To be able to deal with the ecological diversity of agriculture, three hierarchical levels of crop growth can be distinguished: potential growth, limited growth and reduced growth. Each of these growth levels corresponds to a level of crop production: potential, limited and reduced production.
Reality rarely corresponds exactly to one of these growth/ production levels, but it is useful to reduce specific cases to one of them, because this enables you to focus on the principal environmental constraints to crop production, such as light, temperature, water and the macro nutrients nitrogen (N), phosphorus (P) and potassium (K). Other factors can often be neglected because they do not influence the crop's growth rate.
To be able to deal with the ecological diversity of agriculture, three hierarchical levels of crop growth can be distinguished: potential growth, limited growth and reduced growth. Each of these growth levels corresponds to a level of crop production: potential, limited and reduced production. Reality rarely corresponds exactly to one of these growth/production levels, but it is useful to reduce specific cases to one of them, because this enables you to focus on the principal environmental constraints to crop production, such as light, temperature, water and the macro nutrients nitrogen, phosphorus and potassium.
Potential production: Crop growth is determined by CO2 concentration, irradiation, temperature, plant characteristics and planting date only. Potential production represents the absolute production ceiling for a given crop when grown in a given area under specific weather conditions. It is determined by the crop’s response to the temperature and solar radiation regimes during the growing season. Atmospheric CO2-concentration is assumed to be constant. All other factors are assumed to be in ample supply.
Attainable (Limited) production: In addition to irradiation, temperature and plant characteristics, the effect of the availability of water and plant nutrients is considered. If the supply of water or nutrients is sub-optimal during (parts of) the growing season, this leads to water- and/or nutrient-limited production, which is lower than potential production in terms of total plant biomass. In special cases the water-limited yield (harvestable product) may be higher than potential yield because of more favourable harvest index.
Actual (Reduced) production: At this level, the possible reduction in crop yield by mostly biotic factors like weeds, pests and diseases is taken into account.
WOFOST distinguishes three levels of crop production:
- Potential production: determined by crop variety, planting date, CO2 concentration, radiation and temperature;
- Water-limited production, where water availability limits the potential production; For this purpose several waterbalance modules are available with different degrees of complexity and input data requirements.
- Nutrient-limited production where nutrient availability limits the water-limited production.
Nutrient-limited production in WOFOST can be obtained through the use of the QUEFTS model which is basically a post-processing step of the water-limited production results. The other option is to use the (experimental) module for N/P/K limited growth which simulates plant uptake of N/P/K nutrient and allows to determine the impact of different schedules for nutrient applications during the growing season.
Further reducing factors (weeds, pests, frost and diseases) are not taken into account by WOFOST.
From a spatial perspective WOFOST is a one-dimensional simulation model, i.e. without reference to a geographic scale. However, the size of a region to which WOFOST can be applied is limited. This is due to aggregation effects caused by non-linear response of crop models to model inputs. The non-linear behaviour implies that aggregating input data and then running the model provides different results compared to running the model on the original data and then aggregating the model output.
In practice, this is resolved by splitting the model spatial domain into small spatial units where the model inputs (weather, crop, soil, management) can be assumed constant. Aggregation of simulation results is carried out by aggregating the simulation results for the individual spatial units to larger spatial units. In Europe, WOFOST is typically applied at spatial units of 25x25 km for which scaling errors are negligible.
From a temporal perspective, WOFOST typically simulates crop growth with a temporal resolution of one day.
In WOFOST, crop growth is simulated on the basis of eco-physiological processes. The major processes are phenological development, CO2-assimilation, transpiration, respiration, partitioning of assimilates to the various organs, and dry matter formation. The following paragraphs provide a concise description of the main processes implemented in WOFOST.
Assimilation and respiration
The daily gross CO2-assimilation rate of a crop is calculated from the absorbed radiation, and the photosynthesis-light response curve of individual leaves. This response is dependent on temperature and leaf age. The absorbed radiation is calculated from the total incoming radiation and the leaf area. Daily gross CO2 assimilation is obtained by integrating the assimilation rates over the leaf layers and over the day.
Part of the formed assimilates is used for maintenance respiration of plant organs. The remaining carbohydrates are converted into structural plant material, such as cellulose and proteins (dry matter). There is some net loss of carbohydrates due to this conversion, called the growth respiration. Maintenance respiration is estimated on basis of the dry weight of the different organs and their chemical composition, modified by the ambient temperature.
The order and the rate of appearance of vegetative and reproductive organs characterize crop phenological development. The order of appearance is a crop characteristic, which is independent of external conditions. The rate of appearance can vary strongly, notably under the influence of temperature and photoperiod (day-length).
