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Climatic model for dry matter production of winter wheat in Hungary
ELSEVIER
Agricultural
and Forest Meteorology
83 ( 1997) 23 I-246
Climatic model for dry matter production of winter wheat in Hungary L&z16 Lakatos Department
Received
of Agrophysics 16 February
and Agrometeorology,
PO Box 36, H-4015
1995; revised 13 October
1995; accepted
Dehrecen,
1 November
Hungary
1995
Abstract A dynamic model was developed to describe the total above-ground dry matter production and dry matter production of ears for winter wheat, ‘Jubilejnaja 50’. It also estimates the occurrence of phenological stages and yields with an accuracy of approximately f 10 days and f0.5 tha- ‘, respectively. The model uses 4 variables, while the nutrient supply submodel uses 3 variables. These variables are air temperature at 2 m, plant available water at a depth of 1 m, global radiation to characterize the radiation, and a submodel to describe the soil nutrient supply. The 3 variables of the submodel are: temperature at a depth of 1 m, soil moisture content of a 1 m deep soil layer, and precipitation. The results calculated by our model apply to the Eastern part of the Great Hungarian Plain.
1. Introduction The relationship between plant development and weather has attracted the attention of mankind since prehistoric times. Our plant-gathering ancestors must have been the first to find that plant growth is highly dependent upon weather conditions and, consequently, that the quantity and quality of food available varied greatly from year to year. Those communities that were aware of this pattern were less affected by droughts and other calamities than those that had no knowledge of this natural law. The observations that started to accumulate when man began to cultivate the land have gradually led to the scientifically-based description of the relationship between plant development and weather. The simplest yield models involve summing or averaging several variables over the growing season and correlating those variables with yield by multiple regression (Fisher, 1924; Berenyi, 1956; Haun, 1974). The computer-based modeling of plant growth and yield production started in the 1970s. The earliest models described the dependence of basic physiological processes: 0168-1923/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. SSDl 0 168- 1923(95)02322-4
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photosynthesis, respiration with climatic conditions (Dmitrenko, 1973; Sirotenko, 1978). Later models were developed to estimate yield as functions of photosynthetically-active absorbed radiation and temperature, assuming that the remaining factors, water and nutrient supply, were optimal. Such models, e.g. Abranyi (1978) and Hodges and Kanemasu (19771, described the potential biomass production at a particular site. Of course, water supply and transpiration have also got a significant impact on actual yield formation. The first complete dry matter accumulation simulation model for winter wheat was developed by Rickman et al. (I 975). In this model seven daily environmental variables (available soil water, soil N supply, solar radiation, soil temperature, air temperature, wind run and relative humidity) were the primary inputs. Further wheat modelling occurred in the second half of the 1970s (Morgan, 1976; Hochman, 1979). Several models had been developed by the 1980s which could simulate the growth of winter wheat (Porter et al., 1983; Stapper, 1984; Weir et al., 1984; Ritchie and Otter, 1984; Matthaus et al., 1986; Spitters et al., 1989). These models require large computing facilities and extensive data to verify them. Kenworthy (1949) and Richards and Wadleigh (1952) pointed out that plant development is inhibited even before the temporary wilting point is reached. Temperature conditions in a particular geographical area represent decisive criteria for the natural establishment of a plant. All the physiological processes take place within certain tolerance ranges. Thus temperature has to reach a certain minimum at which biological processes can begin. The activity will be at its highest when the temperature is at its optimum. At very high temperatures, however, biological processes will cease. These are the three vital temperature values. They vary widely according to age and development stage, and vary significantly depending on the plant species (Morison and Butterfield, 1990). The models mentioned above use different optimum functions. In many cases these apply only to a specific phenological stage, e.g. emergence. According to most of the authors the optimum temperature for the development of the winter wheat is about 15-25°C (Hubbard and Hanks, 1983). The solar radiation optimum is about 15-25 MJm-* day- ’ (Davidson and Philip, 1958) and the optimum values of the soil moisture is 65% of the available water capacity of the soil (Polevoj, 1983). According to Klages (1930, 1934) the optimum values of the main environmental elements are approximately equal to the climatological average during the growing season. In his research he pointed out that these optimum values keep changing during the growing season of the plant. The model also uses his assumptions that the optimum values of the environmental variables can be substituted by climatological averages.
2. Data The model has to be realistic as well as relatively simple. Obviously, involving a large number of variables would provide more precise results, provided that the effect of each factor is interpreted in the correct way. Being aware of this, and taking physio-
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Days from sowing to maturity Fig. I. The annual average course of the available water of the soil.
requirements into consideration, we decided to use those four variables (air temperature, available water of the soil, global radiation and nutrient supply of the soil) that are essential factors controlling the development of the plant. Air temperature and solar radiation data, as well as meteorological data necessary for the submodel of the production of NO;-N by natural processes, like soil temperature, soil moisture, and precipitation, were observed at the DAU Agrometeorological Observatory (latitude = 47”30’, longitude = 21”42’, altitude 112 m). Measurements of the amount of available water of the soil were taken on lime coated chemozem soil (clay content 47%) samples taken from the observatory area, where the water table was at a depth of 8-10 m. The minimum field water capacity of the soil was 280 mmm- ‘, the wilting point and the available water capacity of this soil water water capacity was 148 mmm-’ therefore 132 mm m- ’. About two thirds of the available water capacity (88 mm m- ’> was freely available. Knowledge of the actual amount of plant available water of the soil during the growing season is very important, especially in a dry area like Hungary. The low amount of available water is generally the primary limiting factor for plant production in Hungary (Fig. 1). Hunk& and Bacsi (1993) found a depth of 1 m satisfactory for running the CERES-model, noting, however, that in dry periods the water supplies from deeper layers can become important. The soil nutrient supply was considered equivalent to the amount of NOT-N naturally available in a 1 m deep soil layer, expressed in mg/lOO g. The annual course of N-formation is well characterized by the degree of the biological activity in the soil. With the submodel predicting the nutrient supply the mineralized NO; amount can be estimated with an accuracy of f 16%, and with a correlation coefficient r = 0.76 significant at the 0.1% level (Lakatos and Szhz, 1991). For plant data, dry matter measurements were supplied by the Experiment Station of the Department of Plant Production, which is located less than 5 km from the Observatory on an identical soil type.
logical
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The complete phenological and grain yield data between 197.5-l 990 were taken at the Variety Experiment Station of the Ministry, which is in the neighborhood of the Observatory, while dry matter data were taken at the Experiment Station of the DAU Department of Plant Production. All the plant data apply to medium duration winter wheat, ‘Jubilejnaja 50’. The meteorological and plant data were collected in years l964- 1994 and 1975 1994, respectively.
