Predicting phasic development of green beans for processing using a model with high temperature reduction of thermal time accumulation

Abstract

Green beans (Phaseolus vulgaris L., Alcade) were sown in the field in Central Portugal in 1992-1993, on eight dates per year, under air temperatures, well above the expected optimum for plant development. It was assumed that the rate of development increases linearly with temperature from a base T(b) to a sharply defined optimum T(o), beyond which this rate decreases linearly, reaching zero at T(c). An algorithm was constructed to fit this piecewise linear model (or any other model) with daily or hourly temperature values. Cardinal temperatures of the developmental process were, for example, 6.8, 24.0 and 34.1°C, when hourly temperatures were used in the phase between emergence and the appearance of the first flower. The standard error (SE) of the estimates of the day of first flower was 2.73 days. A curvilinear model was also validated, but its performance was not significantly better. Using the fitted linear model, thermal time and SE of the estimates of the duration of the phases sowing-emergence, emergence-first trifoliate leaf, first trifoliate leaf-first flowering, first flowering-flowering, flowering-pod development, and pod development-pod filling were calculated. The fitted linear model allows the computation of cardinal temperatures for development under high temperature conditions using limited field data, and can also be used to predict the occurrence of relevant phases of plant development.