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Influence of irrigation on the development and yield of potatoes
Agricultural Water Management, 5 (1982) 171--179
171
Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands
INFLUENCE OF IRRIGATION ON THE DEVELOPMENT AND YIELD OF POTATOES
J. MOSZ l and P. KOWALIK 2
Institute of Agricultural Foundations of Land Improvement, Agricultural Academy, 50950 Wrociaw (Poland) 2Institute of Hydrotechnics, Technical University, 80952 Gdaf~sk (Poland) (Accepted 15 October 1981)
ABSTRACT Mosz, J. and Kowalik, P., 1982. Influence of irrigation on the development and yield o f potatoes. Agric. Water Manage., 5: 171--179. Verification of the model of potential yield developed by De Wit and modified by Rijtema, Feddes et al. and others, was carried out for two varieties of potato grown under different water and fertilization conditions. The anticipated yields were found to be correlated with the measured ones at the 0.99 confidence level, evidenced by correlation coefficients from 0.96 to 0.97. This means that for a given potato variety and under determined water and fertilization conditions the yield can be forecasted with the model. INTRODUCTION
The importance of potato as an edible, fodder and industrial plant makes it a universal crop. Increasing demands for potato necessitate the creation of optimum production conditions, but often water supplies are scarce. Therefore it is of utmost importance to be able to predict the effect of irrigation. Information concerning the effect of water supply on yields of crops is mostly obtained from field experiments. Such experiments are expensive, and labour and time consuming. This is the reason why in agricultural research a tendency has arisen to develop mathematical models to forecast the yields of crops grown under various climatic and agrotechnical conditions (e.g. Rijtema and EndrSdi, 1970; Zelitch, 1971; De Wit and Goudriaan, 1974; Feddes et al., 1978). Such mathematical models have been used already in many countries {e.g. Sirotienko and Bojko. 1977; Slabbers et al. 1979). In Poland, the model for potential rate of biomass accumulation developed by De Wit {1965} has been used to forecast the yields of grassland (Kowalik and Maciejewski, 1976; Brandyk et al., 1979), potatoes (Mosz, 1978), sugar beets (Mosz et al., 1980} and mangolds (Dzie~.yc et al., 1981}. The present paper gives an empirical verification of the mathematical model for yields of potatoes grown under different water and fertilization conditions. 0378-3774/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
172 FIELD EXPERIMENTS
Field experiments with potatoes were carried out at the Agricultural Experimental Station near W r o c h w in the years 1974--1976. The experimental area is situated in the valley of the river Odra at an altitude of 120 m, and at 51007 ' N and 17°10'E. The soil of the experimental field was a brown soil classified in the productivity class IVb and agricultural possibility class 5 {good for rye). The experiment was laid out in randomized subblocks in a system with three variables and four replications. Two potato varieties with different lengths of the growing period were examined, namely the medium-early variety Pola and medium-late variety SokSt. There were t w o watering treatments: W0 = non-irrigated, and W, = irrigated, as well as two nitrogen levels: N, = 80 and N2 = 160 kg N ha-' ; all treatments had the same phosphate and potassium fertilization, namely 80 kg P2Os ha-' and 160 kg K20 h a - ' . In variant W, 20 mm water was applied b y sprinkling when the soil water potential was a b o u t 350 kPa at 20 cm depth. In the years 1974, 1975 and 1976 the additional water supply was 40, 80 and 140 mm, respectively. Every 14 days five plants were taken from each plot to determine their fresh and dry matter contents. The assimilation surface was determined from the weight of 40 discs of known area, cut o u t of undamaged leaves. The weight of all the leaves of one plant as well as the number of plants on a square meter being known, the assimilative surface of crop as well as the leaf area index (LAI) could be calculated. The dry matter production (kg ha-' ) was calculated based upon the yields of fresh matter per plant and the density of plants in the plots. THEORY
De Wit (1965) calculated the daily potential photosynthetic yield of a standard canopy for LAI = 5 at 20°C, for cloudless and totally clouded skies, different latitudes and different days of the year. According to this the maxim u m (potential) dally increases (rates) of biomass for the latitude of W r o c h w are expressed in kg dry matter per ha per day (Table I). TABLE I Daily increase of biomass (kg DM ha -~ day -1 ) Date
Pc (cloudless sky) P0 (clouded sky)
15/05
15/06
15/07
15/08
15/09
15/10
483 250
524 274
510 265
446 226
353 174
253 117
173
For the dally rate of increase of biomass a modified formula based on De Wit's theory (Feddes et al., 1978) was used. This formula reads: P p o t = {P0 + 0.9--~ ( P c - P 0 ) } e 7 ¢
(kg ha-1 day -~)
(1)