3. Method Most of the soil-plant-climate models are based on the examination of the effect that meteorological and other environmental factors (water and nutrient supply) have on plant development. The definition of the function expressing the relationship between development ratio and environmental factors is essential. Most of the environmental conditions have extreme values at which life processes cease. There is an optimum condition between the two extremes. As a rule, authors draw the function for one particular life phase, e.g. the stage emergency (Monteith, 1981). They ignore the rest of the factors or consider them constant. The optimums can be defined for the whole of the vegetational period from climatic chamber experiments, for example. Literature data on the optimum values are usually slightly higher than the climatic averages for most of the growing sites over the given period. However, theoretical ecological averages of these values for wheat and corn, as determined by Schimper (1903) and Klages (1934), equal with the climatic averages at sites that give outstandingly high yields and low annual variations. According to these authors the plant development can be described by a harmonized summation of the annual climatic average schemes. Based on this theoretical assumption, the following method was applied to determine wheat mass increase in our experiment. The mass increase dynamics during the growing season was expressed by the summation of the products of the applied climatic variables, a method also used previously by Baier (19731, Dmitrenko (1973), Rickman et al. (197.51, and Landsberg and Cutting (1977). The long term (30 year) growing season series of input variables was produced using Bessel’s polinomials (expanded trigonometrical series). As the four variables used had different ranges, each of them had to be normalized for their particular minimum and maximum values over the 30 year series. By the summation of the products over the growing season the theoretical ecological curve was produced. As actual conditions, e.g. climatic, nutrient, and soil, have to be taken into consideration, the introduction of relevant weighting functions is required (Schimper, 1903). The weighting functions will have a minimum value if the value for the particular day equals the lowest or the highest value of the 30 year series for that day. They will have a maximum value if it equals with the average value of the 30 year series from that day. The absolute minima and maxima were estimated using the density function of standard normal distribution. From the lowest and highest values produced over the 30 year
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series, a zero impact on plant development is not possible. Thus, the lowest values of the weighting function equal the minimum values of the density functions. As the input variables still remain independent, accurate results could be achieved by multidimensional functions only. According to Liebig’s minimum law, the joint effect of four variables will equal the effect of the lowest value variable, so if the starting and ending times of plant mass increase are known, the actual plant dry matter mass increase as a function of time, can be calculated using the product of 4 response functions and the weight function minimum. 3.1. Response jmctions In the model there are four response functions to characterize the principal factors of plant development i.e. the functions of thermal, hydrological, radiation, nutrient supply conditions. The response functions represent the annual climatic variation of the given variable. According to Schimper (1903) “plants that are well adapted will necessarily acquire a vegetational variation of different climatic elements in the area.” Thus, well-adapted plants, such as the winter wheat, the speed of development and biological activities follow the climatic conditions that are typical of the area. Hungary’s geographical situation, in the centre of the European cereal belt, suggests that winter wheat is well adapted to the area. The response functions can be produced as a trigonometrical series based on the average annual course derived from a long time series. If the maximum and minimum values of the time series are known, normalisation of the series over the range zero to one will produce the following response functions. 1. Temperature function It is known that temperature and day-length regulate the speed of differentiation. The differentiation of the apex, in turn, sets the rate of development (Petr et al., 1985). T(r) 2. Available
= 9.1 + 11 .OSsin (G
+3.06)
water function
H(t)
= 67.98 + 59.49sin (g
3. Solar radiation
- 0.88)
(mmm-‘)
(lb)
(MJm-‘day-‘)
(lc)
function
R( r) = 68.5 + 55.27sin (G-2.63) 4. Nutrient
(“C)
supply function
(m/loo 8)
(‘d)
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1
-
0.9 0.8 0.7 0.6
(
/
/
e w
I
0.5
Available water Temperature v++ Solar radiation
..I_. Nutrient supply
0.4 0.3 0.2 0.1 0
0
50
100 150 200 Days from sowing to maturity
250
300
Fig. 2. Response functions of winter wheat.
The correlation between the measured and calculated values is very high, r = 0.970.99. Normalisation of the above functions over the range 0 to 1 will produce the following response functions (Fig. 2). The standard form of the four response functions is as follows:
X,(f)=
Y(f) - Y, y _y x
n
where Y(t) is the function of the input variables (temperature, available water, solar radiation, nutrient supply), Y, is the minimum value of the given input variable (temperature, available water, solar radiation, nutrient supply), and Y,: maximum value of the given input variable (temperature, available water, solar radiation, nutrient supply). The minimum and maximum values are given in Table 1. The product of the response functions M,(t) demonstrates the average daily dry matter increase of the winter wheat over the growing season (Fig. 3). The response functions have to satisfy the assumption of a normal distribution and the following conditions: 0 < T,(r) < 1, 0 < H,(r) < 1, 0 < R,(r) < 1, and 0
Table I Minimum
maximum minimum
and maximum
values of the input variable functions
T (“Cl
H (mm)
R (MJm-*)
N(mg/lCOg)
21.71 - I .95
127.49 21.82
23.58 3.61
35.68 0
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.?
I
H‘
Measured
DT
* Calculated
-0.1
! 50
I 100
Days Fig. 3. Product
of four response
D,
functions
150 200 250 from sowing to maturity
300
and the average daily development winter wheat.
of the total dry matter mass of
daily variations of the temperature optimum over the growing season corresponds to the long term daily averages. Let us assume that minimum and maximum values equal the long term minima and maxima of the input variables, i.e. the temperature, plant available water, solar radiation, nutrient supply. The examination of the distribution using the Geary test show that the long term 5-day input variables series follow a normal distribution pattern. Let us standardize all the input variables series data between the average sowing and maturity dates for the 30 years investigated. After calculating the standard normal distribution density function and extrapolating its values from the range of O-O.4 to the range of O-l, a function is given which is suitable for weighting. To simplify handling we replaced the extrapolated standard normal distribution density function as ‘weighted function’ with a linear curves below and above mean value (7(T), q(H), q(R), and v(N)) (Fig. 4).
Standardized Fig. 4. Interpretation
values (T,H,R,N)
of weighting
functions.
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As the mean value of the standardized normal distribution is 0 and the dispersion is 1, for such a sample size the average produced will be equal to the mean value and thus the weight of the period will be 1. In the case of a satisfactory length of data, the weight of the minima and maxima would be 0, as it follows from the density function of the standard normal distribution. This, however, is not fulfilled in our case, and, so, the weights of the maxima and minima for each of the 5-day growing season periods have to be determined. As the results showed little variation over the growing season - the value of the coefficient of variation, CV, never exceeded 19% for the ratio of maximum to minimum we assumed that the substitution of the weight of the minimum or maximum values for the average values will not result in errors in the definition of the end value weights of the periods. The minimum values were between 0.1 I-0.27, with a CV between 8-16%. The maximum values were between 0.05-0.20, with a CV between 6-19%. Based on these the weighting function of the variables for a 5day time step over the growing season can be determined for each year. The standard form of the weighting function is as follows: If the given 5-day period’s average value of the given variable is lower than the long term variable average, (X < ??): X-X
I I
rl(x)=l-(l-p”)
x_x
n
where r](X) is the weighting function of the given variable, P, is the probable value of the minimum (Table 2), x is the actual value of the variable over the growing season, X is the long term average value of the 30-year series of the given variables over the growing season, and X, is the absolute minimum value of the 30-year series of the given variables over the growing season. If the given 5-day period’s average value of the given variable is higher than the long term variable average (X > ‘sz>:
I I X-X
77(X)=l-_(l-Px)
y--pj
(3)
x
where q(X) is the weighting function of the given variable, P, is the probable value of the maximum (Table 2), X is the actual value of the variable over the growing season, x is the long term average value of the 30-year series of the given variables over the growing season, and X, is the absolute maximum value of the 30-year series of the given variables over the growing season.
