Tropical Tree Crop Simulation with a Process-Based, Daily Timestep Simulation Model (ALMANAC): Description of Model Adaptation and Examples with Coffee and Cocoa Simulations
by
,
James R. Kiniry
1,*, 
J. G. Fernandez
2,
Fati Aziz
3,
Jacqueline Jacot
4,
Amber S. Williams
1,
Manyowa N. Meki
5,
Javier Osorio Leyton
5,
Alma Delia Baez-Gonzalez
6 and
Mari-Vaughn V. Johnson
7 1
Grassland Soil and Water Research Laboratory, USDA-Agricultural Research Service, Temple, TX 76502, USA
2
Agronomic Institute of Pernambuco (IPA), Bongi, Recife 50761-000, PE, Brazil
3
Department of Ecology and Conservation Biology, Texas A&M University, College Station, TX 77843, USA
4
Oak Ridge Institute for Science and Education, Temple, TX 76502, USA
5
Texas A&M AgriLife Research, Blackland Research and Extension Center, Temple, TX 76502, USA
6
Campo Experimental Pabellón, Instituto Nacional de Investigaciones Forestales, Agricolas y Pecuarias (INIFAP), Km 32.5 Carr. Aguascalientes-Zacatecas, Pabellon de Arteaga 20660, Aguascalientes, Mexico
7
Pacific Islands Climate Adaptation Science Center (PICASC), United States Geological Survey (USGS), Hilo, HI 96720, USA
*
Author to whom correspondence should be addressed.
Agronomy 2023, 13(2), 580; https://doi.org/10.3390/agronomy13020580
Submission received: 23 January 2023
/
Revised: 14 February 2023
/
Accepted: 15 February 2023
/
Published: 17 February 2023
(This article belongs to the Special Issue Recent Advances in Crop Modelling)
Abstract
:Coffee (Coffea species) and Cocoa (Theobroma cacao) are important cash crops grown in the tropics but traded globally. This study was conducted to apply the ALMANAC model to these crops for the first time, and to test its ability to simulate them under agroforestry management schemes and varying precipitation amounts. To create this simulation, coffee was grown on a site in Kaua’i, Hawai’i, USA, and cocoa was grown on a site in Sefwi Bekwai, Ghana. A stand-in for a tropical overstory tree was created for agroforestry simulations using altered parameters for carob, a common taller tropical tree for these regions. For both crops, ALMANAC was able to realistically simulate yields when compared to the collected total yield data. On Kaua’i, the mean simulated yield was 2% different from the mean measured yield, and in all three years, the simulated values were within 10% of the measured values. For cocoa, the mean simulated yield was 3% different from the mean measured yield and the simulated yield was within 10% of measured yields for all four available years. When precipitation patterns were altered, in Ghana, the wetter site showed lower percent changes in yield than the drier site in Hawai’i. When agroforestry-style management was simulated, a low Leaf Area Index (LAI) of the overstory showed positive or no effect on yields, but when LAI climbed too high, the simulation was able to show the detrimental effect this competition had on crop yields. These simulation results are supported by other literature documenting the effects of agroforestry on tropical crops. This research has applied ALMANAC to new crops and demonstrated its simulation of different management and environmental conditions. The results show promise for ALMANAC’s applicability to these scenarios as well as its potential to be further tested and utilized in new circumstances.
Keywords:
coffee; cocoa; Hawai’i; Ghana; ALMANAC; simulation model; tropical agriculture; agroforestry1. Introduction
In 2009, the ALMANAC model [1] was proposed as a tool for simulating agroforestry in the tropics [2]. The model has been applied to several temperate deciduous and evergreen woody species [3,4,5,6,7,8]. However, the application of this model to evergreen, tropical trees producing economically important seeds remains a challenge.
Coffee (Coffea species) is the number two commodity after oil for international trade [9]. In some countries such as Mexico, coffee is traditionally grown in the shady understory of native trees encouraging biodiversity and richness in these agroecosystems and aiding in conservation efforts in biogeographically important habitats [10]. In Columbia, the effect of shade on bean yield and sensory attributes depends on site qualities such as elevation, temperature, and solar radiation [11]. Cocoa (Theobroma cacao), also a hugely important cash crop to the economies of West African countries such as Cote d’lvoire and Ghana, grows as an understory rainforest tree. Realistic simulation of the bean yields of both crops, with a model that is easy to apply, will be useful for management (both irrigation and fertilizer application) as well as yield prediction in various countries. The derivation of soil and weather data for running such simulations will be useful for such applications.
There have been other projects that developed simulation tools for coffee production. These include the complex approach of the ecosystem model of Rodriguez et al. [12] and the simpler, application of remote sensing for phenology simulation of Brunsell et al. [13]. A more recent model “CAF2007” [14,15,16,17] simulates coffee with a daily timestep and with light use efficiency based on canopy-level photosynthesis and carbon partitioning to various plant parts. It simulates the soil water balance with a single layer of soil and simulates light with values of leaf area index and extinction coefficients. However, there is still a need for a daily timestep model with more accurate soil water balance and nutrient balance components that can be useful at any international site without needing extensive calibration at each site.
Thus, the objective of this study is to describe the adaptation of such a model, Agricultural Land Management Alternative with Numerical Assessment Criteria (ALMANAC), and provide steps to derive the necessary soil and weather data for it at any site. A major hurdle restricting the development of any simulation model, but especially those for tree crops, is the availability of seed yield data for model development and validation. Often industry and private producers are reluctant to share such data. Thus, for this paper, we demonstrate the reasonableness of yield production for one region for coffee (Hawai’i), and one location for cocoa (Ghana). The hope is that by demonstrating the capacity of the model to simulate such systems, those in the industry and researchers will adopt this simulation tool and apply it to their situations.
A major strength of the ALMANAC model is its ability to simulate competition between plant species [1,18,19]. This becomes especially important for these two tropical tree species, as they are often grown in agroforestry conditions with companion trees much taller than the coffee or cocoa trees. ALMANAC accurately simulates light competition. It also simulates competition for water and nutrients among different plant species growing together [5,18]. In this paper, we will demonstrate seed yields of both tree species, both in a monoculture and in an agroforestry setting.
