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Modelling of plant growth for yield prediction
Agricultural Meteorology, 14(1974) 243--253 ~) Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands MODELLING OF PLANT GROWTH FOR YIELD PREDICTION* W. E. SPLINTER
Agricultural Engineering Department, University of Nebraska, Lincoln, Nebr. (U.S.A.) (Received October 1, 1973; accepted May 20, 1974) ABSTRACT Splinter, W. E., 1974. Modelling of plant growth for yield prediction. Agric. Meteorol., 14: 243--253. A corn growth model is presented which requires three basic input parameters: average daily light intensity (ly), average daily temperature (°C) and soil resistance block reading (Ohms). Comparison with field measurements taken during the summer of 1972 indicates reasonable fit, although the wet season did not allow a test of the soil moisture component of the model. INTRODUCTION Within r e c e n t y e a r s a c o m b i n a t i o n o f f a c t o r s has led to t h e d e v e l o p m e n t o f s i m u l a t i o n m o d e l s o f biological s y s t e m s . T h e r e f i n e m e n t o f e x p e r i m e n t a l techniques and instrumentation which allowed the determination of the r e s p o n s e o f biological s y s t e m s to their e n v i r o n m e n t was an i m p o r t a n t first step. T h e d e v e l o p m e n t o f i m p r o v e d g r o w t h c h a m b e r s , p h y t o t r o n s , i n s t r u m e n t a t i o n f o r m e a s u r i n g e n v i r o n m e n t a l p a r a m e t e r s , d a t a logging s y s t e m s a n d c o m p u t e r i z e d d a t a r e d u c t i o n has a l l o w e d m e a s u r e m e n t s w i t h g r e a t l y i m p r o v e d precision. M o s t i m p o r t a n t , h o w e v e r , was t h e d e v e l o p m e n t o f c o m p u t e r languages a n d s o f t w a r e w h i c h a l l o w e d t h e u t i l i z a t i o n o f exp e r i m e n t a l l y derived d a t a in direct m o d e l building b y biological scientists as well as p h y s i c a l scientists. T h e r e is, t o d a y , an increasing i n t e r p l a y b e t w e e n t h e p l a n t p h y s i o l o g i s t and t h e e n g i n e e r t o w a r d t h e d e v e l o p m e n t o f a generalized, r a t h e r t h a n a q u a n t i t a t i v e u n d e r s t a n d i n g o f m a n y biological processes. APPROACHES TO MODELLING OF PLANT GROWTH FOR YIELD PREDICTION As o n e m i g h t readily e x p e c t t h e a p p r o a c h t a k e n reflects the b a c k g r o u n d a n d t h e r e s e a r c h o b j e c t i v e s o f t h e m o d e l l e r . R e i t z ( 1 9 7 4 ) , in his o p e n i n g address, has p o i n t e d o u t t h a t t h e o b j e c t i v e o f this c o n f e r e n c e is t h e i m p r o v e * This paper is published with the approval of the Director of the Agricultural Experiment Station, University of Nebraska, Lincoln, Nebr., as Paper No. 3892 of the Journal Series.
244 ment of water-use efficiency which he has defined as the ratio of dry matter production to evapotranspiration. Irrigationists use the term water application efficiency to reflect the a m o u n t of water appearing in the root zone versus the a m o u n t applied through irrigation. The total picture must consider the a m o u n t of marketable product-grain or forage-produced per increment of water added, with storage, time of application and rate of use being critical inputs. Several models deal with water transport through the plant. These models range from resistance or resistance-capacitance simulations of evapotranspiration or water movement through plants to models predicting irrigation needs. Jensen (1968) has developed an irrigation prediction model which deals with evapotranspiration in fairly precise detail, but the whole area of crop response is simply taken care of by "crop coefficients" for various crops at different stages of growth. The preceding paper on modelling the soil--plant--atmosphere continuum given by Shawcroft et al. (1974) has presented the state-of-the-art in prediction of evapotranspiration. The plant modellers on the other hand, have approached modelling on the basis of predicting dry-matter weight as a function of the environmental parameters. This paper will be concerned with prediction of plant growth. Duncan et al. {1967) were among the earliest to publish a model of photosynthesis. Basically, Duncan's approach is to divide the leaf canopy into horizontal layers and then determine the light intensity, CO2 concentration, rate of photosynthesis, and rate of dry matter increase by layers. Inputs to the model are experimentally determined relationships which are stored in the computer. Duncan (private communication, 1974) is currently working on a SIMAIZ program for corn which extends his original model to include many details such as soil moisture level and development of the ear. De Wit et al. (1969} developed the ELCROS model for plant growth. This model approaches the problem from the basis of a total crop mass, which has a reservoir of stored, available carbohydrate energy. This reservoir is contributed to by photosynthesis while the activities of respiration, leaf growth, stem growth and root growth pull from this reservoir. Since only a part of the total biological mass is growing or is photosynthetically active De Wit uses a " b o x c a r " train bookkeeping system to keep track of new growth and to depreciate the activity level of this growth with age. The model is quite comprehensive from an operational sense and De Wit is now using CSMP/360, a reactive language, to program his model. At this stage his model assumes adequate soil moisture and is concerned with forage, rather than grain production. Curry (1971) and Curry and Chen (1971 ) developed a CSMP simulation model for corn. The model considers photosynthesis by layers, individual growth of leaves, stems and roots and respiration as a loss function with evapotranspiration modulating soil-water potential. In the second paper a system of allocating photosynthate to roots, stems and leaves was developed. No system for storage of available energy is included in this model.