where Ppot = daily rate of increase of biomass (kg ha -~ day-~); Pc, P0 = gross potential dally photosynthesis of standard canopy for clouded (P0) and cloudless (Pc) sky; 0.9 = atmosphere purity coefficient; n = duration of full insolation on a given day (min); N = the length of day for a determined latitude (min); ~ = coefficient considering the effect of temperature on the increase of biomass (nondimensional, from 0 to 1); 7 = coefficient o f leaf covering of the soil (LAI/5); ¢ = respiration coefficient (nondimensional, from 0 to 1). According to the above equation the production of biomass is limited by the respiration coefficient ¢the temperature coefficient ~ and the leaf covering coefficient 7. For potatoes, the respiration coefficient is a b o u t 0.8 (Burton, 1964). O p t i m u m air temperatures for photosynthesis are different for different plants. The sensitivity of p o t a t o photosynthesis to temperature was examined by Winkler (1961, 1971). He found that at 0°C the increase o f biomass was completely inhibited. At 5, 10 and 15°C he found values of 50, 90 and 98% respectively. In the range 18--20°C the intensity reached 100% and it fell to below 80% at 25°C. From these data the following values for the temperature coefficient a are as shown in Table II. TABLE II T (°C)
0
3
5
0
0
0.5
10
15
0.9
0.98
18 1.0
20 1.0
25 0.8
The coefficient 7 is introduced to take into account the influence of total leaf surfaces different from that of a standard canopy. If LAI = 5, then 7 = 1, where LAI is the total assimilative surface of leaves per unit area. The final yield has been calculated from the dally rates following from (1) according to the formula: i=te Qpot = ~ i=t o
Ppot,i
(kg h a -1)
(2)
where Qpot = final potential yield (kg ha-1 ); i = consecutive day o f the year; t0, te = first and last days of production, respectively. The above formula gives the so-caUed productivity, i.e. the total biomass of the crop. In potatoes only the t u b e r production is of importance. Therefore the tuber yield is calculated from the productivity by using the yield co-
174 efficient ~, defined by:/3 = (dry matter in tubers) / (total dry matter production). To calculate the potential increase of tubers on a given day, the daily potential production rate has to be multiplied by ~, hence: Ppot,u =/~Ppot
(kg ha -1 day -1 )
(3)
where Ppot, u = potential increase of tuber yield on a given day. The formula for the cumulative tuber yield Qpot, u then simply reads:
i=te Ppot, u,i
Qpot, u = ~
(kg
ha -1)
(4)
i=to POTENTIAL INCREASE OF THE BIOMASS
The potential yields of the biomass of potatoes and tubers were calculated for each treatment separately. Daily rates for a standard canopy were calculated from meteorological data. Coefficients 7 and/3 were determined based upon measurements taken every two weeks. Fig. 1 shows the effect of irrigation on the magnitude of 7 for the two varieties and two levels of nitrogen fertilization. In all treatments irrigation brought about a pronounced increase of the coefficient -f especially in spring, because the assimilative surface developed faster. A similar dependence was I~O kgN ha -1
160 I~jN ha -1 1974
10£
t
,'"
/'<, f ' .. _ "~,
'\
OSC Q6C non- irT'~ated "~
Q40 .
.
.
.
.
irr~J=tea"
Q20 O0
.I/, , ~ 04
.
c
~
0
I
1976
o8o~04ol/ o2oF
.
J vor~e~y Sok&
. . . . . non-irMgated ~ . . . . . . . irrigated j variety Pola
.,:S::-. "~
......
/
\
/5" . . . . ~':'..~ "-::"-.'~.
~
.
.......
,.,--
oJ 180190 2 0 0 2 1 0 ~ 0 230 240 2 5 0 2 6 0
\-
'.:',. ""~:
-.~. "....
180190 2 0 0 210 220 290 240 250 2£~0
Consecutive (Jay of the yeor
Fig. 1. The value of coefficient ~ during the vegetative period of potatoes.
175 obtained by Rijtema and EndrSdi (1970). They state that to obtain high yields, the period of incomplete soil cover should be as short as possible. The largest effect of irrigation on the magnitude of 7 was found in the higher nitrogen treatments. For the 160-kg N ha -1 treatment the increase o f 7 was from 14.6 to 34.2%, while with the lower dose o f 80 kg N ha -'1 it was from 0 to 25%. VERIFICATION OF THE PRODUCTION MODEL The calculated results of Qpot and Qpot,u of the model were compared with measured (empirical) data on total biomass Qemp and tuber production Qemp,uFor this purpose the correlation between measured (Qemp, Qemp,u) and calculated values (Qpot, Qpot,u ) was established by means of linear regression. The significance of the regression was assessed with Fischer's F-test and that of the correlation coefficient with Student's t-test. The correlation between measured and calculated values for the total biomass production is shown in Fig. 2. The data for all years and both nitrogen levels lie along the same straight line. The yields of biomass of irrigated and non-irrigated plants of both varieties are shown separately because of considerable differences between them. This was the reason for carrying out the verification jointly for fertilizer levels and separately for the variety and irrigation. For the results o f the analysis as far as it concerns the biomass, all treatments gave a rectilinear dependence:
(5)
Qemp = a + b Qpot at a confidence level o f p = 0.99.
