## The Kraalingen Approach To Crop Simulation

The crop simulation model considered in this study is the one developed by Kraalingen [Kra95]. This approach uses the rate-state concept of simulation modeling [PL82], Calculations and statements are divided into four categories: Initialization, rate calculations, integration calculations, and the output of results. These calculations are executed sequentially. The simulation starts at the beginning of a time step with a certain value for its state variables; therefore, the initialization step must be performed first. Rate and integration calculations are repeated a certain number of time steps until a termination condition is satisfied. For crop growth, a complete simulation run simulates growth from emergence to harvest. Final calculations and statements are made at the end of a simulation run (e.g., by writing final crop yields to an output file). A detailed description of the model and the FSE (Fortran Simulation Environment) can be found in [BTKOO].

Kraalingen has used a modular approach when each module should:

• Read its own parameters;

• Initialize its own variables;

• Accept variables passed to it from other modules and the environment;

• Pass variables that are computed within the module;

• Own its set of state variables;

• Compute rates of change for its state variables;

• Integrate its state variables;

• Write its own variables as output.

In this model, the effect of temperature on daily plant growth is calculated by the equation:

PT = 1-0.0025((0.25*Tmin+0.75*Tmax)-26**2 Equation 1 where:

PT = temperature based limiting factor, Tmin = minimum daily temperature, Tmax = maximum daily temperature. The plant cycle is divided in two phases: Vegetative and reproductive. The vegetative phase goes on until the plant reaches a genetically determined maximum leaf number [PBJ99]. In the vegetative phase, the delta leaf area index is calculated by equation:

dLAI = SWF A C * PT * PD * EMP\ *dN* (a /(I + a)) Equation 2 where:

dLAI = delta leaf area index, SWF AC = soil water factor, PT = temperature-based limiting factor, PD = plant density, dN = leaf number increase, EMP1 = empirical coefficient for LAI computation, maximum leaf area expansion per leaf, and a is calculated by the equation:

where:

EMP2, nb = coefficients in the expolinear equation, N = plant development stage.

In the vegetative phase, the assimilates are partitioned between canopy and roots whereas in the reproductive phase, all growth occurs in the grain. During the reproductive phase, the difference between daily mean temperature and a base temperature is used to calculate the rate of plant development. Total rate of development towards maturity is accumulated in each step of the simulation [PBJ99].

Our goal is not to make a detailed description of the Kraalingen approach. We are presenting only some of the equations that explain the relationships between simulation elements, plant, soil, and weather. [PBJ99] provide a detailed description of the equations used in this crop simulation model.

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