Hi-sAFe: A 3D Agroforestry Model for Integrating Dynamic Tree–Crop Interactions
Abstract
:1. Introduction
- systems across pedoclimatic environments and management regimes;
- above- and belowground interactions for light, water, and nutrients;
- the multiple possible yields, including food, fiber, and fuel; and
- ecosystem services such as the capture of excess nutrients, soil erosion, and carbon sequestration [17].
- three-dimensional tree–crop interactions for light, water, and nitrogen;
- plastic aboveground and belowground tree architecture responsiveness to resource availability;
- the full lifetime of the system, from tree planting to harvest, on a daily time-step; and
- the principal agroforestry design and management strategies, such as branch pruning, tree thinning, root pruning, and the incorporation of an uncropped area around each tree or strip along the tree row.
2. Model Specification
2.1. Hi-sAFe Scene
2.2. STICS Crop Model in Hi-sAFe
2.3. Water and Nitrogen Cycles
2.4. sAFe-Tree Model
2.4.1. Tree Architecture
2.4.2. Phenology
2.4.3. Light Interception
2.4.4. Carbon Assimilation
2.4.5. Carbon Allocation
2.4.6. Growth and Allometry
2.4.7. Water Demand and Rain Interception
2.4.8. Nitrogen Demand and Allocation
2.4.9. Tree Management Interventions
2.5. Water Competition and Uptake
2.6. Nitrogen Competition and Uptake
- A weighted mean root diameter was used to account for differences in root diameter among plant species;
- To account for differences in current demand that may make the zero-sink assumption an overestimation for some plants, current demand per unit root length at the plant level was used as an additional weighing factor;
- To prevent plant uptake in a mixture from being more than it would be in a monoculture, a series of constraints were added to ensure that including roots of a nondemanding plant does not increase uptake by others.
3. Discussion
3.1. Model Approach
3.2. Model Applications
3.3. Model Limitations
3.4. Model Implementation and Distribution
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter Definition | Units | Allowed Values |
---|---|---|
Latitude | degrees | (−90, 90] |
Cell width | m | (0, -) |
Orientation of north | degrees clockwise relative to +y axis | [0, 360) |
Plot length (y) | m | [cell width, -) |
Plot width (x) | m | [cell width, -) |
Magnitude of the slope of the soil surface | degrees downward from horizontal | [0, 90) |
Aspect of the slope of the soil surface | degrees clockwise from north | [0, 360) |
Maximum thickness of a voxel | m | [0.01, -) |
Distance from the tree to the alley crop edge | m | [0, plot width) |
PBC in the +x direction | - | on/off |
PBC in the -x direction | - | on/off |
PBC in the +y direction | - | on/off |
PBC in the -y direction | - | on/off |
Parameter | Definition | Units | Allowed Values |
---|---|---|---|
Phenology | |||
D0 | Date to start accumulation of temperature for budburst | Julian day | [1, 365] |
ST | Threshold of accumulated degree-days to trigger budburst | °C-days | [0, -) |
DLE | Duration of leaf expansion | days | [1, 365] |
DV | Bud burst to leaf fall duration | days | [1, 365] |
TLF | Threshold for frost mortality of leaves | °C | (-, -) |
DLF | Duration of leaf fall | days | [1, 365] |
Light interception | |||
μ | Correction parameter to account for leaf clumping. A clumping coefficient below 1, equal to 1, or above 1 indicates a clumped, random, or regular distribution of leaves inside the crown, respectively. | - | [0, -) |
σPAR | Leaf light absorption coefficient for photosynthetically active radiation | - | [0, 1] |
σNIR | Leaf light absorption coefficient for near infrared radiation | - | [0, 1] |
WAD | Wood area density for light interception by tree branches | m2 m−3 | [0, -) |
Carbon assimilation | |||
LUEmax | Maximum potential light-use efficiency | g C MJ−1 | (0, -) |
ωLUE | Sensitivity of LUE to water stress | - | [0, -) |
ηLUE | Sensitivity of LUE to N stress | - | [0, -) |
τmax | Leaf age at which maximum LUE occurs | days | [1, 365] |
τleaves | Leaf senescence time constant | days−2 | (0, -) |
Carbon allocation | |||
aNSC | Threshold imbalance above which remobilization of CNSC is triggered | - | (0, 1] |
bNSC | Limits maximum daily ΔCNSC as a fraction of CNSC | - | (0, 1] |
cNSC | Limits maximum daily ΔCNSC as a fraction of Cleaves | - | (0, 1] |