(kg
DM
/~//
Pola
Soko+
Y ha -~)
/ -
8
I~,
-
y= f:,~. 2 . 0 6 4 x 7 •
r :o.g8
oy///~ ~)/~A
•
e Y=395.7*O.77x 7
~°0~
A~//
-,~/~;
6
o ,
8.052x
•
&A~O ° &
O~
4
r=O.g8
~-e //7 Z~/ ~e f~lw
yield) =Oemp(empirical yield)
x = Opot (potent~l
Y 0 • & •
fertihzoti~ 80 I~gN f e r t i l i z a t ~ 10:) t~jN fertilizotionSOkgN fertilization 160 kg N
9on-irrigoted
- ....
2
4
6
irrigat~-~d
8
10
12
14
x ( l O 3 kg D~t ha -1)
Fig. 2. Measured (y) and calculated (x) yield of total biomass.
~-1 -~ . tx:1-1.J non-rrrrgated ha-l-) I~ -1 ~ mrlgoted
176
The calculated yields were highly correlated with the measured ones, which was shown by correlation coefficients of 0.94--0.98. This means that the biomass production of a given variety under determined meteorological conditions can be calculated by means of a simple regression (5) shown in Fig. 2. The somewhat higher correlation coefficients for the higher nitrogen level are probably due to other factors like soil temperature, diseases, pests, etc. VERIFICATION OF TUBER YIELDS
After having proved that the calculated yields of biomass are highly correlated with the measured ones, the anticipated yields Qpot,u, i.e. the yields of tubers, were calculated by applying the coefficient/3. Fig. 3 shows the value of coefficient ~. 80 kgN ha -~
,
.-
160 kgN ha-1
/
,;i / /
.t
-Dcrl-lrP ted . . . . . . . irrl~,qll~ t variety Sokof
~. . . . . . . . .
nc~% irrigated ?
.......... irrigated
0 4
j variety Pole
#/"
02 /
//''
o; 06
-" ~ ..--"
1976
oLJ. o
.~;: ~;. . . . . .
.'" .z / /
~o'2~o~=o~o~oLr~o , ~ I
~
2oo~J2o~3o~4o~r,o ' ~
Consecut~e day of the year
Fig. 3. T h e value o f c o e f f i c i e n t ~ d u r i n g t h e vegetative p e r i o d o f p o t a t o e s .
In experiments carried out by Bodleander and Algra (cited after Sibma, 1977), the tubers made up 85% of the biomass by the end of the vegetative period (/3 = 0.85), while Rijtema and EiidrSdi (1970) report 62% for the lowest final biomass and 75% for the highest (/~ = 0.62 or 0.75). In the present investigation the value of the coefficient for two p o t a t o varieties by the end of the vegetative period was on an average between 0.60 and 0.70 in nonirrigated treatments and between 0.59 and 0.67 in the irrigated ones. The variation of the coefficient during the vegetative period is presented in Fig. 3. Except for the non-irrigated treatments in 1976, the higher nitrogen level brought about a decrease of ~ during the entire vegetative period.
177
The decrease found was in the range 2.5--8.4% for non-irrigated treatments and 1.7--9.2% for the irrigated ones. This was particularly evident in the variety Pola where the decrease o f fl ranged from 0.6 to 2.2% in the low N-level and from 0.5 to 4.8% in the higher N-level. Irrigation-induced decrease of fl in the variety Sokot was higher and reached up to 8.9% for the higher N-levels. Fig. 4 shows the relation between calculated (Qpot, u) and determined tuber yields (Qemp, u ) for both varieties. As in the case of biomass, the experimental points lie along the same straight line, although there is a difference between the irrigation treatments. Therefore the verification o f the model for t u b e r yields was done in the same way as that for the whole biomass.
Soko~
POlO
Y
//
(kg DM m-~)
1
y--~:C~.*.O{~:~x ///~/ y:3~O÷O54x
,'--o.~
"-/Y,./'~0~
/
y:31964DF4x ///~ Y=-34.4.3..,.Of~x
~,ZA z~ , ~ A O,,t~ o ~,~ .~ ]~l r=
2 4 6
8 1'0 12
4
x: y: o • ~, •
6
O~(l:xYcentnl y~eld) Oe~l:~(efnprical yield) fer'tilizotton 80kgN r~:1-1 b . . fertiliz~don 1601~jN ha'l~ nOtl-lr'r'~x:~'ed fert zetonEOl~jN 1"=3-1? fertil!zeticn 160kgN he-l~ irrigcrted
8 10 --X(103 kg DIM hQ-1)
Fig. 4. Measured (y) and calculated (x) yield of tubers.
