Approaches for sensitivity and uncertainty analyses of dynamic mathematical models of greenhouse climate: an overview

Recently it has been reported that models of greenhouse climate have mostly used ordinary differential equations. Those dynamic models have mostly been founded on the first law of thermodynamics, namely energy/enthalpy and matter conservation analysis. However, although almost all the models developed for greenhouse climate have been calibrated and evaluated, surveys have revealed that there is a lack of the application of any uncertainty analysis (UA) and sensitivity analysis (SA). Therefore, the aim of the current research is a review of the main methods available for UA and SA potentially applicable for dynamic models of greenhouse climate. The aim of a SA is quantifying the effects of input factors variations on model outputs, whereas the purpose of a UA is to assess the effects of input factors uncertainties on the uncertainties of the model outputs. Results show that SA methods roughly are classified as local and global. Local sensitivity analysis methods are based on derivatives calculation in order to solve the so-called sensitivity equations whereas global approaches rely on the use of probability density functions (PDFs), sampling strategies and Monte Carlo simulation in order to calculate sensitivity indices. Main global SA procedures are variance-based methods, density-based methods, correlation and regression analysis, multiple start perturbation methods and Monte Carlo Filtering (regional sensitivity analysis). Also it was found that in spite of that several UA methods are found in the literature two main approaches are Monte Carlo (MC) simulation and generalized likelihood uncertainty estimation (GLUE) procedure. MC analysis uses PDFs, sampling and Monte Carlo (MC) simulation in order to calculate statistics associated to model's predictions. In contrast the GLUE method is a kind of Bayesian method that calculates prior and posterior statistics. The application of both local and global SA methods and confident UA could increase the reliability of models of the greenhouse environment.