B.J. Choudhury Agricultural and Forest Meteorology 101 2000 217–234 223
The following equation is used to calculate R
g
mol CO
2
m
− 2
per day Amthor, 1989 pp. 11–12: R
g
= 1 − Y
G
A
g
− R
m
T 31
where Y
G
is the growth conversion efficiency, taken to be 0.74 as the average of three values for wheat given
in Amthor 1989 p. 79. For estimating net carbon accumulation over the global land surface, Ruimy et al.
1996 had taken Y
G
to be 0.72. According to Johnson and Thornley 1983, Y
G
is typically about 0.75. While it is recognized that Y
G
may not be constant during growth due to changes in biochemical composition of
plant Lafitte and Loomis, 1988; Amthor, 1989 pp. 41–43, there is insufficient measurement for wheat
to prescribe such changes. Nevertheless, possible effect of changes in Y
G
during growth is assessed while presenting the results.
Respiration R is obtained as the sum of the values from Eqs. 30 and 31, viz.,
R = 1 − Y
G
A
g
+ Y
G
R
m
T 32
2.3. Net carbon accumulation and radiation use efficiency
Daily gross photosynthesis A
g
and respiration R values are used in Eq. 1 to obtain net carbon accu-
mulation dCdt. Using Eq. 32 one obtains, dC
dt =
Y
G
A
g
− R
m
T 33
Note that use of a constant Y
G
in Eq. 33 implies that plant is in a steady state with respect to nonstruc-
tural cabohydrate pool. For sorghum, McCree 1988 shows that Y
G
increases with plant growth see Sec- tion 4.3.4, Eq. 35.
Then, the corresponding radiation use efficiency e; mol CO
2
mol
− 1
photon intercepted is calculated as the ratio of dCdt and IPAR.
3. Input data and methods
3.1. Canopy characteristics The canopy characteristics leaf area index and ni-
trogen content used in the present calculations are summarized in Table 1 and elaborated further.
Harper et al. 1987 present measurements of leaf area index, and nitrogen content of live foliage,
stem and roots for winter wheat cv. Coker planted at Southern Piedmont Conservation Research Cen-
ter near Watkinsville GA. The planting density was 25 plants m
− 2
. The crop was fertilized with 112 kg N ha
− 1
as ammonium nitrate in split applica- tion at planting in November 1982 39.2 kg N ha
− 1
and in March 1983 72.8 kg N ha
− 1
. These data are presented as best-fit curves to the measurements. The
canopy characteristics for 14 days have been extracted from these curves covering the period from middle of
March to middle of May.
Gregory et al. 1979 and Monteith private com- munication, 1986 present biomass and nitrogen con-
centration of foliage, stem and roots of winter wheat cv. Mans Huntsman grown on a field of University
of Nottigham Farm at Sutton Bonington Leics.. The plant density of the established crop was 250 plants
m
− 2
. No fertilizer was applied at planting October 1974, but 97 kg N ha
− 1
was applied in May 1975. The leaf area index has been determined from the foliage
biomass and specific leaf weight of 525 mg dm
− 2
for this cultivar given by Austin et al. 1982. The canopy
characteristics for 9 days have been used, covering the period from middle of March to middle of June. The
data after anthesis have not been considered to mini- mize inclusion of senescing leaves.
McNeal et al. 1966 present biomass and nitrogen content of foliage, stem and roots as average values
for five cultivars of spring wheat cvs. Thatcher, Min- dum, Chinook, P. I. 266148, and C.I. 13636 grown at
Bozeman MT without fertilizer. The leaf area index has been determined from foliage biomass and spe-
cific leaf area of 18.5 m
2
kg
− 1
obtained by van den Boogaard et al. 1997 as the average value for 10
spring wheat cultivars. The canopy characteristics for 4 days covering the period from middle of June tiller-
ing stage to middle of July flowering stage, have been used.
The data presented in Table 1 show considerable differences in partitioning of total plant nitrogen into
foliage, stem and roots for winter and spring wheat. The average fraction of total nitrogen in foliage, stem
and roots for winter wheat is, respectively, about 48, 38 and 14, while it is 70, 26 and 4 for spring
wheat. Factors contributing to this difference are not known, although we note that spring wheat was not
224 B.J. Choudhury Agricultural and Forest Meteorology 101 2000 217–234
fertilized and one of the varieties cv. Mindum was durum type.
3.2. Air temperature and incident radiation Both air temperature and incident radiation change
during the growing season of wheat, and they also vary with location. On a monthly basis, these two en-
vironmental variables are not totally uncorrelated. To have some guidance in specifying air temperature and
radiation for model calculations, weather conditions corresponding to the data given in Table 1 was con-
sidered, as summarized further.
From March to May at Watkinsville GA, mean daily air temperature increased from 5 to 20
◦
C Sharpe et al., 1988, while irradiance increases from about 32
to 45 mol m
− 2
per day Lof et al., 1966; 1 J solar ra- diation has been taken to be equal to 2
m
mol photon. At Sutton Bonington UK, mean daily air tempera-
ture and irradiance increased, respectively, from 3.5 to 15.5
◦
C and from 15 to 34 mol m
− 2
per day dur- ing the period, March to June Gregory et al., 1981.
