maize.model: The basic Maize model.
In ZeBook: Working with Dynamic Models for Agriculture and Environment
Description
Usage
Arguments
Details
Value
See Also
Examples
Description
Model description.
This model is a dynamic model of crop growth for Maize cultivated in potential conditions.
The crop growth is represented by three state variables, leaf area per unit ground area (leaf area index, LAI), total biomass (B) and cumulative thermal time since plant emergence (TT). It is based on key concepts included in most crop models, at least for the "potential production" part. In fact, this model does not take into account any effects of soil water, nutrients, pests, or diseases,...
Usage
1
maize.model(Tbase, RUE, K, alpha, LAImax, TTM, TTL, weather, sdate, ldate)
Arguments
Tbase
: parameter the baseline temperature for growth (degreeCelsius)
RUE
: parameter radiation use efficiency (?)
K
: parameter extinction coefficient (relation between leaf area index and intercepted radiation) (-)
alpha
: parameter the relative rate of leaf area index increase for small values of leaf area index (?)
LAImax
: parameter maximum leaf area index (-)
TTM
: parameter temperature sum for crop maturity (degreeC.day)
TTL
: parameter temperature sum at the end of leaf area increase (degreeC.day)
weather
: weather data.frame for one single year
sdate
: sowing date
ldate
: last date
Details
The tree state variables are dynamic variables depending on days after emergence: TT(day), B(day), and LAI(day). The model has a time step dt of one day.
The model is defined by a few equations, with a total of seven parameters for the described process.
(1) TT(day+1) = TT(day)+dTT(day)
(2) B(day+1) = B(day)+dB(day)
(3) LAI(day+1) = LAI(day)+dLAI(day)
(4) dTT(day) = max((TMIN(day)+TMAX(day))/2-Tbase ; 0)
(5) dB(day) = RUE*(1-e^{-K*LAI(day)*I(day)}), if TT(day)<= TTM
dB(day) = 0, if TT(day)>TTM
(6) alpha*dTT(day)*LAI(day)*max(LAImax-LAI(day);0), if TT(day)<= TTL
dLAI(day) = 0 if TT(day)>TTL
Value
data.frame with daily TT, LAI,B
See Also
maize.model2, maize.define.param, maize.simule, maize.multisy,
maize.simule240,maize.simule_multisy240
Examples
1
2
3
weather = maize.weather(working.year=2010, working.site=30,weather_all=weather_EuropeEU)
maize.model(Tbase=7, RUE=1.85, K=0.7, alpha=0.00243, LAImax=7, TTM=1200, TTL=700,
weather, sdate=100, ldate=250)
Example output
day TT LAI B
1 100 0.00 0.01000000 1.000000
2 101 5.70 0.01096818 1.280034
3 102 8.85 0.01155496 1.570097
4 103 10.90 0.01195722 1.897970
5 104 13.90 0.01256635 2.158567
6 105 18.60 0.01356919 2.448584
7 106 22.50 0.01446761 2.833340
8 107 27.35 0.01565870 3.263947
9 108 33.00 0.01716024 3.741912
10 109 40.30 0.01928585 4.272062
11 110 47.95 0.02178854 4.649134
12 111 55.45 0.02455956 5.307182
13 112 62.35 0.02743198 6.000904
14 113 69.60 0.03080170 6.437204
15 114 71.60 0.03184496 7.218537
16 115 79.40 0.03605087 8.193251
17 116 87.10 0.04074839 9.129116
18 117 93.95 0.04546869 10.315255
19 118 102.15 0.05176956 11.706170
20 119 112.70 0.06099118 13.325867
21 120 122.70 0.07127538 14.849096
22 121 130.05 0.08009575 16.559796
23 122 136.85 0.08925426 18.244323
24 123 142.30 0.09742303 20.653345
25 124 146.00 0.10346920 21.933894