245 NEBRASKA
CORN MODEL
The basic parameters upon which this model is based were set forth by Beeman (1966). The plant is considered as a machine deriving its energy from the sun. Leaf area is the primary growth determining factor. If we assume that the growth will be some function of the total leaf area present then this can be expressed as:
(1)
dA = kA
dt
where A is area in cm 2 , t is time in hours, and k is a parameter analogous to the reaction rate constant in chemical kinetics. Separating variables and integrating, this relationship becomes: A' = e kt
(2)
where A ' is the normalized area in units of initial area and where initial area is assumed to be unity at time t = 0. This exponential relationship has long been recognized and values over short time intervals during initial stages of growth can be experimentally determined (Eide, 1965). The value of k is, however, a function of many variables such as light intensity, carbon dioxide level, soil-water potential, etc. The following corn growth model was developed from a growth model for tobacco (Fig.l) by Chen et al. (1969}. In order to more accurately determine k, we assume that it is a function of the rate of respiration per unit area (considered on a whole plant basis). We Day temP.
Radiant energy
I. . . . .
~2 H20
'll
Day temp.
P h o t o p e r iod
Id
"l I
r I I
I
I
',
,
02
Night temp.
. . dr Respiration ( ~ - ) -
CO 2
--------~ I
I_
H20
1OI t
i
.........
• I
,
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I
IIL]gl
II I ~--~I
I I
/L~
I I 1 I
Heat
,,. . . . .
b ~--C-~I I
Ill
StoPage cells
Assimilation
Fig.1. Schematic relationship between photosynthesis, respiration and growth.
246 f u r t h e r assume t h a t the p r o p o r t i o n of respirational activity going into p h o t o respiration will be available during the night period for assimilation. Then:
dR
(3)
k d = a b c d-~
(4)
k n = a (a + b) c d R
dt
where k d is the g r o w t h rate c o n s t a n t during the light period; kn is the g r o w t h rate c o n s t a n t during the night period; a is an e x p e r i m e n t a l c o n s t a n t = 1.719; a is the f r a c t i o n o f respirational energy used in p h o t o r e s p i r a t i o n = 0.015; b is the f r a c t i o n o f respirational energy used in assimilation = 0.01 ; c is the units o f p h o t o s y n t h a t e assimilated per unit o f respiration = 3.0; R is mg c a r b o h y d r a t e respired per d m 2 o f leaf area; and t is time in i n c r e m e n t s of hours with to for any day beginning at the initiation o f the light period. For any given day the value o f k will be the sum of k d and kn s u m m e d over hours of daylight or dark period, respectively. Values of a, a, b and c were d e t e r m i n e d for t o b a c c o by iterative fitting f r o m growth d a t a t a k e n in 20 g r o w t h cabinets in the N o r t h Carolina State University P h y t o t r o n . These values are being used in the c o r n m o d e l until individual values for c o r n can be d e t e r m i n e d . The rate o f respiration is assumed to be a f u n c t i o n of t e m p e r a t u r e and level o f available c a r b o h y d r a t e for respiration. E x p e r i m e n t a l results b y Chert et al., showed, for the day period: dR _ ( 0 . 0 0 3 8 5 7 + 0 . 0 0 3 8 2 9 T ) h = gh dt
(5)
where T is t e m p e r a t u r e in °C; h is level of available c a r b o h y d r a t e in the leaves and stem; and g = 0 . 0 0 3 8 5 7 + 0 . 0 0 3 8 2 9 T . Respiration during the night period was 0.8 t h a t for the day period (gn -- 0.Sg). The a m o u n t of available c a r b o h y d r a t e in the leaves is determined from: dh
dC
dR
dt
dt
dt
(6)
bc
dt
where d C / d t is the a m o u n t of c a r b o h y d r a t e a d d e d t h r o u g h p h o t o s y n t h e s i s , d R / d t is the c a r b o h y d r a t e lost t h r o u g h respiration; b c d R / d t is the carboh y d r a t e used f o r assimilation; and d H / d t is the c a r b o h y d r a t e t r a n s l o c a t e d t o the roots. For c o r n we assume t h a t the above g r o u n d stem-leaf system is o n e system in which readily available c a r b o h y d r a t e s for respiration and assimilation are stored in the pith and stem p h l o e m tissue. T r a n s l o c a t i o n is assumed t o be
247 roughly equal to the rate of respiration (eq.5) up to 25 ° C. Above 25°C (Bohning et al., 1953): dH dt - [0.1 - - 0 . 0 0 3 8 2 9 ( T - - 25)] h = qh
(7)
where q = [0.1 - - 0 . 0 0 3 8 2 9 (T -- 25)]. The function dC/dt is assumed to be proportional to light intensity and inversely proportional to the level of h in the leaf tissue: dC P dt -- h
(8)
0 . 4 9 9 6 ( • - 0.084) where P =1 + 0.912(1 -- 0.084)
(9)
and I is in langleys (cal. em -2 see -1 ). This function is adapted from Hesketh and Musgrave (1962), by converting light-intensity units from foot-candles to langleys and assuming no photosynthesis below 0.084 ly. For this corn model the average light intensity for the day period is used. Day length is programmed in as determined from published tables. Temperature is assumed to vary sinusoidally a b o u t the average temperature for the day with a 7.°C temperature variation from the mean. Substituting eqs.5, 7 and 8 into eq.6 and integrating from to to time t to determine h from an initial h0 we find:
P h= { (l+b~g+q
II--exp{--2[(k+bc)g+O](t--to)}]
+ hl exp{ --2[(l+bc)g+q] (t -- to )}}';:
(10)
This can be substituted into eqs.5 and 3 to obtain:
P k d = abcg {(l+bc)g+q
[1--exp{--2[(l+bc)g+q](t--to)}
+ h E exp
(11)
Using the a m o u n t of photosynthate accumulated during the day period for h0 during the night period and observing that there is no photosynthesis at night, then h for the night period can be found to be: h = h0 exp {--([l+(a+b)c]g+q)(t-- to )}
