Experimental fields

The farm ‘Katharinentaler Hof’ (48°55′N, 8°42′E, 319 m a.s.l.) is located north of Pforzheim at the southern edge of the Kraichgau. Three research units or ‘eddy-covariance stations’ (RU EC1-3) were outfitted on separate fields (16–24 ha) to record weather and soil conditions at half-hourly resolution, subsequently aggregated to daily values; a detailed description is given in Ingwersen et al. (Reference Ingwersen, Steffens, Högy, Warrach-Sagi, Zhunusbayeva, Poltoradnev, Gäbler, Wizemann, Fangmeier, Wulfmeyer and Streck2011) and Gayler et al. (Reference Gayler, Ingwersen, Priesack, Wöhling, Wulfmeyer and Streck2013). The weather data recorded at experimental fields was used for calibration of the crops grown on them. Winter wheat, silage maize and winter rapeseed were grown on four fields in 2009 and three fields in 2010/2011 as part of normal crop rotations, grown over five, three and two seasons, respectively, to provide bi-weekly or monthly plant development (BBCH 1997) and leaf area index (LAI, 0+) measurements plus intermittent measurements on whole plant and generative biomass partitioned dry weight (DW, kg/ha) and nitrogen (N) concentration (% DW) (Högy et al. Reference Högy, Zörb, Langenkämper, Betsche and Fangmeier2009; Ingwersen et al. Reference Ingwersen, Steffens, Högy, Warrach-Sagi, Zhunusbayeva, Poltoradnev, Gäbler, Wizemann, Fangmeier, Wulfmeyer and Streck2011). Table 1 shows the number of plant measurements provided by field surveys for crop model calibration.

Table 1.

Weather source and number of data sets per observation and crop used for crop model calibration

DW, dry weight.

* Own field observations at research unit (RU) eddy covariance (EC) stations.

† Source: LTZ (2013).

The differences between plot-measured and farmer-reported yields were averaged by crop and taken as a measurement bias to be applied to crop model results. Modelled yields were thus corrected by −19% for wheat, −18% for rapeseed and +4% for maize.

Supplemental data

The German Weather Service maintains a network of both weather (DWD 2012a) and phenological (DWD 2012b) observatories, often in close enough proximity to allow derivation of causal relationships between them (Menzel Reference Menzel and Schwartz2013). The DWD weather station at Eppingen was moved to a nearby location in 2002 and renamed Eppingen-Elsenz. Records from the two stations were merged and deemed to be from one location. Phenological observations indicate the local onset of crop phases, including the artificial ones used below, planting and harvest. The DWD Phenology station at Oberderdingen was chosen because of its location between the experimental fields and Eppingen.

Experimental fields were not sown with summer or winter barley during the period used for calibration so less detailed data, limited to development stage and final crop yield, were taken from Baden-Württemberg state field trial stations as close as possible to the experimental fields (LTZ Augustenberg 2013). One advantage provided by the LTZ data is multiple years of trials using specific cultivars, so that barley cvar Braemar and cvar Lomerit were chosen as representative of spring and winter cultivars, respectively, in the region. Experimental data covering several years were available for spring barley at the Kraichtal site, close enough that soil parameters from a Katharinentaler Hof field and DWD weather from Eppingen were used for calibration. For winter barley, the nearest source of LTZ experimental data was in Boxberg (Fig. 1). For this site, soil data were derived from the Soil Map of the Federal State of Baden-Württemberg (LGRB 1997) and weather data were taken from the nearest station (Bad Mergentheim) with records of each weather variable needed for simulation. The DWD phenological records for spring barley end in 1990, so they were amalgamated with planting and harvest data from various LTZ trials sites for validation 1991–2010. Table 2 gives a statistical summary of locations with sources of data.

Table 2.

Summary statistics (2010/2011) on data source locations

* Sources: own field observations from research unit (RU) eddy covariance (EC) stations.

† DWD (2012a).