At a confidence level o£ P = 0.99 all the experimental treatments showed a linear dependence: (6)
Qemp,u = a + b Q p o t , u
High values of the correlation coefficient in all cases, reaching up to 0.96-0.97, testify that the tuber yields can be forecasted by means of a simple regression equation. For b o t h varieties, the relationship between the calculated and measured yields was different in the irrigated treatments from that in the non-irrigated ones (see Fig. 4). One should expect in (6): a = 0, b = 1 and Qemp,u = Qpot,u, but it was found that even for irrigated plants with higher N-level, the measured yield was much lower than the potential one. Differences are pronounced because of the values of b which are: b
SokSl
Pola
irrigated non-irrigated
0.54 0.65
0.66 0.74
178
This is due to diseases and pests, and tion of stems in the above-ground mass ticipation of stems in photosynthesis is by respiration and so they decrease the
probably also to the large contribuin the irrigated treatments. The parlow and they cause loss of assimilates productivity.
CONCLUSIONS
Under determined water and fertilizer conditions, the yield of potatoes can be forecasted by a theoretical model for potential yields. The applied regression equation has proved to give a high correlation between the measured Qemp, u and the calculated tuber yield Qpot,u- This is evident from correlation coefficients reaching up to 0.96--0.97. The interpretation of the results of irrigation experiments by means of a mathematical model has appeared to be useful and reliable. More research is needed to find out how to implement a plan for water management fertilizer application to increase yield, and what should be done if water is a limiting resource.
REFERENCES Brandyk, T., Kowalik, P. and Trzeciecki, F., 1980. Attempt of modeling of maximal soil productivity of 7.utawy. Fen. Rocz. Nauk Roln. Ser. F, t. 80, 1 : 145--154 (In Polish with English summary). Burton, W.G., 1964. Respiration of developing potato tubers. Eur. Potato J., 7: 90--101. De Wit, C.T., 1965. Photosynthesis of Leaf Canopies. Agric. Res. Rep. 663. Pudoc, Wageningen, The Netherlands, 57 pp. De Wit, C.T. and Goudriaan, J., 1974. Simulation of Ecological Processes. Simulation of Ecological Processes. Simulation Monograph. Pudoc, Wageningen, The Netherlands, 159 pp. Dzie~yc, D., Kowalik, P. and Mosz, J., 1981. Prognosis of potential rate of growth of beets in different water and fertilizer conditions. Zesz. Probl. Postepow Nauk Roln. (In press, In Polish with English summary). Feddes, R.A., Kowalik, P. and Zaradny, H., 1978. Simulation of field water use and crop yield. Simulation Monograph, Pudoc, Wageningen, The Netherlands, 189 pp. Kowalik, P. and Maciejewski, S., 1976. Example of calculation of potential yield of grasslands. Wiad. Mel. i L~k, 2 : 4 5 (In Polish with English summary). Mosz, J., 1978. Influence of sprinkler irrigation and different nitrogen fertilization on development, yield and quality of tubers of two new varieties of potatoes (mathematical model and empirical verification). Doctor's Thesis, Agricultural University of Wroctaw, 83 pp. (In Polish with English summary). Mosz, J., Kowalik, P. and Dzie~.yc, S., 1981. Prognosis of potential rate of growth of sugar beets in different water and fertilizer conditions. Zesz. Probl. Postepow Nauk Roln. (In press, In Polish). Rijtema, P.E. and EndrSdi, G., 1970. Calculation of production of potatoes. Neth. J. Agric. Sci., 18: 26--36. Sibrna, L., 1977. Maximization of arable crop yields in the Netherlands. Neth. J. Agric. Sci., 25: 278--287. Sirotienko, O.D. and Bojko, A.P., 1977. Dinamiczeskaja model agrocenoza. Trudy Institut ERsperimental' noi Meteorologii S.U., Minsk, Wyp. 8 (67): 12--36.
179 Slabbers, P.J., Sorbello Herrendorf, V. and Stapper, M., 1979. Evaluation of simplified water-crop yield models. Agric. Water Manage., 2: 95--129. Waggoner, P.E., 1969. Environmental manipulation for higher yields. In: J.O. Eastin et al. (Editors), Physiological Aspects of Crop Yield. ASA and CSSA, Madison, WI, pp. 343-373. Winkler, E., 1961. Assimilationsverm~gen, Atmung und Ertr'~ge der Kartoffel-sorten Oberambacher Friihe, Planet, Lori und Anges im Tal (610 m) und an der Waldgrenze bei Innsbruck und Vent (1880 m bzw. 2014 m). Flora (Jena), 151: 621---622. Winkler, E., 1971. Kartoffelbau in Tiroll. II. PhotosynthesevermSgen und Respiration von verschiedenen Kartoffelsorten. Potato Res., 14: 1--18. Zelitch, I., 1971. Photosynthesis, Photorespiration and Plant Productivity. Academic Press, New York, 419 pp.