(12)
and
kn = a(a + b)cgho exp { - - ( [ l + ( a + b)clg+q)(t-- to)}
(13)
248 Eide (1965) f o u n d that mutual shading of small individual corn plants could be taken care of by decreasing the k parameter in eq.1 by 0.0015A0 where A0 is the initial area. For larger field plants hd is decreased linearly by: k' d = k d -- 0.009D
(14)
when D is day number. Leaf area increase for corn essentially stops at onset of flowering. Since onset of flowering is primarily a function of the degree days accumulated, the corn growth model accumulates 450 degree days from initiation of field measurements (A0 = 24 in. 2 ), based on the average t e m p e r a t u r e for each day, minus 10°C and then arrests leaf area increase. The plant continues to accumulate dry matter, so the program runs until kernel moisture is an estimated 30%. At present we do not have an exact relationship predicting black layer formation, a more recently developed criteria for maturity, but this may also be a degree-day p h e n o m e n o n . Around 1,400 degree days from germination are required for corn at the 30% kernel moisture stage depending on variety. In our irrigation research program resistance blocks are used extensively to mo n ito r soil moisture. Although these are relatively simple to use it must be recognized t ha t there is a great deal of variability between individual block readings at a given moisture level. Useable results have been obtained by averaging readings f r om four separate blocks. Splinter (1971) f o u n d a linear relationship between growth rate of corn and moisture block resistance. Therefore, the rate of photosynthesis in the model is decreased in accordance with: p, = P ( 0 . 1 3 5 -- 0.000021p) 0.135
(15)
where p is resistance block reading in ohms (average of 4). This will give 0 p h o t o s y n t h a t e p r o d u c t i o n at 6,430 ~2 soil resistance as shown in Fig.2. This corresponds to roughly --6 bar moisture tension in the soil used. The model therefore requires three data inputs: Average light intensity (ly), average daily t e m p e r a t u r e (°C), and average resistance block reading in the r o o t zone. VERIFICATION During the summer of 1972 ten plants were selected random l y in an irrigated corn research plot area under a center pivot sprinkler and ten plants of the same variety were selected in the non-irrigated area outside of the sprinkler circle at the University of Nebraska Field L a b o r a t o r y at Mead, Nebraska. Beginning on June 21 the stem diameter of each plant was measured every Monday, Wednesday and Friday until August 23. Light
249 0.15. light intensity = 0.376 ly/min max. temp.= 86°F; rain. temp.= 6 5 ' F length = 14.5 h
" ~ day "x.
No:o, p,~.ts:9
:
-~ 0.10c~ O~ U1D
o
0.05.
o
lO6O
36o0
~x~bo
Resistance (Ohms)
Fig.2. R e l a t i o n s h i p b e t w e e n m o i s t u r e b l o c k resistance a n d p l a n t g r o w t h rate for c o r n g r o w n in a g r o w t h c h a m b e r .
intensity and daily temperature were obtained from a microclimatological station one mile distant operated by Dr. Norman l{osenberg. Average light intensity was determined from the light intensity at solar noon and average daily temperature was determined from the arithmetic average of day temperature taken at 06h00 and at 14h00. z~ 0 -
300200-
*r
g%:p:,:n A = mD n
~100-
~5ot~
m 30-
-J 20-
10 0.1
.t
?
O:2 0:3 0:5 lb DiameteP (inches)
2b
Fig.3. R e l a t i o n s h i p b e t w e e n p l a n t leaf area a n d s t e m d i a m e t e r for corn. This r e l a t i o n s h i p h o l d s o n l y u n t i l tasseling.
25O Leaf area was d e t e r m i n e d f r o m stem d i a m e t e r m e a s u r e m e n t s f r o m the relation (Splinter and Beeman, 1968; see Fig.3): (16)
A =mD n
Although resistance block readings were available, there were no measureable differences b e t w e e n the d r y l a n d and irrigated corn plots as 1 9 7 2 had an unusually wet s u m m e r season. Differences b e t w e e n d r y l a n d and irrigated corn plots were f o u n d in o t h e r areas b u t n o t for the areas being used for this test. In general the c o r n plants in b o t h test plots were n o t subjected to a m o i s t u r e stress during the g r o w t h period o f the test. Results o f the m e a s u r e d plant leaf areas and the p r e d i c t e d areas f r o m the c o m p u t e r p r o g r a m are s h o w n in Fig.4. The p l o t t e d points for the field results are the average values for the ten plants in each plot. The m o d e l is capable of printing out, o n a daily basis, such p a r a m e t e r s as the daily g r o w t h rate c o n s t a n t , plant leaf area, assimilation and dry m a t t e r weight o f the above g r o u n d p o r t i o n of the plant. H o u r l y growth rates can be either printed o u t or displayed although these e x c e e d the precision of the i n p u t data at this time. S h o u l d there be a need for this precision, h o u r l y t e m p e r a t u r e s and light intensities c o u l d be i n t r o d u c e d .
• 1200
,
LE*F
'
AREA
MEAO
I-
fOR
CORN
NEBR.,
• "
1972
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"
"
"
'
"
"
" ' " "
*
IOOO
-
, i
-
." *
i
i
q ,
_~i
"
~" 4 0 0
..~-FiIM
Plot 2
Field Ptol I
i
•
~- 2 0 0
•°
i !* ~,:~
" ....
,0 J. . . . . . . . .
20 J .......... TIME,
IN
30 L ........
40 .J- . . . . . . . .
5,0 ~--
DAYS
Fig.4. Computer printout of field data and model prediction. Each field plot is the average of 10 plants. With ample rain in July the unirrigated plots (2) grew essentially the same as the irrigated plots.
