Agriculture Reference
In-Depth Information
temperature occur during the time interval. Selec-
tion of the time interval depends on availability of
data and the problem, but most frequently a daily
time interval is used, with day/night and hourly
intervals sometimes used. Somewhat problematic
is that equation 2.1 has been interpreted in differ-
ent ways, resulting in over a 20% difference in
the estimation of
T
avg
for a growing season using
the same weather data, and it often is unclear
how the equation is being interpreted (McMaster
and Wilhelm 1997).
Once
T
avg
is determined, a key area of diver-
gence in thermal time approaches is the tempera-
ture-response function. The most basic version is
to estimate thermal time (TT) linearly above the
base temperature (
T
base
) at which the development
rate is zero (Fig. 2.3a):
secondary importance and usually affect only
certain developmental processes or events (Masle
et al., 1989). Further, factors such as water and
nutrients often seem to have threshold levels
before infl uencing development. Given the
importance of temperature in controlling and
predicting wheat development, this section
focuses primarily on the role of temperature.
Temperature
Reamur (1735) formalized the relationship
between phenology and temperature by creating
the concept of heat units, which is more com-
monly known today as thermal time. Thermal
time acknowledges that, for most developmental
processes, temperature is a better predictor than
calendar time (i.e., days, hours, etc.). Many
studies (Friend et al., 1962; Cao and Moss 1989;
Jame et al., 1998; Yan and Hunt 1999; Streck
et al., 2003; Xue et al., 2004) show a curvilinear
response of the developmental process to tem-
perature. Thermal time is an attempt to
explain the observed differential response to tem-
perature. Many forms of describing and quantify-
ing thermal time have been developed, yet all
forms are empirical in approach as the direct
mechanisms of temperature effects are not
well known (Wang 1960; Shaykewich 1995;
Jamieson et al., 2007).
Estimation of thermal time has two elements:
(i) average temperature (
T
avg
) over some time
interval and (ii) use of
T
avg
in a temperature-
response function to estimate the rate of the
developmental process or “passage of time” (i.e.,
the effectiveness of a specifi c temperature on
development rate). The most accurate calculation
of
T
avg
is to use the integral of temperatures over
the time interval of interest, but in practice the
maximum (
T
max
) and minimum (
T
min
) tempera-
ture of the interval are used:
(
)
(2.2)
TT
=−
T
T
,
TT
≥
0
avg
base
Thermal time in this instance is often expressed
as growing degree-days (GDD, ºC
.
days), and the
value can be either summed or used directly in an
algorithm. For example, it may require an average
of 105 GDD for a leaf blade to grow completely
(Frank and Bauer 1995), or if the fi nal blade
length is 105 mm the rate of growth can be 1 mm
GDD
−1
. Normally, predicting when a develop-
mental event begins or ends assumes a summation
of thermal time.
The base temperature is important in defi ning
the minimum temperature at which development
can occur;
T
base
can be diffi cult to directly measure,
and it likely changes both among cultivars and
possibly with progression through the life cycle
(Angus et al., 1981; Weir et al., 1984; McMaster
and Smika 1988; Slafer and Rawson 1995a,b;
Madakadze et al., 2003). Yet often this does not
introduce signifi cant error for predicting develop-
ment in the fi eld, as little development occurs
near
T
base
, inaccuracies in calculating
T
avg
mask
slight differences in setting
T
base
, and little differ-
ence in predictive accuracy is noted by using a
range of temperatures for
T
base
(McMaster and
Smika 1988). Often
T
base
is set to 0 ºC (Gallagher
1979; Baker and Gallagher 1983a,b; Slafer and
Rawson 1994; McMaster et al., 2008).
(
)
TTT
avg
=
+
2
(2.1)
max
min
This simple estimation of
T
avg
is generally
accurate, but errors increase as day length
deviates from 12 hours and if sudden changes in