2. Materials and Methods
2.1. General Description of ALMANAC Model
Daily timestep, process-based model ALMANAC has been described previously [1,20,21,22] and is described at (https://www.ars.usda.gov/plains-area/temple-tx/grassland-soil-and-water-research-laboratory/docs/193226 accessed on 16 January 2023). ALMANAC has been parameterized and validated for many crops [23,24,25,26,27,28] and grasses [1,21,29,30,31] as well as the northern tree species lodgepole pine (Pinus contorta Douglas ex Loudon), white spruce (Picea glauca var. glauca), black spruce (Picea mariana), and trembling aspen (Populus tremuloides Michx.) [7]. As described below, the model uses USDA-NRCS soils data for the U.S. and soils data for the country of Mexico [32,33]. It uses solar, daily temperature, and rainfall data. It can also use international soil and weather data as described below and shown in Druille et al. [34]. Plant growth simulation processes involves light interception, dry matter production, and biomass partitioned into plant parts [22,35]. Biomass is simulated via light interception and species-specific radiation use efficiency (RUE), which is the dry biomass produced per unit of intercepted light [30,36]. Potential plant growth simulation depends on RUE, LAI, and the light extinction coefficient (k) used to calculate the fraction of light intercepted by leaves [37]. LAI has already been shown to be a promising indicator of coffee yield, especially when combined with other data such as fertilizer use and precipitation [38].
Phenological development (the duration of various plant growth stages) defines the length of each growing season. Phenological development is simulated with a growing degree day (GDD) system, species-specific base temperature, and optimum growing temperature. The GDD sum (Potential Heat Units or PHU) determines the duration of the growing season. Date of anthesis is simulated as a defined fraction of PHU (DLAI). Simulated leaf area growth is on a whole canopy basis. The potential leaf area index (LAI) is defined for each species/ecotype/variety. The potential leaf area growth is defined as an “S” curve over the growing season. Thus, LAI is simulated with this 0.0 to 1.0 “S” curve defined for each species. Daily dry matter production is simulated using radiation use efficiency (RUE). Potential dry matter produced is calculated from the amount of photosynthetically active radiation (PAR) intercepted by the leaf canopy on that day. The RUE value is species-specific and the units are g of dry matter per MJ of intercepted PAR. Plant part partitioning is also on a whole canopy basis. Partitioning between roots and shoots is defined by two parameters. Plants partition more of the total dry matter production into the roots initially. The fraction going to roots decreases as plants approach anthesis. Drought stress reduces the above-ground dry matter production more than the root dry matter production. Thus drought stress changes the simulated root:shoot ratio.
Seed production is simulated with a harvest index (HI) approach. A species-specific HI parameter determines the fraction of the total above-ground plant weight in the seed at maturity relative to the total plant weight. Seeds begin growth after anthesis and seed growth stops at physiological maturity. Leaf area expansion and dry matter accumulation are reduced by environmental stresses. In addition, drought stress near anthesis can decrease this HI value. Water stress yield factor (WSYF) defines the lowest HI value for a plant species under severe drought stress.
A variety of stresses are simulated each day. Leaf area growth and dry matter accumulation are constrained by the most severe stress each day. Leaf area growth is more sensitive to drought than is dry matter growth. Potential evapotranspiration (PET) is used to calculate drought stress. PET is calculated with weather variables. Plant available soil water is calculated based on rainfall, soil infiltration, and soil water-holding capacity. The model simulates a drought stress response if plant available soil water is insufficient to meet the plant’s demand (based on PET and leaf area index).
Nitrogen (N) and phosphorus (P) stresses reduce plant growth in the model. These stresses are simulated with a supply and demand approach. Plant nutrient uptake is calculated with three parameters defining how nutrient demand changes during the growing season. Optimum concentrations of N and P are defined early in plant development, near anthesis, and at physiological maturity for each species. These values define the potential nutrient uptake from the soil each day and if insufficient to meet demand, ALMANAC simulates nutrient stress.
ALMANAC simulates temperature stress when the temperature is below the defined base temperature or above the defined optimum temperature.
Winter dormancy is simulated when day length gets sufficiently short in the fall. The DORMNT parameter defines this interval as the hours of photoperiod near the minimum when plants are dormant.
Plant height is simulated from the fraction of GDD relative to the physiological maturity value and a species-specific plant height parameter (CHT).
ALMANAC simulates competition between crops and weeds and simulates communities of plants including woody plants competing with forages and native range sites. ALMANAC simulates competition for light, water, and nutrients. Fraction of incoming solar radiation intercepted by a leaf canopy (FIPAR) is:
FIPAR = 1.0 − exp (−k × LAI)
The light extinction coefficient (k) for Beer’s law [39] is calculated as:
where ln = natural log of the number. Values for k have been calculated for several plant species [21,23,30,31,36]. Simulation of LAI is critical for these equations describing light interception. Simulated light competition [40] is computed as LAI × k using the LAI of each plant species in the mixture. These products (LAI × k) of each species are summed and then used in Beer’s law to calculate the fraction of light interception by the whole plant community. This fraction for the whole plant community is divided among the competing species by weighted fractions. The weights accommodate for differences in plant heights and LAI × k of the species. Taller species and those with higher LAI and higher k intercept more of the total light intercepted by the community. In addition, potential plant transpiration is simulated with the potential evapotranspiration and the total community LAI. Simulated water and nutrient competition use a balance sheet approach. After each plant species’ intercepted light is computed as described above, each one’s potential daily biomass growth is calculated as RUE multiplied by the intercepted PAR, assuming 45% of the total daily incident solar radiation is PAR [41,42].
k = ln (1.0 − FIPAR)/(−LAI)
ALMANAC accounts for variability in root scavenging capacities between species through differences in the current rooting depth of each species. Potential rooting depths are derived from measurements reported in the literature (such as in [36]). A deeper-rooted plant species may have access to soil water (and nutrients) not available to any competing shallower-rooted species. A deeper-rooted species can have adequate soil water and nutrients at the same time as when a shallower-rooted species is stressed.
2.2. Adaptation of ALMANAC to Tropical Trees
For this project, coffee, cocoa, and a tropical overstory tree were simulated. The parameters for coffee came from parameters developed by Josimar Gurgel Fernandes (personal communication). The parameters for cocoa were based on the coffee parameters but adapted according to supplementary information from Fati Aziz (personal communication). Lastly, a new aspect of the model developed for this study is a generic, stand-in for tropical overstory trees. This was developed from parameters for carob trees (Ceratonia siliqua) by Josimar Gurgel Fernandes, but our tropical tree was simulated as a non-legume. These trees take a few years to develop and they are evergreen, therefore we set the total degree days (PHU) to values that allow development over five years for coffee and cocoa and ten years for the overstory tropical tree. Once that number of years is reached, the leaf area index is assumed to be fairly stable and does not change except when trees are pruned and the leaves regrow.
