Modeling of Agricultural Systems [AGS721]
LAB 3
Relationship between variables:
Curve fitting
1. Given observed rice yield corresponse to nitrogen application rate in
the table below:
Nitrogen (kg/ha) |
Grain yield (kg/ha) |
0 |
5500 |
25 |
5700 |
50 |
6400 |
75 |
6600 |
100 |
6800 |
125 |
7000 |
150 |
7100 |
175 |
7000 |
200 |
6300 |
225 |
6100 |
Construct an empirical model that explain the relationship between rice yield and the nitrogen application rate. From the model, what is the optimum nitrogen rate ?
2. The following table illustrates the observation of corn mean total dry weight per plant and mean total leaf area per plant, (a) construct the mathematical function to describe the dynamic change of both variables through time (b) give reason(s) why you decide to use the function used in a.
Day in the year |
Mean total dry wt per plant (g.) |
Mean total leaf area per plant (m2) |
140 |
0.3282 |
n.a. |
148 |
0.328 |
n.a. |
155 |
0.287 |
n.a. |
162 |
0.255 |
0.00179 |
169 |
0.308 |
0.00292 |
176 |
0.637 |
0.01244 |
183 |
2.319 |
0.04192 |
190 |
4.654 |
0.07622 |
197 |
9.019 |
0.1301 |
204 |
20.001 |
0.2136 |
211 |
34.557 |
0.2805 |
218 |
57.587 |
0.3384 |
225 |
70.095 |
0.3047 |
232 |
85.165 |
0.3025 |
239 |
111.649 |
0.2976 |
246 |
124.76 |
0.2684 |
253 |
121.99 |
0.2387 |
Source: Kreusler, Prehn and Hornberger (1879)
3. Given data on grain yield (kg/ha) of wheat from USA and the former USSR during 1950-1982 -- (a) compare and describe the dynamic behavior of wheat grain yield of both countries during that period (b) project grain yield in the next 10 years (1983-1993). Do you think your projection results are resonable ? Why ?
| Year | USA | USSR | Year | USA | USSR |
| 1950 | 1600 | 800 | 1966 | 3000 | 1300 |
| 1951 | 1600 | 800 | 1967 | 3200 | 1200 |
| 1952 | 1700 | 900 | 1968 | 3200 | 1300 |
| 1953 | 1600 | 800 | 1969 | 3500 | 1300 |
| 1954 | 1700 | 800 | 1970 | 3200 | 1600 |
| 1955 | 1800 | 900 | 1971 | 3700 | 1500 |
| 1956 | 2000 | 1000 | 1972 | 3900 | 1400 |
| 1957 | 2100 | 800 | 1973 | 3700 | 1800 |
| 1958 | 2400 | 1100 | 1974 | 3000 | 1500 |
| 1959 | 2300 | 1100 | 1975 | 3500 | 1000 |
| 1960 | 2500 | 1100 | 1976 | 3500 | 1700 |
| 1961 | 2500 | 1100 | 1977 | 3700 | 1500 |
| 1962 | 2700 | 1100 | 1978 | 4000 | 1800 |
| 1963 | 2800 | 800 | 1979 | 4400 | 1500 |
| 1964 | 2700 | 1100 | 1980 | 3800 | 1600 |
| 1965 | 3000 | 1000 | 1981 | 4300 | 1300 |
| 1982 | 4400 | 1400 |
References:
Gomez, K.A. and A.A. Gomez. 1976. Statistical Procedures for Agricultural Research, with Emphasis on Rice. The International Rice Research Institute, Los Banos, Philippines.
Hunt, R. Plant Growth Analysis: The Rationale Behind the Use of the Fitted Mathematical Function. 1979. Ann. Bot. 43,245-249.
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