Table 2 Probable values of minimum
Maximum Minimum
and maximum
from extrapolated
standard normal density function
T
H
R
N
0.1 I 0.14
0.27 0.05
0.13 0.15
0.18 0.2
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The CV value of the minimum and maximum values of the temperature weighting function were 12 and 14%, respectively. The CV values for the available water weighting function were 8 and 6%. The distribution analysis shows that values deviate towards the lower values compared to a normal distribution of available water for the soil series. There is higher probability of low values than of high ones, which is a consequence of the climatic conditions in the basin. It has been shown that the efficiency of the solar energy utilization in winter wheat is only l-2% at a maximum. It is also known that the intensity of the photosynthesis is proportionate to the number of photons. Moreover, unlike temperature and soil moisture, solar radiation is not a continues process. As stated earlier solar radiation is considered equivalent to the global radiation using the standard normal distribution density investigations, the CV of minimum and maximum values were found to be 13 and 14%. As mentioned above, the soil nutrient supply is considered equivalent to the amount of naturally produced NO;-N in a 1 m deep soil layer. These values were calculated with our model developed earlier. Using the standard normal distribution density investigations, the CV values of minimum and maximum from the density functions were 16 and 19%.
4. Biometeorological
time
For the description of the development of a certain plant part (ear, spike, leaf, stem) as a function of time, an appropriate time scale is needed. Mass increase (total above ground or ear mass) will start at a certain stage of the plant development. For the determination of the starting point we have to introduce a biometeorological time scale, a name introduced by Robertson (1968). It has to be stressed, however, that our scale is not identical with the scale used by Robertson because, besides daily temperature maxima and minima, he introduced day and night length also. The word ‘scale’ is only used to indicate that more than thermal time derived from temperature summation is meant (Monteith, 1981). The character of the scale is determined by the temperature only, the daily increases, however, are in complete accordance with the plant physiological requirements. When constructing the scale, the external effects were taken into consideration from both meteorological and biological aspects. It was presupposed that the daily temperature optimum of wheat equals the long term temperature averages for the particular geographical area. Thus variation in the temperature daily optimum over the growing season correspond to the long term temperature averages. Thus, if the products of multiplying the values of the 5-day time step temperature weighting function by the corresponding values of the temperature response function are summed over the period between sowing and maturity, we will obtain the ’biometeorological’ time. So, the time scale is based on statistical data and along with its deterministic
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character it is capable with dealing with the stochastic effects, which appear as a sum of effects taken at any point of plant development. maturity ‘b=
c I=
*dr)dT(‘))
(4)
sowing
where 7’,(t) is the temperature response function, function, and I is the time (in 5-day time steps).
5. Estimating
n(T(t))
is the temperature
weighting
the starting point of the phenological phases
The biometeorological time scale characterizes the development speed of the plant. If the scale is correctly defined, it is expected to truly express the occurrence of the phenological phases. Comparison between the measured and calculated values gave correlation coefficients of 0.77-0.88 with the difference between the real and calculated occurrence of the phenological phases never exceeded 10 days during the 20 years studied. If the biometeorological time is known, fitting the data from the 20 year series, the occurrence of the phenological phases can be estimated by the following regression equations: Emergence
(t,,) = 18.15tb + 6.24
Head development
( tb) = 6.11 I, + 38.12
Heading
( tb) = 4.82rb + 48.25
Flowering
(r,)
= 6.59rb + 96.18
Vaxen ripeness
( tb) = 9.36tb + 156.86
Maturity
( tb) = 8.19tb + 163.27
(5)
where rb is biometeorological time (dimensionless). The weakest fitting was found with estimating emergence time r = 0.77. Flowering, maturity heading, head development, and vaxen ripeness times were estimated with correlations r = 0.83, r = 0.84, r = 0.85, r = 0.86, and r = 0.88, respectively. This shows that our model is suited for the estimation of the occurrence of phenological phases and that it provides results with acceptable precision.
6. The dynamics of dry matter accumulation According to Vrkoc (1973), soil and climatic conditions have a significant effect on the amount and dynamics of above soil biomass formation. This and our previous observations of plant physiology eventually led us to the conclusion that biomass development as a function of time can be described with four variables, i.e. air temperature, solar radiation, available water of the soil, nutrient supply. The joint effect of the four variables can be interpreted by additive or multiplicative
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relations. The multiplicative approach is supported by the fact that each of the variables is essential for survival which means that minimum conditions of any of the four factors will result in a significant decrease in their overall effect Varga-Haszonits (1986). In the additive case it is not realized to the same extent. Consequently, the product of the four response functions is suitable for predicting the dynamics of daily dry matter formation over the growing season. By quadratic fitting the averages total above ground daily dry matter and ear dry matter increase can be calculated with the following equation:
D,= -11.49M;+6.03M,+0.01 D, = 11.83M;
- 0.26M,
r = 0.99 + 0.01
(6)
r = 0.98
where D, is the total daily dry matter production (gplant-‘1, M, is the product of the four response functions, and D, is the ear daily dry matter production (g plan-’ ). Knowing the response functions and probability weights of each variable, using Liebig’s minimum law, the summation of the products of the four response functions multiplied by the lowest value of the weighting function, the dry matter production of winter wheat can be described. Accordingly, the model equation is this: DM(%)
=
E PM&)} r,=O
x I&f(~tJ~
(7)
where D,(t,):plant mass increase as a function of biometeorological time, t, is the biometeorological time (from sowing to maturity), M,(r,)= TR(fb)HR(rb)SR(fb)NR(tb), NW(fb>= min[v(T(t,)). v(H(r,)), rl(R(t,)), 77(N(tb))l, TR(tb) is the temperature response function, H,(t,)is the soil available water response function, S,(t,) is the solar radiation response function, NR( tb) is the nutrient supply response function, q(T( t,)) is the temperature weighting function, q(H(tb))is the soil available water weighting function, T&R( t,)) is the solar radiation weighting function, and T(N( t,)) is the nutrient supply weighting function.
Calculated ( dimensionless Fig. 5. Relationship
between measured
)
above soil total biomass and total calculated
by our model.
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’
DM=2.78dmc$c0.39
E s.6 S -
I r=0.96
I
(n=20)
5-
“0
015
Fig. 6. Relationship
1 Calculated
115
2
( dimensionless
between measured and calculated
2.5
) ear dry matter by our model.