ALMANAC plant parameters are calculated for physical descriptions, leaf area development, development rate response to temperature, radiation-use efficiency, and nitrogen and phosphorous concentrations in plant biomass (Table 1). ALMANAC simulates effects of stresses on plant biomass and LAI such as from nutrient deficiency, drought, and temperature [1]. Plant parameter values and plant growth curves are optimized through ALMANAC application using the field data. Values for these curves are used to reproduce growth curves generated with measured field data of LAI. ALMANAC has simulated a wide range of species, including evergreen shrubs like creosote bush (Larrea tridentata [DC.] Cov.). For this study, plant and management parameters that will be discussed are listed in Table 1 and Table 2.
2.3. Deriving Values for Tree Phenology
The following values listed in Table 3 were used for coffee, cocoa, and an overstory tropical tree. Parameters in bold font were altered to simulate these three tree species. These were largely based on measured coffee parameters derived in Brazil by Josimar Gurgel Fernandes (personal communication). Values for others were the default values for trees previously derived [4,5].
2.4. Deriving Soils Data
For the U.S., the model’s required soil data is from USDA-NRCS (https://www.nrcs.usda.gov/wps/portal/nrcs/main/soils/survey/ accessed on 19 October 2022). This is publicly available, verified, and the most extensive soil database for the U.S. This data can be downloaded for any state, as described in the ALMANAC model documentation (https://www.ars.usda.gov/plains-area/temple-tx/-grassland-soil-and-water-research-laboratory/docs/193226/ accessed on 11 October 2022).
Soil data inputs are the texture, depth, and the amount of rocks by soil layer. The model uses the values for saturation, drained upper limit, and lower limit for each soil layer. Soil organic matter impacts plant-available water and soil carbon balances in the model. Runoff is calculated using the traditional runoff curve number system. Runoff is simulated with the type of ground cover and slope.
Soil and weather data for Mexico are available for the ALMANAC model (https://www.ars.usda.gov/plains-area/temple-tx/grassland-soil-and-water-research-laboratory/docs/almanacmex/ accessed on 11 October 2022). When ALMANAC is applied outside of these two countries, soils, weather, and plant species growth curve data can be developed through cooperation with the senior author of this project. Accessing international soils data for other sites can be determined from available country data. Then the data can be input manually into the ALMANAC interface or database. First, a site with a similar latitude and soil is input, then the soil data is augmented to match that from a country outside the U.S. or Mexico.
2.5. Accessing Weather Data
The input data is designed to make this model easily applied and readily available. The required daily weather inputs consist of solar radiation, wind speed, relative humidity, rainfall, and maximum and minimum temperatures. Solar radiation can be approximated when unavailable for a given location derived from wind speed and relative humidity. The U.S. National Oceanic and Atmospheric Administration (NOAA) website’s weather data are readily downloaded for the U.S. via the steps in the model documentation (see website link above). Weather in both U.S. and Mexico ALMANAC models are also available with the included weather generator. When needing observed weather that is unavailable in NOAA or internationally, this website from NASA provides all required weather inputs using satellite data from the latitude and longitude of the location (https://power.larc.nasa.gov/data-access-viewer/ accessed on 11 October 2022).
2.6. Datasets Used for Model Demonstration
2.6.1. Coffee at Sites in Hawai’i
Coffee yields were published from 2003–2021 by NASS (www.nass.usda.gov accessed on 3 October 2022) for all of Hawai’i, while yields for the island of Kaua’i were only shown for 2014–2016 on a grower’s website (https://bigislandcoffeeroasters.com/blogs/blog/hawaii-coffee-production-statistics accessed on 3 October 2022). We focused on Kaua’i using a known coffee field for the simulation 21.8994, −159.5617. The soil (Table 4) and weather for the island were downloaded using USDA-NRCS and NASA websites listed previously. Soil at the site was Makaweli stony silty clay loam, with 0 to 6 percent slopes, and all weather parameters were downloaded from 1998 to 2021. Crop parameters used for coffee were discussed above in Section 2 and shown in Table 3. Management for coffee simulations in Hawai’i was described in a video from a local company’s website. The simulation’s management schedule lasted for twenty-four years. Coffee was planted on 10 March of the first year. PHU was set at 25,000 and POP was set to 10 (see Table 2 for management parameter definitions). Every year 200 kg/Ha Nitrogen was applied on 10 March. In year six, coffee is harvested on 30 September. The standard harvest operation for grapes (HARVGRAPE) was augmented and the newly created HarvCoffee operation was used with HE changed to 0.43. The HE values for coffee here and for cocoa below take into account the non-seed portions of the harvested cherries or pods as well as losses due to poor quality seed and underdeveloped seed and fruit. New tillage operations were created in ALMANAC for the pruning events used in coffee and cocoa. The standard prune operation was augmented to create PruneCoffee with a harvest operation for a fraction of the total plant biomass (ORHI) set to 0.15. In year seven, on 10 March the coffee was pruned with the PruneCoffee operation. In year eight, coffee is pruned in March and harvested in September. The following year it is only pruned in March. Management alternates the same as years eight and nine as a year of pruning and harvesting with a year of only harvesting until the schedule completes. We ran 19 years beginning in 2003 to obtain even-numbered harvest year yields, and 18 years beginning in 2004 for the odd-numbered harvest years.
2.6.2. Cocoa at Sites in Ghana
Cocoa was simulated by selecting Kaua’i, Hawai’i in ALMANAC (coordinates 21.9270, −159.5443) because it was similar in latitude and climate to the site in Ghana. The soil Pohakupu silty clay loam, 0 to 8 percent slopes, MLRA 158 was amended to match those in Ghana (Table 5). Observed temperature and precipitation were provided by the Ghana Meteorological Agency (GMet) for the years 1998 to 2016. Remaining weather parameters were downloaded from NASA for Ghana at 6.2, −2.33 for 1998–2021. Measured cocoa yields were reported from 2012 to 2015 by Daymond et al. [43]. Management data for cocoa in Ghana, obtained from the manual for cocoa extension in Ghana [44] and from personal interviews with cocoa farmers in Ghana, was simulated in ALMANAC. Crop parameters used were discussed in Section 2 and shown in Table 3. The operation schedule lasted twenty years beginning in 2002. Cocoa was planted October 15 with PHU 24,000 and POP 3. From year four onward, on April 15 the new PruneCoffee operation was utilized in this crop as well, then cocoa was harvested twice a year on 15 June and 15 September with a new operation called HarvCocoa. This harvest operation is the same as HARVGRAPE but with HE set to 0.21. This yearly single pruning and double harvest continue until the end of our simulation in 2020.