The mean air temperature and radiation at Bozeman MT during June–July period are, respectively, about
16.7
◦
C and 50 mol m
− 2
per day. Near Manhattan KS, where chamber measure-
ments and calculations were done to obtain gross photosynthesis and net carbon accumulation by win-
ter wheat cv. Newton Wall and Kanemasu, 1990, air temperature ranged between 13 and 25
◦
C and in- cident PAR fluctuated between ca. 10 and 70 mol m
− 2
per day Wall et al., 1990. From these measurements, the mean daily irradiance is estimated to be about
48 mol m
− 2
per day. Considering the above environmental conditions,
calculations have been done for a base value of temper- ature as 15
◦
C, while sensitivity results are presented for 10 and 20
◦
C. Incident direct and diffuse irradiances were calcu-
lated at 15 min interval for 34
◦
N Watkinsville, GA by prescribing atmospheric conditions and time peri-
ods of a day being cloudy Choudhury, 1982, 1987. A sample of 13 realizations of daily total irradiance
and its diffuse fraction, obtained by varying the time periods of a day being cloudy, used in the present
calculations are given in Table 2. Cloud cover varies from zero Realization 1 to 100 Realization
Table 2 Possible realizations of incident total irradiance used in the
calculations I, mol m
− 2
per day and the fraction of this irradiance which is diffuse f
dif a
I f
dif
e
g,10
e
10
e
g,20
e
20
1 65
0.20 0.0195
0.0134 0.0184
0.0123 2
64 0.20
0.0195 0.0134
0.0184 0.0113
3 61
0.20 0.0195
0.0134 0.0184
0.0113 4
59 0.20
0.0194 0.0133
0.0184 0.0114
5 55
0.22 0.0204
0.0143 0.0183
0.0124 6
52 0.24
0.0214 0.0143
0.0193 0.0124
7 48
0.27 0.0224
0.0153 0.0213
0.0134 8
39 0.36
0.0265 0.0184
0.0244 0.0154
9 30
0.49 0.0316
0.0225 0.0285
0.0174 10
23 0.68
0.0398 0.0276
0.0356 0.0215
11 17
0.88 0.0488
0.0336 0.0426
0.0255 12
15 0.97
0.0527 0.0355
0.0465 0.0276
13 14
1.00 0.0537
0.0365 0.0465
0.0277 All
b
42 0.33
0.03044 0.02043
0.02741 0.01637
a
Totally clear and cloudy sky conditions are presented here as, respectively, Realization 1 and 13. Also given are calculated
mean radiation use efficiency mol CO
2
mol
− 1
photon intercepted for gross photosynthesis e
g
, 10 and e
g
, 20, and for net carbon accumulation e
10
and e
20
when air temperature is 10 and 20
◦
C for the 27 canopies in Table 1. The coefficient of variation in
percent of the efficiency values for the 27 canopies are given in parenthesis.
b
The last line gives the mean irradiance and diffuse fraction, together with the summary of efficiency values for all realiza-
tion. These efficiency values are for randomly oriented leaves and A
max
= 20
m
mol m
− 2
s
− 1
.
13. It is commonly observed that the diffuse frac- tion does not change significantly at high irradiances,
but then it increases as the total irradiance decreases Collares-Pereira and Rabl, 1979, as seen in Table 2.
These irradiances will be considered to provide pos- sible realizations of day-to-day fluctuations. While
it was desirable to use an ensemble of measured diurnal values of direct and diffuse PAR, such mea-
surements were not available to me for the present calculations.
3.3. Summary of parameters and sensitivity Calculation of the efficiency values for the 27
canopies Table 1 has been done for all realizations of the incident irradiance Table 2 assuming the
base values of maximum leaf photosynthesis A
max
as 20
m
mol m
− 2
s
− 1
, curvature factor θ in the light response function for leaf photosynthesis as 0.8, leaf
B.J. Choudhury Agricultural and Forest Meteorology 101 2000 217–234 225
inclination index χ as 0 and temperature T as 15
◦
C Base Case. Sensitivity analysis considers A
max
to be either 18 or 22
m
mol m
− 2
s
− 1
, θ being either 0.7 or 0.9,
x
being either −0.2 or +0.2, and T being either 10 or 20
◦
C Sensitivity results. The sensitiv- ity results are presented in terms of relative change
in . Thus, for example, sensitivity of e
g
to A
max
has been calculated as: 100 [e
g
A
max
= 22 or 18 –e
g
A
max
= 20]e
g
A
max
= 20.
Fig. 1. Variation of the radiation use efficiency mol CO
2
mol
− 1
photon intercepted for, a gross photosynthesis, and b net carbon accumulation, with leaf area index of the 27 canopies at four irradiances, as annotated within the figure.
4. Results and discussion
