A Dynamic Model of Crop Growth Rate of Italian Ryegrass after Cutting

YELi POHJONEN1 and PERTII HARI2

1 Department of Plant Husbandry, University of Helsinki, Viikki, SF-00710 Helsinki 71, 2Department of Silviculture• University of Helsinki, Unionink. 40 B, SF-00170 Helsinki 17, Finland

The growth of grasses is preceded by the follow­ing three stages, (i) photosynthesis, (ii) trans­location of carbohydrates, and (iii) biochemical processes during cell division and enlargement. The energy for the first stage is provided by sun­light, and the energy for the second and third stages is released during respiration, from com­pounds photosynthesized earlier. Provided that the plant is kept at full turgor, then the respira­tion is mainly controlled by temperature (Utaa­ker, 1968). In most temperate grasslands, the growth is largely limited by the periods of low temperature and drought (Spedding, 1971).

The photosynthesis of a grass plant is restricted for a short period after cutting, but the grass can still grow using carbohydrates which have been accumulated in the roots. Under favourable conditions, the removal of carbohydrates from the roots ceases after a few days and the photo­synthesis level returns to normal (Davidson & Milthorpe, 1965).

In growth analysis (cf. Radford, 1967; Black­man, 1968), the concept of the Crop Growth Rate (CGR) of a canopy cover, at any instant in time t, is defined as the increase in plant material W, per unit of time (CGR ~ dW/dt). It is commonly given the dimensions: kg ha- 1 day-1 or g m- 2

day-1 (dry matter). The main difficulty in per­forming the growth analysis is to find the relation­ship between plant material W and time t. This relationship is approximated as a rule by a polynom (e.g. Kornher, 1971):

W ~ a +bt + ct• +dt", (1)

where a, b, c and d are constants estimated empirically. According to Eq. (1) CGR depends only on time t. However, environmental factors have a very strong effect, for example, on the daily height increment in woody plants as in spruce (Dahl & Mork, 1959) and in Scots pine (Hari et al. 1970).

Direct determination of CGR of the sward is difficult. If samples are taken, then the yield in the same place cannot be determined contin­uously, and sampling from different places de­creases the accuracy of the determinations. How­ever, CGR can be determined by measuring the height of individual plants in the sward re­peatedly. The plant material W can be approx­imated by means of regression. In this way W can be measured after short intervals and the variance caused by the experimental field can be diminished. However, the genetic variance be­tween measured plants cannot always be avoided.

In this study CGR was approximated with the daily height increments. Attempts were made to find a model for the dependence of the daily height increment of Italian ryegrass (Lolium multif lorum Lam.) on temperature and the growth rhythm in North Finnish conditions.

Material and Methods

An Italian ryegrass sward was established at the Arctic Circle Agricultural Experimental Station, near Rovaniemi, on peat land in spring 1972 using the seed of 'Barmultra' variety. The peat land was fertilized in spring with 87 kg P (as superphosphate), 250 kg K (as potassium chlo­ride), and 100 kg N (as urea) per hectare. The Crop Growth Rate of the aftermath after six different cuttings in June-September was studied. The first three of them were primary cuttings and the last three were aftermath cuttings. The height of the stubble which remained was about 5 cm. More nitrogen was given immediately after cutting: in the first two cases 150 kg N/ha, in the others 200 kg N/ha (as urea). These nitrogen amounts were added with the aim of making the nitrogen supply adequate for rapid growth during the regrowth.

The daily height increments of the same in-

A eta A griculturre Scandinavica 23 (1973)

122 V. Pohjonen and P. Hari

dividual plants were the primary observations. After each cutting, 20-30 plants in the sward were marked for measurements. Measurements were performed to an accuracy of 1 mm at 8: 00 hours every morning. The day therefore begins in this study at 8 :00 hours and ends at 8 :00 hours the following morning.

Daily measurement was somewhat harmful to the plants, especially in the last stages of the first two series when the plants were tall and in autumn after night frosts. The accuracy of the method decreased in those cases.

During the first two measurement series, the dry matter was sampled 2- 3 times a week over an area of 0.2 m 2

• The stubble which remained was about 5 cm high. The temperature observa­tions were made with a thermohygrograph (Lambrecht 252) in a standard weather chamber located in the sward so that the measuring point was 25 cm above the ground. The temperature was read once in an hour.

Growth model of daily height incre­ment of Italian ryegrass after cutting

The daily height increment of Italian ryegrass depends to a certain degree on the growth rhythm and the temperature conditions of that day. In order to include the influence of the growth rhythm in the model, a variable must be chosen to describe the physiological stage of develop­ment in the aftermath. Environmental conditions regulate the activity of the vital processes of plants. When the weather is cold the progress of development goes on slowly, but when the weather becomes warmer the progress is speeded up. Let M be the rate of maturation (which describes the activity of the vital processes) and x be the temperature. Supposing that the rate of maturation depends only on temperature, then the physiological stage of development s at time t can be determined as follows (Hari, 1968, 1972; Sarvas, 1972):

s(t)= f M(x(t))dt (2)

