The Modelling module allows you to write **dynamic models** consisting of **algebraic and/or (first order) differential equations**. Dynamic models are characterized by the fact that the model variables change over time (or space). This is a property of most biological systems, including plant based systems.

One of the goals of PhytoSim is to make modelling as easy as possible without trying to lose the connection to the mathematics behind the models. As such the PhytoSim Modelling module should be useful to both novice and expert modellers.

- Compilation free modelling: Type your equations and start simulating directly (no intermediate compilation steps required).
- Real-time model syntax checking: Know instantly if you wrote something wrong.
- Real-time unit validation: Check if the units of your equations are consistent.
- Syntax highlighting: Color coded functions, model components for optimal readability.
- Built-in model library: Use one of the built-in models as the starting point for your own modelling work.

More details in the Modelling User Guide.

- Crop Models
**SUCROS1 (Simple and Universal CROp growth Simulator, Version September 1997, SUCROS1_97 v1.0)**- Description:

SUCROS is a mechanistic model that explains crop growth on the basis of the underlying processes, such as CO2 assimilation and respiration, as influenced by environmental conditions.

SUCROS simulates potential growth of a crop, i.e. its dry matter accumulation under ample supply of water and nutrients in a pest-, disease- and weed-free environment under the prevailing weather conditions. The rate of dry matter accumulation is a function of irradiation, temperature and crop characteristics. The basis for the calculation is the rate of CO2 assimilation (photosynthesis) of the canopy. That rate is dependent on the radiant energy absorbed by the canopy, which is a function of incoming radiation and crop leaf area. From the absorbed radiation and the photo- synthetic characteristics of individual leaves, the daily rate of gross CO2 assimilation of the crop is calculated.

Part of the carbohydrates (CH2O) produced is used to maintain the existing biomass. The remaining carbohydrates are converted into structural dry matter (plant organs). In the process of conversion, part of the weight is lost in growth respiration. The dry matter produced is partitioned among the various plant organs, using partitioning factors defined as a function of the phenological development stage of the crop. The dry weights of the plant organs are obtained by integration of their growth rates over time. - Main reference:

J. Goudriaan and H.H. van Laar (1994). Modelling Potential Crop Growth Processes. Textbook with Exercises. Kluwer Academic Publishers, Dordrecht, The Netherlands, 238 pp. (http://www.springer.com/life+sciences/plant+sciences/book/978-0-7923-3219-0)

- Description:

- Irrigation
**Penman-Monteith**- Description:

Implementation of the Penman-Monteith crop evapotranspiration model according to: "Crop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56".

Currently the Reference crop evapotranspiration and the crop evapotranspiration under standard conditions are calculated (using the single crop coefficient approach). The crop evapotranspiration under various management and environmental conditions is not yet implemented, but the model can be easily extended. - Main reference:

http://www.fao.org/docrep/X0490E/x0490e00.htm

- Description:
**Staci**- Description:

The Staci model is a simplified version of the mechanistic water flow and storage model RCGro, developed by Steppe et al. (2006). Is was originally developed for use in the STACI research tool (Software Tool for Automatic Control of Irrigation). This tool was developed to optimally combine continuous plant measurements, mathematical modelling and real-time irrigation scheduling. The RCGro model was simplified to only describe the processes in the stem compartment and uses sap flow measured near the crown as the only model input. - Main reference:

Steppe K., De Pauw D.J.W. and Lemeur R. (2008). A step towards new irrigation scheduling strategies using plant-based measurements and mathematical modelling. Irrigation Science, 26(6), 505-517. (http://dx.doi.org/10.1007/BF00386231)

- Description:

- Plant Physiology
**CarbohydrateSupplyDemand**- Abstract:

Photosynthesis is the limiting factor in crop growth models, but metabolism may also limit growth.We hypothesize that, over a wide range of temperature, growth is the minimum of the supply of carbohydrate from photosynthesis, and the demand of carbohydrate to synthesize new tissue. Biosynthetic demand limits growth at cool temperatures and increases exponentially with temperature. Photosynthesis limits growth at warm temperatures and decreases with temperature. Observations of tomato seedlings were used to calibrate a model based on this hypothesis. Model predictions were tested with published data for growth and carbohydrate content of sunflower and wheat. The model qualitatively fitted the response of growth of tomato and sunflower to both cool and warm temperatures. The transition between demand and supply limitation occurred at warmer temperatures under higher light and faster photosynthesis. Modifications were required to predict the observed non-structural carbohydrate (NSC). Some NSC was observed at warm temperatures, where demand should exceed supply. It was defined as a required reserve. Less NSC was found at cool temperatures than predicted from the difference between supply and demand. This was explained for tomato and sunflower, by feedback inhibition of NSC on photosynthesis. This inhibition was much less in winter wheat. - Main reference:

Gent M.P.N and Seginer I. (2012). A Carbohydrate Supply and Demand Model of Vegetative Growth: Response to Temperature and Light. Plant, Cell & Environment, 35(7), 1274-1286. (http://dx.doi.org/10.1111/j.1365-3040.2012.02488.x)

- Abstract:
**Farquhar**- Description:

Implementation of the photosynthesis model of Farquhar at leaf level.

The model has two input data variables: temperature (°C) and irradiance (umol.m^-2.s^-1). - Main reference:

Farquhar, G. D., Caemmerer, S. and Berry, J. A. (1980). A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta, 149(1), 78-90. (http://dx.doi.org/10.1007/BF00386231)

- Description:
**HydR**- Description:

The model uses the osmotic potential of the perfused solution (Psi_xylem) as an input and links this directly to changes in twig diameter through radial water transport across a radial hydraulic resistance (R_s = 1 / L_p). Water transport out of the elastic bark tissues into the xylem induces changes in bark water content (W_bark) and, hence, bark turgor (Psi_bark_p), causing the twig diameter (D_outer) to shrink accordingly. Measurements of D_outer were used to calibrate the model and estimate L_p. - Main reference:

Steppe K., Cochard H., Lacointe A. and Ameglio T. (2012). Could rapid diameter changes be facilitated by a variable hydraulic conductance? Plant, Cell & Environment, 35(1), 150-157. (http://dx.doi.org/10.1111/j.1365-3040.2011.02424.x)

- Description:
**Penman-Monteith_Tree**- Description:

Model to calculate potential transpiration based on the single-leaf model of Penman-Monteith. By calibrating some of the model parameters, the simulated course of potential transpiration can be made to fit to a measured course of sap flow but not fall below it. - Main reference:

Zweifel, R., Böhm, J. P., & Häsler, R. (2002). Midday stomatal closure in Norway spruce--reactions in the upper and lower crown. Tree physiology, 22(15-16), 1125-36. (http://www.ncbi.nlm.nih.gov/pubmed/12414372)

- Description:
**RCGro**- Description:

RCGro is a model for simulation of sap flow dynamics and stem diameter variations in individual trees.

- Whole-tree leaf transpiration is used as the only input.

- Constant capacitance of the storage tissues (electrical analogue approach).

- Radial stem growth based on Lockhart's equation for irreversible cell expansion.

- Constant soil water potential - Main reference:

Steppe K., De Pauw D.J.W., Lemeur R. and Vanrolleghem P.A. (2006). A mathematical model linking tree sap flow dynamics to daily stem diameter fluctuations and radial stem growth. Tree Physiology, 26(3), 257-273. (http://dx.doi.org/10.1093/treephys/26.3.257)

- Description:
**RCGro2**- Description:

RCGro2 is a modified version of the original RCGro model by Steppe et al. (2006)

Differences with respect to RCGro:

- Whole-tree leaf transpiration and soil water potential are used as model inputs

- Dynamic soil water potential: simple linear factor converting soil water potentials into root water potentials

- No distinction between crown xylem and crown storage water potential

- Calculations of the storage water potentials are based on the ratio of the difference between current and maximal water content of the storage tissue and its capacitance - Main reference:

De Pauw D.J.W., Steppe K. and De Baets, B. (2008). Identifiability analysis and improvement of a tree water flow and storage model. Mathematical Biosciences, 211(2), 314-32. (http://dx.doi.org/10.1016/j.mbs.2007.08.007)

- Description:

- Can't find the model you are looking for?
- Do you know a model you would like to see implemented in PhytoSim?
- Have you implemented a model in PhytoSim that you would like to see distributed with PhytoSim?

Contact **support@phyto-it.com** and, if possible, we will be happy to include it.