2.7. Demonstration of the Model at the Two Sites
2.7.1. Sensitivity to Changes in Rainfall
Each daily rainfall amount was increased or decreased by different factors to demonstrate the model’s sensitivity to water stress. Each rainfall event was adjusted by factors calculated from 1 standard deviation or 1.5 standard deviations calculated from all the years we used for weather data in Table 6. These two factors were chosen simply to demonstrate how variability in daily rainfall amounts affected the simulated values. We analyzed 24 years of annual rainfall for Ghana and 25 years of data for Hawai’i. The means and standard deviations were 1487 and 194 mm for Ghana and 755 and 312 mm for Hawai’i. Thus, the fractions we used for this sensitivity analysis (multiplying each rainfall event by the fraction) were 1.20, 1.13, 0.87, and 0.80 for Ghana. For Hawai’i, these fractions were 1.62, 1.41, 0.59, and 0.38.
2.7.2. Sensitivity to Overstory Trees
We also simulated agroforestry with different shading intensities of overstory trees. We developed a generic tropical tree to provide the overstory. This tree was simulated with 52,000 PHU five years before the previously described management for coffee and cocoa trees began. This value for PHU represents what is accumulated in the first 5 years. We simulated different densities of the overstory trees and thus different fractions of shading for the shorter coffee and cocoa trees. These were calculated from tree densities of 0.05, 0.2, 0.5, 1, 1.5, 2, and 2.5 plants per 100 m2. The maximum leaf area index (DMLA) values for these densities were 0.013, 0.057, 0.16, 0.39, 0.69, 1.05, and 2.0, respectively. In addition to reduced solar radiation for the coffee and cocoa trees, water competition and nutrient competition were simulated by the ALMANAC model.
3. Results and Discussion
The ALMANAC model did an acceptable job simulating the yields of coffee. For coffee (Table 7), the statewide mean coffee yield for Hawai’i over ten years was 0.983 Mg/ha. For 10 years of statewide yields, the average simulated over measured ratio was also 0.983. While the correlation coefficient was low (0.554) due to the low variability in measured yields, the simulations show promise for future projects with more diverse simulated yields. For the three years of available yield data for the island of Kaua’i, the average simulated over measured ratio was 1.022 (Table 7). Thus, for both types of data, the model was realistically close to the mean simulated values. For individual years, for the statewide yields, the simulated values were within 10% of the measured values for 8 of 10 years and within 5% of measured values for 6 of 10 years. For Kaua’i, in all three years, the simulated values were within 10% of the measured values. Looking graphically at the results (Figure 1), after the first year, the simulated values showed the same pattern as the measured ones, showing higher values in the higher measured years and lower values in the lower measured years.
For cocoa, the ALMANAC model showed similarly promising results. The simulated values were within 10% of the measured values for all four years (Table 8). As shown in Figure 2, the simulated values were somewhat more stable over years than the measured values, likely due to the high rainfall for this site. The measured values varied around the simulated values over the four years. Likewise, while the correlation coefficient was again low (0.577) due to the low variability in measured yields, the simulations also show promise for future projects with more diverse simulated yields.
For the sensitivity analyses for rainfall, ALMANAC showed the expected response, with the wettest site (Ghana) showing lower percent changes in yield than the drier site (Hawai’i) (Table 9). This demonstrates how differences among locations in rainfall variability are reflected in the simulated yields for such tropical trees.
The responses to “tropical tree” densities showed interesting results, with the lower densities and thus lower potential LAI of the tropical tree having little or no impact on the coffee or cocoa yields (Table 10 and Table 11). Eventually, as the tropical tree density increased, the coffee and cocoa yields decreased until eventually, they yielded zero. Thus, as the tropical tree potential LAI exceeded 1, coffee had zero simulated yields. As this LAI reached 0.69, cocoa in the wetter site, showed zero simulated yields. Shade is the cause of the reduced yield as shown by stress Table 12 as the overall number of stress days per year was low. As the canopy density increased, the reduced light available for coffee reduced plant size and reduced demand for water. Likewise, nitrogen, phosphorus, temperature, and aeration stress all stayed relatively stable, indicating that light competition was the major stress. This is similar to Ref. [46], who found that in a coffee-growing system shaded by macadamia trees, there was no significant difference between its LAI and that of a similar system in full sun. Although the shade trees do not impact LAI, there is evidence to show it can impact flowering and cherry development, increase the infiltration rate of water in the soil, and improve N fixation. Despite the alternative ecosystem services provided, shade trees did not impact coffee growth as much as climatic conditions, especially drought. Coffee grown in shade experienced less hydric stress than its peers in full sun [46]. Under stressful conditions, light requirements may decrease and shaded trees may not experience notable deprivation compared to trees in full sun [47].
4. Conclusions
The ALMANAC model shows great promise in simulating coffee and cocoa yields in tropical conditions.
The model shows reasonable responses to changes in rainfall at two diverse sites.
The model is a realistic tool to simulate agroforestry of these trees at these sites. The model shows realistic responses to an overstory of a taller tropical tree at different planting densities and thus different LAI. The low leaf cover of the overstory tree had little or no impact on the coffee and cocoa yields. The model showed that with sufficient leaf cover of the overstory tree, the taller tree causes the coffee and cocoa to produce no yield.
The ALMANAC model parameters for cocoa and coffee can be applied to assist with management questions specific to diverse sites. More measured data will improve the values derived here. These current values are a promising start to tropical tree crops for ALMANAC and its related models.
Author Contributions
Conceptualization F.A., A.D.B.-G., J.J., M.-V.V.J., J.R.K., J.O.L. and A.S.W.; Methodology F.A., J.G.F., J.R.K. and A.S.W.; Validation J.J. and A.S.W.; Formal Analysis J.J., J.R.K. and A.S.W.; Investigation J.J., J.R.K. and A.S.W.; Resources A.S.W.; Data Curation J.J. and A.S.W.; Writing—Original Draft Preparation J.R.K.; Writing—Review and Editing F.A., A.D.B.-G., J.J., J.R.K., M.N.M. and A.S.W. Visualization J.R.K. and A.S.W.; Supervision J.R.K.; Project Administration, J.R.K. All authors have read and agreed to the published version of the manuscript.
Funding
This research was supported in part by an appointment to the Agricultural Research Service (ARS) Research Participation Program administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and the U.S. Department of Agriculture (USDA), Agricultural Research Service Agreement #60-3098-0-002.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
Relevant data applicable to this research are within the paper.