251 To demonstrate the activity of the moisture block reading feature three drought periods of two days each were inserted into the program at days 10 and 11, 23 and 24, and 40 and 41. A resistance of 500 ~2 was assumed. The effect on plant growth is shown in Fig.5. Data from the 1972 season do not allow verification of this part of the program but field tests will be run in 1973 to check this out.
~
1200
*I
~1000
LEAF
AREA
WITH
SIMULATED
DROUGHT
FOR
CORN
PERIODS
-600
~
* a * ~w,.~pfltdicttd
5 0 0 . ( ' L Resistonce
I
[::]:] .'
_" . . . . . . .
Jr'2' 3. . . . . . .
30
. . L _ _ L"L"I_ . . . . TIME,
1 . . . . . . . . . . . . . . .
50 J--
DAYS
Fig. 5. Simulated stress effects imposing 500 ~ resistant block readings at three dates.
DISCUSSION
The Nebraska Corn Model lacks many of the points of sophistication found in several of the other models under development. For example, CO2 level is recognized as an important factor and prediction of CO2 levels in the canopy has received a considerable level of attention. However, the CO2 depression seldom amounts to over 15 p.p.m, out of roughly 300 p.p.m. Therefore the error in not including this factor is probably well within the precision of measurement of plant growth in the field. E T models exist which are oriented toward prediction of soil moisture levels. Such a model will have to be coupled in with the corn model to allow prediction of alternative programs of irrigation.
252 Results of simulation using the ELCROS model and the Curry model are shown in Figs.6 and 7. At the present state of the art it is safe to say that activities toward further refinement are needed in all cases. If reasonably accurate modelling can be obtained with relatively simple inputs, it would appear to have certain advantages toward adoption by plant Kg shoot ha
1 = California 2 = Iowa 3 = Neth./Germany -average 2 exp -- simulated factors : Mc Cree
1/ /
2/ /
/ / /
/"/ //
if3
//
ljJ/ //
0
25
2
/
15,000-
5,000]
/
//i
/j3
/
//
50
75
100
Days a f t e r e m e r g e n c e
Fig.& Results o f simulation o f corn growth by ELCROS, comparing predicted and actual growth in California, I o w a and G e r m a n y (from De Wit et al., 1 9 6 9 ) . 6007
Total growth
1
/jA
vs. time
CuUrvVee~ [ ~°thete[eendbaCkinfeedback t ~ Curve C - et feedback
Soil
moisture vs. t~rne
CurVe D - both et and rain feedback curve E - et feedback but .o rai~
480i i
Rain is indicated by the nistograrn
? ," E 360q
/
[~
B
but no rain
[!
.,-JJ iJj
2/
Y~d
,,e
~3
•
30
D
_~o~ 15 § 120 -I
1
~ , ~ : i ~ 30 40 50 60 Time (days) Fig.7. Results o f s i m u l a t i o n run with weather s e q u e n c e i m p o s e d (from Curry and Chen, 1971). 0
l!' 10
' I 20
253
breeders and others. Further model development is needed before effects of fertility elements or varieties can be evaluated. REFERENCES Beeman, J. F., 1966. Growth Dynamics of Small Tobacco Plants. Unpublished Ph.D. thesis, Biological and Agricultural Engineering Department, North Carolina State University, Greensboro, N.C. Bohning, R. H., Kendall, W. A. and Linck, A. J., 1953. Effect of temperature and sucrose on growth and translocation in tomato. Am. J. Bot., 40:150--153. Chen, L. H., Huang, G. K. and Splinter, W. E., 1969. Developing a physical-chemical model for a plant growth system. ASAE Trans., 12:698--702. Curry, R. B., 1971. Dynamic simulation of plant growth, I. Development of a model. ASAE Trans., 14(5):946--959. Curry, R. B. and Chen, L. H., 1971. Dynamic simulation of plant growth, II. Incorporation of actual daily weather and partitioning of net photosynthate. ASAE Trans., 14:1170--1175. De Wit, C. T., Brouwer, R. and Penning DeVries, F. W. T., 1969. The simulation of photosynthesis systems. Conf. Productivity of Photosynthetic Systems, I. Models and Methods, Trebon, Czechoslovakia, September 14--21, 1969. Duncan, W. G., Loomis, R. S., Williams, W. A. and Hanau, R., 1967. A model for simulating photosynthesis in plant communities. Hilgardia, 38:181--205. Eide, R. L., 1965. Simulation of a Weather Sequence in a Plant Growth Chamber. Unpublished M.S. thesis, Biological and Agricultural Engineering Department, North Carolina State University, Greensboro, N.C. Hesketh, J. D. and Musgrave, R. B., 1962. Photosynthesis under field conditions, IV. Light studies with individual corn leaves. Crop Sci., 2:311--315. Jensen, M. E., 1968. Water consumption by agricultural plants. In: T. T. Kozlowski (Editor), Water Deficits and Plant Growth, vol. II. Academic Press, New York, N.Y., pp.l--22. Reitz, L. P., 1974. Breeding for more efficient water use -- is it real or a mirage? In: J. F. Stone (Editor), Plant Modification for More Efficient Water Use. Agric. Meteorol., 1 4 : 3 - - 1 1 {this issue). Shawcroft, R. W., Lemon, E. R., Allen, L. H., Stewart, D. W. and Jensen, S. E., 1974. The soil--plant--atmosphere model and some of its predictions. In: J. F. Stone (Editor), Plant Modification for More Efficient Water Use. Agric. Meteorol., 1 4 : 2 8 7 - - 3 0 7 (this issue). Splinter, W. E., 1971. Growth rate of corn (Zea mais L.) at differing soil water levels. ASAE Pap., 71--592. Splinter, W. E. and Beeman, J. F., 1968. Relationship between plant stem diameter and total leaf area for certain plants exhibiting apical dominance. Tobacco Sci., 12: 139--143.
