Simulating Winter Wheat Development Response to Temperature: Modifying Molo's Exponential Sine Equation

Authors: LI, LONGHUI - CHINESE ACAD. OF SCIENCES; McMaster, Gregory; YU, QIANG - CHINESE ACAD. OF SCIENCES; DU, JUN - LHASA METEOROLOGIC BUREAU

Submitted to: Computers and Electronics in Agriculture
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/27/2008
Publication Date: 5/9/2008
Citation: Li, L., Mcmaster, G.S., Yu, Q., Du, J. 2008. Simulating Winter Wheat Development Response to Temperature: Modifying Molo's Exponential Sine Equation. Computers and Electronics in Agriculture 63 (2008) 274-281.

Interpretive Summary: Predicting crop developmental events is fundamental to crop management decisions. Many approaches to predict developmental events have been created, however, most only simulate the mean time for reaching a developmental event. An exponential sine equation was developed by Malo in 2002 to predict the pattern of flower appearance over time, and this 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 meaning. 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 R2 for the modified temperature response function was 0.74 and 0.91 for two different experiments and compared very well (identical mean R2’s) to an existing function (Beta model). 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.

Technical Abstract: 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 (2002, Func. 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 R2 for the modified temperature response function was 0.74 and 0.91 for two different experiments and compared very well (identical mean R2’s) to an existing function (Beta model, Yin et al., 1995, Agric. For. 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.