αNSC* | Target CNSC as a fraction of the tree woody C pool | - | (0, 1] |
LFR*0 | Initial LFR* at tree planting | kg kg−1 | (0, 1) |
ΔLFR*max | Maximum daily change in LFR* | kg kg−1 | [0, -) |
δLFR | Target daily upward drift in LFR* | kg kg−1 | [0, -) |
εLFR | Sensitivity of LFR* to N satisfaction when there is no stress | day−1 | [0, -) |
ωLFR | Sensitivity of LFR* to water stress | - | [0, -) |
ηLFR | Sensitivity of LFR* to N stress | - | [0, -) |
LFR*min | Minimum allowed LFR* | kg kg−1 | (0, 1) |
LFR*max | Maximum allowed LFR* | kg kg−1 | (0, 1) |
Growth and senescence | |||
SLM | Leaf dry mass per unit leaf area | kg m−2 | (0, -) |
θleaves | Leaf C content | g C g−1 dry biomass | (0, 1) |
θwood | C content of all compartments except leaves | g C g−1 dry biomass | (0, 1) |
ρwood | Wood density of branches, stems, stump, and coarse roots | kg m−3 | (0, -) |
γ | Ratio of coarse root cross-sectional area to fine root length | m2 m−1 | (0, -) |
SRL | Fine root length per unit dry mass | m g−1 of dry matter | (0, -) |
τfr | Mean lifespan of fine roots not in anoxic voxel | days | (0, -) |
τfr,anoxia | Mean lifespan of fine roots in anoxic voxel | days | (0, -) |
τcr | Number of days of anoxia to kill coarse roots | days | (0, -) |
Root growth algorithm [47] | |||
α | Threshold for root colonization | m of root m−3 voxel | (0, -) |
β | The proportion of C allocated to fine roots that is allocated to colonization | - | (0, 1) |
λ | Fraction of root colonization to horizontal voxels | - | [0, 1] |
η | Fraction of vertical root colonization to lower voxel | - | [0, 1] |
ϕ | Fine root proliferation weighting factor for water uptake efficiency | - | [0, -) |
υ | Fine root proliferation weighting factor for N uptake efficiency | - | [0, -) |
ρ | Fine root proliferation weighting factor for voxel–stem base topological distance | - | [0, -) |
Water demand and rain interception | |||
Γ | Scaling coefficient for transpiration | - | (0, -) |
ω | Wettability of leaves | mm lai−1 | [0, -) |
SFmax | Maximum fraction of intercepted rain routed to stem flow | - | [0, 1] |
cSF | Scaling coefficient for stem flow | - | [0, -) |
Nitrogen demand | |||
ηbranches | Functional optimum N/C ratio in branches | kg N kg C−1 | (0, -) |
ηcr | Functional optimum N/C ratio in coarse roots | kg N kg C−1 | (0, -) |
ηfr | Functional optimum N/C ratio in fine roots | kg N kg C−1 | (0, -) |
ηleaves | Functional optimum N/C ratio in foliage | kg N kg C−1 | (0, -) |
ηstem | Functional optimum N/C ratio in stem | kg N kg C−1 | (0, -) |
ηstump | Functional optimum N/C ratio in stump | kg N kg C−1 | (0, -) |
αN | Coefficient applied to optimum N content to define target N content | - | [1, -) |
βN | Coefficient defining “luxury” N content | ||
κleaves | Fraction of N content recovered from leaves during senescence | - | [0, 1] |
κfr | Fraction of N content recovered from fine roots during senescence | - | [0, 1] |
(A1) | |
(A2) | |
(A3) | |
(A4) | |
(A5) | |
(A6) | |
(A7) |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Dupraz, C.; Wolz, K.J.; Lecomte, I.; Talbot, G.; Vincent, G.; Mulia, R.; Bussière, F.; Ozier-Lafontaine, H.; Andrianarisoa, S.; Jackson, N.; et al. Hi-sAFe: A 3D Agroforestry Model for Integrating Dynamic Tree–Crop Interactions. Sustainability 2019, 11, 2293. https://doi.org/10.3390/su11082293
Dupraz C, Wolz KJ, Lecomte I, Talbot G, Vincent G, Mulia R, Bussière F, Ozier-Lafontaine H, Andrianarisoa S, Jackson N, et al. Hi-sAFe: A 3D Agroforestry Model for Integrating Dynamic Tree–Crop Interactions. Sustainability. 2019; 11(8):2293. https://doi.org/10.3390/su11082293
Chicago/Turabian StyleDupraz, Christian, Kevin J. Wolz, Isabelle Lecomte, Grégoire Talbot, Grégoire Vincent, Rachmat Mulia, François Bussière, Harry Ozier-Lafontaine, Sitraka Andrianarisoa, Nick Jackson, and et al. 2019. "Hi-sAFe: A 3D Agroforestry Model for Integrating Dynamic Tree–Crop Interactions" Sustainability 11, no. 8: 2293. https://doi.org/10.3390/su11082293
APA StyleDupraz, C., Wolz, K. J., Lecomte, I., Talbot, G., Vincent, G., Mulia, R., Bussière, F., Ozier-Lafontaine, H., Andrianarisoa, S., Jackson, N., Lawson, G., Dones, N., Sinoquet, H., Lusiana, B., Harja, D., Domenicano, S., Reyes, F., Gosme, M., & Van Noordwijk, M. (2019). Hi-sAFe: A 3D Agroforestry Model for Integrating Dynamic Tree–Crop Interactions. Sustainability, 11(8), 2293. https://doi.org/10.3390/su11082293