Agricultural Engineering Department, University of Nebraska, Lincoln, Nebr. (U.S.A.) (Received October 1, 1973; accepted May 20, 1974) ABSTRACT Splinter, W. E., 1974. Modelling of plant growth for yield prediction. Agric. Meteorol., 14: 243--253. A corn growth model is presented which requires three basic input parameters: average daily light intensity (ly), average daily temperature (°C) and soil resistance block reading (Ohms). Comparison with field measurements taken during the summer of 1972 indicates reasonable fit, although the wet season did not allow a test of the soil moisture component of the model. INTRODUCTION Within r e c e n t y e a r s a c o m b i n a t i o n o f f a c t o r s has led to t h e d e v e l o p m e n t o f s i m u l a t i o n m o d e l s o f biological s y s t e m s . T h e r e f i n e m e n t o f e x p e r i m e n t a l techniques and instrumentation which allowed the determination of the r e s p o n s e o f biological s y s t e m s to their e n v i r o n m e n t was an i m p o r t a n t first step. T h e d e v e l o p m e n t o f i m p r o v e d g r o w t h c h a m b e r s , p h y t o t r o n s , i n s t r u m e n t a t i o n f o r m e a s u r i n g e n v i r o n m e n t a l p a r a m e t e r s , d a t a logging s y s t e m s a n d c o m p u t e r i z e d d a t a r e d u c t i o n has a l l o w e d m e a s u r e m e n t s w i t h g r e a t l y i m p r o v e d precision. M o s t i m p o r t a n t , h o w e v e r , was t h e d e v e l o p m e n t o f c o m p u t e r languages a n d s o f t w a r e w h i c h a l l o w e d t h e u t i l i z a t i o n o f exp e r i m e n t a l l y derived d a t a in direct m o d e l building b y biological scientists as well as p h y s i c a l scientists. T h e r e is, t o d a y , an increasing i n t e r p l a y b e t w e e n t h e p l a n t p h y s i o l o g i s t and t h e e n g i n e e r t o w a r d t h e d e v e l o p m e n t o f a generalized, r a t h e r t h a n a q u a n t i t a t i v e u n d e r s t a n d i n g o f m a n y biological processes. APPROACHES TO MODELLING OF PLANT GROWTH FOR YIELD PREDICTION As o n e m i g h t readily e x p e c t t h e a p p r o a c h t a k e n reflects the b a c k g r o u n d a n d t h e r e s e a r c h o b j e c t i v e s o f t h e m o d e l l e r . R e i t z ( 1 9 7 4 ) , in his o p e n i n g address, has p o i n t e d o u t t h a t t h e o b j e c t i v e o f this c o n f e r e n c e is t h e i m p r o v e * This paper is published with the approval of the Director of the Agricultural Experiment Station, University of Nebraska, Lincoln, Nebr., as Paper No. 3892 of the Journal Series.
244 ment of water-use efficiency which he has defined as the ratio of dry matter production to evapotranspiration. Irrigationists use the term water application efficiency to reflect the a m o u n t of water appearing in the root zone versus the a m o u n t applied through irrigation. The total picture must consider the a m o u n t of marketable product-grain or forage-produced per increment of water added, with storage, time of application and rate of use being critical inputs. Several models deal with water transport through the plant. These models range from resistance or resistance-capacitance simulations of evapotranspiration or water movement through plants to models predicting irrigation needs. Jensen (1968) has developed an irrigation prediction model which deals with evapotranspiration in fairly precise detail, but the whole area of crop response is simply taken care of by "crop coefficients" for various crops at different stages of growth. The preceding paper on modelling the soil--plant--atmosphere continuum given by Shawcroft et al. (1974) has presented the state-of-the-art in prediction of evapotranspiration. The plant modellers on the other hand, have approached modelling on the basis of predicting dry-matter weight as a function of the environmental parameters. This paper will be concerned with prediction of plant growth. Duncan et al. {1967) were among the earliest to publish a model of photosynthesis. Basically, Duncan's approach is to divide the leaf canopy into horizontal layers and then determine the light intensity, CO2 concentration, rate of photosynthesis, and rate of dry matter increase by layers. Inputs to the model are experimentally determined relationships which are stored in the computer. Duncan (private communication, 1974) is currently working on a SIMAIZ program for corn which extends his original model to include many details such as soil moisture level and development of the ear. De Wit et al. (1969} developed the ELCROS model for plant growth. This model approaches the problem from the basis of a total crop mass, which has a reservoir of stored, available carbohydrate energy. This reservoir is contributed to by photosynthesis while the activities of respiration, leaf growth, stem growth and root growth pull from this reservoir. Since only a part of the total biological mass is growing or is photosynthetically active De Wit uses a " b o x c a r " train bookkeeping system to keep track of new growth and to depreciate the activity level of this growth with age. The model is quite comprehensive from an operational sense and De Wit is now using CSMP/360, a reactive language, to program his model. At this stage his model assumes adequate soil moisture and is concerned with forage, rather than grain production. Curry (1971) and Curry and Chen (1971 ) developed a CSMP simulation model for corn. The model considers photosynthesis by layers, individual growth of leaves, stems and roots and respiration as a loss function with evapotranspiration modulating soil-water potential. In the second paper a system of allocating photosynthate to roots, stems and leaves was developed. No system for storage of available energy is included in this model.