171
Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands
INFLUENCE OF IRRIGATION ON THE DEVELOPMENT AND YIELD OF POTATOES
J. MOSZ l and P. KOWALIK 2
Institute of Agricultural Foundations of Land Improvement, Agricultural Academy, 50950 Wrociaw (Poland) 2Institute of Hydrotechnics, Technical University, 80952 Gdaf~sk (Poland) (Accepted 15 October 1981)
ABSTRACT Mosz, J. and Kowalik, P., 1982. Influence of irrigation on the development and yield o f potatoes. Agric. Water Manage., 5: 171--179. Verification of the model of potential yield developed by De Wit and modified by Rijtema, Feddes et al. and others, was carried out for two varieties of potato grown under different water and fertilization conditions. The anticipated yields were found to be correlated with the measured ones at the 0.99 confidence level, evidenced by correlation coefficients from 0.96 to 0.97. This means that for a given potato variety and under determined water and fertilization conditions the yield can be forecasted with the model. INTRODUCTION
The importance of potato as an edible, fodder and industrial plant makes it a universal crop. Increasing demands for potato necessitate the creation of optimum production conditions, but often water supplies are scarce. Therefore it is of utmost importance to be able to predict the effect of irrigation. Information concerning the effect of water supply on yields of crops is mostly obtained from field experiments. Such experiments are expensive, and labour and time consuming. This is the reason why in agricultural research a tendency has arisen to develop mathematical models to forecast the yields of crops grown under various climatic and agrotechnical conditions (e.g. Rijtema and EndrSdi, 1970; Zelitch, 1971; De Wit and Goudriaan, 1974; Feddes et al., 1978). Such mathematical models have been used already in many countries {e.g. Sirotienko and Bojko. 1977; Slabbers et al. 1979). In Poland, the model for potential rate of biomass accumulation developed by De Wit {1965} has been used to forecast the yields of grassland (Kowalik and Maciejewski, 1976; Brandyk et al., 1979), potatoes (Mosz, 1978), sugar beets (Mosz et al., 1980} and mangolds (Dzie~.yc et al., 1981}. The present paper gives an empirical verification of the mathematical model for yields of potatoes grown under different water and fertilization conditions. 0378-3774/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
172 FIELD EXPERIMENTS
Field experiments with potatoes were carried out at the Agricultural Experimental Station near W r o c h w in the years 1974--1976. The experimental area is situated in the valley of the river Odra at an altitude of 120 m, and at 51007 ' N and 17°10'E. The soil of the experimental field was a brown soil classified in the productivity class IVb and agricultural possibility class 5 {good for rye). The experiment was laid out in randomized subblocks in a system with three variables and four replications. Two potato varieties with different lengths of the growing period were examined, namely the medium-early variety Pola and medium-late variety SokSt. There were t w o watering treatments: W0 = non-irrigated, and W, = irrigated, as well as two nitrogen levels: N, = 80 and N2 = 160 kg N ha-' ; all treatments had the same phosphate and potassium fertilization, namely 80 kg P2Os ha-' and 160 kg K20 h a - ' . In variant W, 20 mm water was applied b y sprinkling when the soil water potential was a b o u t 350 kPa at 20 cm depth. In the years 1974, 1975 and 1976 the additional water supply was 40, 80 and 140 mm, respectively. Every 14 days five plants were taken from each plot to determine their fresh and dry matter contents. The assimilation surface was determined from the weight of 40 discs of known area, cut o u t of undamaged leaves. The weight of all the leaves of one plant as well as the number of plants on a square meter being known, the assimilative surface of crop as well as the leaf area index (LAI) could be calculated. The dry matter production (kg ha-' ) was calculated based upon the yields of fresh matter per plant and the density of plants in the plots. THEORY
De Wit (1965) calculated the daily potential photosynthetic yield of a standard canopy for LAI = 5 at 20°C, for cloudless and totally clouded skies, different latitudes and different days of the year. According to this the maxim u m (potential) dally increases (rates) of biomass for the latitude of W r o c h w are expressed in kg dry matter per ha per day (Table I). TABLE I Daily increase of biomass (kg DM ha -~ day -1 ) Date
Pc (cloudless sky) P0 (clouded sky)
15/05
15/06
15/07
15/08
15/09
15/10
483 250
524 274
510 265
446 226
353 174
253 117
173
For the dally rate of increase of biomass a modified formula based on De Wit's theory (Feddes et al., 1978) was used. This formula reads: P p o t = {P0 + 0.9--~ ( P c - P 0 ) } e 7 ¢
(kg ha-1 day -~)
(1)