The activity of the vital processes in grass is fairly well described by the dark iespiration R and thus we can say that M = R. The dark respiration of plants has been found to be an exponential function of temperature (e.g. in Italian ryegrass Murata & Iyama, 1963). The dark respiration of Paa alpinum (Fig. 1) was used

Acta Agricultura: Scandinavica 23 (1973)

4

3

2

I I

I I

I

I I

I I

I I

I I

..,_----,~~~~~~~~~~ -5 0 5 10 15 20 :25 30

Fig. 1. The dark respiration rate of Paa alpinum according to Scott & Billings (1964).

in this study because it had earlier been measured over a wide temperature range: - 5 .. . + 22°c. The values over the range + 22 . . . + 30°C were extrapolated. However, the dark respiration R was normalized so that R(IO) = 1.0 (cf. Utaaker, 1968), which means that if the temperature is constant at 10°C during one day, then the physiological stage of development increases by one unit.

Let ti be the point at which the jth day begins and ri the theoretical cumulative dark respiration for that day. Then

t; - 1

r ; = R(x(t))dt (3) I;

Variable r; is a generalization of the temperature sum on thejth day.

Let s; be the physiological stage of develop­ment at the beginning of the jth day (si is defined by Eq. _)) and gi the height increment for that day. Let us suppose that the height increment on the jth day depends on the physiological stage of development si at the beginning of the day and also on the cumulative dark respiration r i for that day. Then

(4)

To make Eq. (4) operational, it is assumed that g is a linear function of r (Hari et al., 1970), i.e.

g(s,r) = f(s)·a ·(r-b) (5)

The function f is actually a complex function of

L ,-.-.ct;""'on,-.-1 _,_--,,:::-.,'.:'1;o::::n°2 ___ _,_,(S"O)

Fig. 2. The functi on fused in the model.

s. Here it is supposed that f is composed of two linear sections (Fig. 2):

1st section: steady daily height increment after cutting, and

2nd section: diminishing daily height incre­ment.

The parameters of the model can be estimated from the dai ly height increment data. The para­meters can be interpreted as follows: a determines the level of the daily height incre­

ment, b is the theoretical daily dark respiration level

at which the growth ceases, s2 (in function f) is the physiological stage of

development in which the daily height incre­ment begins to decrease . and

sc (in function f) i the physiological stage of development ' ·here the height growth ceases.

Results

Testing the growth model

The parameters for each measurement series were determined by computer iteration' (Table 1). As the value 0.3 3 was chosen for parameter b, then according to the model, growth ceases at + 2°C. In this way the number of parameters was decreased .

The measured and calculated height increments are shown in Figs 3-8.

Crop growth rate of Italian ryegrass after cutting

The estimate for the Crop Growth Rate of Italian ryegrass after cutting was computed from the daily height increments. The following regression equation was found between the average height of the plants in the first series and the dry matter yie ld in the surrounding sward:

1 FORTRAN programs used in computing the integral in Eq . (3) and in fitting the model of Eq . (5) into daily height increments a re ava ilable from the authors.

Crop growth rate of Italian ryegrass 123

Table I . The parameters in the growth model of the daily height increment of Italian ryegrass after cutting and the correlation coefficients between measured and calculated hei1<ht increments

Parameters Corre-Series lation no. Period a Sz Sc r

72-06-30 1.75 17.27 45.41 0.979 72-07-27

2 72-07- 12 2.25 6.86 35.34 0.949 72-08-01

3 72-07-29 2.25 1.55 32.45 0.982 72-08-18

4 72-08-06 1.90 8.87 31.87 0.985 72-09-04

5 72-08-25 1.61 1.94 23.50 0.876 72-09-19

6 72-09-06 1.50 12.36 23.66 0.956 72-10-03

Y = exp(0.96291 + 1.81174 · Log.h), where (6) Y = the dry matter yield, kg/ha, h = the average height (cm) of the measured p lants.

Coefficient of determination R " = 0.92 The corresponding equation in the second series:

Y = exp( - 0.59561 + 2.16429 · Log.h) (7)

Coefficient of determination R" = 0.95 The estimates of the Crop Growth Rate, which

Figs. 3-8. The measured (thick line) and calculated dail y height increments in the series. 3: in the !st series; 4 : in the 2nd series; 5: in the 3rd series; 6: in the 4th ser ies ; 7: in the 5th series; 8: in the 6th series.

3

4 0 m m

30

20

10

30 June

16 July

24

Acta Agricultur<E Scandinavica 23 (1973)

124 V. Pohjonen and P. Hari

40

30

20

10

4

40

30

'.20

10

5

40

30

20

6

mm

12

mm

29 July

mm

6

2 0 July

14

28

14 Augu<t

22 August

Acta Agriculturre Scandinavica 23 (1973)

5 -

22

30

20 mm

10

10,

14

8

10 September

22 September

18

30

are computed from the measured and calculated height increments for three series, as examples, are shown in Figs. 9- 11. The maximum Crop Growth Rate occurred later than the maximum height increment because of the non-linear regression.