With the help of the equation above, the daily (averaged over 5 days) plant mass increase can be determined. The relationship between the dimensionless cumulative final value of our model and the final measured dry matter content is shown in Fig. 5 and Fig. 6, and can be characterized by a single linear equation: M, = 2.970,
- 0.49
for above soil biomass total
M, = 2.780,
- 0.39
for ear mass
(8)
where M, E is the measured cumulated and D, is the calculated dry matter content. There is a’significant relation between the measured and the calculated values of above soil biomass total and grain mass accumulation growing r = 0.96 and r = 0.97 at p = 0.1%. The testing of a model is usually done against an independent data set. In our case it was the dry matter mass increase prediction for year 1994. If the starting point of ear formation which can be read on the biometeorological time scale (on the basis of 3 investigated years it had a value of 8.6, with very slight
4
Fig. 7. Cumulative
6
8 IO Biometeorological time
measured and calculated
above-ground
12
14
total and grain dry matter increase in 1994
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differences) and the final point, i.e. the maturity date (the value was 12.4, also with a very slight differences) are known, the ear dry matter mass increase can be calculated with the model being run between these two points. As can be seen in Fig. 7, both above soil biomass total and grain mass increase as a function of time can be predicted with the precision of f6%.
7. Prediction of the grain yield amount The total plant and grain dry matter mass increase data are essential for making yield estimations. The data of the available 4 test years, the period between 1991- 1994, show a significant, at p = 0.1 %, connection between the measured dry matter content maximum value and the grain yield amount; the correlation coefficient is r = 0.96. The regression equation is: Y = 1.18{ ME,x} - 0.27 where Y is the quantity of grain yield in (tha-I), and M,,, is the cumulated ear dry matter content maximum value in (g plant- ’>. This equation can be generalized only if the stem numbersha -’ is the same in every investigated year (it was about 6 million stem ha- ’ in our case). Let us suppose that this assumption is correct in every investigated year. Independent control data, which are necessary for testing, were available between 1975-1990 from the Variety Research Station. If we run the model from the starting point of grain formation determined earlier, i.e. from 8.6, to the maturity date, i.e. 12.4 biometeorological time points, the ear dry matter content maximum value can be determined. In the investigated period of 1975-1990, the values calculated show a significant relation with grain yields (r = 0.92) at p = 1%. The average error of measured and calculated values was below 0.5 tha- ’ (Fig. 8).
1975
1980
1985
1990
Years Fig. 8. Measured and calculated
grain yields during the period of 1975- 1990.
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remarks
The results apply to a medium-duration winter wheat ‘Jubilejnaja 50’. This is the major variety cultivated in Eastern Hungary, and in other regions of the country. The average annual yield of a large cultural area involves the yields of several different varieties and there are large differences in their productivity, drought and disease resistance. Varieties with new traits can show significant differences in their weather tolerance - their tolerance to certain climatic effects may increase, to others it may decrease. Cultivation of a variety over a long period may cause changes in certain characteristics. Thus, we cannot expect a plant-weather model developed for a variety with certain genetic characteristics to work perfectly for varieties with different genetic characteristics. The model presented here did not take the dry matter decrease during the growing period into consideration. We assumed that the dry matter mass increase was a monotonically increasing process. We think that this assumption could be correct if the principal controls (thermal, hydrological, radiation, nutrient condition) were near the optimum. The model uses a low number of input parameters which makes it easier to deal with. Moreover, the incorporation of a variety function would widen the range of use of the model. The results calculated by our model apply to the Eastern part of the Great Hungarian Plain and to any other place where the average annual variation of climatological elements is similar.
Appendix
T(t) H(t) R(t) N(t)
X,(r) 17(X) p, PX ‘b
DT DE MR
A. Notation temperature function, with trigonometrical series expanded available water of the soil function, with trigonometrical series expanded solar radiation function, with trigonometrical series expanded nutrient supply function, with trigonometrical series expanded standard form of the four response function, with trigonometrical series expanded standard form of the four weighting functions probable values of minima probable values of maxima the time (in five day time steps) biometeorological time the total daily dry matter production the ear daily dry matter production the product of the four response function
“C
mmm-’ MJm-*
day- ’
w/100 g dimensionless dimensionless
day dimensionless g plant- ’ g plant- ’ dimensionless
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MT ME Divl
-
Y Subscripts R n : T E W D
the the the by the
und Forest Meteorohgy
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function
245
dimensionless g plant- ’ g plant- ’ g plant- ’ tha-’
response function minimum maximum biometeorological total ear weighting function model
References Abrinyi, A., 1978. Analysis of the crop yield of winter wheat by using a photosynthetical model (in Hungarian). Beszamolok az 1975-ben vegzett Tud. kut.-rbl, pp. 133-136. Baier, W., 1973. Crop-weather analysis model: review and model development. J. Appl. Meteorol., 12: 931-947. Berenyi, D., 1956. The maturity time of wheat and the weather (in Hungarian). Idojads, 60(4): 250-252. Davidson, J.L. and Philip, J.R., 1958. Ligh and pasture growth. In: Climatology and Microclimatology. UNESCO, pp. 181-187. Dmitrenko, V.P., 1973. Determine the effect of precipitation on the yield formation of arable crops (in Russian). Trudi UNIGI, 128: 3-22. Fisher, R.A., 1924. The influence of rainfall upon the yield of wheat at Rothampsted. Philos. Trans. R. Sot. London, Ser. B., 113: 89- 142. Harm, J.R., 1974. Prediction of spring wheat yields from temperature and precipitation data. Agron. J., 66: 405-409. Hochman, 2.. 1979. Wheat in semi-arid environment: a field and simulation study of the effects of water stress on yield. MSc. Thesis, University of Sydney. Hodges, T. and Kanemasu, E.T., 1977. Modelling daily dry matter production of winter wheat. Agron. J., 69: 974-978. Hubbard, KG. and Hanks, R.J., 1983. Climate model for winter wheat yield simulation. J. Clim. Appl. Meteorol., 22: 698-703. Hunk&r, M. and Bacsi, Zs., 1993. Attempts by soil-plant weather models (in Hungarian). Meteoroldgia es niivtnytermesztes, 59: 59-65. Kenworthy, A.L., 1949. Soil moisture and growth of apple trees. Am. Sot. Hortic. Sci. Pro., 54: 29-39. Klages, K.H.W., 1930. Geographical distribution of variability in the yields of field crops in the states of the Mississippi Valley. Ecology, 1 I : 293-306. Klages, K.H.W., 1934. Geographical distribution of variability in the yields of cereal crops in South Dakota. Ecology, 12: 334-345. Lakatos, L. and Szasz, G., 1991. Climatic effects on the changes of N-supplying power of the soil (in Hungarian), IdojjLas, 95: 289-301. Landsberg, J.J. and Cutting, C.V., 1977. Environmental effects on Crop Physiology. Academic Press, London. Matthaus, E., Mirschel, W., Kretschmer, H., Kinkel, K. and Klank, I., 1986. The winter wheat crop model TRITSIM of the Agroecosystem AGROSIM-W. In: Computer Aided Modelling and Simulation of the