245 NEBRASKA
CORN MODEL
The basic parameters upon which this model is based were set forth by Beeman (1966). The plant is considered as a machine deriving its energy from the sun. Leaf area is the primary growth determining factor. If we assume that the growth will be some function of the total leaf area present then this can be expressed as:
(1)
dA = kA
dt
where A is area in cm 2 , t is time in hours, and k is a parameter analogous to the reaction rate constant in chemical kinetics. Separating variables and integrating, this relationship becomes: A' = e kt
(2)
where A ' is the normalized area in units of initial area and where initial area is assumed to be unity at time t = 0. This exponential relationship has long been recognized and values over short time intervals during initial stages of growth can be experimentally determined (Eide, 1965). The value of k is, however, a function of many variables such as light intensity, carbon dioxide level, soil-water potential, etc. The following corn growth model was developed from a growth model for tobacco (Fig.l) by Chen et al. (1969}. In order to more accurately determine k, we assume that it is a function of the rate of respiration per unit area (considered on a whole plant basis). We Day temP.
Radiant energy
I. . . . .
~2 H20
'll
Day temp.
P h o t o p e r iod
Id
"l I
r I I
I
I
',
,
02
Night temp.
. . dr Respiration ( ~ - ) -
CO 2
--------~ I
I_
H20
1OI t
i
.........
• I
,
I d¢
I
IIL]gl
II I ~--~I
I I
/L~
I I 1 I
Heat
,,. . . . .
b ~--C-~I I
Ill
StoPage cells
Assimilation
Fig.1. Schematic relationship between photosynthesis, respiration and growth.
246 f u r t h e r assume t h a t the p r o p o r t i o n of respirational activity going into p h o t o respiration will be available during the night period for assimilation. Then:
dR
(3)
k d = a b c d-~
(4)
k n = a (a + b) c d R
dt
where k d is the g r o w t h rate c o n s t a n t during the light period; kn is the g r o w t h rate c o n s t a n t during the night period; a is an e x p e r i m e n t a l c o n s t a n t = 1.719; a is the f r a c t i o n o f respirational energy used in p h o t o r e s p i r a t i o n = 0.015; b is the f r a c t i o n o f respirational energy used in assimilation = 0.01 ; c is the units o f p h o t o s y n t h a t e assimilated per unit o f respiration = 3.0; R is mg c a r b o h y d r a t e respired per d m 2 o f leaf area; and t is time in i n c r e m e n t s of hours with to for any day beginning at the initiation o f the light period. For any given day the value o f k will be the sum of k d and kn s u m m e d over hours of daylight or dark period, respectively. Values of a, a, b and c were d e t e r m i n e d for t o b a c c o by iterative fitting f r o m growth d a t a t a k e n in 20 g r o w t h cabinets in the N o r t h Carolina State University P h y t o t r o n . These values are being used in the c o r n m o d e l until individual values for c o r n can be d e t e r m i n e d . The rate o f respiration is assumed to be a f u n c t i o n of t e m p e r a t u r e and level o f available c a r b o h y d r a t e for respiration. E x p e r i m e n t a l results b y Chert et al., showed, for the day period: dR _ ( 0 . 0 0 3 8 5 7 + 0 . 0 0 3 8 2 9 T ) h = gh dt
(5)
where T is t e m p e r a t u r e in °C; h is level of available c a r b o h y d r a t e in the leaves and stem; and g = 0 . 0 0 3 8 5 7 + 0 . 0 0 3 8 2 9 T . Respiration during the night period was 0.8 t h a t for the day period (gn -- 0.Sg). The a m o u n t of available c a r b o h y d r a t e in the leaves is determined from: dh
dC
dR
dt
dt
dt
(6)
bc
dt
where d C / d t is the a m o u n t of c a r b o h y d r a t e a d d e d t h r o u g h p h o t o s y n t h e s i s , d R / d t is the c a r b o h y d r a t e lost t h r o u g h respiration; b c d R / d t is the carboh y d r a t e used f o r assimilation; and d H / d t is the c a r b o h y d r a t e t r a n s l o c a t e d t o the roots. For c o r n we assume t h a t the above g r o u n d stem-leaf system is o n e system in which readily available c a r b o h y d r a t e s for respiration and assimilation are stored in the pith and stem p h l o e m tissue. T r a n s l o c a t i o n is assumed t o be
247 roughly equal to the rate of respiration (eq.5) up to 25 ° C. Above 25°C (Bohning et al., 1953): dH dt - [0.1 - - 0 . 0 0 3 8 2 9 ( T - - 25)] h = qh
(7)
where q = [0.1 - - 0 . 0 0 3 8 2 9 (T -- 25)]. The function dC/dt is assumed to be proportional to light intensity and inversely proportional to the level of h in the leaf tissue: dC P dt -- h
(8)
0 . 4 9 9 6 ( • - 0.084) where P =1 + 0.912(1 -- 0.084)
(9)
and I is in langleys (cal. em -2 see -1 ). This function is adapted from Hesketh and Musgrave (1962), by converting light-intensity units from foot-candles to langleys and assuming no photosynthesis below 0.084 ly. For this corn model the average light intensity for the day period is used. Day length is programmed in as determined from published tables. Temperature is assumed to vary sinusoidally a b o u t the average temperature for the day with a 7.°C temperature variation from the mean. Substituting eqs.5, 7 and 8 into eq.6 and integrating from to to time t to determine h from an initial h0 we find:
P h= { (l+b~g+q
II--exp{--2[(k+bc)g+O](t--to)}]
+ hl exp{ --2[(l+bc)g+q] (t -- to )}}';:
(10)
This can be substituted into eqs.5 and 3 to obtain:
P k d = abcg {(l+bc)g+q
[1--exp{--2[(l+bc)g+q](t--to)}
+ h E exp
(11)
Using the a m o u n t of photosynthate accumulated during the day period for h0 during the night period and observing that there is no photosynthesis at night, then h for the night period can be found to be: h = h0 exp {--([l+(a+b)c]g+q)(t-- to )}