‡ LTZ Augustenberg (2013).

‘Shifting’ triggers

A mechanism for shifting triggers was developed so that each day after the start of the planting period, triggers were constantly relaxed to a calibrated degree. It was a daily check whether t: t ≥ base − shift × day for a minimum trigger, or: t ≤ base + shift × day for a maximum trigger, each day during the time window. This can be very restrictive early in the period when only exceptionally favourable combinations of environmental conditions will permit action, and also allow progressively sub-optimal combinations late in the period, facing the risk of late or failed action.

‘Fuzzy’ triggers

Fuzzy logic has already been applied to crop modelling (Wieland et al. Reference Wieland, Mirschel, Nendel and Specka2013). Here, it was implemented as an option for simulating how a farmer determines the suitability of a day for action. The hard logic behind the fuzzy is the existence of a trade-off dynamic among reasons not to work a field, effectively measures of temperature and moisture.

Each trigger is given a base value and a degree of ‘fuzziness’ stipulating the range where the fulfilment of the trigger gradually moves from 0 (impossible) to 1 (perfectly suitable) for an action (Fig. 2). A composite of all triggers is calculated each day and must exceed a given threshold (for the current work: 0·50 or ‘half-perfect’) for action. This composite t* is the geometric mean of the normalized fulfilment t of each fuzzy trigger k and is calculated as:

$${t^{\ast}} = {[\Pi _{k = 0}^n \,{t_k}]^{1/n}}$$

Where t = [υ − (b − f/2)]/f for minimum triggers and t = [b + (f/2)−υ]/f for maximum triggers, n is the number of triggers, b is the minimum or maximum base value for each, f is its band of fuzziness (halved between greater and less than the base) and v is the currently simulated value. All ts are truncated to be between 0 and 1.

Fig. 2.

Membership functions of fuzzy triggers for the planting of winter wheat. (a) Maximum mean daily air temperature, (b) maximum soil moisture (c) maximum 3-day minimum of mean daily air temperature and (d) maximum total daily precipitation. b: Trigger base value, f: fuzziness of trigger (source: own depiction)

This was implemented in FarmActor at daily resolution using the programming language Java. It provides a clear interface to simulated behaviour, an entry point for experiments in actor profiles.

Crop model calibration

Two crop growth models, Genotype-by-Environment interaction on CROp growth Simulator (GECROS) and Crop Environment REsource Synthesis (CERES), were applied separately within Expert-N to provide a broader perspective on the effects of climate on crop performance. Both were calibrated using identical weather data, soil parameters and crop performance observations. See Table 3 for details of soil properties and hydraulic parameters.

Table 3.

Soil properties and hydraulic parameters

* LGRB reference profile DE6517-5 (LGRB 1997).

Both models were iteratively calibrated using UCODE (Poeter et al. Reference Poeter, Hill, Banta, Mehl and Christensen2005). Phenological parameters were optimized first and then, with these fixed, drivers of crop growth and yield formation were calibrated. Default parameters that were not adjusted are available for CERES in Priesack (Reference Priesack2006) and GECROS in Yin & Van Laar (Reference Yin and Van Laar2005).

Dynamic genetics

One of the latest capacities of crop modelling is accounting for the diversity of cultivars (Jeuffroy et al. Reference Jeuffroy, Casadebaig, Debaeke, Loyce and Meynard2014). While technological progress including the breeding of new crop cultivars has been credited with much of the yield increases in recent decades, allowing for this element has been elusive to crop modellers, leading to statistical correction of yields (Ewert et al. Reference Ewert, Rounsevell, Reginster, Metzger and Leemans2005). Further, simulating crop performance over a range of decades with static crop model parameters calibrated to specific years has resulted in failure to capture trends in crop yields and phenology (Aurbacher et al. Reference Aurbacher, Parker, Calberto Sánchez, Steinbach, Reinmuth, Ingwersen and Dabbert2013). Thus, one of the areas for improvement in crop modelling is a process-based way to account for the evolution of genotypes. To demonstrate how this can improve model accuracy, trends in some genetic parameters interpreted by the crop models were incorporated.