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Winter Wheat Agroecosystem for Integrated Pest Management. Academic der Ladwirtschwissenschaften der DDR. pp. 43-77. Monteith, J.L., 1981. Climatic variation and the growth of crops. Q. J. R. Meteorol. Sot., 107: 7499774. Morgan, J.M., 1976. A simulation model of the growth of the wheat plant. Ph.D. Thesis, Macquarie University. Morison, J.I.L. and Butterfield, R.E., 1990. Cereal crop damage by frosts, Spring 1990. Weather, 4_5(8): 308-313. Petr, J., Cemy, V. and Hruska, L., 1985. Yield Formation of Main Arable Crops (in Hungarian). Mezogazdasagi Kiad6, Budapest. Polevoj, A.N., 1983. Theory and Calculation of the Productivity of Plant. Gidrometeoizdat, Leningrad. Porter, J.R., Bragg, P.L., Rayner, J.H., Weir, A.H. and Landsberg, J.J., 1983. The ARC wheat simulation model-principles and progress. In: A. Hawkins and B. Jeffcoat (Editors), Opportunities for Manipulations of Cereal Productivity. British Plant Growth Regulator Group. Richards, L.A. and Wadleigh, C.H., 1952. Soil water and plant growth. In: Soil Physical Conditions and Plant Growth. Academic Press, New York. Rickman, R.W., Raming, R.E. and Allmaras, R.R., 1975. Modeling dry matter accumulation in dryland winter wheat. Agron. J., 67: 283-289. Ritchie, J.T. and Otter, S., 1984. CERES wheat: a user oriented wheat yield model. Preliminary documentation, Agristars publication no. YM-U3-04442-JSC-18892. Robertson, G.W., 1968. A biometeorological time scale for a cereal crop involving day and night temperatures and photo period. hit. J. Biometeorol., 12: 191-223. Schimper, A.F.W.. 1903. Plant Geography on a Physiological Basis. Clarendon, Oxford. Sirotenko, O.D., 1978. Physico-mathematical modelling in agrometeorology (in Russian). Meteorologija i Gidrologija, 3: 80-88. Spitters, C.J.T., Van Keulen, H. and Van Kraalingen, D.W.G., 1989. A simple and universal crop growth simulator SUCROS 87. In: R. Rabbinge, S.A. Ward and H.H. van Laar (Editors). Simulation and Systems Management in Crop Protection. Simulation Monographs, PUDOC, Wageningen, pp. 147- 181. Stapper, M., 1984. SIMTAG: a simulation model of wheat genotypes. Model documentation, Farming Systems Programme. International Centre for Agricultural Research in the Dry Areas. Varga-Haszonits, Z., 1986. Methodical principles of multiplicative crop-weather model building (in Hungarian). Beszkmolok 1983. OMSZ. Bp. pp. 1555 164. Vrkoc, F., 1973. Yield formation of cereals. In: J. Petr-V., Cemy-L. Hruska (Editors), Yield Formation of Main Arable Crops (in Hungarian). Bp. Mezogazd, pp. 115-116. Weir, A.H., Bragg, P.L., Porter, J.R. and Rayner, J.H., 1984. A winter wheat crop simulation model without water or nutrient limitation. J. Agric. Sci., 102: 371-382.
Agricultural
and Forest Meteorology
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Climatic model for dry matter production of winter wheat in Hungary L&z16 Lakatos Department
Received
of Agrophysics 16 February
and Agrometeorology,
PO Box 36, H-4015
1995; revised 13 October
1995; accepted
Dehrecen,
1 November
Hungary
1995
Abstract A dynamic model was developed to describe the total above-ground dry matter production and dry matter production of ears for winter wheat, ‘Jubilejnaja 50’. It also estimates the occurrence of phenological stages and yields with an accuracy of approximately f 10 days and f0.5 tha- ‘, respectively. The model uses 4 variables, while the nutrient supply submodel uses 3 variables. These variables are air temperature at 2 m, plant available water at a depth of 1 m, global radiation to characterize the radiation, and a submodel to describe the soil nutrient supply. The 3 variables of the submodel are: temperature at a depth of 1 m, soil moisture content of a 1 m deep soil layer, and precipitation. The results calculated by our model apply to the Eastern part of the Great Hungarian Plain.
1. Introduction The relationship between plant development and weather has attracted the attention of mankind since prehistoric times. Our plant-gathering ancestors must have been the first to find that plant growth is highly dependent upon weather conditions and, consequently, that the quantity and quality of food available varied greatly from year to year. Those communities that were aware of this pattern were less affected by droughts and other calamities than those that had no knowledge of this natural law. The observations that started to accumulate when man began to cultivate the land have gradually led to the scientifically-based description of the relationship between plant development and weather. The simplest yield models involve summing or averaging several variables over the growing season and correlating those variables with yield by multiple regression (Fisher, 1924; Berenyi, 1956; Haun, 1974). The computer-based modeling of plant growth and yield production started in the 1970s. The earliest models described the dependence of basic physiological processes: 0168-1923/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. SSDl 0 168- 1923(95)02322-4
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photosynthesis, respiration with climatic conditions (Dmitrenko, 1973; Sirotenko, 1978). Later models were developed to estimate yield as functions of photosynthetically-active absorbed radiation and temperature, assuming that the remaining factors, water and nutrient supply, were optimal. Such models, e.g. Abranyi (1978) and Hodges and Kanemasu (19771, described the potential biomass production at a particular site. Of course, water supply and transpiration have also got a significant impact on actual yield formation. The first complete dry matter accumulation simulation model for winter wheat was developed by Rickman et al. (I 975). In this model seven daily environmental variables (available soil water, soil N supply, solar radiation, soil temperature, air temperature, wind run and relative humidity) were the primary inputs. Further wheat modelling occurred in the second half of the 1970s (Morgan, 1976; Hochman, 1979). Several models had been developed by the 1980s which could simulate the growth of winter wheat (Porter et al., 1983; Stapper, 1984; Weir et al., 1984; Ritchie and Otter, 1984; Matthaus et al., 1986; Spitters et al., 1989). These models require large computing facilities and extensive data to verify them. Kenworthy (1949) and Richards and Wadleigh (1952) pointed out that plant development is inhibited even before the temporary wilting point is reached. Temperature conditions in a particular geographical area represent decisive criteria for the natural establishment of a plant. All the physiological processes take place within certain tolerance ranges. Thus temperature has to reach a certain minimum at which biological processes can begin. The activity will be at its highest when the temperature is at its optimum. At very high temperatures, however, biological processes will cease. These are the three vital temperature values. They vary widely according to age and development stage, and vary significantly depending on the plant species (Morison and Butterfield, 1990). The models mentioned above use different optimum functions. In many cases these apply only to a specific phenological stage, e.g. emergence. According to most of the authors the optimum temperature for the development of the winter wheat is about 15-25°C (Hubbard and Hanks, 1983). The solar radiation optimum is about 15-25 MJm-* day- ’ (Davidson and Philip, 1958) and the optimum values of the soil moisture is 65% of the available water capacity of the soil (Polevoj, 1983). According to Klages (1930, 1934) the optimum values of the main environmental elements are approximately equal to the climatological average during the growing season. In his research he pointed out that these optimum values keep changing during the growing season of the plant. The model also uses his assumptions that the optimum values of the environmental variables can be substituted by climatological averages.
