Simulating winter wheat development response to temperature: Modifying Malo's exponential sine equation

Predicting crop developmental events is fundamental to simulation models and crop management decisions. Many approaches to predict developmental events have been developed, however, most only simulate the mean time for reaching a developmental event. An exponential sine equation developed by Malo [Malo, J.E., 2002. Modelling unimodal flowering phenology with exponential sine equation. Funct. Ecol. 16,413-418] to predict flower number over time was modified to incorporate the response of crop development rate to temperature. The revised model (ExpSine model) uses the base, optimum, and maximum cardinal temperatures specific to a crop or genotype. Most model parameters were estimated from the literature, and four of the five model parameters have physiological significance. Model evaluation for winter wheat (Triticum aestivum L.) was based on two controlled environment studies from the literature and two field experiments conducted in the North China Plain (NCP) and the Tibet Plateau (TPC). The r(2) for the modified temperature response function was 0.74 and 0.91 for two different experiments and compared very well (identical mean r(2)'s) to an existing function (Beta model) [Yin, X., Kropff, M.J., McLaren, G., Visperas, R.M., 1995. A nonlinear model for crop development rate as a function of temperature. Agric. Forest Meteorol. 77, 1-16]. Differences between observed and predicted flowering dates ranged from -2 to 3 days in the NCP and from -7 to 4 days on the TPC, with the mean percent error in both sites less than 1% and no apparent bias observed in the model. This modification of Malo's exponential sine equation expanded the predictive ability of the original equation to simulate phenology across a broader range of environments. The ExpSine model developed can be used as a phenological module in various crop or ecological simulation models. (C) 2008 Elsevier B.V. All rights reserved.