The genetic contribution to increased wheat and barley yields over recent decades has, through extensive cultivar trials, been largely attributed to grain number per ear (Ahlemeyer & Friedt Reference Ahlemeyer and Friedt2012) so that breeding has resulted in an increase of around 0·15 grains/ear/year between 1966 and 2007. However, Ahlemeyer & Friedt (Reference Ahlemeyer and Friedt2012) also showed complementary improvements in disease resistance as a result of breeding. Further, technological and climatic factors, including atmospheric CO₂ fertilization, have contributed to yield trends (Lobell et al. Reference Lobell, Schlenker and Costa-Roberts2011). This precludes an exaggerated use of dynamic grain number to match observed historic yields.

Based on yield sensitivity, the initial leaf N content in GECROS was used to create a trend in simulated winter rapeseed yields. Another option would be to adjust thousand kernel weight, since its genetic advance has been well documented (Ali et al. Reference Ali, Javidfar, Elmira and Mirza2003; Marjanović-Jeromela et al. Reference Marjanović-Jeromela, Marinković, Ivanovska, Jankulovska, Mijić and Hristov2011).

Silage maize yields in Karlsruhe District show only a slight upward trend (+0·067 t/year) between 1981 and 2010. Phenological records at Oberderdingen however, show the start of local maize harvest trending later by 1·35 days/year. Bassu et al. (Reference Bassu, Brisson, Durand, Boote, Lizaso, Jones, Rosenzweig, Ruane, Adam, Baron, Basso, Biernath, Boogaard, Conijn, Corbeels, Deryng, De Sanctis, Gayler, Grassini, Hatfield, Hoek, Izaurralde, Jongschaap, Kemanian, Kersebaum, Kim, Kumar, Makowski, Müller, Nendel, Priesack, Pravia, Sau, Shcherbak, Tao, Teixeira, Timlin and Waha2014) propose that adaptation to greater cumulative temperatures in future growing seasons are likely to include the selection of later-ripening maize cultivars. This can be realistically achieved in simulations with an annual increase in the temperature requirement for the crop's juvenile stage, evidence for which has been established in German maize (Estrella et al. Reference Estrella, Sparks and Menzel2007).

Calibration of field management

Adaptive crop management in the face of global change could mean the difference between increasing and decreasing future yields, varying by crop (Leclère et al. Reference Leclère, Jayet and de Noblet-Ducoudré2013). To track historic climatic adaptation by local farmers and consequently project the same into the future, FarmActor conducts daily integration of Expert-N with database soil and weather records and internal management decision-making. Sensitivity analysis of simulated wheat yields produced by the coupled models during simulation years 2001–2010 showed a 370 kg/ha increase when planting a week earlier compared with a 121 kg/ha decrease when planting a week later than the average simulated planting date. Respective equivalents were: for winter barley, 47·8 and 1·0 kg/ha; spring barley, 114 and 142 kg/ha; oilseed rape, 342 and 449 kg/ha and silage maize, 131 and 323 kg/ha. FarmActor's dynamic crop rotation (Aurbacher & Dabbert Reference Aurbacher and Dabbert2011) was omitted to simplify the extraction of annual performance measures of each crop and to determine planting and harvest dates based on daily crop, soil and weather conditions, in addition to learning. Ten-year moving averages of soil temperature for spring crops and cumulative air temperature for winter crops were used to represent farmer learning from historic weather (Aurbacher et al. Reference Aurbacher, Parker, Calberto Sánchez, Steinbach, Reinmuth, Ingwersen and Dabbert2013). To accommodate the lack of crop rotation, soil nutrient values were reset each year.