where Ppot = daily rate of increase of biomass (kg ha -~ day-~); Pc, P0 = gross potential dally photosynthesis of standard canopy for clouded (P0) and cloudless (Pc) sky; 0.9 = atmosphere purity coefficient; n = duration of full insolation on a given day (min); N = the length of day for a determined latitude (min); ~ = coefficient considering the effect of temperature on the increase of biomass (nondimensional, from 0 to 1); 7 = coefficient o f leaf covering of the soil (LAI/5); ¢ = respiration coefficient (nondimensional, from 0 to 1). According to the above equation the production of biomass is limited by the respiration coefficient ¢the temperature coefficient ~ and the leaf covering coefficient 7. For potatoes, the respiration coefficient is a b o u t 0.8 (Burton, 1964). O p t i m u m air temperatures for photosynthesis are different for different plants. The sensitivity of p o t a t o photosynthesis to temperature was examined by Winkler (1961, 1971). He found that at 0°C the increase o f biomass was completely inhibited. At 5, 10 and 15°C he found values of 50, 90 and 98% respectively. In the range 18--20°C the intensity reached 100% and it fell to below 80% at 25°C. From these data the following values for the temperature coefficient a are as shown in Table II. TABLE II T (°C)
0
3
5
0
0
0.5
10
15
0.9
0.98
18 1.0
20 1.0
25 0.8
The coefficient 7 is introduced to take into account the influence of total leaf surfaces different from that of a standard canopy. If LAI = 5, then 7 = 1, where LAI is the total assimilative surface of leaves per unit area. The final yield has been calculated from the dally rates following from (1) according to the formula: i=te Qpot = ~ i=t o
Ppot,i
(kg h a -1)
(2)
where Qpot = final potential yield (kg ha-1 ); i = consecutive day o f the year; t0, te = first and last days of production, respectively. The above formula gives the so-caUed productivity, i.e. the total biomass of the crop. In potatoes only the t u b e r production is of importance. Therefore the tuber yield is calculated from the productivity by using the yield co-
174 efficient ~, defined by:/3 = (dry matter in tubers) / (total dry matter production). To calculate the potential increase of tubers on a given day, the daily potential production rate has to be multiplied by ~, hence: Ppot,u =/~Ppot
(kg ha -1 day -1 )
(3)
where Ppot, u = potential increase of tuber yield on a given day. The formula for the cumulative tuber yield Qpot, u then simply reads:
i=te Ppot, u,i
Qpot, u = ~
(kg
ha -1)
(4)
i=to POTENTIAL INCREASE OF THE BIOMASS
The potential yields of the biomass of potatoes and tubers were calculated for each treatment separately. Daily rates for a standard canopy were calculated from meteorological data. Coefficients 7 and/3 were determined based upon measurements taken every two weeks. Fig. 1 shows the effect of irrigation on the magnitude of 7 for the two varieties and two levels of nitrogen fertilization. In all treatments irrigation brought about a pronounced increase of the coefficient -f especially in spring, because the assimilative surface developed faster. A similar dependence was I~O kgN ha -1
160 I~jN ha -1 1974
10£
t
,'"
/'<, f ' .. _ "~,
'\
OSC Q6C non- irT'~ated "~
Q40 .
.
.
.
.
irr~J=tea"
Q20 O0
.I/, , ~ 04
.
c
~
0
I
1976
o8o~04ol/ o2oF
.
J vor~e~y Sok&
. . . . . non-irMgated ~ . . . . . . . irrigated j variety Pola
.,:S::-. "~
......
/
\
/5" . . . . ~':'..~ "-::"-.'~.
~
.
.......
,.,--
oJ 180190 2 0 0 2 1 0 ~ 0 230 240 2 5 0 2 6 0
\-
'.:',. ""~:
-.~. "....
180190 2 0 0 210 220 290 240 250 2£~0
Consecutive (Jay of the yeor
Fig. 1. The value of coefficient ~ during the vegetative period of potatoes.
175 obtained by Rijtema and EndrSdi (1970). They state that to obtain high yields, the period of incomplete soil cover should be as short as possible. The largest effect of irrigation on the magnitude of 7 was found in the higher nitrogen treatments. For the 160-kg N ha -1 treatment the increase o f 7 was from 14.6 to 34.2%, while with the lower dose o f 80 kg N ha -'1 it was from 0 to 25%. VERIFICATION OF THE PRODUCTION MODEL The calculated results of Qpot and Qpot,u of the model were compared with measured (empirical) data on total biomass Qemp and tuber production Qemp,uFor this purpose the correlation between measured (Qemp, Qemp,u) and calculated values (Qpot, Qpot,u ) was established by means of linear regression. The significance of the regression was assessed with Fischer's F-test and that of the correlation coefficient with Student's t-test. The correlation between measured and calculated values for the total biomass production is shown in Fig. 2. The data for all years and both nitrogen levels lie along the same straight line. The yields of biomass of irrigated and non-irrigated plants of both varieties are shown separately because of considerable differences between them. This was the reason for carrying out the verification jointly for fertilizer levels and separately for the variety and irrigation. For the results o f the analysis as far as it concerns the biomass, all treatments gave a rectilinear dependence:
(5)
Qemp = a + b Qpot at a confidence level o f p = 0.99.
