Modelling impact of freezing temperatures on reproductive organs of deciduous fruit trees

This study arises from the need for quantitative methods to assess risks of frost damage in agriculture. Classical mathematical functions were used to model damage due to freezing temperatures and a simple method based on experimental data is described to estimate the model parameters. Using survival data of vegetative and flower buds of deciduous fruit trees reported in the specialized literature, three sigmoidal functions were tested: logistic, Gompertz and Richards. The logistic function was chosen as the best model through the analysis of three comparative criteria: Root Mean Square Error (RMSE), statistical significance of parameters and Akaike Information Criterion (AIC). A parameter estimation method was developed based on a solution of a linear equation system of 2 × 2 fed only by two pairs of data, obtained from the simulated evolution of LT10 and LT90 for buds of apricot, cherry, apple and pear. The evolution of lethal temperatures (LT10 and LT90) fit well to a monomolecular function (r2 between 0.907 and 0.997, mean errors fluctuating between 0.5 °C and 1.3 °C). The method proved to be a good estimator of survival of buds and flowers, starting from published values of lethal temperatures. However, the model is highly sensitive to errors in the estimation of lethal temperatures during the flowering period. This study shows that it is possible to model crop response to freezing temperature, on the basis of limited data on freezing damage. Considering the simplicity of the method, it may be a useful tool to assess risks of frost damage and to improve models of climate change impacts.