26 125 149.00 0.10867119 24.622403
27 126 152.20 0.11449455 27.915290
28 127 156.90 0.12349833 30.836220
29 128 161.95 0.13391973 33.379546
30 129 167.75 0.14687922 36.210373
31 130 172.90 0.15947608 37.638354
32 131 180.50 0.17962282 41.487959
33 132 185.90 0.19569852 44.089083
34 133 189.20 0.20637655 48.044265
35 134 192.50 0.21761955 52.448912
36 135 197.10 0.23411804 58.042912
37 136 201.70 0.25182415 64.083200
38 137 207.60 0.27618779 69.644344
39 138 214.65 0.30800158 77.872254
40 139 221.85 0.34406339 86.626852
41 140 230.40 0.39164291 97.317953
42 141 239.35 0.44793056 109.694301
43 142 249.00 0.51675184 123.686229
44 143 260.60 0.61118813 139.521234
45 144 273.40 0.73264198 157.873692
46 145 287.55 0.89052630 179.101874
47 146 299.70 1.05115868 192.489004
48 147 309.20 1.19551326 209.738054
49 148 318.60 1.35402168 228.302225
50 149 328.75 1.54257628 256.513034
51 150 337.10 1.71339170 268.973607
52 151 347.95 1.95221121 295.985642
53 152 358.60 2.20723686 314.178892
54 153 368.15 2.45273294 338.338515
55 154 377.60 2.70885017 359.131052
56 155 388.75 3.02379886 404.883330
57 156 402.35 3.42114265 451.421204
58 157 416.50 3.84213895 496.143699
59 158 428.15 4.18561644 534.079555
60 159 439.30 4.50478776 570.854938
61 160 449.70 4.78885519 601.315946
62 161 460.90 5.07704139 630.058253
63 162 473.35 5.37240451 671.211106
64 163 481.90 5.55407633 710.060627
65 164 493.75 5.78532638 748.295828
66 165 505.70 5.98938815 789.013649
67 166 514.70 6.12176609 828.005548
68 167 525.20 6.25894347 845.703438
69 168 534.85 6.36770767 885.528927
70 169 545.50 6.47190508 916.980053
71 170 556.35 6.56201656 941.136877
72 171 566.40 6.63220528 964.760404
73 172 573.60 6.67488310 1005.251552
74 173 582.00 6.71917954 1056.567241
75 174 592.95 6.76938667 1106.981101
76 175 606.00 6.81889183 1159.244697
77 176 620.95 6.86375597 1212.074317
78 177 636.95 6.90011444 1264.000439
79 178 652.90 6.92682764 1316.854951
80 179 669.85 6.94770413 1363.660196
81 180 686.00 6.96196308 1411.572232
82 181 702.60 6.97264505 1458.386460
83 182 719.30 6.97264505 1509.793270
84 183 736.95 6.97264505 1560.098505
85 184 753.40 6.97264505 1589.106633
86 185 769.00 6.97264505 1621.786676
87 186 784.85 6.97264505 1667.502018
88 187 798.95 6.97264505 1706.975104
89 188 812.60 6.97264505 1758.198317
90 189 829.10 6.97264505 1811.257489
91 190 848.60 6.97264505 1862.113511
92 191 866.80 6.97264505 1910.399193
93 192 884.30 6.97264505 1961.806003
94 193 899.70 6.97264505 2005.501791
95 194 915.05 6.97264505 2038.549026
96 195 929.40 6.97264505 2081.510431
97 196 941.80 6.97264505 2109.233389
98 197 954.65 6.97264505 2155.315922
99 198 967.40 6.97264505 2181.753710
100 199 979.85 6.97264505 2227.469051
101 200 994.10 6.97264505 2278.508669
102 201 1010.80 6.97264505 2329.181096
103 202 1026.95 6.97264505 2378.017565
104 203 1041.40 6.97264505 2417.490651
105 204 1054.85 6.97264505 2461.186439
106 205 1067.50 6.97264505 2500.475929
107 206 1080.75 6.97264505 2538.480249
108 207 1094.15 6.97264505 2572.078271
109 208 1109.25 6.97264505 2618.895187
110 209 1126.25 6.97264505 2664.977720
111 210 1142.25 6.97264505 2705.919572
112 211 1157.25 6.97264505 2745.576254
