Mathematical consequences of using various empirical expressions of crop yield as a function of temperature

Different expressions for the sensitivity of crops to temperature are commonplace. Sometimes absolute values in t ha−1 °C−1 are quoted and sometimes relative values expressed as % °C−1. Values for the sensitivity are often calculated from curves fitted statistically to the data for yield and temperature. Mechanistic models of crop growth were built to avoid the difficulties of assessing the effects on yield of environmental variables that are often correlated with each other. Choosing an arbitrary mathematical relationship between yield and temperature can have bizarre implications for the expressions of temperature sensitivity; especially if the temperature range is small and the relationship is applied outside the range of data. We used a very simple analysis to illustrate the consequences of choosing different ways of expressing the effect of temperature on crop yield. The analysis presented shows that in the mean daily temperature range 22–32 °C, rice yields decline by −0.6 t ha−1 °C−1.