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Crop models

"AquaCrop output variables over time"

AquaCrop

AquaCrop (Steduto et al., 2009; Raes et al., 2009) is a process-based crop growth model designed for use in predicting crop yield response to water conditions. It simulates plant growth over time — including canopy cover, phenology, biomass, yield, and other variables — based on physical and physiological processes. The model also incorporates management practices and environmental input data. Inside Persefone, the AquaCrop.jl (Dı́az Iturry et al., 2025) implementation of the AquaCrop model was used, which is a direct translation of the original AquaCrop Fortran code to the Julia programming language.

The AquaCrop model focuses on the yield response to water availability. It is designed to use a relatively low number of parameters, which are expected to be easy to estimate. The model emphasises the fundamental processes involved in crop productivity and the responses to water deficits, both from physiological and agronomic perspectives. In addition to crop parameters, AquaCrop also relies on climate input data and soil type characterization. Temperature data are used to track crop development through the calculation of growing degree days (GDD). Rainfall and soil properties are used to estimate the soil water content within the root zone. Based on these calculations, the model estimates the crop’s canopy cover (CC). Subsequently, using reference evapotranspiration (ETo) and the water productivity (WP) parameter, it estimates biomass production. Finally, the harvest index (HI) is applied to convert biomass into yield, as described in (Steduto et al., 2009; Raes et al., 2009). Daily sunshine radiation is not an explicit AquaCrop model input, but it’s effect enters only indirectly via the reference evapotranspiration. We expanded the model by adding a functionality to calculate plant height from biomass.

Model inputs

To simulate with AquaCrop and predict plant yields for given conditions, the following data is needed:

  • climate data: min./max. daily air temperature, rainfall, reference evapotranspiration
  • soil type: 5 horizons, each with hydraulic conductivity, water content at saturation, field capacity, and permanent wilting point. These parameters can be set from preset soil types such as “silty loam” etc.
  • crop type and parameters
  • sowing date, sowing density

Model outputs

The outputs relevant to Persefone are:

  • canopy cover
  • dry biomass and yield

Model calibration

To calibrate crop parameters to empirical crop data, the following is needed:

  • input data as above
  • biomass or yield per crop type
  • phenological phase dates per crop type (date of germination, flowering, etc)

ALMaSS

ALMaSS (Animal, Landscape and Man Simulation System) is an agent-based landscape simulation framework developed to study fauna and management in agricultural environments (Topping, Hansen, et al., 2003; Topping and Duan, 2024). It includes a vegetation/crop growth submodel that provides daily vegetation state (e.g., height, biomass, fractional cover) to the animal agents. The crop module is a simple, semi-mechanistic light-use-efficiency model driven primarily by solar radiation and temperature (growing degree-days), with stage changes driven by crop management (sowing, harvest) or calendar time (January 1st, March 1st). The model does not consider water availability or transpiration, and assumes that an adequate amount of water is available. In Persefone, the ALMaSS vegetation model has been reimplemented in the Julia programming language, following the original publication and source code.

Each crop stage has its own set of three piecewise linear growth curves that determine the daily change in plant height, green and total leaf area index of the plant in terms of growing degree-days.

The amount of radiation absorbed by the plant canopy can be calculated from the green leaf area index with the Beer-Lambert law of extinction. Finally, the change in dry matter is calculated from the amount of solar energy with a simple multiplicative model of crop- and temperature-dependent factors.

The total accumulated dry matter over the course of a simulation can be calculated as the sum of daily changes, which are determined by the leaf area index, temperature, incoming radiation:

\[W = \sum_{d = 1}^{n} \varepsilon \, f(T(d)) \, \phi(L(d)) \, R(d) \, p(d)\]

  • W : accumulated dry matter (g/m2 ) at day n
  • ε: radiation use efficiency (g/MJ), depends on plant species
  • f (T ): effect of temperature T (°C) on radiation use efficiency, depends on plant species
  • ϕ: fraction of incoming light intercepted by canopy; estimated as ϕ(L(d)) = 1 − e−kL(d) from leaf area index L, with extinction coefficient k = 0.4
  • R: incoming daily radiation (MJ/m2 )
  • p: effect of fertiliser use

Model inputs

A simulation with the ALMaSS vegetation model needs the following input data:

  • climate data: min./max. daily air temperature, incoming daily radiation
  • crop parameters: growth curves for height and green/total leaf area index in terms of growing-degree days (GDD), radiation use efficiency for crop type,
  • sowing date

Model outputs

  • canopy height, green leaf area index, total leaf area index
  • accumulated dry matter (biomass)

Literature

  • Díaz Iturry, G., Matthies, M. C., Pe’er, G., & Vedder, D. (2025). AquaCrop.jl: A Process-Based Model of Crop Growth. Journal of Open Source Software, 10(110), 7944. https://doi.org/10.21105/joss.07944
  • Hsiao, T. C., Heng, L., Steduto, P., Rojas‐Lara, B., Raes, D., & Fereres, E. (2009). AquaCrop—The FAO Crop Model to Simulate Yield Response to Water: III. Parameterization and Testing for Maize. Agronomy Journal, 101(3), 448–459. https://doi.org/10.2134/agronj2008.0218s
  • Raes, D. (2023). AquaCrop Training Handbooks—Book I. Understanding AquaCrop. Food and Agriculture Organization of the United Nations. https://www.fao.org/3/cc2380en/cc2380en.pdf
  • Raes, D., Steduto, P., Hsiao, T. C., & Fereres, E. (2009). AquaCrop—The FAO Crop Model to Simulate Yield Response to Water: II. Main Algorithms and Software Description. Agronomy Journal, 101(3), 438–447. https://doi.org/10.2134/agronj2008.0140s
  • Steduto, P., Hsiao, T. C., Raes, D., & Fereres, E. (2009). AquaCrop—The FAO Crop Model to Simulate Yield Response to Water: I. Concepts and Underlying Principles. Agronomy Journal, 101(3), 426–437. https://doi.org/10.2134/agronj2008.0139s
  • Topping, C. J., & Duan, X. (2024). ALMaSS Landscape and Farming Simulation: Software classes and methods. Food and Ecological Systems Modelling Journal, 5, e121215. https://doi.org/10.3897/fmj.5.121215
  • Topping, C. J., Hansen, T. S., Jensen, T. S., Jepsen, J. U., Nikolajsen, F., & Odderskær, P. (2003). ALMaSS, an agent-based model for animals in temperate European landscapes. Ecological Modelling, 167(1), 65–82. https://doi.org/10.1016/S0304-3800(03)00173-X