Acknowledgments
This work was supported in part by the USDA, Agricultural Research Service. Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the USDA. USDA is an equal opportunity provider and employer.
Conflicts of Interest
The authors declare no conflict of interest.
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Figure 1.
Coffee yields (in Hawai’i) measured and simulated with the ALMANAC model.
Figure 2.
Cocoa yields (in Ghana) measured and simulated with the ALMANAC model.
Table 1.
Relevant Plant Parameter Descriptions. These parameters were altered to simulate these three tree species. Values for others were the default values for trees previously derived [4,5].
| Parameter | Description |
|---|---|
| WA | The radiation use efficiency times 10; Biomass-energy ratio, g per MJ of IPAR |
| HI | Harvest index; fruit yield/above-ground biomass |
| TB | Optimal temperature for plant growth: °C |
| TG | Minimum temperature for plant growth: °C |
| DMLA | Maximum leaf area index (LAI) |
| DLAI | Fraction of season when maximum LAI is reached and anthesis is assumed to occur |
| LAP1 | First point on optimal LAI curve; Numbers before decimal are % of growing seasons. Numbers after decimal are fractions of maximum potential leaf area index |
| LAP2 | Second point on optimal LAI curve; Numbers before decimal are % of growing seasons. Numbers after decimal are fractions of maximum potential leaf area index |
| PPL1 | First plant population parameter; Number before decimal is plants/m2. Number after decimal is fraction of species LAI at that population (plants/100 m2 for trees) |
| PPL2 | Second plant population parameter; Number before decimal is plants/m2 Number after decimal is fraction of species LAI at that population (plants/100 m2 for trees) |
| RLAD | Leaf area index decline rate parameter. Estimated LAI decline between DLAI and harvest. 1 is linear, >1 accelerated decline, <1 retards decline rate |
| RDMB | Biomass energy ratio decline rate parameter. Reduces efficiency of bio-mass-energy conversion due to creation of seeds or N translocation |
| WAC2 | An “S” curve number used to describe the effect of CO2 concentration on the crop parameter WA. The value on the left of the decimal is a value of CO2 concentration higher than ambient. The value on the right of the decimal is the corresponding value WA |
| CLAIYR | Number of years until maximum LAI |
| HMX | Maximum crop height (m) |
| RDMX | Maximum root depth (m) |
| WSYF | The minimum value for HI when severe drought stress occurs near anthesis |
| Tree1 | First point on multi-year S-curve function for trees’ LAI and height increase; Numbers before decimal are % of years to maturity. Numbers after decimal are fractions of maximum potential leaf area index and height increase |
| Tree2 | Second point on multi-year S-curve function for trees’ LAI and height increase; Numbers before decimal are % of years to maturity. Numbers after decimal are fractions of maximum potential leaf area index and height increase |
| BN1 | Normal fraction of N in crop biomass at emergence |
| BN2 | Normal fraction of N in crop biomass at midseason |
| BN3 | Normal fraction of N in crop biomass at maturity |
| BP1 | Normal fraction of P in crop biomass at emergence |
| BP2 | Normal fraction of P in crop biomass at midseason |
| BP3 | Normal fraction of P in crop biomass at maturity |
| EXT | Extinction coefficient for calculating light interception; Kc |
| DORMNT | Defines the day length in the fall when dormancy begins (1 h greater than the minimum for the latitude). Value is hours of day length which is added to the minimum day length of the year for that location |
| DMPHT | Tree parameter, minimum grams of biomass per meter of height |
| CHTYR | Tree parameter, number of years to maximum height |
Table 2.
Relevant Management Parameter Descriptions.
| Parameter | Description |
|---|---|
| POP | Plant density (plants/100 m2 for trees) |
| PHU | Potential heat units (degree days or GDD) |
| N | Nitrogen applied kg/ha |
| HE | Harvest efficiency. This is the ratio of seed yield removed from the field to total fruit yield |
Table 3.
Plant parameters used in this study. Parameters in bold font were adjusted from measured data by Josimar Gurgel Fernandes (personal communication) to simulate these three tree species.
Table 3.
Plant parameters used in this study. Parameters in bold font were adjusted from measured data by Josimar Gurgel Fernandes (personal communication) to simulate these three tree species.
| ALMANAC Plant Parameters | Coffee | Cocoa | Tropical Tree |
|---|---|---|---|
| WA | 12.0 | 12.0 | 16.1 |
| HI | 0.05 | 0.05 | 0.05 |
| TB | 24 | 24 | 30 |
| TG | 10 | 10 | 10 |
| DMLA | 3.5 | 6 | 3.9 |
| DLAI | 0.65 | 0.65 | 0.99 |
| LAP1 | 5.05 | 5.05 | 5.05 |
| LAP2 | 95.95 | 95.95 | 40.95 |
| PPL1 | 1.1 | 1.1 | 1.1 |
| PPL2 | 10.99 | 10.99 | 10.9 |
| RLAD | 0.01 | 0.01 | 0.05 |
| RBMD | 0.01 | 0.01 | 0.1 |
| WAC2 | 660.18 | 660.18 | 660.18 |
| CLAIYR | 5 | 5 | 10 |
| HMX | 2 | 2 | 6 |
| RDMX | 2 | 2 | 3.5 |
| WSYF | 0.005 | 0.005 | 0.01 |
| TREE1 | 1.95 | 1.95 | 1.95 |
| TREE2 | 2.99 | 2.99 | 2.99 |
| BN1 | 0.02 | 0.02 | 0.006 |
| BN2 | 0.01 | 0.01 | 0.002 |
| BN3 | 0.008 | 0.008 | 0.0015 |
| BP1 | 0.0007 | 0.0007 | 0.0007 |
| BP2 | 0.0004 | 0.0004 | 0.0004 |
| BP3 | 0.0003 | 0.0003 | 0.0003 |
| EXT | 0.61 | 0.72 | 0.65 |
| DORMNT | 0.5 | 0.5 | 0 |
| DMPHT | 120 | 120 | 120 |
| CHTYR | 10 | 10 | 10 |
Table 4.
Soil parameters used for coffee simulations in Hawai’i. SALB is soil albedo, Z is depth (m), BD is bulk density (Mg/m3), U is wilting point (m/m), CBN is organic carbon (%), SIL is silt content (%), SAN is sand content (%), ROK is coarse fragment content (%).
Table 4.