2. Data The model has to be realistic as well as relatively simple. Obviously, involving a large number of variables would provide more precise results, provided that the effect of each factor is interpreted in the correct way. Being aware of this, and taking physio-
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Days from sowing to maturity Fig. I. The annual average course of the available water of the soil.
requirements into consideration, we decided to use those four variables (air temperature, available water of the soil, global radiation and nutrient supply of the soil) that are essential factors controlling the development of the plant. Air temperature and solar radiation data, as well as meteorological data necessary for the submodel of the production of NO;-N by natural processes, like soil temperature, soil moisture, and precipitation, were observed at the DAU Agrometeorological Observatory (latitude = 47”30’, longitude = 21”42’, altitude 112 m). Measurements of the amount of available water of the soil were taken on lime coated chemozem soil (clay content 47%) samples taken from the observatory area, where the water table was at a depth of 8-10 m. The minimum field water capacity of the soil was 280 mmm- ‘, the wilting point and the available water capacity of this soil water water capacity was 148 mmm-’ therefore 132 mm m- ’. About two thirds of the available water capacity (88 mm m- ’> was freely available. Knowledge of the actual amount of plant available water of the soil during the growing season is very important, especially in a dry area like Hungary. The low amount of available water is generally the primary limiting factor for plant production in Hungary (Fig. 1). Hunk& and Bacsi (1993) found a depth of 1 m satisfactory for running the CERES-model, noting, however, that in dry periods the water supplies from deeper layers can become important. The soil nutrient supply was considered equivalent to the amount of NOT-N naturally available in a 1 m deep soil layer, expressed in mg/lOO g. The annual course of N-formation is well characterized by the degree of the biological activity in the soil. With the submodel predicting the nutrient supply the mineralized NO; amount can be estimated with an accuracy of f 16%, and with a correlation coefficient r = 0.76 significant at the 0.1% level (Lakatos and Szhz, 1991). For plant data, dry matter measurements were supplied by the Experiment Station of the Department of Plant Production, which is located less than 5 km from the Observatory on an identical soil type.
logical
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The complete phenological and grain yield data between 197.5-l 990 were taken at the Variety Experiment Station of the Ministry, which is in the neighborhood of the Observatory, while dry matter data were taken at the Experiment Station of the DAU Department of Plant Production. All the plant data apply to medium duration winter wheat, ‘Jubilejnaja 50’. The meteorological and plant data were collected in years l964- 1994 and 1975 1994, respectively.
3. Method Most of the soil-plant-climate models are based on the examination of the effect that meteorological and other environmental factors (water and nutrient supply) have on plant development. The definition of the function expressing the relationship between development ratio and environmental factors is essential. Most of the environmental conditions have extreme values at which life processes cease. There is an optimum condition between the two extremes. As a rule, authors draw the function for one particular life phase, e.g. the stage emergency (Monteith, 1981). They ignore the rest of the factors or consider them constant. The optimums can be defined for the whole of the vegetational period from climatic chamber experiments, for example. Literature data on the optimum values are usually slightly higher than the climatic averages for most of the growing sites over the given period. However, theoretical ecological averages of these values for wheat and corn, as determined by Schimper (1903) and Klages (1934), equal with the climatic averages at sites that give outstandingly high yields and low annual variations. According to these authors the plant development can be described by a harmonized summation of the annual climatic average schemes. Based on this theoretical assumption, the following method was applied to determine wheat mass increase in our experiment. The mass increase dynamics during the growing season was expressed by the summation of the products of the applied climatic variables, a method also used previously by Baier (19731, Dmitrenko (1973), Rickman et al. (197.51, and Landsberg and Cutting (1977). The long term (30 year) growing season series of input variables was produced using Bessel’s polinomials (expanded trigonometrical series). As the four variables used had different ranges, each of them had to be normalized for their particular minimum and maximum values over the 30 year series. By the summation of the products over the growing season the theoretical ecological curve was produced. As actual conditions, e.g. climatic, nutrient, and soil, have to be taken into consideration, the introduction of relevant weighting functions is required (Schimper, 1903). The weighting functions will have a minimum value if the value for the particular day equals the lowest or the highest value of the 30 year series for that day. They will have a maximum value if it equals with the average value of the 30 year series from that day. The absolute minima and maxima were estimated using the density function of standard normal distribution. From the lowest and highest values produced over the 30 year
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series, a zero impact on plant development is not possible. Thus, the lowest values of the weighting function equal the minimum values of the density functions. As the input variables still remain independent, accurate results could be achieved by multidimensional functions only. According to Liebig’s minimum law, the joint effect of four variables will equal the effect of the lowest value variable, so if the starting and ending times of plant mass increase are known, the actual plant dry matter mass increase as a function of time, can be calculated using the product of 4 response functions and the weight function minimum. 3.1. Response jmctions In the model there are four response functions to characterize the principal factors of plant development i.e. the functions of thermal, hydrological, radiation, nutrient supply conditions. The response functions represent the annual climatic variation of the given variable. According to Schimper (1903) “plants that are well adapted will necessarily acquire a vegetational variation of different climatic elements in the area.” Thus, well-adapted plants, such as the winter wheat, the speed of development and biological activities follow the climatic conditions that are typical of the area. Hungary’s geographical situation, in the centre of the European cereal belt, suggests that winter wheat is well adapted to the area. The response functions can be produced as a trigonometrical series based on the average annual course derived from a long time series. If the maximum and minimum values of the time series are known, normalisation of the series over the range zero to one will produce the following response functions. 1. Temperature function It is known that temperature and day-length regulate the speed of differentiation. The differentiation of the apex, in turn, sets the rate of development (Petr et al., 1985). T(r) 2. Available
= 9.1 + 11 .OSsin (G
+3.06)
water function
H(t)
= 67.98 + 59.49sin (g
3. Solar radiation
- 0.88)
(mmm-‘)
(lb)
(MJm-‘day-‘)
(lc)
function
R( r) = 68.5 + 55.27sin (G-2.63) 4. Nutrient
(“C)
supply function
(m/loo 8)
(‘d)
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1
-
0.9 0.8 0.7 0.6
(
/
/
e w
I
0.5
Available water Temperature v++ Solar radiation
..I_. Nutrient supply
0.4 0.3 0.2 0.1 0
0
50
100 150 200 Days from sowing to maturity
250
300
Fig. 2. Response functions of winter wheat.
The correlation between the measured and calculated values is very high, r = 0.970.99. Normalisation of the above functions over the range 0 to 1 will produce the following response functions (Fig. 2). The standard form of the four response functions is as follows:
X,(f)=
Y(f) - Y, y _y x
n
where Y(t) is the function of the input variables (temperature, available water, solar radiation, nutrient supply), Y, is the minimum value of the given input variable (temperature, available water, solar radiation, nutrient supply), and Y,: maximum value of the given input variable (temperature, available water, solar radiation, nutrient supply). The minimum and maximum values are given in Table 1. The product of the response functions M,(t) demonstrates the average daily dry matter increase of the winter wheat over the growing season (Fig. 3). The response functions have to satisfy the assumption of a normal distribution and the following conditions: 0 < T,(r) < 1, 0 < H,(r) < 1, 0 < R,(r) < 1, and 0
Table I Minimum
maximum minimum
and maximum
values of the input variable functions
T (“Cl
H (mm)
R (MJm-*)
N(mg/lCOg)
21.71 - I .95
127.49 21.82
23.58 3.61
35.68 0
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237
.?