In WOFOST phenology is described by the dimensionless state variable development stage (DVS). For most annual crops, DVS is set to 0 at seedling emergence, 1 at flowering (for cereals) and 2 at maturity. The development rate is a crop/cultivar specific function of ambient temperature, possibly modified by photoperiod.
To account for the effect of temperature on development stage, the concept of thermal time is applied, sometimes called temperature sum or heat sum. Thermal time is the integral over time of the daily effective temperature (Te) after crop emergence. Te is the difference between the daily average temperature and a base temperature below which no development occurs. Above a certain maximum effective temperature, Te remains constant. DVS is calculated by dividing the thermal time by the thermal time required to pass to the next development stage.
The phenological development of some crops is also influenced by photoperiod. This phenomenon is treated in WOFOST through a photoperiod reduction factor for the development rate until flowering, based on an optimum and a critical photoperiod.
The development stage determines, among other things, the assimilate partitioning over the organs (leaves, stems, roots, storage organs), the specific leaf area and the maximum leaf CO2 assimilation rate.
Transpiration is the loss of water from a crop to the atmosphere. Water loss is caused by diffusion of water vapours from the open stomata to the atmosphere. The stomata need to be open to exchange gasses (CO2 and O2) with the atmosphere. To avoid desiccation, a crop must compensate for transpiration losses, by water uptake from the soil.
In WOFOST, an optimum soil moisture range for plant growth is determined as function of the evaporative demand of the atmosphere (reference potential transpiration of a fixed canopy), the crop group and total soil water retention capacity. Within the optimum range, the transpiration losses are fully compensated. Outside the optimum range, the soil can either be too dry or too wet. Both conditions lead to reduce water uptake by the roots, in a dry soil due to water shortage, in a wet soil due to oxygen shortage. A crop reacts to water stress with closure of the stomata. As a consequence, the exchange of CO2 and O2 between the crop and the atmosphere diminishes, and hence CO2-assimilation is reduced. WOFOST applies the ratio of actual over potential crop transpiration as a reduction factor to the gross assimilation rate.
Partitioning of dry matter
Partitioning is the subdivision of the net assimilates over the different plant organs. After germination, most assimilates are converted into leaf and root tissue and later into stem tissue. The partitioning to root tissue gradually diminishes and is zero if the development stage equals 1 (anthesis in cereals). From then on, the storage organs receive most of the available assimilates.
In WOFOST partitioning is implemented through so-called partitioning tables which describe the fraction of assimilates partitioned to the various organs as a function of the crop development stage. In the calculations, a fraction of the assimilates is assigned to the roots first, the remainder is divided over the above-ground organs (including below ground storage organs such as tubers).
The moisture content in the root zone follows from the daily calculation of the water balance. In WOFOST four different soil water sub models are distinguished (depending on the implementation). The first and most simple soil water balance applies to the potential production situation. Assuming a continuously moist soil, the crop water requirements are quantified as the sum of crop transpiration and evaporation from the shaded soil under the canopy.
The second water balance in the water-limited production situation applies to a freely draining soil, where groundwater is so deep that it cannot have influence on the soil moisture content in the rooting zone. The soil profile is divided in two compartments, the rooted zone and the lower zone between actual rooting depth and maximum rooting depth. The subsoil below the maximum rooting depth is not defined. The second zone merges gradually with the first zone as the roots grow deeper towards the maximum rooting depth. This water balance applies to regional applications with limited information on soil properties.
The third water balance takes into account the impact of different soil layers and the influence of groundwater. This water balance uses a simple but elegant solution to estimate water flow through the soil taking into account both gravitational flow as well flow due to differences in matric suction. It is targeted at making good estimates of crop water availability under conditions when properties of the soil are well known, but without going into the complexity of Richards equation type of soil water models.
Finally, the WOFOST implementation connected to the SWAP model has a detailed water balance including solute transport which allows to make detailed simulations of the behaviour of water and solutes in the soil and its impact on plant growth.
WOFOST is a dynamic, explanatory model that simulates crop growth with time steps of one day, based on knowledge of processes at a lower level of integration. To ensure that the results of the simulation are correct, the different types of calculations (integration, driving variables and rate calculations) should be strictly separated. In other words, first all states should be updated, then all driving variables should be calculated, after which all rates of change should be calculated. If this rule is not applied rigorously, there is a risk that some rates will pertain to states at the current time whereas others will pertain to states from the previous time step.
In WOFOST, the calculations of rates and states are not mixed during a time step but are all executed separately. This is taken care of by grouping all the state calculations into one block as do all the rate calculations for the different components of the model.