A previously developed model of wheat growth, designed for convenient incorporation into system level models of advanced space life support systems is described. The model is applied to data from an experiment that grew wheat under controlled conditions and measured fresh biomass and cumulated transpiration as a function of time. The adequacy of modeling the transpiration as proportional to the inedible biomass and an age factor that varies during the life cycle are discussed

Rummel, John D.

Volk, Tyler

English

NASA Technical Reports Server

N91-8i795
TRANSPIRATION DURING LIFE CYCLE
IN CONTROLLED WHEAT GROWTH
Tyler Volk* and John D. Rummel**
*Earth Systems Group, Department of Applied Science,
New York University, New York, NY 10003, U.S.A.
** Code EBR, Life Sciences, NASA Headquarters,
Washington, D.C. 20546, U.S.A.
ABSTRACt
We use a previously-developed model of wheat growth, which was designed for convenient incorporation into
system-level models of advanced space life support systems. We apply the model to data from an experiment that
grew wheat under controlled conditions and measured fresh biomass and cumulated transpiration as a function of
time. We examine the adequacy of modeling the transpiration as proportional to the inedible biomass and an age
factor, which varies during the life cycle. Results indicate that during the main phase of vegetative growth in the
first half of the life cycle, the rate of transpiration per unit mass of inedible biomass is more than double the rate
during the phase of grain development and maturation during latter half of the life cycle.
THE GROWTH MODEL
We developed a model for the growth of wheat/1/, which proved useful for coupling the wheat with other
components in a system-level model of a Controlled Ecological Life Support System (CELSS). The rationale for
the model's form is that growth curves of most crops prominently show the S-shaped or sigrnoidal curve typical of
biological systems. The solution to the logistic differential equation imitates this S-shape of exponential growth
followed by a leveling-off. In the logistic equation, dM/dt = rM(I-MIIO, where M is the biomass and I is time,
there are two parameters: r and K. The • is the growth rate for the purely exponential part of the system. K, the
carrying-capacity in an ecological system, in this case is the maximum biomass reached by the crop. The logistic
equation thus contains some biologically meaningful parameters.
While the logisdc ¢quadon can be applied directly to the growth of the inedible biomass of a crop, the equation for
the edible crop parts is here somewhat differently structured (see abo/2,3/). Like the inedible cells, the edible cells
reproduce and the total edible growth must be proportional to the edible mass (Meal). However, the edible parts do
not produce their growing mass through photosynthesis, but rather receive photosynthetic products from the
inedible parts (in particular, the leaves); therefore, the inedible biomass (Mined) should also appear in the edible
equation. Furthermore, since the edible growth occurs substantially after the beginning of the inedible growth
(about halfway through the life cycle for wheat), a time that initiates the growth of the edible mass (t*) is
incorporated into the edible equation. Before t* the edible biomass is assumed equal to zero, and its growth is
initiated at t* with a minimum edible mass (Emin). The full set of equations is (see also/2,3/):
t<t*: ---_= 0
(1)
(2a)
(2b)
The parameters t and r* are in units of time, rined and red arc in units of rime'l, and all other parameters (Med, Mined,
Me.d, Kined, Emin) arc in identical units of either dry mass ordry mass per unit area. The system of equations (In-c)
above was used for wheat, soybean, and potato/2L The total fresh biomass (B) is the sum of the fresh edible and
inedible masses, expressed using their respective ratios (wi's) of their wet (fresh) mass to dry mass:
B = Wed Med + Wine d Mined (3)
355
https://ntrs.nasa.gov/search.jsp?R=19910022481 2020-03-17T14:58:58+00:00Z
We compare the model to data provided by S. Schwartzkopf/4/. He grew wheat at the NASA Ames Research
Center under controlled conditions of temperature, humidity, and atmospheric CO2 (1200 ppm). Since we are not
concerned here with how growth is affected by changes in these vmiables (except for humidity, see below), or
other parameters (such as planting density), this data has been normalized to the total fresh biomass at day 60
(B60), which in his experiment was the maximum total fresh biomus reached during the seed maturation. Figure
I a plots this normalized value of BIB60 as a function of time for lhe wheat data.
Equations (1, 2a-b, and 3) are run with Wed = 1.13 (gm fresh per gm dry)/5/and wined = 5.7 (gin fresh per gm
