Mathematical Description of Rooting Profiles of Agricultural Crops and its Effect on Transpiration Prediction by a Hydrological Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mathematical Description of Root Density Profiles
2.2. Mean Half-Distance between Roots
2.3. Experimental Data
2.4. Parameter Estimation and Model Selection
2.5. Sensitivity of Agro-Hydrological Model Output to Root Profile Shape
3. Results
3.1. Function Selection and Parameter Values
3.2. Sensitivity of Agro-Hydrological Model Output to Root Profile Shape
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
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- Agron. J. 67, 519 523; 77, 1015 1017; 79, 434 438; 80, 271 275; 82, 606 612; 85, 1058 1060; 87, 1210 1216; 90, 511 518; 91, 426 431; 94, 136 145; 72, 981 986
- Aust. J. Exp. Agr. 28, 249 252; 39, 709 720
- Aust. J. Plant Physiol. 5, 169 177
- Can. J. Plant Sci. 44, 240 248
- Crop Sci. 34, 810 812; 42, 773 780
- Eur. J. Agron. 19, 225 237; 8, 117 125.
- Field Crops Res. 11, 325 333; 21, 215 226; 22, 45 57; 37, 205 213; 66, 81 99; 93, 223 236
- Hydrol. Process. 18, 2275 2287
- Irrig. Sci. 12, 45 51; 12, 135 140; 12, 141 144; 12, 145 152; 12, 153 159; 12, 161 168; 17, 69 75
- J. Agr. Sci. (Cambridge) 137, 251 270
- JARQ Jpn. Agr. Res. Q. 34, 81 86
- Plant Soil 200, 107 112; 201, 149 155; 206, 123 136; 207, 87 96; 253, 301 309; 255, 169 177; 255, 387 397; 267, 309 318
- Soil Sci. Soc. Am. J. 68, 529 537; 69, 197 205
- Soil Till. Res. 23, 41 59; 33, 91 108; 41, 25 42; 55, 99 106; 68, 153–161; 80, 103 114
- Z. Pflanz. Bodenkunde 163, 481 489
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Equation # | Df | D50 | D95 | |
---|---|---|---|---|
Generalized logistic | (2) | |||
Logistic | (4) | m | ||
Exponential (Mitscherlich) | (12) | |||
Gompertz | (14) |
Crop Group | Contains Species | Species Local Name | Relative Proportion of the Area | Number of Sources in Database |
---|---|---|---|---|
Wheat | Triticum aestivum Triticum turgidum xTriticosecale | Bread wheat Durum wheat Triticale | 22 | 12 |
Maize | Zea mays | 13 | 9 | |
Rice | Oryza sativa Oryza glaberrima | 11 | 7 | |
Barley | Hordeum vulgare | 9 | 2 | |
Soybean | Glycine max | 5 | 6 | |
Pulses | Cajanus cajan Phaseolus aureus Pisum sativum Vicia faba Vigna unguiculata (= Vigna sinensis) | Pigeon pea Mung bean Pea Faba bean Cowpea | 4 | 6 |
Cotton | Gossypium hirsutum | 3 | 6 | |
Potato | Solanum tuberosum | 3 | 3 | |
Sunflower | Helinathus annuus | 2 | 4 | |
Rye | Secale cereale | 2 | 3 | |
Rapeseed | Brassica napus Brassica rapa | 2 | 4 | |
Sugarbeet | Beta vulgaris saccharifera | 1 | 3 | |
Other | Arachis hypogea Avena sativa Lolium multiflorum Pennisetum glaucum Raphanus sativus oleiformis Sorghum bicolor Trifolium incarnataum Vicia villosa | Peanut Oats Italian ryegrass Pearl millet Fodder radish Sorghum Crimson clover Hairy vetch | 11 |
Depth (m) | θr | θs | α (m−1) | n | λ | Ks (m·d−1) |
---|---|---|---|---|---|---|
0.00–0.30 | 0.01 | 0.43 | 2.27 | 1.548 | −1.983 | 0.1965 |
0.30–2.00 | 0.02 | 0.38 | 2.14 | 2.075 | −1.039 | 0.2556 |
Development Stage | Leaf Area Index (m2 m−2) | Crop Height (m) | Rooting Depth (m) |
---|---|---|---|
0 | 0.05 | 0.01 | 0.05 |
0.30 | 0.14 | 0.15 | 0.2 |
0.50 | 0.61 | 0.40 | 0.5 |
0.70 | 4.1 | 1.40 | 0.8 |
1.0 | 5.0 | 1.70 | 0.9 |
1.4 | 5.8 | 1.80 | 0.9 |
2.0 | 5.2 | 1.75 | 0.9 |