Soil parameters used for coffee simulations in Hawai’i. SALB is soil albedo, Z is depth (m), BD is bulk density (Mg/m3), U is wilting point (m/m), CBN is organic carbon (%), SIL is silt content (%), SAN is sand content (%), ROK is coarse fragment content (%).
| Attributes | ||||
|---|---|---|---|---|
| Layer | 1 | 2 | 3 | 4 |
| SALB | 0.09 | |||
| Z | 0.01 | 0.30 | 0.64 | 1.52 |
| BD | 1.10 | 1.10 | 1.25 | 1.25 |
| U | 0.173 | 0.173 | 0.133 | 0.195 |
| CBN | 2.06 | 2.06 | 0.56 | 0.44 |
| SIL | 44.0 | 44.0 | 54.6 | 44.0 |
| SAN | 18.5 | 18.5 | 20.9 | 18.5 |
| ROK | 20.0 | 20.0 | 0.0 | 0.0 |
Table 5.
Altered soil parameters used for cocoa simulations in Ghana [45] SALB is soil albedo, Z is depth (m), BD is bulk density (Mg/m3), U is wilting point (m/m), CBN is organic carbon (%), SIL is silt content (%), SAN is sand content (%), ROK is coarse fragment content (%).
Table 5.
Altered soil parameters used for cocoa simulations in Ghana [45] SALB is soil albedo, Z is depth (m), BD is bulk density (Mg/m3), U is wilting point (m/m), CBN is organic carbon (%), SIL is silt content (%), SAN is sand content (%), ROK is coarse fragment content (%).
| Attributes | ||||||
|---|---|---|---|---|---|---|
| Layer | 1 | 2 | 3 | 4 | 5 | 6 |
| SALB | 0.15 | |||||
| Z | 0.05 | 0.15 | 0.30 | 0.60 | 1.00 | 2.00 |
| BD | 1.571 | 1.583 | 1.612 | 1.616 | 1.621 | 1.649 |
| U | 0.25 | 0.26 | 0.23 | 0.23 | 0.23 | 0.23 |
| CBN | 2.02 | 1.81 | 1.37 | 1.05 | 0.80 | 0.61 |
| SIL | 23.0 | 22.8 | 21.7 | 20.6 | 20.3 | 20.6 |
| SAN | 56.2 | 55.0 | 53.1 | 47.9 | 46.5 | 46.4 |
| ROK | 10.4 | 10.7 | 12.5 | 15.05 | 16.1 | 19.8 |
Table 6.
Analysis of the annual rainfall data for twenty-four years at the two sites.
| Year | Annual Precipitation in Sefwi Bekwai, Ghana (Cocoa) in mm | Annual Precipitation in Kaua’i, Hawai’i (Coffee) in mm |
|---|---|---|
| 1998 | 1368 | 210 |
| 1999 | 1694 | 313 |
| 2000 | 1328 | 203 |
| 2001 | 1253 | 456 |
| 2002 | 1304 | 998 |
| 2003 | 1480 | 899 |
| 2004 | 1277 | 1185 |
| 2005 | 1273 | 792 |
| 2006 | 1451 | 1249 |
| 2007 | 1375 | 207 |
| 2008 | 1684 | 805 |
| 2009 | 1398 | 672 |
| 2010 | 1507 | 678 |
| 2011 | 1462 | 899 |
| 2012 | 1360 | 1027 |
| 2013 | 1390 | 965 |
| 2014 | 1708 | 1203 |
| 2015 | 1502 | 577 |
| 2016 | 1224 | 542 |
| 2017 | 1705 | 619 |
| 2018 | 1743 | 1178 |
| 2019 | 1789 | 757 |
| 2020 | 1930 | 826 |
| 2021 | 851 | |
| Average | 1487 | 755 |
| Std Dev | 194 | 312 |
| Mean +1 std (% of mean) | 1681 (113%) | 1067 (141%) |
| Mean +1.5 std | 1778 (120%) | 1223 (162%) |
| Mean −1 std | 1293 (87%) | 442 (59%) |
| Mean −1.5 std | 1196 (80%) | 286 (38%) |
Table 7.
Hawai’i simulated coffee yields and measured statewide averages in Mg/ha.
| Year | Simulated | Statewide | Kaua’i | ||
|---|---|---|---|---|---|
| Measured | Simulated/Measured | Measured | Simulated/Measured | ||
| 2012 | 0.95 | 1.13 | 0.84 | ||
| 2013 | 0.94 | 0.98 | 0.96 | ||
| 2014 | 1.07 | 1.1 | 0.97 | 1.01 | 1.06 |
| 2015 | 1.04 | 1.09 | 0.95 | 1.09 | 0.95 |
| 2016 | 0.99 | 0.99 | 1.00 | 0.94 | 1.05 |
| 2017 | 0.93 | 0.83 | 1.12 | ||
| 2018 | 0.98 | 0.91 | 1.08 | ||
| 2019 | 0.97 | 0.93 | 1.04 | ||
| 2020 | 0.99 | 0.93 | 1.06 | ||
| 2021 | 0.97 | 0.94 | 1.03 | ||
| Avg | 0.98 | 0.98 | 1.01 | 1.01 | 1.02 |
| Std Dev | 0.04 | 0.09 | 0.06 | ||
| CV% | 4 | 9 | 6 | ||
| RMSE | 0.08 | 0.10 | |||
Table 8.
Cocoa simulated yields in Ghana compared to measured yields in Mg/ha. For these simulations, Harvest Efficiency (HE) was 0.21, Harvest Index (HI) was 0.05, and PHU was 24,000.
Table 8.
Cocoa simulated yields in Ghana compared to measured yields in Mg/ha. For these simulations, Harvest Efficiency (HE) was 0.21, Harvest Index (HI) was 0.05, and PHU was 24,000.
| Year | Simulated Yield | Actual Yield | Simulated/Measured |
|---|---|---|---|
| 2011 | 0.78 | ||
| 2012 | 0.78 | 0.73 | 1.08 |
| 2013 | 0.77 | 0.78 | 0.99 |
| 2014 | 0.77 | 0.70 | 1.10 |
| 2015 | 0.76 | 0.79 | 0.96 |
| 2016 | 0.75 | ||
| 2017 | 0.74 | ||
| 2018 | 0.75 | ||
| 2019 | 0.74 | ||
| 2020 | 0.73 | ||
| 2021 | 0.74 | ||
| Average | 0.76 | 0.75 | 1.03 |
| Standard Deviation | 0.02 | ||
| CV% | 2.2 | ||
| RMSE | 0.05 |
Table 9.