113 212 1171.75 6.97264505 2789.455638
114 213 1186.85 6.97264505 2830.213894
115 214 1200.45 6.97264505 2861.975959
116 215 1214.55 6.97264505 2861.975959
117 216 1229.75 6.97264505 2861.975959
118 217 1242.80 6.97264505 2861.975959
119 218 1255.15 6.97264505 2861.975959
120 219 1268.70 6.97264505 2861.975959
121 220 1283.50 6.97264505 2861.975959
122 221 1298.30 6.97264505 2861.975959
123 222 1313.05 6.97264505 2861.975959
124 223 1326.95 6.97264505 2861.975959
125 224 1340.60 6.97264505 2861.975959
126 225 1353.50 6.97264505 2861.975959
127 226 1366.30 6.97264505 2861.975959
128 227 1378.05 6.97264505 2861.975959
129 228 1389.10 6.97264505 2861.975959
130 229 1402.35 6.97264505 2861.975959
131 230 1415.75 6.97264505 2861.975959
132 231 1428.85 6.97264505 2861.975959
133 232 1443.30 6.97264505 2861.975959
134 233 1459.25 6.97264505 2861.975959
135 234 1477.55 6.97264505 2861.975959
136 235 1493.10 6.97264505 2861.975959
137 236 1507.65 6.97264505 2861.975959
138 237 1519.20 6.97264505 2861.975959
139 238 1533.65 6.97264505 2861.975959
140 239 1551.30 6.97264505 2861.975959
141 240 1565.25 6.97264505 2861.975959
142 241 1577.05 6.97264505 2861.975959
143 242 1587.80 6.97264505 2861.975959
144 243 1598.40 6.97264505 2861.975959
145 244 1609.30 6.97264505 2861.975959
146 245 1621.50 6.97264505 2861.975959
147 246 1634.90 6.97264505 2861.975959
148 247 1649.90 6.97264505 2861.975959
149 248 1663.75 6.97264505 2861.975959
150 249 1679.95 6.97264505 2861.975959
151 250 1694.55 6.97264505 2861.975959
ZeBook documentation built on May 1, 2019, 9:48 p.m.
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Description Usage Arguments Details Value See Also Examples
Description
Model description. This model is a dynamic model of crop growth for Maize cultivated in potential conditions. The crop growth is represented by three state variables, leaf area per unit ground area (leaf area index, LAI), total biomass (B) and cumulative thermal time since plant emergence (TT). It is based on key concepts included in most crop models, at least for the "potential production" part. In fact, this model does not take into account any effects of soil water, nutrients, pests, or diseases,...
Usage
1 | maize.model(Tbase, RUE, K, alpha, LAImax, TTM, TTL, weather, sdate, ldate)
|
Arguments
Tbase |
: parameter the baseline temperature for growth (degreeCelsius) |
RUE |
: parameter radiation use efficiency (?) |
K |
: parameter extinction coefficient (relation between leaf area index and intercepted radiation) (-) |
alpha |
: parameter the relative rate of leaf area index increase for small values of leaf area index (?) |
LAImax |
: parameter maximum leaf area index (-) |
TTM |
: parameter temperature sum for crop maturity (degreeC.day) |
TTL |
: parameter temperature sum at the end of leaf area increase (degreeC.day) |
weather |
: weather data.frame for one single year |
sdate |
: sowing date |
ldate |
: last date |
Details
The tree state variables are dynamic variables depending on days after emergence: TT(day), B(day), and LAI(day). The model has a time step dt of one day.
The model is defined by a few equations, with a total of seven parameters for the described process.