dry)/6/. Other parameters used here are Ked = 2500, Kined ffi 3700, £mia " 80, initial Mined = 10. In previous
models these units have been gm dry mass m -2, but here the units may he considered arbitrary since to facilitate
comparison to Schwartzkopf's data, the model's output is nomudized Is a ratio between total fresh biomass and the
total fresh biomass at day 60. This ratio, BIB60, is plotted in figure It. Note also that the harvest index, defined
as the fraction of the edible dry biomass--here approximately 2500/(2300+3700)----is consistent with the value of
0.4 from data/51. The only major unknowns that can influence the Rape of the growth curve significantly are the
growth rates; these are adjusted to produce a reasonably accurate fit to data. The model curve shown in figure la
uses red = rined = 0.2 day -!,
TRANSPIRATION FORMULATION
Transpiration will probably account for about half tbe energy balance in the plant growth system ofa CELSS. By
definition, the total transpiration rote (I") is proportional to the trlmspiratlon rate per unit of inedible biomass (7) and
to the total inedible biomass. Therefore
r -- _ M_d (4)
Following general reasoning such as that given in Gates/71, 7 is I function of the difference between the partial
pressures of water vapor in the leaf (PH20,lc.af) and atmosphere (PH20a_ir) and a function of the stomatal resistance
(/'s), which itself a complex function of various environmental factors including light, temperature, and CO2.
Y = "_' _fsh (5)
Here we have written y as a product of a humidity factor 0rE is a function of PH20.leaf - PH20,air), a stomatal
resistance factor q's), a unit normalizing constant 7*, and an age factor _, which accounts for changes in the
plant's transpiration rate per unit inedible biomass during its life cycle even when all environmental factors ffh, fs)
are constant. A y = constant = 2.4 gm H20 per gm dry inedible blomiss per day (this gives a rough average of
typical wheat under controlled environments/8/) was used by Rmnmel _ Volk IlL but could not be tested against
data during the plant's life cycle at that time. S. Sehw_.kopf hal _ able to take detmled transpiration data from
wheat/41. To facilitate comparison between model and dat!t lbe eumulatnd mmsptred water at lime t ( 0 Jt rdt ) is
normalized to the cumulated transpired water at day 60 ( 0_ rdi, ). This ratio---- _t rdt (o _ rdt )-t_ is plotted
as a function of time in figure I b. It is also useful to consider the instantaneous transpiration rate F (here calculated
from the data on cumulated water for any point using the c,qrevious and subsequent points), also normalized to the
cumulated transpired water at day 60. This ratio---.- r ( 0_ F_ )-t_lms the units of day "-t , and should he read Is
the fraction of the total transpired water during the life cycle transpired during a given day; this ratio is plotted in
figure Ic.
Normalized cumulated transpiration = _ (6a)
d_ rd,
V
Normalized transpiration rate = _ (6b)
0Jw rd,
Schwartzkoprs humidity controls kept the relative humidity (rh) at 0.35 at the beginning of the experiment, but
only maintained rh near 0.45 at the end/4/; the change was gradual and approximately linear. Assuming leaf rh =
1.0 and air rh varied from 035 to 0.45, the humidity factor[h, exprested in terms ofrh and non-dimensionalized
to the final condition, is taken here to have varied linearly from !.18 at the beginning of the experiment ((1-
035)/(t-0.45)) to 1.00 at the end. Furthermore, we set y *= 2.4 gm H20 per gm dry inedible biomass per day,
and since environmental conditions were approximately constant, fs = 1.0 folr the duration of the experiment. We
test several cases of the age factor fa.
The first case hasfa = ! .0 = constant (or, ct = O, see below). Output from the model for cumulated transpiration
;lnd transpiration rate is nomlalized to the cumulated transpiration at day 60 using equations 6a-b, like the
experimental data, Note this normalization effectively eliminates dependence oftbe results on "_'. Results with[a
356
= constant are plotted against data in figures lb and lc. Although the general shape of the cumulated transpiration
data is matched by the model (see figure Ib), the empirical value is significantly underestimated during the middle
one-third of the life cycle. The underestintadon is even clearer in the rate results, shown in figure lc. For the first
one-half of the life cycle, the transpiration rate in the model is much too low.
A second case explores the possibility that the transpiration rate per unit inedible biomass is substantially higher
when the plant is younger than when mature. A convenient way of parameterizing this process that takes into