Description | Parameter | Value | Unit |
---|---|---|---|
Plant maximum height | Hmax | 175 | cm |
Reflection coefficient, Albedo | Cref | 0.20 | ‒ |
Minimum canopy resistance | RSC | 131 | s m−1 |
Extinction coefficient for diffuse visible light | Kdif | 0.60 | ‒ |
Extinction coefficient for direct visible light | Kdir | 0.75 | ‒ |
Length of crop cycle - fixed | LCC | 120 | d |
Interception coefficient Von Hoyningen-Hune and Braden | COFAB | 0.25 | cm |
Sigmoid Function | Convergence (n = 570) | D95 > Dmax | R2adj | Mean D50 (m) | Mean D95 (m) |
---|---|---|---|---|---|
Generalized logistic (Equation (2)) | 54 | 5 | 1.00 | 0.322 | 0.644 |
Logistic (Equation (4)) | 568 | 48 | 0.98 | 0.267 | 0.560 |
Exponential (Equation (12)) | 568 | 422 | 0.98 | 0.460 | 1.942 |
Gompertz (Equation (14)) | 568 | 174 | 0.99 | 0.272 | 0.699 |
Crop | D50 (± Standard Error) (m) | D95 (± Standard Error) (m) | n | rn (± Standard Error) (mm) | nr | c | Rx (mm−1) |
---|---|---|---|---|---|---|---|
All crops | 0.27 (±0.24) | 0.56 (±0.48) | 568 | 5.6 (±5.7) | 494 | −3.969 | 10.2 |
Wheat | 0.22 (±0.10) | 0.49 (±0.25) | 80 | 6.4 (±6.1) | 50 | −3.677 | 8.5 |
Maize | 0.39 (±0.20) | 0.80 (±0.40) | 48 | 6.5 (±4.7) | 40 | −4.071 | 7.4 |
Rice | 0.13 (±0.07) | 0.27 (±0.13) | 87 | 5.2 (±5.3) | 87 | −4.048 | 11.6 |
Barley | 0.17 (±0.06) | 0.33 (±0.09) | 10 | 4.8 (±3.7) | 7 | −4.286 | 12.9 |
Soybean | 0.27 (±0.17) | 0.60 (±0.33) | 42 | 7.1 (±8.0) | 40 | −3.716 | 6.8 |
Pulses | 0.28 (±0.12) | 0.59 (±0.25) | 39 | 4.7 (±0.7) | 37 | −3.942 | 14.6 |
Cotton | 0.32 (±0.10) | 0.67 (±0.22) | 97 | 5.4 (±1.3) | 97 | −3.989 | 10.9 |
Potato | 0.32 (±0.06) | 0.62 (±0.13) | 40 | 3.2 (±0.6) | 40 | −4.482 | 27.7 |
Sunflower | 0.35 (±0.19) | 0.79 (±0.46) | 26 | 4.3 (±1.2) | 23 | −3.596 | 19.1 |
Rye | 0.22 (±0.06) | 0.47 (±0.13) | 7 | 4.6 (±2.1) | 6 | −3.955 | 15.2 |
Rapeseed | 0.18 (±0.04) | 0.39 (±0.09) | 30 | 2.7 (±0.9) | 21 | −3.858 | 45.3 |
Sugar beet | 0.48 (±0.15) | 0.95 (±0.28) | 13 | 3.9 (±1.8) | 7 | −4.349 | 19.2 |
Other | 0.28 (±0.18) | 0.56 (±0.37) | 49 | 10.3 (±13.3) | 39 | −4.194 | 2.9 |
Autumn Maize (February–June) | Summer Maize (November–February) | |||||
---|---|---|---|---|---|---|
D50 (m) | 0.15 | 0.30 | 0.45 | 0.15 | 0.30 | 0.45 |
c = −1 | 0.017 (23%) | 0.006 (23%) | 0 | 0.010 (53%) | 0.004 (65%) | 0 |
c = −3 | 0.049 (17%) | 0.035 (18%) | 0.019 (22%) | 0.030 (48%) | 0.018 (56%) | 0.008 (68%) |
c = −5 | 0.053 (16%) | 0.041 (18%) | 0.026 (21%) | 0.033 (47%) | 0.021 (56%) | 0.011 (68%) |
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Metselaar, K.; Pinheiro, E.A.R.; de Jong van Lier, Q. Mathematical Description of Rooting Profiles of Agricultural Crops and its Effect on Transpiration Prediction by a Hydrological Model. Soil Syst. 2019, 3, 44. https://doi.org/10.3390/soilsystems3030044
Metselaar K, Pinheiro EAR, de Jong van Lier Q. Mathematical Description of Rooting Profiles of Agricultural Crops and its Effect on Transpiration Prediction by a Hydrological Model. Soil Systems. 2019; 3(3):44. https://doi.org/10.3390/soilsystems3030044
Chicago/Turabian StyleMetselaar, Klaas, Everton Alves Rodrigues Pinheiro, and Quirijn de Jong van Lier. 2019. "Mathematical Description of Rooting Profiles of Agricultural Crops and its Effect on Transpiration Prediction by a Hydrological Model" Soil Systems 3, no. 3: 44. https://doi.org/10.3390/soilsystems3030044