(kg
DM
/~//
Pola
Soko+
Y ha -~)
/ -
8
I~,
-
y= f:,~. 2 . 0 6 4 x 7 •
r :o.g8
oy///~ ~)/~A
•
e Y=395.7*O.77x 7
~°0~
A~//
-,~/~;
6
o ,
8.052x
•
&A~O ° &
O~
4
r=O.g8
~-e //7 Z~/ ~e f~lw
yield) =Oemp(empirical yield)
x = Opot (potent~l
Y 0 • & •
fertihzoti~ 80 I~gN f e r t i l i z a t ~ 10:) t~jN fertilizotionSOkgN fertilization 160 kg N
9on-irrigoted
- ....
2
4
6
irrigat~-~d
8
10
12
14
x ( l O 3 kg D~t ha -1)
Fig. 2. Measured (y) and calculated (x) yield of total biomass.
~-1 -~ . tx:1-1.J non-rrrrgated ha-l-) I~ -1 ~ mrlgoted
176
The calculated yields were highly correlated with the measured ones, which was shown by correlation coefficients of 0.94--0.98. This means that the biomass production of a given variety under determined meteorological conditions can be calculated by means of a simple regression (5) shown in Fig. 2. The somewhat higher correlation coefficients for the higher nitrogen level are probably due to other factors like soil temperature, diseases, pests, etc. VERIFICATION OF TUBER YIELDS
After having proved that the calculated yields of biomass are highly correlated with the measured ones, the anticipated yields Qpot,u, i.e. the yields of tubers, were calculated by applying the coefficient/3. Fig. 3 shows the value of coefficient ~. 80 kgN ha -~
,
.-
160 kgN ha-1
/
,;i / /
.t
-Dcrl-lrP ted . . . . . . . irrl~,qll~ t variety Sokof
~. . . . . . . . .
nc~% irrigated ?
.......... irrigated
0 4
j variety Pole
#/"
02 /
//''
o; 06
-" ~ ..--"
1976
oLJ. o
.~;: ~;. . . . . .
.'" .z / /
~o'2~o~=o~o~oLr~o , ~ I
~
2oo~J2o~3o~4o~r,o ' ~
Consecut~e day of the year
Fig. 3. T h e value o f c o e f f i c i e n t ~ d u r i n g t h e vegetative p e r i o d o f p o t a t o e s .
In experiments carried out by Bodleander and Algra (cited after Sibma, 1977), the tubers made up 85% of the biomass by the end of the vegetative period (/3 = 0.85), while Rijtema and EiidrSdi (1970) report 62% for the lowest final biomass and 75% for the highest (/~ = 0.62 or 0.75). In the present investigation the value of the coefficient for two p o t a t o varieties by the end of the vegetative period was on an average between 0.60 and 0.70 in nonirrigated treatments and between 0.59 and 0.67 in the irrigated ones. The variation of the coefficient during the vegetative period is presented in Fig. 3. Except for the non-irrigated treatments in 1976, the higher nitrogen level brought about a decrease of ~ during the entire vegetative period.
177
The decrease found was in the range 2.5--8.4% for non-irrigated treatments and 1.7--9.2% for the irrigated ones. This was particularly evident in the variety Pola where the decrease o f fl ranged from 0.6 to 2.2% in the low N-level and from 0.5 to 4.8% in the higher N-level. Irrigation-induced decrease of fl in the variety Sokot was higher and reached up to 8.9% for the higher N-levels. Fig. 4 shows the relation between calculated (Qpot, u) and determined tuber yields (Qemp, u ) for both varieties. As in the case of biomass, the experimental points lie along the same straight line, although there is a difference between the irrigation treatments. Therefore the verification o f the model for t u b e r yields was done in the same way as that for the whole biomass.
Soko~
POlO
Y
//
(kg DM m-~)
1
y--~:C~.*.O{~:~x ///~/ y:3~O÷O54x
,'--o.~
"-/Y,./'~0~
/
y:31964DF4x ///~ Y=-34.4.3..,.Of~x
~,ZA z~ , ~ A O,,t~ o ~,~ .~ ]~l r=
2 4 6
8 1'0 12
4
x: y: o • ~, •
6
O~(l:xYcentnl y~eld) Oe~l:~(efnprical yield) fer'tilizotton 80kgN r~:1-1 b . . fertiliz~don 1601~jN ha'l~ nOtl-lr'r'~x:~'ed fert zetonEOl~jN 1"=3-1? fertil!zeticn 160kgN he-l~ irrigcrted
8 10 --X(103 kg DIM hQ-1)
Fig. 4. Measured (y) and calculated (x) yield of tubers.