Sensitivity analysis of yield responses to changes in rainfall.
| Coffee Yields (Mg/ha) | ||
|---|---|---|
| Rainfall Changes Standard Deviation (%) | Average | Fraction of Average |
| +1.5 (162%) | 1.31 | 1.41 |
| +1 (141%) | 1.20 | 1.29 |
| 0 (100%) | 0.93 | 1.00 |
| −1 (59%) | 0.54 | 0.58 |
| −1.5 (38%) | 0.29 | 0.31 |
| Cocoa Yields (Mg/ha) | ||
| Rainfall Changes Standard Deviation (%) | Average | Fraction of Average |
| +1.5 (120%) | 0.73 | 1.01 |
| +1 (113%) | 0.73 | 1.01 |
| 0 (100%) | 0.72 | 1.00 |
| −1 (87%) | 0.71 | 0.99 |
| −1.5 (80%) | 0.70 | 0.97 |
Table 10.
Coffee simulation with tropical tree overstory growth planted five years prior to coffee. POP is the plants per 100 m2 of the tropical trees. DMLA is the potential LAI of the overstory trees. The fraction of light intercepted by the overstory tree (FI) and the fraction transmitted beneath the overstory (Trans) are calculated from the potential LAI (DMLA) and Beer’s Law with the appropriate extinction coefficient. Simulated coffee yield in Mg/ha is indicated and the yield divided by the control is in parentheses.
Table 10.
Coffee simulation with tropical tree overstory growth planted five years prior to coffee. POP is the plants per 100 m2 of the tropical trees. DMLA is the potential LAI of the overstory trees. The fraction of light intercepted by the overstory tree (FI) and the fraction transmitted beneath the overstory (Trans) are calculated from the potential LAI (DMLA) and Beer’s Law with the appropriate extinction coefficient. Simulated coffee yield in Mg/ha is indicated and the yield divided by the control is in parentheses.
| POP of Overstory Tropical Tree | Control, No Overstory Tree | 0.05 | 0.2 | 0.5 | 1.0 | 1.5 | 2.0 |
|---|---|---|---|---|---|---|---|
| DMLA of Overstory Tropical Tree | NA | 0.013 | 0.057 | 0.16 | 0.39 | 0.69 | 1.05 |
| FI by Overstory Tropical Tree | NA | 0.008 | 0.0036 | 0.0099 | 0.224 | 0.361 | 0.495 |
| Trans by Overstory Tropical Tree | NA | 0.992 | 0.964 | 0.901 | 0.776 | 0.639 | 0.505 |
| Year | Simulated Coffee Yield | ||||||
| 2010 | 0.76 | 0.73 (0.96) | 0.73 (0.96) | 0.73 (0.96) | 0.69 (0.91) | 0.37 (0.49) | 0 (0) |
| 2011 | 0.79 | 0.79 (1.00) | 0.79 (1.00) | 0.78 (0.99) | 0.74 (0.94) | 0.65 (0.82) | 0 (0) |
| 2012 | 0.95 | 0.98 (1.03) | 0.98 (1.03) | 0.97 (1.02) | 0.92 (0.97) | 0.47 (0.49) | 0 (0) |
| 2013 | 0.94 | 1.00 (1.06) | 1.00 (1.06) | 0.99 (1.05) | 0.94 (1.00) | 0.80 (0.85) | 0 (0) |
| 2014 | 1.07 | 1.14 (1.07) | 1.14 (1.07) | 1.13 (1.06) | 1.07 (1.00) | 0.51 (0.48) | 0 (0) |
| 2015 | 1.04 | 1.13 (1.09) | 1.13 (1.09) | 1.12 (1.08) | 1.06 (1.02) | 0.85 (0.82) | 0 (0) |
| 2016 | 0.99 | 1.09 (1.10) | 1.09 (1.10) | 1.08 (1.09) | 1.02 (1.03) | 0.52 (0.53) | 0 (0) |
| 2017 | 0.93 | 1.06 (1.14) | 1.06 (1.14) | 1.05 (1.13) | 0.99 (1.06) | 0.80 (0.86) | 0 (0) |
| 2018 | 0.98 | 1.11 (1.13) | 1.11 (1.13) | 1.09 (1.11) | 1.03 (1.05) | 0.48 (0.49) | 0 (0) |
| 2019 | 0.97 | 1.16 (1.20) | 1.16 (1.20) | 1.14 (1.18) | 1.08 (1.11) | 0.76 (0.78) | 0 (0) |
| 2020 | 0.99 | 1.20 (1.21) | 1.20 (1.21) | 1.18 (1.19) | 1.12 (1.13) | 0.43 (0.43) | 0 (0) |
| 2021 | 0.97 | 1.22 (1.26) | 1.22 (1.26) | 1.20 (1.24) | 1.13 (1.16) | 0.69 (0.71) | 0 (0) |
| Averages | 0.95 | 1.05 | 1.05 | 1.04 | 0.98 | 0.61 | 0 |
| Fraction of Control | 1.10 | 1.10 | 1.09 | 1.03 | 0.65 | 0 | |
Table 11.
Cocoa simulation with tropical tree overstory growth planted five years prior to cocoa. POP is the plants per 100 m2 of the tropical trees. DMLA is the potential LAI of the overstory trees. The fraction of light intercepted by the overstory tree (FI) and the fraction transmitted beneath the overstory (Trans) are calculated from the potential LAI (DMLA) and Beer’s Law with the appropriate extinction coefficient. Simulated cocoa yield in Mg/ha is indicated and the yield divided by the control is in parentheses.
Table 11.
