Thermal Time

2.7 Thermal Time

The forgoing example takes the viewpoint that clock or calendar time is the correct basis for measuring development, and that the rate of develop- ment of an ectotherm (an organism whose temperature is environmentally determined) varies depending on environmental temperature. Another viewpoint is that there exists a time scale in which the rate of devel- opment of organisms is constant, and

like that in Fig. 2.7 provides a means of transforming

time to clock or calendar time. Monteith (1977) uses the term thermal time to describe a time scale in which the development rate of organisms is constant. It has also been referred to as physiological time or p-time. Units of thermal time are day-degrees or hour-degrees. Units for p-time are p-days or p-hours.

Thermal Time

The formal transforms which convert one time scale to the other, for an organism whose development rate depends only on temperature, is

where is the thermal time and R is the rate of development at temperature T (which, in turn, depends on time). The function g is the inverse of R

and allows, in principle, the conversion of thermal time back to clock time.

In practice, the integral in (2.6) is always approximated as a sum because temperature generally is not a predictable function of time. For the usual calculation of thermal time we assume a straight line relation- ship between development rate and temperature, such as that shown in

Fig. 2.7. We also assume that temperatures are always within the range

.. . where

the base temperature (low temperature at which development stops) and

is the temperature at which the development rate is maximum. Thermal time, and therefore organism development, is then directly proportional to the sum of products of (I;: - and the length of the time increment, where I;: is the temperature at a particular

time, with the condition that I;: - Given these assumptions, the equation for thermal time increments is

0. (2.7) The time step, At, is chosen so that temperature is fairly constant during

(I;: -

when I;:

otherwise =

one time increment. The units of A t are day-degrees, or hour-degrees, depending on the units of At. No thermal time is accumulated when I;: is at or below the base temperature. Thermal time is computed as:

From Fig. 2.7, it can be seen that the rate is 1.35 when the temperature is

C, the time for completion is 111.35 =

= 33" C. The base temperature is

C. At

0.74 days. The thermal time for completion at this constant temperature is 0.74 days, or (33" C - 10"

= 17.0 day-degrees. When the temperature of the melon fly eggs varies during germination, we can use the varying temperature, with Eq.

to find since the start of the stage. Once reaches 17.0 day-degrees, the stage will be complete. The inverse operation indicated by the second of

(2.6) is used to find the calendar or clock time required to complete a developmental stage. An analytical form of the inverse is not possible except in the trivial case where temperature is constant. To find the calendar time required for completion of the egg stage in the example just presented, we would construct a table of and the corresponding . We would then enter the

Temperature

table at =

17.0 day-degrees and find how many calendar days were required to reach that value. The term heat unit has been used in connection with the day-degree, but this is clearly inappropriate. The unit has nothing to do with heat or its accumulation, but defines a quantity which bears a simple linear relationship to biological time.