The Wofost model
Heart of the CGMS is the crop growth model Keulen and Wolf, 1986; van Diepen et al., 1988; van Diepen et al., 1989; Hijmans et al., 1994). WOFOST is a simulation model for the quantitative analysis of the growth and production of annual field crops. It is a mechanistic model that explains crop growth on the basis of the underlying processes, such as photosynthesis, respiration and how these processes are influenced by environmental conditions.(
With WOFOST, you can calculate attainable crop production, biomass, water use, etc. for a location given knowledge about soil type, crop type, weather data and crop management factors (e.g. sowing date). WOFOST has been used by many researchers over the World and has been applied for many crops over a large range of climatic and management conditions.
The model computes the instantaneous photosynthesis, at three depths in the canopy and for three moments of the day. These instant values are integrated over the depth of the canopy and over the day light period to achieve daily total canopy photosynthesis. After subtracting the maintenance respiration, assimilates are partitioned over roots, stems, leaves and grains as a function of the development stage of the crop. The development stage is calculated by integrating the daily development rate, described as a function of temperature. Assimilates are then converted into structural plant material taking into account growth respiration. The accumulation of dry matter and it's distribution over roots, stems, leaves and grains are simulated from sowing to maturity on a hectare basis.
The CGMS simulates two situations: potential and water-limited. The potential situation is defined by temperature, day length, solar radiation and crop parameters (e.g. leaf area dynamics, assimilation characteristics, dry matter partitioning, etc.). For this situation the effect of soil moisture on crop growth is not considered and a continuously moist soil is assumed. In the water-limited situation soil moisture determines whether the crop growth is limited by drought stress. Therefore a soil water balance is calculated that applies to a freely draining soil, where groundwater is so deep that it does not influence the soil moisture content in the rooting zone.
In both situations optimal supply of nutrients is assumed and damage caused by pests, diseases, weed and/or extreme weather events is not considered. To save disk space the results onlevel are only saved for the last day of a decade.
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.
Crop growth is determined by irradiation, temperature and plant characteristics 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, crop management, radiation and temperature;
- Water-limited production, where water availability limits the potential production.
- Nutrient-limited production where nutrient availability limits the water-limited production
However, nutrient-limited production in WOFOST but is not implemented in a biophysical way (see section 2.1.2 of the WOFOST manual). Nutrient-limited production is obtained through post-processing of the water-limited production results. Further reducing factors (weeds, pests, frost and diseases) are not taken into account in WOFOST.
Temporal and spatial scale
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 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 or 50x50 km for which scaling errors are negligible.
From a temporal perspective, WOFOST typically simulates crop growth with a temporal resolution of one day. Some versions of WOFOST still support dekadal (10-daily) or monthly time-steps, but given the general availability of daily weather data nowadays, this option is hardly used anymore and may be dropped in future versions of WOFOST.
Crop growth simulation
Assimilation and respiration
The daily gross CO2-assimilation rate of a crop is calculated from the absorbed radiation (Ia), 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. Because photosynthesis responds to light intensity in a non-linear way, variation in radiation level have been taken into account.
|Variation in radiation|
|One kind of variation occurs in the canopy along the vertical plane, because upper leaves receive more light than lower leaves. This is accounted for by dividing the canopy in different leaf layers. The intercepted radiation by each leaf layer is calculated on the basis of the radiation flux at the top of the canopy and the transmission by overlying layers. On the basis of the photosynthesis-light response curve for individual leaves, the assimilation of each leaf layer is calculated. The variation in the horizontal plane, e.g. the effect of plant rows, is not accounted for.
The second kind of variation is temporal, caused by the daily cycle of the sun. On a clear day, the radiation level at the top of the canopy equals the solar constant multiplied by the sine of the angle between the sun and the earth’s surface:
The canopy reflects part of the PAR. The reflection coefficient is a function of solar elevation, leaf angle distribution, and reflection and transmission properties of the leaves. The complementary fraction is potentially available for absorption by the canopy. Radiation flux decreases more or less exponentially with increasing leaf area within the canopy. This is described by the equation below.
