Predicting Crop Phenology (1991) p. 8-9
Tom Hodges

II. TEMPERATURE

A. THERMAL TIME ACCUMULATION

The effect of temperature or thermal time accumulation on crop growth and development has recently been reviewed by Ritchie and NeSmith.4

The basic concept of thermal time is as follows.5,6 Many crop phenological and growth processes proceed in direct relation to the accumulated temperature or thermal time experienced by the crop. Below a base temperature, no thermal time accumulates and crop development ceases. The rate of thermal time accumulation and the crop growth or development rate increase with increasing temperature up to an optimum temperature value or range of values (plateau). Above that temperature value or plateau the rate of thermal time accumulation and the crop response decrease with further increases in temperature until no further accumulation curs and crop development ceases7,8 (Figure 1). Various linear9,10 and nonlinear11-14 algorithms have been developed to calculate the accumulated thermal time that a crop experiences. Wassink14 shows how some exponential functions may generate a nearly linear response over part of a range, while being curvilinear over other parts. Innumerable greenhouse, growth chamber, and field studies have been carried out in an attempt to determine the cardinal (minimum, optimum, and maximum) temperatures for development in the several stages of different varieties of many crops. Studies and reviews include those by Barlow et al.,15 and Boersma,15 Bunting,16 Cross and Zuber,10 Frank et al.,17 Hesketh et al.,18 Hodges,19 Hodges and French,20 Major and Johnson,7 Major et al.,13 Ritchie  and NeSmith,4 and Warrington and Kanemasu.21,22

For soybean,20,23 maize,24,25 and wheat,26 thermal time accumulation functions have been modified by the effects of daylength, solar radiation, and sometimes water stress.

Theoretically, if thermal time is accumulated correctly for a given crop variety, then crop development should be directly related to thermal time accumulation, with a characteristic amount of accumulation required for each growth stage or for the appearance of each plant organ (phyllochron) regardless of the time or location of planting. The chapters on phenology models for wheat, maize, sorghum/millet. rice, and cotton show how various modelers have attempted to calculate the accumulation of thermal time, with a considerable degree of success. As can be seen from the leaf and stem development chapters, however, the situation can be quite complicated and is not fully understood.

FIGURE 1. Days for the plant to reach some stage as a function of temperature.

1. Simple Thermal Time Equations

Simple thermal time equations or growing degree day (GDD) equations accumulate thermal time linearly with increasing temperature above a constant crop-specific base temperature. There is usually no optimum temperature, although sometimes there is an upper limit above which accumulation is constant. Many such equations have been reviewed by Cross and Zuber,10 Robertson,27 Major et al.,28 and Zur et al.29 Numerous researchers have expressed reservations about the theoretical validity of simple thermal time equations. Wang30 noted the base temperature changes throughout the life of the plant. Thornthwaite,31 Wang,32 and Padol'skii13 reported that using various base temperatures or time periods for accumulation did not improve the accuracy of degree day summations as predictors of crop development. Simple thermal time equations ignore thermoperiodicity, the range of temperature between day and night, which has been shown to affect plant response,34,35 and daylength, which is discussed in a later chapter. In general, these equations are effective only for locally adapted varieties or hybrids over a small geographic range and within a narrow range of planting dates. The equations will have to be rederived for application outside of a limited range of conditions.

2. Photothermal Equations

Photothermal equations are similar to simple thermal time equations, except that daily accumulated thermal time is multiplied by a factor based on daylength. These equations were discussed by Coligado and Brown36 and by Major et al.28 Williams,37 and Major et al.13 developed iterative regression equations combining temperature and daylength effects. Photothermal equations may be usable over a wider range of conditions than simple thermal time equations. However, equations that ignore the negative effects of extremely high temperatures are not suitable for areas with high daytime temperatures during the growing season. They may be used in areas with mild growing season temperatures.

3. Daily Thermal Time Equations

Daily thermal time (DTT) equations accumulate thermal time linearly, with increasing temperature up to an optimum temperature or temperature range and thereafter at a decreasing rate with further increases in temperature. Daily maximum and minimum temperatures are used to estimate interpolated temperatures at 3-h intervals throughout the day.24,26 The rate of daily accumulation is modulated by daylength,24,26 solar radiation,25 or daylength and water stress factors.20

4. Nonlinear Thermal Time Equations

A set of nonlinear equations have been presented by Kiniry and Keener12 in which plant development is modeled based on the response of enzymatic reactions to temperature and other factors. Mahan et al.38 and Burke et al.39 discuss the reaction rates of several wheat and cotton enzymes over a range of temperatures in terms of crop management and breeding for high yields.

For predicting crop growth stages, the daily thermal time equations have generally been most effective, especially over a range of environments. However, there has been very little experience in the use of the nonlinear, enzymatic-based equations to predict crop phenology under field conditions.