(12)
and
kn = a(a + b)cgho exp { - - ( [ l + ( a + b)clg+q)(t-- to)}
(13)
248 Eide (1965) f o u n d that mutual shading of small individual corn plants could be taken care of by decreasing the k parameter in eq.1 by 0.0015A0 where A0 is the initial area. For larger field plants hd is decreased linearly by: k' d = k d -- 0.009D
(14)
when D is day number. Leaf area increase for corn essentially stops at onset of flowering. Since onset of flowering is primarily a function of the degree days accumulated, the corn growth model accumulates 450 degree days from initiation of field measurements (A0 = 24 in. 2 ), based on the average t e m p e r a t u r e for each day, minus 10°C and then arrests leaf area increase. The plant continues to accumulate dry matter, so the program runs until kernel moisture is an estimated 30%. At present we do not have an exact relationship predicting black layer formation, a more recently developed criteria for maturity, but this may also be a degree-day p h e n o m e n o n . Around 1,400 degree days from germination are required for corn at the 30% kernel moisture stage depending on variety. In our irrigation research program resistance blocks are used extensively to mo n ito r soil moisture. Although these are relatively simple to use it must be recognized t ha t there is a great deal of variability between individual block readings at a given moisture level. Useable results have been obtained by averaging readings f r om four separate blocks. Splinter (1971) f o u n d a linear relationship between growth rate of corn and moisture block resistance. Therefore, the rate of photosynthesis in the model is decreased in accordance with: p, = P ( 0 . 1 3 5 -- 0.000021p) 0.135
(15)
where p is resistance block reading in ohms (average of 4). This will give 0 p h o t o s y n t h a t e p r o d u c t i o n at 6,430 ~2 soil resistance as shown in Fig.2. This corresponds to roughly --6 bar moisture tension in the soil used. The model therefore requires three data inputs: Average light intensity (ly), average daily t e m p e r a t u r e (°C), and average resistance block reading in the r o o t zone. VERIFICATION During the summer of 1972 ten plants were selected random l y in an irrigated corn research plot area under a center pivot sprinkler and ten plants of the same variety were selected in the non-irrigated area outside of the sprinkler circle at the University of Nebraska Field L a b o r a t o r y at Mead, Nebraska. Beginning on June 21 the stem diameter of each plant was measured every Monday, Wednesday and Friday until August 23. Light
249 0.15. light intensity = 0.376 ly/min max. temp.= 86°F; rain. temp.= 6 5 ' F length = 14.5 h
" ~ day "x.
No:o, p,~.ts:9
:
-~ 0.10c~ O~ U1D
o
0.05.
o
lO6O
36o0
~x~bo
Resistance (Ohms)
Fig.2. R e l a t i o n s h i p b e t w e e n m o i s t u r e b l o c k resistance a n d p l a n t g r o w t h rate for c o r n g r o w n in a g r o w t h c h a m b e r .
intensity and daily temperature were obtained from a microclimatological station one mile distant operated by Dr. Norman l{osenberg. Average light intensity was determined from the light intensity at solar noon and average daily temperature was determined from the arithmetic average of day temperature taken at 06h00 and at 14h00. z~ 0 -
300200-
*r
g%:p:,:n A = mD n
~100-
~5ot~
m 30-
-J 20-
10 0.1
.t
?
O:2 0:3 0:5 lb DiameteP (inches)
2b
Fig.3. R e l a t i o n s h i p b e t w e e n p l a n t leaf area a n d s t e m d i a m e t e r for corn. This r e l a t i o n s h i p h o l d s o n l y u n t i l tasseling.
25O Leaf area was d e t e r m i n e d f r o m stem d i a m e t e r m e a s u r e m e n t s f r o m the relation (Splinter and Beeman, 1968; see Fig.3): (16)
A =mD n
Although resistance block readings were available, there were no measureable differences b e t w e e n the d r y l a n d and irrigated corn plots as 1 9 7 2 had an unusually wet s u m m e r season. Differences b e t w e e n d r y l a n d and irrigated corn plots were f o u n d in o t h e r areas b u t n o t for the areas being used for this test. In general the c o r n plants in b o t h test plots were n o t subjected to a m o i s t u r e stress during the g r o w t h period o f the test. Results o f the m e a s u r e d plant leaf areas and the p r e d i c t e d areas f r o m the c o m p u t e r p r o g r a m are s h o w n in Fig.4. The p l o t t e d points for the field results are the average values for the ten plants in each plot. The m o d e l is capable of printing out, o n a daily basis, such p a r a m e t e r s as the daily g r o w t h rate c o n s t a n t , plant leaf area, assimilation and dry m a t t e r weight o f the above g r o u n d p o r t i o n of the plant. H o u r l y growth rates can be either printed o u t or displayed although these e x c e e d the precision of the i n p u t data at this time. S h o u l d there be a need for this precision, h o u r l y t e m p e r a t u r e s and light intensities c o u l d be i n t r o d u c e d .
• 1200
,
LE*F
'
AREA
MEAO
I-
fOR
CORN
NEBR.,
• "
1972
""
"
"
"
'
"
"
" ' " "
*
IOOO
-
, i
-
." *
i
i
q ,
_~i
"
~" 4 0 0
..~-FiIM
Plot 2
Field Ptol I
i
•
~- 2 0 0
•°
i !* ~,:~
" ....
,0 J. . . . . . . . .
20 J .......... TIME,
IN
30 L ........
40 .J- . . . . . . . .
5,0 ~--
DAYS
Fig.4. Computer printout of field data and model prediction. Each field plot is the average of 10 plants. With ample rain in July the unirrigated plots (2) grew essentially the same as the irrigated plots.