The extinction coefficient is radiation (direct or diffuse) specific and a function of solar elevation, leaf angle distribution and the scattering coefficient of individual leaves (Spitters et al., 1989).
The decline in radiation flux is a measure for its adsorption by the leaf layers. This can be described by the equation below, obtained by taking the derivative of the previous equation with respect to L.
The instantaneous assimilation rate of a leaf layer can now be described by equation:
The calculations on light interception and assimilation as performed by WOFOST proceed along these lines but are more complex. You are referred to Supit et al. (1994) for the exact description. Both ε and Am in equation 2-4 are temperature-dependent. k, Ρ and Am are crop specific. Generally, Am of C4 crops are higher than that of C3 crops (Penning de Vries et al., 1989). This is illustrated in the figure showing the photosynthesis-light response curves of individual leaves for a C3 (barley) and a C4 (maize) crop with an Am of 35 and 60 kg • ha-1 • h-1, respectively and both with ε of 0.40 kg • ha-1 • h-1 • (J • m-2 • s-1)-1. Measured at 340 vvpm CO2 and Am at optimum temperatures and ε at a low temperature (data from Penning de Vries et al., 1989).
Daily gross CO2 assimilation is obtained by integrating the assimilation rates over the leaf layers and over the day.
|For the integration over the day, a sinusoidal course of incoming radiation over the day is assumed and a three-point Gaussian integration method is applied as described by Goudriaan (1986).
In CO2-assimilation, or photosynthesis, CO2 is reduced to carbohydrates (CH2O) using the energy supplied by the adsorbed light:
CO2 + H2O → CH2O + O2
Part of the formed assimilates is used for maintenance respiration. 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 (roughly 0.01-0.03 g • g-1) (Penning de Vries, 1975; Penning de Vries et al., 1989).
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) (Van Keulen and Van Diepen, 1990).
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 (Van Keulen and Van Diepen, 1990).
To account for the effect of temperature on development stage, the concept of thermal time is applied, sometimes called temperature sum or heat sum (see e.g. Ritchie, 1991a). Thermal time is the integral over time of the daily effective temperature after crop emergence. The daily effective temperature is the difference between the daily average temperature and a base temperature below which no development occurs. The development stage is calculated by dividing the thermal time by the thermal time required to pass to the next development stage.
To calculate the time between sowing and emergence of a crop, WOFOST uses an additional set of thermal time variables. 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). 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.
|Formula's and graphs|
|The formula's and graphs of effective temperature, development, photoperiod reduced development and partitioning are explained in this section.
Te equals (T - Tbase)
In the formula all temperatures are expressed in °C. Te is non-negative. Above a certain maximum effective temperature Tmax,e, Te remains constant. Between Tmax,e and Tbase, the daily increase in thermal time is obtained by linear interpolation. The figure is an example of the relation between daily average temperature (°C) and daily increase in the thermal time (°C • d) for the calculation of the development stage of a crop with a Tbase of 8 °C and Tmax,e of 27 °C.
DVS equals ∫Te/Treq
Photoperiod reduced development stage
Fpr equals (P - Pc)/(P0 - Pc)
The figure below is an example of the relation between Fpr and P for a short-day crop (with a P0 of 10 hours and Pc of 12 hours) and for a long-day crop (with P0 of 12 hours and Pcof 10 hours).
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). To initiate the simulation, the dry weight (kg•ha-1) and the leaf area index [m2•m-2 or ha•ha-1] of the crop at emergence must be known. From the outset of crop growth, the supply of assimilates to the leaves determines the increase in leaf area, calculated by multiplying the dry matter weight of the leaves (kg•ha-1) with specific leaf area (ha•kg-1). However, leaf area expansion may be limited by the maximum daily increase in leaf area index (i.e. a maximum rate of cell division and extension), that is temperature dependent. The increase in leaf area leads to a higher (potential) light interception, and, consequently, to a higher potential growth rate. This leads to exponential crop growth, that lasts until nearly all light is intercepted (leaf area index ≥ 3). From then on, the growth rate is constant, until the leaf area and its photosynthetic capacity decrease because of senescence of the crop.