The simulated farmer, in seeking to maximize crop yield and minimize risk, has an inevitably simplified set of criteria for each action, crop and field. Field-specific soil properties determine the moisture level corresponding to a favourable response to action, and that at which traffic and tillage can be withstood without the long-term damage of compaction (Rotz & Harrigan Reference Rotz and Harrigan2005). Recent and immediate weather determine soil moisture and are themselves direct criteria for action, varying with crop-specific temperature requirements.

Use of a genetic algorithm to calibrate management

The proper specification of action triggers is crucial for the functioning of the model. Although they are based in principle on expert knowledge, there remains a certain range of reasonable settings. The goal was to set the triggers such that the model optimally reproduced observed actions of farmers. To systematically apply the information from observations to trigger settings a genetic algorithm was used with a (μ + λ) evolutionary strategy, according to Schöneburg et al. (Reference Schöneburg, Heinzmann and Feddersen1994), where all former generations are retained.

Functioning of the genetic algorithm proceeded as follows (see also Fig. 3): The first step was to define the possible range for each action-specific trigger based on agronomic principles. A population of potential values was created by assigning a number of intervals within the possible range to each trigger. The resultant population size was the product of the number of intervals of the different triggers. In the first iteration, the population was generated by choosing the centre of each interval within each trigger range (with one interval the value was at midpoint of the range, two intervals gave values at one and three quarters, three intervals at one-sixth, half and five-sixths, etc.). The model was then run for all population members and a fitness function evaluated upon completion. Root Mean Squared Error (RMSE) in days between observed and modelled action dates was used as the measure of fitness. Additionally, for every simulated year in which a combination of triggers resulted in a failed planting (by being too restrictive) a ‘penalty’ of 10 days was added to the RMSE to lead the algorithm away from that solution. The members of the population (trigger set) were then ranked according to fitness and if identical fitness values arose the rank was assigned randomly. The penalty ensured that population members with failed runs always ranked behind completely successful runs.

Fig. 3.

Schematic representation of genetic algorithm for calibration of management action triggers (source: own depiction).

Next a propagation probability function was used to assign to each member of the population the likelihood that it would be one of the starting points of the following iteration. The function used was:

$$p(r) = \displaystyle{{3{{(n + 1 - r)}^2}} \over {{n^3}}}$$

where p is the assigned probability, n is the size of the population and r is the rank of each population member (1 being the best, n the worst). This quadratic function assigned the probability 3/n to the first-ranked member (equal to a multiplication of the ‘fair chance’ 1/n by the factor 3) and the probability 3/n ³ (slightly larger than zero) to the one deemed of worst fitness. About 0·60 of the population members were assigned a value lower than fair chance while those remaining were privileged.

A new population of the same size was drawn from the preceding population using the assigned probabilities. Members of the new population were not exact copies of their ‘ancestors’, as ‘mutation’ occurred. Each trigger parameter was modified by adding a normally distributed random number with a pre-defined standard deviation. The standard deviation employed was reduced by the factor 0·9 in each successive iteration.

The model was re-run with the new generation of parameters, evaluated and successively propagated with respect to fitness rank. Members of previous iterations were not discarded but also included in the ranking and selection process of further iterations.

The parameter bounds, interval number and standard deviation used to find optimum values for each trigger were the same for winter wheat, barley and rapeseed, likewise for spring barley and maize. These values are given in Supplementary Table 1 (available from: http://journals.cambridge.org/AGS).

A drawback of this approach was the need to run the model repeatedly, resulting in a potentially long calibration time. To calibrate planting criteria, a population of 12 trigger sets was run for ten iterations from 1981–2010 for winter wheat, winter rapeseed and maize, establishing learning (expectations) for the first 10 years and comparing simulated planting dates during 1991–2010 to phenological observations at Oberderdingen. This left the years 1981–1990 at Oberderdingen available for validation of simulated planting of these crops. Summer and winter barley were likewise run from 1971–1990, calibrating to the latest available phenological observations at Oberderdingen and Helmstadt, respectively, while validation for spring barley depended on state field trial records.