WWDM model

WWDM as an agronomic model

WWDM (Winter Wheat Dry Matter) is a dynamical model with 2 equations and 2 state variables.


Above ground biomass : U(t+1) = U(t) + Eb * Eimax * ( 1 - e^(K * LAI(t)) ) * PAR(t)

Leaf area index : LAI(t) = Lmax * ( 1 / ( 1 + e^(-A*(ST(t)-TI)) ) - e^(-B*(ST(t)-Tr)) )

with : Tr = (1/B) * log(1+e^(A * TI)) , U_1 = 0 , LAI_1 = 0

Input variables

  • PAR(t) : photosynthetically active radiation
  • ST(t) : cumulative degree day


Eb Radiation use efficiency g/m^2 1.85 0.9-2.8
Eimax Max ratio of intercepted to incident radiation   0.94 0.9-0.99
K Coefficient of extinction   0.7 0.6-0.8
Lmax Maximal value of LAI   7.5 3-12
TI Temperature threshold degre C 900 700-1100
A Coefficient of LAI increase   0.0065 0.0035-0.01
B Coefficient of LAI decrease   0.00205 0.0011-0.0025

WWDM as a model of the Record platform

The WWDM model has been developed as an agronomic model of the Record platform, and so as a vle model.

Simulator, model, models repository

The WWDM model is the vle model named ‘wwdm’. This model (also called a vle package) contains some simulators (also called vpz files). The simulator that will be used in this example is the ‘wwdm.vpz’ simulator of the ‘wwdm’ model.

In the ‘wwdm.vpz’ simulator, the crop model of the ‘wwdm’ model is coupled with a climate series reader model of another vle model, the ‘meteo’ model. The model for weather (of ‘meteo’ model) reads climatic datas contained in a file. It provides to the crop model (of ‘wwdm’ model) datas for RG (Global Radiation), Tmin (minimal daily temperature) and Tmax (maximal daily temperature), from which the crop model computes PAR and ST.

The ‘wwdm.vpz’ simulator is part of the ‘wwdm’ model. The ‘wwdm’ model (and its ‘meteo’ model dependency) are distributed by the Record platform into its record models distribution http://recordb.toulouse.inra.fr/distributions/1.1. This distribution of the Record platform corresponds in erecord with the ‘recordb’ models repository.

Thus the ‘wwdm.vpz’ simulator, that belongs to the ‘wwdm’ model, is going to be used by relying on the ‘recordb’ models repository of erecord.

WWDM into erecord databases

For more about the erecord databases, see Databases.

The erecord databases contain some available models repositories, their models, and their simulators. A simulator can be recorded into the erecord databases as a VleVpz that is attached to a model recorded as a VlePkg that is attached to a models repository recorded as a VleRep.

In our example case, the ‘wwdm.vpz’ simulator is attached to the ‘wwdm’ model that is attached to the ‘recordb’ models repository. The erecord databases contain in particular :

  • the ‘recordb’ models repository (VleRep, vle rep)
    • the ‘wwdm’ model (VlePkg, vle pkg, vle package, agronomic model)
      • the ‘wwdm.vpz’ simulator (VleVpz, vle vpz, vpz file, simulator)


The simulator of the example is ‘wwdm.vpz’. It belongs to the ‘wwdm’ model that is hosted by the ‘recordb’ models repository.