(1) TT(day+1) = TT(day)+dTT(day)
(2) B(day+1) = B(day)+dB(day)
(3) LAI(day+1) = LAI(day)+dLAI(day)
(4) dTT(day) = max((TMIN(day)+TMAX(day))/2-Tbase ; 0)
(5) dB(day) = RUE*(1-e^{-K*LAI(day)*I(day)}), if TT(day)<= TTM
dB(day) = 0, if TT(day)>TTM
(6) alpha*dTT(day)*LAI(day)*max(LAImax-LAI(day);0), if TT(day)<= TTL
dLAI(day) = 0 if TT(day)>TTL
Value
data.frame with daily TT, LAI,B
See Also
maize.model2, maize.define.param, maize.simule, maize.multisy,
maize.simule240,maize.simule_multisy240
Examples
1 2 3 | weather = maize.weather(working.year=2010, working.site=30,weather_all=weather_EuropeEU)
maize.model(Tbase=7, RUE=1.85, K=0.7, alpha=0.00243, LAImax=7, TTM=1200, TTL=700,
weather, sdate=100, ldate=250)
|
Example output
day TT LAI B
1 100 0.00 0.01000000 1.000000
2 101 5.70 0.01096818 1.280034
3 102 8.85 0.01155496 1.570097
4 103 10.90 0.01195722 1.897970
5 104 13.90 0.01256635 2.158567
6 105 18.60 0.01356919 2.448584
7 106 22.50 0.01446761 2.833340
8 107 27.35 0.01565870 3.263947
9 108 33.00 0.01716024 3.741912
10 109 40.30 0.01928585 4.272062
11 110 47.95 0.02178854 4.649134
12 111 55.45 0.02455956 5.307182
13 112 62.35 0.02743198 6.000904
14 113 69.60 0.03080170 6.437204
15 114 71.60 0.03184496 7.218537
16 115 79.40 0.03605087 8.193251
17 116 87.10 0.04074839 9.129116
18 117 93.95 0.04546869 10.315255
19 118 102.15 0.05176956 11.706170
20 119 112.70 0.06099118 13.325867
21 120 122.70 0.07127538 14.849096
22 121 130.05 0.08009575 16.559796
23 122 136.85 0.08925426 18.244323
24 123 142.30 0.09742303 20.653345
25 124 146.00 0.10346920 21.933894
26 125 149.00 0.10867119 24.622403
27 126 152.20 0.11449455 27.915290
28 127 156.90 0.12349833 30.836220
29 128 161.95 0.13391973 33.379546
30 129 167.75 0.14687922 36.210373
31 130 172.90 0.15947608 37.638354
32 131 180.50 0.17962282 41.487959
33 132 185.90 0.19569852 44.089083
34 133 189.20 0.20637655 48.044265
35 134 192.50 0.21761955 52.448912
36 135 197.10 0.23411804 58.042912
37 136 201.70 0.25182415 64.083200
38 137 207.60 0.27618779 69.644344
39 138 214.65 0.30800158 77.872254
40 139 221.85 0.34406339 86.626852
41 140 230.40 0.39164291 97.317953
42 141 239.35 0.44793056 109.694301
43 142 249.00 0.51675184 123.686229
44 143 260.60 0.61118813 139.521234
45 144 273.40 0.73264198 157.873692
46 145 287.55 0.89052630 179.101874
47 146 299.70 1.05115868 192.489004
48 147 309.20 1.19551326 209.738054
49 148 318.60 1.35402168 228.302225
50 149 328.75 1.54257628 256.513034
51 150 337.10 1.71339170 268.973607
52 151 347.95 1.95221121 295.985642
53 152 358.60 2.20723686 314.178892
54 153 368.15 2.45273294 338.338515
55 154 377.60 2.70885017 359.131052
56 155 388.75 3.02379886 404.883330
57 156 402.35 3.42114265 451.421204
58 157 416.50 3.84213895 496.143699
59 158 428.15 4.18561644 534.079555
60 159 439.30 4.50478776 570.854938
61 160 449.70 4.78885519 601.315946
62 161 460.90 5.07704139 630.058253
63 162 473.35 5.37240451 671.211106
64 163 481.90 5.55407633 710.060627
65 164 493.75 5.78532638 748.295828
66 165 505.70 5.98938815 789.013649
67 166 514.70 6.12176609 828.005548
68 167 525.20 6.25894347 845.703438
69 168 534.85 6.36770767 885.528927
70 169 545.50 6.47190508 916.980053