account the apparent steadiness of the transpiration rate during the second one-half of the life cycle, when the
inedible biomass it_lf is relatively maximum and constant, is to wrltefa as a function of Mined:
fa -- 1 + a(l M'n- _) (7)
Here the term ct is an enhancement of transpiration rate per unit biomass when the plant is young. Notefa = 1.0
when Mined = Kincd. The model output for cumulated transpiration and transpiration rate for this second model--
which uses a = I, rather than ct = 0--is shown in figures Ib and lc. Overall better fit to the data is apparent, in
particular, improvement in the transpiration rate during the first one-half of the life cycle. However, also clear is
that even higher rates (in other words, higher ct's) are needed in the first one-third of the life cycle. Without fitting
the data even further, we have nevertheless demonstrated the possibility of representing the transpiration to varying
degrees of accuracy with formulations that have physical meaning.
CONCLUSION
Models such as these are the best way of examining the "interactions of assumptions"/9/. Considering the overall
results, the logistic growth equations combined with the assumption that the rate of transpiration per unit inedible
mass decreases during the life cycle of the crop will generally reproduce the data and will probably be adequate in
highly aggregated models of a CELSS, for example, the BLSS model/1L A physiological interpretation of this
transpiration formulation and comparison of these findings to the transpiration formulations in more detailed
models of non-hydroponic wheat/10,11/(which, however, are presently not applicable to a CELSS model) will
help the crop model shown here develop more complex dynamics and allow better pntliminary designs of space
agricultural systems.
ACKNOWLEDGEMENTS
Research time for T. V. was partially provided by NASA-Ames Joint Research Interchange NCA2-101. We thank
T. Tibbins fox a thoughtful and important review.
REFERENCES
I. J. D. Rummel and T. Volk, A Modular BLSS Simulation Model, Adv. Space Res., 7, # 4, 59-67 (1987).
2. T. Volk, Modeling the growth dynamics of four candidate crops for controlled ecological life support systems,
Final report to NASAJASEE Summer Faculty Fellowship Program at Johnson Space Center, NGT44-001-800,
33-1 to 33-17 (1987).
3. T. Volk and H. Cullingfoxd, Crop growth and associated life support for a lunar farm, Lunar Bases and Space
Activities of tl, e 21st Century, in press (1989).
4. S. Schwartzkopf, private communication (1987).
5. B. G. Bugbee and F. B. Salisbury, Studies on maximum yield of wheat for the controlled environments of
space, in Controlled Ecological Life Support Systems: CELSS "85 Workshop, eds. R, D. MacEIroy, N. V.
Martello, and D. T. Smernoff, NASA-TM-88215, p. 447-486 (1986).
6. B.G. Bugbee, private communication (1988).
7. D. M. Gates, Biophysical Ecology, Springer-Verlag, New York (1980).
8. B.G. Bugbee, private communication (1986).
9. J. F. Reynolds and B. Acock, Modeling approaches for evaluating vegetation responses to carbon dioxide
concentration, eds. B. R. Strain and J. D. Cure, Direct Effects o.f Increasing Carbon Dioxide on Vegetation,
DOE/ER-0238, U. S. Dept. of Energy, Wash., D. C., p. 33-51 (1985).
357
10. T. Hodges and E. T. Kanemasu, Modeling daily dry matter production of winter wheat, Agronomy Journal,
69, 974-978 (1977).
11. S. J. Maas and G. F. Arkin, TAMW: A wheat growth and development simulation n'gxt¢l, (Research Center
Program and Model Documentation. No. 78-1), Blackland Research Center at Temple, Texas Agriculture
Experiment Station, College Stafon, Texas (1980).
E
O
t.-i
r--
.N
E
O
z
e-
.9
c:
I,--
3
E
-'.s¢o
'10
N
;=
m
E
O
z
1,0
0.8
0.6
0.4
0.2"
0.C
0
1.0
0.8-
0.6
0.4
0.2
0.0
0
• i . i . i . i . i .j t
10 20 30 40 50 60
O_
• i • i . i . i . i
• ! _ | • ; . | . | .
10 20 30 40 50 60
DW
_. 0.04
c
O
'.,= 0.03
c 0.02
I--
"O
,0,)
N 0,01
E
O
z 0.00
0¢ o:0
• I • i - ! - ! - !
10 20 30 40 50 60
Day
Fig. 1. Model results (lines) and empirical data (points) of (a, top) fresh biomass, (b, middle)
cumulated transpiration, and (c, bottom) transpiration rate, all normalized as described in the text.
Results in (b) and (c) are shown for two values of Qt;a controls the time-dependence of the age
factor fa in the transpiration rate. When ot = O,fa is constant; when 0t = l,fa decreases non-
linearly from about 2 in early growth to about ! in late growth (see text). Results for biomass in (a)
do not vary as a function of ct. See equations 6a-b for definition of the normalized cumulated
transpiration and nomlalized transpiration rate.
358


Transpiration during life cycle in controlled wheat growth

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server