251 To demonstrate the activity of the moisture block reading feature three drought periods of two days each were inserted into the program at days 10 and 11, 23 and 24, and 40 and 41. A resistance of 500 ~2 was assumed. The effect on plant growth is shown in Fig.5. Data from the 1972 season do not allow verification of this part of the program but field tests will be run in 1973 to check this out.
~
1200
*I
~1000
LEAF
AREA
WITH
SIMULATED
DROUGHT
FOR
CORN
PERIODS
-600
~
* a * ~w,.~pfltdicttd
5 0 0 . ( ' L Resistonce
I
[::]:] .'
_" . . . . . . .
Jr'2' 3. . . . . . .
30
. . L _ _ L"L"I_ . . . . TIME,
1 . . . . . . . . . . . . . . .
50 J--
DAYS
Fig. 5. Simulated stress effects imposing 500 ~ resistant block readings at three dates.
DISCUSSION
The Nebraska Corn Model lacks many of the points of sophistication found in several of the other models under development. For example, CO2 level is recognized as an important factor and prediction of CO2 levels in the canopy has received a considerable level of attention. However, the CO2 depression seldom amounts to over 15 p.p.m, out of roughly 300 p.p.m. Therefore the error in not including this factor is probably well within the precision of measurement of plant growth in the field. E T models exist which are oriented toward prediction of soil moisture levels. Such a model will have to be coupled in with the corn model to allow prediction of alternative programs of irrigation.
252 Results of simulation using the ELCROS model and the Curry model are shown in Figs.6 and 7. At the present state of the art it is safe to say that activities toward further refinement are needed in all cases. If reasonably accurate modelling can be obtained with relatively simple inputs, it would appear to have certain advantages toward adoption by plant Kg shoot ha
1 = California 2 = Iowa 3 = Neth./Germany -average 2 exp -- simulated factors : Mc Cree
1/ /
2/ /
/ / /
/"/ //
if3
//
ljJ/ //
0
25
2
/
15,000-
5,000]
/
//i
/j3
/
//
50
75
100
Days a f t e r e m e r g e n c e
Fig.& Results o f simulation o f corn growth by ELCROS, comparing predicted and actual growth in California, I o w a and G e r m a n y (from De Wit et al., 1 9 6 9 ) . 6007
Total growth
1
/jA
vs. time
CuUrvVee~ [ ~°thete[eendbaCkinfeedback t ~ Curve C - et feedback
Soil
moisture vs. t~rne
CurVe D - both et and rain feedback curve E - et feedback but .o rai~
480i i
Rain is indicated by the nistograrn
? ," E 360q
/
[~
B
but no rain
[!
.,-JJ iJj
2/
Y~d
,,e
~3
•
30
D
_~o~ 15 § 120 -I
1
~ , ~ : i ~ 30 40 50 60 Time (days) Fig.7. Results o f s i m u l a t i o n run with weather s e q u e n c e i m p o s e d (from Curry and Chen, 1971). 0
l!' 10
' I 20
253
breeders and others. Further model development is needed before effects of fertility elements or varieties can be evaluated. REFERENCES Beeman, J. F., 1966. Growth Dynamics of Small Tobacco Plants. Unpublished Ph.D. thesis, Biological and Agricultural Engineering Department, North Carolina State University, Greensboro, N.C. Bohning, R. H., Kendall, W. A. and Linck, A. J., 1953. Effect of temperature and sucrose on growth and translocation in tomato. Am. J. Bot., 40:150--153. Chen, L. H., Huang, G. K. and Splinter, W. E., 1969. Developing a physical-chemical model for a plant growth system. ASAE Trans., 12:698--702. Curry, R. B., 1971. Dynamic simulation of plant growth, I. Development of a model. ASAE Trans., 14(5):946--959. Curry, R. B. and Chen, L. H., 1971. Dynamic simulation of plant growth, II. Incorporation of actual daily weather and partitioning of net photosynthate. ASAE Trans., 14:1170--1175. De Wit, C. T., Brouwer, R. and Penning DeVries, F. W. T., 1969. The simulation of photosynthesis systems. Conf. Productivity of Photosynthetic Systems, I. Models and Methods, Trebon, Czechoslovakia, September 14--21, 1969. Duncan, W. G., Loomis, R. S., Williams, W. A. and Hanau, R., 1967. A model for simulating photosynthesis in plant communities. Hilgardia, 38:181--205. Eide, R. L., 1965. Simulation of a Weather Sequence in a Plant Growth Chamber. Unpublished M.S. thesis, Biological and Agricultural Engineering Department, North Carolina State University, Greensboro, N.C. Hesketh, J. D. and Musgrave, R. B., 1962. Photosynthesis under field conditions, IV. Light studies with individual corn leaves. Crop Sci., 2:311--315. Jensen, M. E., 1968. Water consumption by agricultural plants. In: T. T. Kozlowski (Editor), Water Deficits and Plant Growth, vol. II. Academic Press, New York, N.Y., pp.l--22. Reitz, L. P., 1974. Breeding for more efficient water use -- is it real or a mirage? In: J. F. Stone (Editor), Plant Modification for More Efficient Water Use. Agric. Meteorol., 1 4 : 3 - - 1 1 {this issue). Shawcroft, R. W., Lemon, E. R., Allen, L. H., Stewart, D. W. and Jensen, S. E., 1974. The soil--plant--atmosphere model and some of its predictions. In: J. F. Stone (Editor), Plant Modification for More Efficient Water Use. Agric. Meteorol., 1 4 : 2 8 7 - - 3 0 7 (this issue). Splinter, W. E., 1971. Growth rate of corn (Zea mais L.) at differing soil water levels. ASAE Pap., 71--592. Splinter, W. E. and Beeman, J. F., 1968. Relationship between plant stem diameter and total leaf area for certain plants exhibiting apical dominance. Tobacco Sci., 12: 139--143.