Cocoa simulation with tropical tree overstory growth planted five years prior to cocoa. POP is the plants per 100 m2 of the tropical trees. DMLA is the potential LAI of the overstory trees. The fraction of light intercepted by the overstory tree (FI) and the fraction transmitted beneath the overstory (Trans) are calculated from the potential LAI (DMLA) and Beer’s Law with the appropriate extinction coefficient. Simulated cocoa yield in Mg/ha is indicated and the yield divided by the control is in parentheses.
| POP of Overstory Tropical Tree | Control, No Overstory Tree | 0.05 | 0.2 | 0.5 | 1.0 | 1.5 | 2.0 |
|---|---|---|---|---|---|---|---|
| DMLA of Overstory Tropical Tree | NA | 0.013 | 0.57 | 0.16 | 0.39 | 0.69 | 1.05 |
| FI by Overstory Tropical Tree | NA | 0.008 | 0.0036 | 0.0099 | 0.224 | 0.361 | 0.495 |
| Trans by Overstory Tropical Tree | NA | 0.992 | 0.964 | 0.901 | 0.776 | 0.639 | 0.505 |
| Year | Simulated Cocoa Yield | ||||||
| 2007 | 0.52 | 0.52 (1.00) | 0.52 (1.00) | 0.52 (1.00) | 0.50 (0.96) | 0 (0) | 0 (0) |
| 2008 | 0.63 | 0.63 (1.00) | 0.63 (1.00) | 0.63 (1.00) | 0.60 (0.95) | 0 (0) | 0 (0) |
| 2009 | 0.71 | 0.72 (1.01) | 0.72 (1.01) | 0.71 (1.00) | 0.68 (0.68) | 0 (0) | 0 (0) |
| 2010 | 0.75 | 0.76 (1.01) | 0.76 (1.01) | 0.75 (1.00) | 0.72 (0.96) | 0 (0) | 0 (0) |
| 2011 | 0.78 | 0.79 (0.99) | 0.79 (0.99) | 0.78 (1.00) | 0.75 (0.96) | 0 (0) | 0 (0) |
| 2012 | 0.78 | 0.79 (1.01) | 0.79 (1.01) | 0.78 (1.00) | 0.75 (0.96) | 0 (0) | 0 (0) |
| 2013 | 0.77 | 0.79 (1.02) | 0.79 (1.09) | 0.78 (1.01) | 0.75 (0.97) | 0 (0) | 0 (0) |
| 2014 | 0.77 | 0.78 (1.01) | 0.78 (1.01) | 0.78 (1.01) | 0.75 (0.97) | 0 (0) | 0 (0) |
| 2015 | 0.76 | 0.78 (1.02) | 0.78 (1.02) | 0.77 (1.01) | 0.74 (0.97) | 0 (0) | 0 (0) |
| 2016 | 0.75 | 0.76 (1.01) | 0.76 (1.01) | 0.75 (1.00) | 0.72 (0.96) | 0 (0) | 0 (0) |
| 2017 | 0.74 | 0.76 (1.02) | 0.76 (1.02) | 0.75 (1.01) | 0.72 (0.97) | 0 (0) | 0 (0) |
| 2018 | 0.75 | 0.76 (1.01) | 0.76 (1.01) | 0.76 (1.01) | 0.73 (0.97) | 0 (0) | 0 (0) |
| 2019 | 0.74 | 0.77 (1.04) | 0.77 (1.04) | 0.76 (1.02) | 0.73 (0.99) | 0 (0) | 0 (0) |
| 2020 | 0.73 | 0.77 (1.05) | 0.77 (1.05) | 0.76 (1.04) | 0.73 (1.00) | 0 (0) | 0 (0) |
| 2021 | 0.74 | 0.77 (1.04) | 0.77 (1.04) | 0.76 (1.03) | 0.73 (0.99) | 0 (0) | 0 (0) |
| Averages | 0.73 | 0.74 | 0.74 | 0.74 | 0.71 | 0 | 0 |
| Fraction of Control | 1.01 | 1.01 | 1.01 | 0.97 | 0 | 0 | |
Table 12.
Simulated days of stress listed by type of stress per species at each density of overstory tropical tree. Coffee and cocoa simulations with tropical tree overstory growth planted five years prior to crop. POP is the plants per 100 m2 of the tropical trees. Water is drought stress, N is nitrogen, P is phosphorus, Temp is temperature, and Air is aeration (flooding) stress. The bold values are the stress that was highest for the plant at that density.
Table 12.
Simulated days of stress listed by type of stress per species at each density of overstory tropical tree. Coffee and cocoa simulations with tropical tree overstory growth planted five years prior to crop. POP is the plants per 100 m2 of the tropical trees. Water is drought stress, N is nitrogen, P is phosphorus, Temp is temperature, and Air is aeration (flooding) stress. The bold values are the stress that was highest for the plant at that density.
| POP of Overstory Tropical Tree | No Tree | 0.05 | 0.2 | 0.5 | 1.0 | 1.5 | 2.0 | |
|---|---|---|---|---|---|---|---|---|
| Coffee Stress Days | Water | 115.4 | 84.3 | 84.5 | 85.5 | 79.9 | 27.9 | 0.0 |
| N | 3.1 | 3.7 | 3.7 | 3.7 | 3.6 | 5.5 | 7.3 | |
| P | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Temp | 1.4 | 1.6 | 1.6 | 1.5 | 2.0 | 2.2 | 2.6 | |
| Air | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Cocoa Stress Days | Water | 13.6 | 2.3 | 6.7 | 2.6 | 3.7 | 0.0 | 0.0 |
| N | 3.8 | 4.0 | 4.1 | 4.0 | 4.0 | 4.1 | 4.1 | |
| P | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Temp | 24.1 | 26.9 | 21.5 | 26.9 | 26.6 | 28.2 | 28.2 | |
| Air | 0.1 | 0.2 | 0.1 | 0.2 | 0.1 | 0.1 | 0.1 | |
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Kiniry, J.R.; Fernandez, J.G.; Aziz, F.; Jacot, J.; Williams, A.S.; Meki, M.N.; Leyton, J.O.; Baez-Gonzalez, A.D.; Johnson, M.-V.V. Tropical Tree Crop Simulation with a Process-Based, Daily Timestep Simulation Model (ALMANAC): Description of Model Adaptation and Examples with Coffee and Cocoa Simulations. Agronomy 2023, 13, 580. https://doi.org/10.3390/agronomy13020580
AMA Style
Kiniry JR, Fernandez JG, Aziz F, Jacot J, Williams AS, Meki MN, Leyton JO, Baez-Gonzalez AD, Johnson M-VV. Tropical Tree Crop Simulation with a Process-Based, Daily Timestep Simulation Model (ALMANAC): Description of Model Adaptation and Examples with Coffee and Cocoa Simulations. Agronomy. 2023; 13(2):580. https://doi.org/10.3390/agronomy13020580
Chicago/Turabian StyleKiniry, James R., J. G. Fernandez, Fati Aziz, Jacqueline Jacot, Amber S. Williams, Manyowa N. Meki, Javier Osorio Leyton, Alma Delia Baez-Gonzalez, and Mari-Vaughn V. Johnson. 2023. "Tropical Tree Crop Simulation with a Process-Based, Daily Timestep Simulation Model (ALMANAC): Description of Model Adaptation and Examples with Coffee and Cocoa Simulations" Agronomy 13, no. 2: 580. https://doi.org/10.3390/agronomy13020580
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