In the figure below an example is presented of dry matter allocation to the above-ground organs in relation to development stage (barley in the Netherlands, simulated).
Soil water balance
The moisture content in the root zone follows from the daily calculation of the water balance. In WOFOST three 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 can not 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 rooting depth rooting depth is not defined. The second zone merges gradually with the first zone as the roots grow deeper.
The third water balance is for water-limited production on soils having influence of shallow groundwater in the rooting zone. The principles are similar to the freely draining situation. Different is that the soil moisture retention capacity is determined by the depth of the groundwater, as is the percolation rate. There is capillary rise if the rooted soil dries out. The groundwater level can be controlled by artificial drainage and the moisture content within the root zone does not vary with depth.
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 ration of actual over potential crop transpiration as a reduction factor to the gross assimilation rate.
|The reduction of CO2-assimilation is quantified assuming a constant ratio of transpiration to gross assimilation. This is done according to equation below, were the assimilation rate is the product of the potential assimilation rate and the ratio of the actual (water-limited) transpiration rate and the potential transpiration rate (Van Keulen and Wolf, 1986).
The potential transpiration rate depends on the leaf area and the evaporative demand of the atmosphere. The evaporative demand is characterised by radiation level, vapour pressure deficit and wind speed. In WOFOST, potential transpiration is calculated according to the Penman formula (Penman, 1948), adapted according to Frère and Popov (1979). The potential transpiration is calculated for a reference crop. Differences between crops can be accounted for with a correction factor, having a value of 1.0 for most crops. A plausible range for this factor is 0.8 for water saving crops and 1.2 for crops spending relatively much water. The ratio between the actual and potential evapotranspiration indicates to which extent the crop suffers from drought. This ratio Ta/Tp is effected by the soil moisture as shown in the figure below.
The dashed line represents either a more drought resistant species under the same field conditions, or the same species under a lower evaporative demand, caused by different weather conditions (Penning de Vries et al., 1989; van Laar et al., 1992).
Between the critical soil moisture content (θcr) and field capacity (θfc), the ratio is 1, allowing potential transpiration. Outside this range, the ratio is smaller than 1, leading to reduced transpiration. At the permanent wilting point (θwp) and at the saturation point (θst) transpiration and hence crop growth, come to a halt. The θwp, θfc and θst are related to the Soil Physical Groups. The θcr depends on crop type and weather. A combination of high evaporative demand and drought-sensitive crops lead to high values of θcr. A crop’s drought-tolerance is indicated with a soil depletion number, within the range of 1.0 for drought-sensitive crops and 5.0 for drought tolerant crops (van Keulen and Wolf, 1986; Doorenbos et al., 1979).
The soil moisture is calculated by running a soil water balance that applies to a freely draining soil, where groundwater is so deep that it does not influence 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 rooting depth is not defined. The second zone merges gradually with the first zone as the roots grow deeper. The maximum rooting depth is determined by the crop type and by the depth to which the soil allows root growth. The principle of the soil water balance is a cascade (overflowing bucket). The rainfall infiltrates, a part may be temporarily stored above the surface or runs off. Evapotranspiration loss is calculated. The infiltrated water that exceeds the retention capacity of a soil compartment percolates downward. The required soil parameters rooting depth, AWC and infiltration capacity are described in the section 'soil data used in the CGMS'. The latter two relate only to one soil compartment: the rooting zone.
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).
Implementation of crop dynamics
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 allexecuted 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. When looking at the WOFOST model code, the separate execution of initialization, rate calculation and state updates is governed by the value of the ITASK variable (1=initialization, 2=rate calculation, 3=state update, 4=finish).