Using Conditional Containers to Simulate Crop Growing Seasons

 Posted by Jason Lillywhite

Modeling sequential, time-dependent processes lies at the heart of many dynamic simulations. But what happens when the duration of each step is uncertain or changing during the simulation? Consider simulating crop growth stages based on the FAO Irrigation and Drainage paper 56 for modeling crop water demand. Accurately capturing the variability in crop stage durations is important, and ensuring stages trigger correctly using traditional conditional logic can become complex and error-prone under uncertain conditions.  A previous version of the model described here that I built years ago relied heavily on nested IF statements to manage stage transitions. I was always bothered by this implementation, knowing that if the precise duration of each stage wasn't fixed at the simulation start, dynamically ensuring the correct sequence could become extremely difficult to implement reliably.

Screen Capture of the Crop Growing Season Scheduler using Conditional Containers

This post explores how GoldSim's Conditional Containers provide an improved solution. I'll walk through the new version where each growth stage resides in its own Container, dynamically triggered by the completion of the previous one (as shown in the model structure pictured). Discover how this approach not only simplifies the representation of sequential logic but also seamlessly integrates stochastic durations, leading to a more robust, understandable, and maintainable model for Monte Carlo analysis. Read on to see this powerful technique in action! 

This model simulates the daily Crop Coefficient (Kc) for one or more crops throughout their respective growing seasons. The resulting Kc time series can be used, typically by multiplying with Reference Evapotranspiration (ETo), to estimate Crop Evapotranspiration (ETc) for irrigation scheduling or water resource management studies.

The model implements the crop coefficient approach as described in the FAO Irrigation and Drainage Paper 56. It simulates the four standard crop growth stages:

1. Initial Stage: Germination, to 10% ground cover
2. Crop Development Stage: Rapid vegetative growth, increasing ground cover to around 70-80%
3. Mid-Season Stage: Full canopy, maximum ground cover, peak physiological activity, and maximum evapotranspiration
4. Late Season Stage: Maturation and Senescence, fruit ripening, grain filling completion and drying, leaf senescence, general decline

Kc values are user defined, including the initial (Kc_ini), mid-season (Kc_mid), and end-of-late-season (Kc_end) stages.

• Kc remains constant during the Initial (Kc_ini) and Mid-Season (Kc_mid) stages.
• Kc is linearly interpolated between Kc_ini and Kc_mid during the Crop Development stage.
• Kc is linearly interpolated between Kc_mid and Kc_end during the Late Season stage.

A Time History of the Kc for each crop for a single realization

A key feature of this new version of the model is the use of stochastic durations for each growth stage (Dur_Init, Dur_Dev, Dur_Mid, Dur_Final). Instead of fixed average values often cited in literature, durations are sampled from user-defined probability distributions (e.g., Normal). This approach allows the model to represent the natural variability and uncertainty inherent in crop development timing while ensuring robust sequential progression through the stages across multiple simulation realizations (Monte Carlo runs). While conceptually aligned with the FAO 56 framework, this method explicitly incorporates uncertainty in stage length.

GoldSim Implementation using Conditional Containers

This model leverages GoldSim's dynamic simulation capabilities, particularly Conditional Containers, to manage the progression through crop growth stages and calculate the Crop Coefficient (Kc). This containerized approach was adopted specifically to overcome limitations encountered in previous model version. The earlier structure, relying on complex conditional expressions and nested IF statements, made it difficult to robustly manage the sequential dependencies where the start of one stage depends precisely on the end of the previous. This complexity was a barrier to effectively incorporating uncertain (stochastic) durations, as the logic would need to simultaneously evaluate multiple potential stage timings.

Interconnected Conditional Containers representing crop growth stages

Nested IF statements used in the old version of this model, shown for comparison

The Conditional Containers inherently handle these dynamic dependencies. Each of the four growth stages is primarily managed within its own dedicated Container. The Containers are linked chronologically. The activation of each subsequent stage's Container is typically triggered by the Completion_Event or Completion_Status output of the preceding stage's Container. This ensures the correct sequence (Initial -> Development -> Mid -> Late) is maintained dynamically during the simulation.

This containerized, conditional activation approach automatically adapts to the stochastic stage durations sampled for each realization. Since each Container only activates when the previous one signals completion, the model doesn't need to pre-calculate stage end dates and inherently prevents stage overlap issues. Allowing for stochastic representation of the crop stage timing provides a range of curves that appears smooth when viewing the mean of all realizations, as shown below.

Stochastic Time History of Kc for each crop (mean of 100 realizations)

Furthermore, for the Development and Late Season stages requiring linear interpolation, the logic resides within the respective Containers. The interpolation logic can reference the Container's own properties, such as its total scheduled duration (the sampled stochastic value for that realization) and its elapsed active time (the internally available ~Duration property), to calculate the correct interpolation fraction (elapsed active time / total scheduled duration) for determining the daily Kc value.

Conditional Container property "~Duration" used internally

This structure creates a robust and modular simulation where the timing and internal calculations for each stage are encapsulated, allowing for dynamic and interconnected behavior that accurately reflects the sequential nature of crop growth under uncertainty.

Time History of ETc for each crop for multiple seasons