I
H‘
Measured
DT
* Calculated
-0.1
! 50
I 100
Days Fig. 3. Product
of four response
D,
functions
150 200 250 from sowing to maturity
300
and the average daily development winter wheat.
of the total dry matter mass of
daily variations of the temperature optimum over the growing season corresponds to the long term daily averages. Let us assume that minimum and maximum values equal the long term minima and maxima of the input variables, i.e. the temperature, plant available water, solar radiation, nutrient supply. The examination of the distribution using the Geary test show that the long term 5-day input variables series follow a normal distribution pattern. Let us standardize all the input variables series data between the average sowing and maturity dates for the 30 years investigated. After calculating the standard normal distribution density function and extrapolating its values from the range of O-O.4 to the range of O-l, a function is given which is suitable for weighting. To simplify handling we replaced the extrapolated standard normal distribution density function as ‘weighted function’ with a linear curves below and above mean value (7(T), q(H), q(R), and v(N)) (Fig. 4).
Standardized Fig. 4. Interpretation
values (T,H,R,N)
of weighting
functions.
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As the mean value of the standardized normal distribution is 0 and the dispersion is 1, for such a sample size the average produced will be equal to the mean value and thus the weight of the period will be 1. In the case of a satisfactory length of data, the weight of the minima and maxima would be 0, as it follows from the density function of the standard normal distribution. This, however, is not fulfilled in our case, and, so, the weights of the maxima and minima for each of the 5-day growing season periods have to be determined. As the results showed little variation over the growing season - the value of the coefficient of variation, CV, never exceeded 19% for the ratio of maximum to minimum we assumed that the substitution of the weight of the minimum or maximum values for the average values will not result in errors in the definition of the end value weights of the periods. The minimum values were between 0.1 I-0.27, with a CV between 8-16%. The maximum values were between 0.05-0.20, with a CV between 6-19%. Based on these the weighting function of the variables for a 5day time step over the growing season can be determined for each year. The standard form of the weighting function is as follows: If the given 5-day period’s average value of the given variable is lower than the long term variable average, (X < ??): X-X
I I
rl(x)=l-(l-p”)
x_x
n
where r](X) is the weighting function of the given variable, P, is the probable value of the minimum (Table 2), x is the actual value of the variable over the growing season, X is the long term average value of the 30-year series of the given variables over the growing season, and X, is the absolute minimum value of the 30-year series of the given variables over the growing season. If the given 5-day period’s average value of the given variable is higher than the long term variable average (X > ‘sz>:
I I X-X
77(X)=l-_(l-Px)
y--pj
(3)
x
where q(X) is the weighting function of the given variable, P, is the probable value of the maximum (Table 2), X is the actual value of the variable over the growing season, x is the long term average value of the 30-year series of the given variables over the growing season, and X, is the absolute maximum value of the 30-year series of the given variables over the growing season.
Table 2 Probable values of minimum
Maximum Minimum
and maximum
from extrapolated
standard normal density function
T
H
R
N
0.1 I 0.14
0.27 0.05
0.13 0.15
0.18 0.2
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The CV value of the minimum and maximum values of the temperature weighting function were 12 and 14%, respectively. The CV values for the available water weighting function were 8 and 6%. The distribution analysis shows that values deviate towards the lower values compared to a normal distribution of available water for the soil series. There is higher probability of low values than of high ones, which is a consequence of the climatic conditions in the basin. It has been shown that the efficiency of the solar energy utilization in winter wheat is only l-2% at a maximum. It is also known that the intensity of the photosynthesis is proportionate to the number of photons. Moreover, unlike temperature and soil moisture, solar radiation is not a continues process. As stated earlier solar radiation is considered equivalent to the global radiation using the standard normal distribution density investigations, the CV of minimum and maximum values were found to be 13 and 14%. As mentioned above, the soil nutrient supply is considered equivalent to the amount of naturally produced NO;-N in a 1 m deep soil layer. These values were calculated with our model developed earlier. Using the standard normal distribution density investigations, the CV values of minimum and maximum from the density functions were 16 and 19%.
4. Biometeorological
time
For the description of the development of a certain plant part (ear, spike, leaf, stem) as a function of time, an appropriate time scale is needed. Mass increase (total above ground or ear mass) will start at a certain stage of the plant development. For the determination of the starting point we have to introduce a biometeorological time scale, a name introduced by Robertson (1968). It has to be stressed, however, that our scale is not identical with the scale used by Robertson because, besides daily temperature maxima and minima, he introduced day and night length also. The word ‘scale’ is only used to indicate that more than thermal time derived from temperature summation is meant (Monteith, 1981). The character of the scale is determined by the temperature only, the daily increases, however, are in complete accordance with the plant physiological requirements. When constructing the scale, the external effects were taken into consideration from both meteorological and biological aspects. It was presupposed that the daily temperature optimum of wheat equals the long term temperature averages for the particular geographical area. Thus variation in the temperature daily optimum over the growing season correspond to the long term temperature averages. Thus, if the products of multiplying the values of the 5-day time step temperature weighting function by the corresponding values of the temperature response function are summed over the period between sowing and maturity, we will obtain the ’biometeorological’ time. So, the time scale is based on statistical data and along with its deterministic
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character it is capable with dealing with the stochastic effects, which appear as a sum of effects taken at any point of plant development. maturity ‘b=
c I=
*dr)dT(‘))
(4)
sowing
where 7’,(t) is the temperature response function, function, and I is the time (in 5-day time steps).
5. Estimating
n(T(t))
is the temperature
weighting
the starting point of the phenological phases
The biometeorological time scale characterizes the development speed of the plant. If the scale is correctly defined, it is expected to truly express the occurrence of the phenological phases. Comparison between the measured and calculated values gave correlation coefficients of 0.77-0.88 with the difference between the real and calculated occurrence of the phenological phases never exceeded 10 days during the 20 years studied. If the biometeorological time is known, fitting the data from the 20 year series, the occurrence of the phenological phases can be estimated by the following regression equations: Emergence
(t,,) = 18.15tb + 6.24
Head development
( tb) = 6.11 I, + 38.12
Heading
( tb) = 4.82rb + 48.25
Flowering
(r,)
= 6.59rb + 96.18
Vaxen ripeness
( tb) = 9.36tb + 156.86
Maturity
( tb) = 8.19tb + 163.27
(5)
where rb is biometeorological time (dimensionless). The weakest fitting was found with estimating emergence time r = 0.77. Flowering, maturity heading, head development, and vaxen ripeness times were estimated with correlations r = 0.83, r = 0.84, r = 0.85, r = 0.86, and r = 0.88, respectively. This shows that our model is suited for the estimation of the occurrence of phenological phases and that it provides results with acceptable precision.
