8.4. Improved degreeday modelThe purpose of modification is to use the model for a wide range of temperatures. Effective temperature (ET) is defined as follows:
This model is nonlinear because the graph is not straight (see the figure above). Thus, temperature cannot be averaged! In particular, you cannot use average daily temperature. Instead, it is necessary to use actual temperature dynamics. Accumulated degreedays are equal to the area under the temperature curve restricted to the temperature interval between t_{min} and t_{max}:
Lightblue area equals to accumulated degreedays. Here the average temperature is below t_{min} but organisms can accumulate some degreedays because daily maximums are above t_{min}. Another example:
Lightblue area again equals to accumulated degreedays. Daily maximum temperature exceeds t_{max} however this excess does not count in the accumulation of degreedays. Nonlinear models of development rate require simulation of diurnal temperature change. In most cases, only daily minimum and maximum temperature are known. There are two most frequently used methods for simulation temperature change. "Rectangular" model assumes that temperature stays at maximum for half of the day and stays at minimum for the other half:
This method is not very accurate but it is simple and fast. "Sinewave" method was developed by Allen (1976; Environ. Entomol. 5: 338396). This model generates smooth temperature changes as in the second figure above. In the paper of Allen you will find a FORTRAN code that can be used for estimation of degreedays.