71 170 556.35 6.56201656 941.136877
72 171 566.40 6.63220528 964.760404
73 172 573.60 6.67488310 1005.251552
74 173 582.00 6.71917954 1056.567241
75 174 592.95 6.76938667 1106.981101
76 175 606.00 6.81889183 1159.244697
77 176 620.95 6.86375597 1212.074317
78 177 636.95 6.90011444 1264.000439
79 178 652.90 6.92682764 1316.854951
80 179 669.85 6.94770413 1363.660196
81 180 686.00 6.96196308 1411.572232
82 181 702.60 6.97264505 1458.386460
83 182 719.30 6.97264505 1509.793270
84 183 736.95 6.97264505 1560.098505
85 184 753.40 6.97264505 1589.106633
86 185 769.00 6.97264505 1621.786676
87 186 784.85 6.97264505 1667.502018
88 187 798.95 6.97264505 1706.975104
89 188 812.60 6.97264505 1758.198317
90 189 829.10 6.97264505 1811.257489
91 190 848.60 6.97264505 1862.113511
92 191 866.80 6.97264505 1910.399193
93 192 884.30 6.97264505 1961.806003
94 193 899.70 6.97264505 2005.501791
95 194 915.05 6.97264505 2038.549026
96 195 929.40 6.97264505 2081.510431
97 196 941.80 6.97264505 2109.233389
98 197 954.65 6.97264505 2155.315922
99 198 967.40 6.97264505 2181.753710
100 199 979.85 6.97264505 2227.469051
101 200 994.10 6.97264505 2278.508669
102 201 1010.80 6.97264505 2329.181096
103 202 1026.95 6.97264505 2378.017565
104 203 1041.40 6.97264505 2417.490651
105 204 1054.85 6.97264505 2461.186439
106 205 1067.50 6.97264505 2500.475929
107 206 1080.75 6.97264505 2538.480249
108 207 1094.15 6.97264505 2572.078271
109 208 1109.25 6.97264505 2618.895187
110 209 1126.25 6.97264505 2664.977720
111 210 1142.25 6.97264505 2705.919572
112 211 1157.25 6.97264505 2745.576254
113 212 1171.75 6.97264505 2789.455638
114 213 1186.85 6.97264505 2830.213894
115 214 1200.45 6.97264505 2861.975959
116 215 1214.55 6.97264505 2861.975959
117 216 1229.75 6.97264505 2861.975959
118 217 1242.80 6.97264505 2861.975959
119 218 1255.15 6.97264505 2861.975959
120 219 1268.70 6.97264505 2861.975959
121 220 1283.50 6.97264505 2861.975959
122 221 1298.30 6.97264505 2861.975959
123 222 1313.05 6.97264505 2861.975959
124 223 1326.95 6.97264505 2861.975959
125 224 1340.60 6.97264505 2861.975959
126 225 1353.50 6.97264505 2861.975959
127 226 1366.30 6.97264505 2861.975959
128 227 1378.05 6.97264505 2861.975959
129 228 1389.10 6.97264505 2861.975959
130 229 1402.35 6.97264505 2861.975959
131 230 1415.75 6.97264505 2861.975959
132 231 1428.85 6.97264505 2861.975959
133 232 1443.30 6.97264505 2861.975959
134 233 1459.25 6.97264505 2861.975959
135 234 1477.55 6.97264505 2861.975959
136 235 1493.10 6.97264505 2861.975959
137 236 1507.65 6.97264505 2861.975959
138 237 1519.20 6.97264505 2861.975959
139 238 1533.65 6.97264505 2861.975959
140 239 1551.30 6.97264505 2861.975959
141 240 1565.25 6.97264505 2861.975959
142 241 1577.05 6.97264505 2861.975959
143 242 1587.80 6.97264505 2861.975959
144 243 1598.40 6.97264505 2861.975959
145 244 1609.30 6.97264505 2861.975959
146 245 1621.50 6.97264505 2861.975959
147 246 1634.90 6.97264505 2861.975959
148 247 1649.90 6.97264505 2861.975959
149 248 1663.75 6.97264505 2861.975959
150 249 1679.95 6.97264505 2861.975959
151 250 1694.55 6.97264505 2861.975959
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