6. The dynamics of dry matter accumulation According to Vrkoc (1973), soil and climatic conditions have a significant effect on the amount and dynamics of above soil biomass formation. This and our previous observations of plant physiology eventually led us to the conclusion that biomass development as a function of time can be described with four variables, i.e. air temperature, solar radiation, available water of the soil, nutrient supply. The joint effect of the four variables can be interpreted by additive or multiplicative
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relations. The multiplicative approach is supported by the fact that each of the variables is essential for survival which means that minimum conditions of any of the four factors will result in a significant decrease in their overall effect Varga-Haszonits (1986). In the additive case it is not realized to the same extent. Consequently, the product of the four response functions is suitable for predicting the dynamics of daily dry matter formation over the growing season. By quadratic fitting the averages total above ground daily dry matter and ear dry matter increase can be calculated with the following equation:
D,= -11.49M;+6.03M,+0.01 D, = 11.83M;
- 0.26M,
r = 0.99 + 0.01
(6)
r = 0.98
where D, is the total daily dry matter production (gplant-‘1, M, is the product of the four response functions, and D, is the ear daily dry matter production (g plan-’ ). Knowing the response functions and probability weights of each variable, using Liebig’s minimum law, the summation of the products of the four response functions multiplied by the lowest value of the weighting function, the dry matter production of winter wheat can be described. Accordingly, the model equation is this: DM(%)
=
E PM&)} r,=O
x I&f(~tJ~
(7)
where D,(t,):plant mass increase as a function of biometeorological time, t, is the biometeorological time (from sowing to maturity), M,(r,)= TR(fb)HR(rb)SR(fb)NR(tb), NW(fb>= min[v(T(t,)). v(H(r,)), rl(R(t,)), 77(N(tb))l, TR(tb) is the temperature response function, H,(t,)is the soil available water response function, S,(t,) is the solar radiation response function, NR( tb) is the nutrient supply response function, q(T( t,)) is the temperature weighting function, q(H(tb))is the soil available water weighting function, T&R( t,)) is the solar radiation weighting function, and T(N( t,)) is the nutrient supply weighting function.
Calculated ( dimensionless Fig. 5. Relationship
between measured
)
above soil total biomass and total calculated
by our model.
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’
DM=2.78dmc$c0.39
E s.6 S -
I r=0.96
I
(n=20)
5-
“0
015
Fig. 6. Relationship
1 Calculated
115
2
( dimensionless
between measured and calculated
2.5
) ear dry matter by our model.
With the help of the equation above, the daily (averaged over 5 days) plant mass increase can be determined. The relationship between the dimensionless cumulative final value of our model and the final measured dry matter content is shown in Fig. 5 and Fig. 6, and can be characterized by a single linear equation: M, = 2.970,
- 0.49
for above soil biomass total
M, = 2.780,
- 0.39
for ear mass
(8)
where M, E is the measured cumulated and D, is the calculated dry matter content. There is a’significant relation between the measured and the calculated values of above soil biomass total and grain mass accumulation growing r = 0.96 and r = 0.97 at p = 0.1%. The testing of a model is usually done against an independent data set. In our case it was the dry matter mass increase prediction for year 1994. If the starting point of ear formation which can be read on the biometeorological time scale (on the basis of 3 investigated years it had a value of 8.6, with very slight
4
Fig. 7. Cumulative
6
8 IO Biometeorological time
measured and calculated
above-ground
12
14
total and grain dry matter increase in 1994
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differences) and the final point, i.e. the maturity date (the value was 12.4, also with a very slight differences) are known, the ear dry matter mass increase can be calculated with the model being run between these two points. As can be seen in Fig. 7, both above soil biomass total and grain mass increase as a function of time can be predicted with the precision of f6%.
7. Prediction of the grain yield amount The total plant and grain dry matter mass increase data are essential for making yield estimations. The data of the available 4 test years, the period between 1991- 1994, show a significant, at p = 0.1 %, connection between the measured dry matter content maximum value and the grain yield amount; the correlation coefficient is r = 0.96. The regression equation is: Y = 1.18{ ME,x} - 0.27 where Y is the quantity of grain yield in (tha-I), and M,,, is the cumulated ear dry matter content maximum value in (g plant- ’>. This equation can be generalized only if the stem numbersha -’ is the same in every investigated year (it was about 6 million stem ha- ’ in our case). Let us suppose that this assumption is correct in every investigated year. Independent control data, which are necessary for testing, were available between 1975-1990 from the Variety Research Station. If we run the model from the starting point of grain formation determined earlier, i.e. from 8.6, to the maturity date, i.e. 12.4 biometeorological time points, the ear dry matter content maximum value can be determined. In the investigated period of 1975-1990, the values calculated show a significant relation with grain yields (r = 0.92) at p = 1%. The average error of measured and calculated values was below 0.5 tha- ’ (Fig. 8).
1975
1980
1985
1990
Years Fig. 8. Measured and calculated
grain yields during the period of 1975- 1990.
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remarks
The results apply to a medium-duration winter wheat ‘Jubilejnaja 50’. This is the major variety cultivated in Eastern Hungary, and in other regions of the country. The average annual yield of a large cultural area involves the yields of several different varieties and there are large differences in their productivity, drought and disease resistance. Varieties with new traits can show significant differences in their weather tolerance - their tolerance to certain climatic effects may increase, to others it may decrease. Cultivation of a variety over a long period may cause changes in certain characteristics. Thus, we cannot expect a plant-weather model developed for a variety with certain genetic characteristics to work perfectly for varieties with different genetic characteristics. The model presented here did not take the dry matter decrease during the growing period into consideration. We assumed that the dry matter mass increase was a monotonically increasing process. We think that this assumption could be correct if the principal controls (thermal, hydrological, radiation, nutrient condition) were near the optimum. The model uses a low number of input parameters which makes it easier to deal with. Moreover, the incorporation of a variety function would widen the range of use of the model. The results calculated by our model apply to the Eastern part of the Great Hungarian Plain and to any other place where the average annual variation of climatological elements is similar.
Appendix
T(t) H(t) R(t) N(t)
X,(r) 17(X) p, PX ‘b
DT DE MR
A. Notation temperature function, with trigonometrical series expanded available water of the soil function, with trigonometrical series expanded solar radiation function, with trigonometrical series expanded nutrient supply function, with trigonometrical series expanded standard form of the four response function, with trigonometrical series expanded standard form of the four weighting functions probable values of minima probable values of maxima the time (in five day time steps) biometeorological time the total daily dry matter production the ear daily dry matter production the product of the four response function
“C
mmm-’ MJm-*
day- ’
w/100 g dimensionless dimensionless
day dimensionless g plant- ’ g plant- ’ dimensionless
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MT ME Divl
-
Y Subscripts R n : T E W D
the the the by the
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function
245
dimensionless g plant- ’ g plant- ’ g plant- ’ tha-’
response function minimum maximum biometeorological total ear weighting function model
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