Objectives  Learning objectives and
requirements 



Production Situation
Production situation PS‑1 represents a land‑use system with the least possible analytical complexity; all land qualities which can be influenced by a farmer through irrigation and drainage, use of fertilizers, weeding and control of pests and diseases are assumed to be optimum. The production calculated for production situation PS‑1 is the highest production possible on a farmer's field. It is the 'biophysical production potential'. The biophysical production potential is determined by the solar radiation and
temperature during the growing period and by the physiological characteristics
of the crop. Analysis of production situation PS‑1 is based on the same
principles as calculation of net biomass production for agro‑ecological
zoning but the procedure is dynamic and considerably more detailed. The basic methods to calculate production potentials are described in Land use systems analysis by P.M. Driessen and N.T. Konijn (1992). Chapter 8 contains the formulas for PS1. The complete book can be downloaded here; to read chapter 8 (page 108 and following), please use the bookmarks in the PDF. 

Photosynthesis  The fundamental process behind plant growth is assimilation, i.e. reduction of atmospheric CO2 to carbohydrates, (CH2O)n. Assimilation requires energy; it is a unique capability of green plants that they can capture solar energy and use it in assimilation:
CO_{2}
+ H_{2}O + solar energy ‑‑> ^{1}/_{n}(CH_{2}O)_{n}
+ O_{2} (1a)
Conversion of (CH_{2}O)_{n} to CO_{2} and H_{2}O occurs also. This process is known as respiration; it releases chemical energy which can be used by the plant.
 
Pathways of photosynthesis  The rate of assimilation under conditions of light saturation and optimum temperature differs among plants. Three different pathways of photosynthesis exist of which two have practical importance.
An important difference between C3‑plants and C4‑plants is that respiration in the sunlit photosynthetic organs (photorespiration) is considerable in C3‑plants and negligible in C4‑plants.
Losses of assimilates incurred in photorespiration increase with temperature and intensity of light. This has practical consequences.
Not surprisingly, C4‑plants stem predominantly from the tropics. Most C3‑crops (not all) have their origin in more temperate regions. Representatives of both groups are included in Table 1. Table 1: Photosynthetic mechanism for various crops (Driessen and Konijn, 1992)
 
Effects of light intensity and temperature on assimilation  The
amount of solar energy at the outer extremity of the atmosphere varies with the
latitude of the site and the time of year. Approximately half the total
global radiation is photosynthetically active radiation (PAR). The
transparancy of the atmosphere determines how much radiation reaches the
canopy. Light response curves relate irradiance with gross assimilation.
Light response curves are described by only two parameters.
light use efficiency at low light intensity (EFF) maximum rate of assimilation (AMAX). AMAX (kg ha^{1} h^{1}) is the gross rate of assimilation at light saturation; AMAX is codetermined by photorespiration and is much greater for C4‑crops than for C3‑crops. AMAX is strongly temperature‑dependent; EFF decreases by only 1% for every degree of temperature increase in C3‑plants, and even less in C4‑plants. For practical purposes EFF is a constant with a value of some 0.5 kg ha^{1} h^{1}/J m^{2} s^{1} (de Wit et al., 1978). The above figure presents light response curves of maize leaves at several temperatures. Observe that ambient temperature has a much more pronounced effect on AMAX (the plateau) than on EFF (the initial angle of the curve). It is unfortunate that curves like those Figure 1 cannot be used to describe the assimilatory potential of field‑grown crops. It appears that the photosynthetic activity of plant leaves is influenced by the radiation and temperature to which the leaves were exposed in the past. It is for this reason that the AEZ team defined crop‑adaptability groups with different AMAX‑to‑temperature relations. The response curves in Figure 2 resemble those used by the AEZ team (FAO, 1978). Note that Figure 2 is a simplification; the optimum temperature for assimilation by a C3‑crop cannot be a steady 18 ^{o}C in cool climates and 27 ^{o}C in the tropics if it is co‑determined by the temperatures to which the crop was actually exposed. Therefore actual assimilation will be calculated as a fraction of assimilation at a reference temperature (T_{ref}). T_{ref} is the temperature to which the assimilating plant 'got used'; it is tentatively defined as the weighted average of the daytime temperatures (T_{day}) over the past 10 days, with a minimum of 15 ^{o}C and a maximum of 30 ^{o}C.
Curves I and II in Figure 2 suggest the following AMAX‑to‑temperature relation for C3‑crops.
AMAX = 1.8 * T_{ref}  0.15 * (T_{ref}  T_{day})2 (8.2a)
Approximate AMAX‑to‑temperature relations for C4‑crops are obtained by dividing response curves III and IV in Figure 2 in three linear trajecta. if T_{day} <= T_{ref} then AMAX = 110  10 * (T_{ref}  T_{day}) (8.2b) if T_{day} > T_{ref} then AMAX = 110  2 * (T_{day}  T_{ref}) (8.2c)
if AMAX > 88 then AMAX = 88 (8.2d) where AMAX is maximum rate of assimilation at actual temperature (kg ha^{1} h^{1}) T_{ref} is reference temperature (^{o}C) T_{day} is daytime temperature (^{o}C).


