The Lingra model

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General description

LINGRA is a crop growth model developed by the former DLO-Winand Staring Centre (SC-DLO) in conjunction with the former Research Institute for Agrobiology and Soil Fertility (AB-DLO), both located in Wageningen and now part of ALTERRA, The Netherlands.

The GRASSLAND GROWTH MODEL - LINGRA (LINTUL GRAssland) was developed to predict growth and development of perennial rye grass across the member states of the EC at the level of potential production and water-limited production. The model is based on the LINTUL (Light INTerception and UtiLisation simulator) concepts as proposed by Spitters (cit. Bouman B. et al., 1996). The main principle of this concept is that crop growth is proportional to the amount of light intercepted by canopy.

The integration level is kept high and the number of processes has been restricted to key parameters, and only a small number of processes involving these parameters are dynamically simulated. On the other hand, parameters that have relatively little impact on crop growth, or which knowledge is scarce, have been treated using a static approach. Common modules with CGMS are: soil water balance and weather parameters (ETP).

In contrast to arable crops, the grassland plants are frequently defoliated due to grazing or management activities. The consequence of defoliation is reduction of photosynthesis rate. After defoliation, new leaves must be formed in order to assure continuation of production. The formation of the new leaves is based on amounts of carbohydrates stored in the stubble of the plant before defoliation. This induces an alternation of the periods with assimilate shortage with periods when the surplus of assimilate is stored. This process is strongly influenced by environmental conditions and cultural practices. Assimilate demand (the sink) is associated with leaves elongation, leaf appearance and tillering rate, where assimilate supply (the source) is controlled by photosynthesis which is depending on the amount of light that is intercepted by canopy.

In LINGRA, the dynamic fluctuation of assimilate demand (ΔWd) and the assimilate supply (ΔWs) are simulated semi-independently. The term “semi-independent” is used because each day, crop-growth rate is estimated from the most limiting process, either ΔWd or ΔWs as driving rate variable. All other state variables are derived from the growth rate at that particular day and are not integrated independently for source or sink limitations. Both hypothetical levels of potential production (depending only on intercepted solar radiation and temperature) and water-limited production are simulated. Soil nutrients are considered to be at optimal level and there is no simulation of mineral nutrition. Also, the effects of pests, diseases and weeds are not taken into consideration.


More information
Bouman et al., 1996: LINGRA-in-CGSM (pdf) .

Main equations LINGRA

Yield formation

The “yield” results from the integration of daily (t) new formed dry matter allocated to “harvestable” organs:

Yield formation lingra.jpg

Intersepted PAR

The quantity of new formed dry matter is dependent on the foliar interception and utilisation efficiency of incoming photosynthetically active radiation (estimated as 50% of global radiation:

Intercepted par lingra.jpg

Leaf area index

PAR interception is depending of existing leaf area index (LAI):

Intercepted par versus lai lingra.jpg

The value for extinction coefficient is taken from the C++ version of LINGRA used in CGMS.

Utilization efficiency

The maximum light utilisation efficiency of intercepted PAR in photosynthesis may be reduced by water stress (estimated by the ratio between actual and potential transpiration), temperatures below Tb2 value (crop and cultivar dependent) and it is also reduced by the high levels of PAR:

Light utilization efficiency lingra.jpg

Leaf elongation

Initial, growth of leaf area after cutting is dependent on the number of tillers that after cutting have a node for leaf elongation. The average width of new leaves is a model parameter (i.e. 0.03 m) and the leaf elongation is described as a function of temperature:

Temperature leaf elongation rate lingra.jpg


The partitioning of the newly formed assimilates is independent from weather the growth is sink or source limited and it is also influenced by water stress:

Transpiration reduction factor lingra.jpg

The two sources of assimilates are the carbohydrates previously stored, and the current photosynthesis. The actual crop growth is the minimum between assimilate demand and assimilate supply. When the assimilates produced by photosynthesis exceed the demand, the difference is stored in carbohydrate pool.

Actual leaves growth is derived from the amount of assimilates available for growth and the death rate of leaves by senescence which is enhanced by internal shading and water stress (Spitters and Schapendonk, 1990). Each tiller produces new leaves and in principle each axil of a leaf contains a bud to produce new tillers. The maximum number of tillers emerging from a bud is considered to be in average 0.69. Just after mowing this number is much less (0.335). This cascade of events is sensitive to light, temperature and stress conditions.