At a confidence level o£ P = 0.99 all the experimental treatments showed a linear dependence: (6)
Qemp,u = a + b Q p o t , u
High values of the correlation coefficient in all cases, reaching up to 0.96-0.97, testify that the tuber yields can be forecasted by means of a simple regression equation. For b o t h varieties, the relationship between the calculated and measured yields was different in the irrigated treatments from that in the non-irrigated ones (see Fig. 4). One should expect in (6): a = 0, b = 1 and Qemp,u = Qpot,u, but it was found that even for irrigated plants with higher N-level, the measured yield was much lower than the potential one. Differences are pronounced because of the values of b which are: b
SokSl
Pola
irrigated non-irrigated
0.54 0.65
0.66 0.74
178
This is due to diseases and pests, and tion of stems in the above-ground mass ticipation of stems in photosynthesis is by respiration and so they decrease the
probably also to the large contribuin the irrigated treatments. The parlow and they cause loss of assimilates productivity.
CONCLUSIONS
Under determined water and fertilizer conditions, the yield of potatoes can be forecasted by a theoretical model for potential yields. The applied regression equation has proved to give a high correlation between the measured Qemp, u and the calculated tuber yield Qpot,u- This is evident from correlation coefficients reaching up to 0.96--0.97. The interpretation of the results of irrigation experiments by means of a mathematical model has appeared to be useful and reliable. More research is needed to find out how to implement a plan for water management fertilizer application to increase yield, and what should be done if water is a limiting resource.
REFERENCES Brandyk, T., Kowalik, P. and Trzeciecki, F., 1980. Attempt of modeling of maximal soil productivity of 7.utawy. Fen. Rocz. Nauk Roln. Ser. F, t. 80, 1 : 145--154 (In Polish with English summary). Burton, W.G., 1964. Respiration of developing potato tubers. Eur. Potato J., 7: 90--101. De Wit, C.T., 1965. Photosynthesis of Leaf Canopies. Agric. Res. Rep. 663. Pudoc, Wageningen, The Netherlands, 57 pp. De Wit, C.T. and Goudriaan, J., 1974. Simulation of Ecological Processes. Simulation of Ecological Processes. Simulation Monograph. Pudoc, Wageningen, The Netherlands, 159 pp. Dzie~yc, D., Kowalik, P. and Mosz, J., 1981. Prognosis of potential rate of growth of beets in different water and fertilizer conditions. Zesz. Probl. Postepow Nauk Roln. (In press, In Polish with English summary). Feddes, R.A., Kowalik, P. and Zaradny, H., 1978. Simulation of field water use and crop yield. Simulation Monograph, Pudoc, Wageningen, The Netherlands, 189 pp. Kowalik, P. and Maciejewski, S., 1976. Example of calculation of potential yield of grasslands. Wiad. Mel. i L~k, 2 : 4 5 (In Polish with English summary). Mosz, J., 1978. Influence of sprinkler irrigation and different nitrogen fertilization on development, yield and quality of tubers of two new varieties of potatoes (mathematical model and empirical verification). Doctor's Thesis, Agricultural University of Wroctaw, 83 pp. (In Polish with English summary). Mosz, J., Kowalik, P. and Dzie~.yc, S., 1981. Prognosis of potential rate of growth of sugar beets in different water and fertilizer conditions. Zesz. Probl. Postepow Nauk Roln. (In press, In Polish). Rijtema, P.E. and EndrSdi, G., 1970. Calculation of production of potatoes. Neth. J. Agric. Sci., 18: 26--36. Sibrna, L., 1977. Maximization of arable crop yields in the Netherlands. Neth. J. Agric. Sci., 25: 278--287. Sirotienko, O.D. and Bojko, A.P., 1977. Dinamiczeskaja model agrocenoza. Trudy Institut ERsperimental' noi Meteorologii S.U., Minsk, Wyp. 8 (67): 12--36.
179 Slabbers, P.J., Sorbello Herrendorf, V. and Stapper, M., 1979. Evaluation of simplified water-crop yield models. Agric. Water Manage., 2: 95--129. Waggoner, P.E., 1969. Environmental manipulation for higher yields. In: J.O. Eastin et al. (Editors), Physiological Aspects of Crop Yield. ASA and CSSA, Madison, WI, pp. 343-373. Winkler, E., 1961. Assimilationsverm~gen, Atmung und Ertr'~ge der Kartoffel-sorten Oberambacher Friihe, Planet, Lori und Anges im Tal (610 m) und an der Waldgrenze bei Innsbruck und Vent (1880 m bzw. 2014 m). Flora (Jena), 151: 621---622. Winkler, E., 1971. Kartoffelbau in Tiroll. II. PhotosynthesevermSgen und Respiration von verschiedenen Kartoffelsorten. Potato Res., 14: 1--18. Zelitch, I., 1971. Photosynthesis, Photorespiration and Plant Productivity. Academic Press, New York, 419 pp.