Implementation 
To calculate AMAX, you can run the MaximumAssimilationAlgorithm, by clicking the following JAVA Webstart link.
The following interface should appear:
AMAX‑to‑temperature response curves relate AMAX to the equivalent daytime temperature (T_{day}), not the average daily temperature (T_{24h}).
 
Additional reading 
Average daily temperature (T_{24h}) is a function of equivalent daytime temperature (T_{day}), equivalent night temperature (T_{night}) and daylength (DL). The equivalent daytime temperature (T_{day}) is found by integrating the temperature curve between sunrise and sunset (M. v.d. Berg, pers. comm.). It is assumed that the maximum temperature occurs at 14.00 hrs and the lowest temperature at sunrise.
T_{day} = Tmid + (SUNSET  14) * AMPL * sin(AUX) / (DL * AUX) (8.3.1) with Tmid = (Tmax + Tmin) / 2 (8.3.2) AMPL = (Tmax  Tmin) / 2 (8.3.3) SUNRISE = 12  DL / 2 (8.3.4) SUNSET = 12 + DL / 2 (8.3.5) AUX = PI * (SUNSET  14) / (SUNRISE + 10) (8.3.6)
where Tmax is maximum daily temperature (^{o}C) Tmin is minimum daily temperature (^{o}C) DL is daylength (h d^{1}) PI is a constant (PI = 3.14159).
The equivalent night temperature (T_{night}) is found by integrating the temperature curve between sunset and sunrise.
T_{night} = Tmid  AMPL * sin(AUX) / (PI  AUX) (8.3.7)
The daylength (DL) is a function of the day in the year and the latitude of the site (de Wit et al., 1978).
DL = 12 * (PI + 2 * asin(SSCC)) / PI (8.4) with SSCC = SSIN / CCOS (8.4.1) SSIN = sin(LAT * RAD) * sin(DEC * RAD) (8.4.2) CCOS = cos(LAT * RAD) * cos(DEC * RAD) (8.4.3) DEC = 23.45 * cos(2 * PI * (DAY+10) / 365) (8.4.4)
where RADis a conversion factor (degree to radian; RAD = PI / 180) LAT is latitude of the site (degree) DEC is declination of the sun (degree) DAY is Julian day number on the northern hemisphere, or Julian day number plus or minus 182 on the southern hemisphere. Note that Equations 8.2, 8.3 and 8.4 relate AMAX to a few readily available data, viz. latitude of the site (LAT, in degree), Julian day number (DAY), and daily maximum and minimum temperatures (Tmax and Tmin). 
Sunflower case 
Well done, continue with the next session. 
7.0.1.0.0 
Data requirements

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