evaporation, crop transpiration, evapotranspiration, crop biomass at maturity, and grain yield, were investigated to study 47 genotypic model parameters on the output time series of the model for wheat in the Qazvin Synoptic Station. The main objective of this study was to find the most critical variables of the AquaCrop model as well as find the probabilistic behavior of inputs to estimate the missing values. The SAFE toolbox in the Matlab was used to study the global sensitivity analysis (GSA) and uncertainty of inputs and their impact on outputs. The uncertainty in the outputs of the AquaCrop model in simulating wheat yield, in the Qazvin Synoptic Station, over 36 years was analyzed using the Generalized Likelihood Uncertainty Estimation (GLUE) method. Using RMSE < 0.9 as the threshold in a 95% confidence level, the best parameter sets included all the observations. Results showed that evaporation and yield rates are the least reliable outputs of the AquaCrop model that have not been calibrated, while others consider them reliable. After that, the new domain of each output was determined based on the two indexes. Then we modified the domain to reduce its size. Finally, the probabilistic distribution of each inputs were introduced by the Easy Fit software. The main result of this study is that the probabilistic distribution of the model parameter that is calibrated for a particular output variable can differ from other output variables. Also, when we trust a specific run of the model (calibrated run) as observed data, the uncertainty bounds covering are very high. So we can find an efficient bound of uncertainty which was one of the main goals of the study. Finally, we utilized the GLUE to optimize multi-output models by introducing one unique, optimized Probability Density Function (PDF) for each model parameter for all outputs estimated by collecting all accepted output series of all target outputs.