F igs. 9-11. The estimates of the Crop Growth Rate which are computed from the measured (thick line) and cal-culated height increments. 9: in 1he 1st series, Eq. (6) IO: int e d series, Eq. (1 : 11: in the 6th series, Eq. (7).

ba->tby-i

9

30 June

16 July

23

200

150

100

50

10

12 5 Aug ult

·:r~ 6 M n ~

September

11

Discussion

Paramerers of the model

The parameters a and sc decreased regularly towards the autumn. Thus, at the Arctic Circle the aftermath of Italian ryegrass grows more rapidly and taller in midsummer than in the autumn. This is not caused by temperature alone. The decrease in growth potential in autumn is probably due to the decrease in the total incom­ing radiation. The level of height increment de­termined by the parameter a, was irregularly small in the first series. The explanation for this may be that the root system was insufficient as a resu.lt of the short primary growing period. Parameter s2 showed irregular variations. This cannot yet be explained.

Crop Growth Rate of Italian ryegrass after cutting

The correlations between the measured and calculated height increments and between the height and the yield of Italian ryegrass aftermath were high. Thus the Crop Growth Rate was highly dependent on both the physiological stage of development and the temperature conditions. A striking feature was that it was not necessary

9 - 733839

Crop growth rate of Italian ryegrass 125

to include the total daily incoming radiation in the model, but it could be supposed that the radiation conditions have an influence on the parameters a and Sc, as discussed earlier. How­ever, this influence varies very little between successive days.

Anslow (1965) points out the importance of internal factors in determining the pattern of growth. By using Eq. (2), the internal factors are defined precisely, and so the model can be made operational. This enables, for example, the prediction and optimization of the yield.

The high level in CGR (Figs. 9 and 10) found in this study can be explained by the favourable temperature conditions and the long summer day (22-24 h) due to the northern latitude (at the Arctic Circle) of the experimental field. In further experiments, attention will be focused on the effect of the incoming radiation and the optimi­zation problems.

Summary

The height and yield of Italian ryegrass was studied in North Finnish conditions. A dynamic model for the Crop Growth Rate was constructed in two stages: (a) model for the daily height increment and (b) regression model between height and yield. The explaining variables for the daily height increment were the growth rhythm and the theoretical daily dark respiration. The effect of temperature and incoming radiation on the Crop Growth Rate was discussed.

Acknowledgements

We wish to express our gratitude to Mr Reijo Heikkila, Head of the Arctic Circle Agricultural Experimental Station, for providing facilities for field experiments. Our thanks are also due to Professor Juhani Paatela, Professor Paavo Yli­Vakkuri and Dr Arvi Valmari for valuable criticism of the manuscript. The study has been supported by August Johannes and Aino Tiura Agricultural Research Foundation and the Acad­emy of Finland.

References

Anslow, R. C. 1965. Grass growth in midsummer. J. Br. Grassl. Soc. 20, 19- 26.

Blackman, G . E. 1968. The application of the concepts of growth analysis to the assessment of productivity.

Acta Agricultura Scandinavica 23 (1973)

126 V. Pohjonen and P. Hari

U NESCO Copenhagen symposium: Functioning of terrestrial ecosystems at the primary productivity level, pp. 243-259.

Dahl , E. & Mork, E. 1959. Om sambandet mellom temperature, anding og vekst hos gran (Picea abies (L.) Karst.) . Meddr. Norske Skogsforsves. 53, 81-93.

Davidson, J. L. & Milthorpe, F. L. 1965. Carbohydrate reserves in the regrowth of cocksfoot (Dactylis glomerata L.). J. Br. Grassl. Soc. 20, 15-18.

Hari , P. 1968. A growth model for a biological popula­tion, applied to a stand of pine. Comm. Inst. For. Fenn. 66, 7.

- 1972. Physiological stage of development in biological models of growth and maturation. Ann. Bot. Fennici 9, 107- 115.

Hari , P., Leikola, M. & Rasanen, P. 1970. A dynamic model of the daily height increment of plants. Ann. Bot. Fennici 7, 375-378.

Kornher, A. 1971. Untersuchungen zur Stoffsproduktion von Futterpflanzenbestanden. I. Acta Agric. Scand. 21, 215- 236.

Acta Agriculturre Scandinavica 23 (1973)

Murata, Y. & l yama, J. 1963. Studies on the photo­synthesis of forage crops. Proc. Crop Sci. Soc. lap . 31 , 315- 323.

Radford, P. J . 1967. Growth analysis formulae- their use and a buse. Crop Sci. 7, 171- 175.

Sarvas, R. 1972. Investigations on the annual cycle of development of forest trees. Comm. Inst. For. Fenn. 76, 3.

Scott, D. & Billings, W. D. 1964. The effect of environ­mental factors on the standing crop and productivity of an alpine tundra. Ecol. Monogr. 34, 243- 270.

Spedding, C. R . W. 1971. Grassland ecology, 221 pp. Oxford.

Utaaker, K. 1968. A temperature growth index- the respiration equivalent-used in climatic studies on the mesoscale in Norway. Agr. Meteorol. 5, 351- 359.

Ms received March 26, 1973

Printed Aug. 7, 1973