Sensitivity types.

The average yield (avy_farm) determines the location of sgy in the yield distribution and allows for the identification of comparative performance between farms for a given crop. We can argue that when avy_farm > avy_region for a given crop, the farmer’s yield distribution and the processes underlying the result are likely to be favorably skewed. This reasoning is based on the assumption that climatic influences are comparable throughout the relatively uniform Kraichgau study region and production conditions, such as the availability of inputs are assumed to be relatively homogenous throughout this region.

If a farmer declares sgy to exceed avy_farm, despite avy_farm being higher than avy_region, the farmer can be considered to be more sensitive to yield for a particular crop as opposed to a farmer that declares his sgy below avy_farm.

A sensitivity type in this context is thus identified by two conditions with regard to a given crop: first, determine if sgy is above or below avy_farm; second, compare the individual average performance of a crop at the farm level avy_farm to the individual avy_farm.

Simulations.

Before the simulation model is able to assess climatic impacts, based on the ARS methodology, the model must be provided with information about what level of mid-season variability is acceptable. The ARS methodology is exemplified using the empirically elicited average sgy from the Kraichgau sample, 69.17 dt/ha (Table 1), to scale the boundaries of the acceptance ranges in the simulation model.

Acceptance ranges for inter-temporal crop conditions embody the experience of a farmer in crop production. This experience pertains to a certain range of tolerable fluctuations in growth patterns from a downside risk perspective at a given point in time during the growing season. To initialize these ranges, it was necessary to simulate a reasonable number of “historical” growing seasons to accumulate an experience pool for the simulated farmer.

To create a knowledge pool, FarmActor’s crop management routine was overridden in order to compile a comprehensive set of simulated agro-ecological states (crop biomass, soil moisture, etc.) arrived at through what-if scenarios using an array of day-of-year (DOY) starting points (sowing dates). A standard production procedure was used for these model runs, and input levels for fertilization were kept constant. All wheat-specific actions, apart from planting (three fertilization applications, harvesting, and preparation of fields; Fig 1) were governed by their existing weather and plant-growth-dependent trigger arrays [32] and [38]. A range of plausible starting points for winter wheat growth processes for the Kraichgau region extends from DOY 283 to 324 (early-mid October to mid-late November) [38]. The later the simulated DOY for sowing, through the associated growth-process simulation, the less likely the yields will be acceptable or greater than sgy, thus justifying the maximum in the sowing DOY chosen for simulation. For each of the 46 DOY, a time series of 30 years (1983–2013) was modeled. This produced “historical” growth processes for each weather year and resulted in 1,380 permutations of the annual growth processes for winter wheat.

Data from the modeled growth processes were then used to initialize the acceptance ranges of all observation points used to monitor the growth processes. A season’s first observation point is the sowing date, OP 0 (see Fig 1). The acceptance range for OP 0 (sowing) is described by the relative frequency in which a DOY led to a yield ≥ sgy (average sgy for the Kraichgau region 69.17 dt/ha (Table 1)) throughout the historical time frame. This value is the ratio of desired to total yield outcomes compiled over all simulation years (n = 30) and stems from that particular sowing DOY. The higher the relative success frequency of a DOY, the more often a yield ≥ sgy is observable in the 30-year times series with this DOY as a starting point, and consequently, the more suitable a DOY is for sowing.

For crop surveillance after sowing, at OP 1 through 7, ten observable field parameters are used for monitoring to give a complete picture of crop response to external influences: aboveground biomass and generative biomass (kg/ha); leaf area index (LAI); crop development stage (BBCH) (BBCH-scale [55]); soil water content at 20, 50 and 120 cm depths (% volume); and soil temperature at 5, 20 and 50 cm depths (°C). The crop development stage is used indirectly; it is incorporated into the decision triggers of the simulation management routine to ensure that observations each year are made at a comparable stage of crop development (compare [32]).

Mid-season indicators of forthcoming yields, or OP 1 to 7, are based on simulated growth processes, however, not all modeled values for a given parameter could serve as a reference for an economically interpretable observation. The base of 1,380 data points for each OP parameter was reduced to those in which the corresponding final yield did not fall below the downside-risk threshold, i.e., the average sgy for the Kraichgau region, 69.17 dt/ha (Table 1). The results represent the farm actor’s “knowledge” that has accrued over a 30-year time-span. These data provide a simulated knowledge base to generate expectations about crop response to seasonal variability, with reference to a yield benchmark, which implies agronomic utility.

Because the states of physical growth processes are compiled as observational data, it is important to determine acceptance ranges that cover a wide range of outcomes to prevent the model from being too sensitive to fluctuations. When plotting the data with boxplots, the limits for each observation point parameter were set at the whiskers of selected point-specific outcomes for a given parameter. The outliers represent a result of rare combinations of plant response and environmental conditions that still resulted in a yield ≥ sgy and were thus excluded. The outliers are data points that lie below the first quartile minus 1.5 times the inter quartile range (x_0.25−1.5 IQR) or above the third quartile plus 1.5 times the inter quartile range (x_0.75 + 1.5 IQR). Whiskers are assigned to the next inner data points, which are not considered outliers. Boxplots were calculated with STATA [56]. We examined the result of the data extraction further to test whether it made any difference in our acceptance ranges when all 1,380 data points were plotted. The acceptance ranges were consequently much greater in both directions.

Acceptance ranges.

Table 2 gives an overview of all acceptance ranges we obtained from extracting simulation data for all OPs in winter wheat production in the Kraichgau using the FarmActor model.

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Table 2. Observation trigger ranges for winter wheat production in the Kraichgau region for the production years 1983–2013 and 10 observation parameters throughout 7 observation points; average regional sgy level: 69.17 dt/ha (Table 1); weather data from Eppingen station (see details [32]).

https://doi.org/10.1371/journal.pone.0181954.t002

Acceptance ranges represent tolerable fluctuation during the growth process from a downside-risk point of view. The values between the boundaries are not ranges that indicate the optimal state. The upper boundaries of the acceptance ranges, therefore, can be more than twice the value of the lower boundary, especially in the earlier observation point ranges. The later the observation point is, the closer the boundary values are. After initialization, the attained acceptance ranges with farmers’ revealed preferences for yield fluctuations are used to test and exemplify the approach. Thus, in the next section, the knowledge pool based on past climatic impacts is used to test how changes in future climatic conditions can be perceived by the model farmer using the ARS methodology.

Application to future climate.

Future simulations for winter wheat production in the Kraichgau were performed using the coupled FarmActor-Expert-N models forced with simulated future climate in the form of daily weather parameters in ten realizations (25002–00 and 25002–99) of WETTREG 2010 future scenarios [57], corresponding to the German Weather Service [58] weather station at Eppingen (Kraichgau study site) and based on the IPCC scenario A1B [59]. For each WETTREG future realization, the model simulated a 20-year (2014–2034) time series for winter wheat with only one standard production procedure each year on a representative field [32]. FarmActor’s management routine was not manipulated in this case. These ten time series, each with 20 years of future growth processes, were then used to comprehensively test the methodological approach. All growth processes were evaluated with the ARS mechanism by comparing them to their acceptance range at each observation point (OP 0–7) to conduct a comparative analysis and investigate the performance of the proposed approach under diverse climatic conditions.

As described above, observations outside the acceptance ranges are assigned a binary utility value of 1 (0 otherwise). At the end of each year, from evaluating all observations made during the production season, the ARS is compiled. With 10 observation parameters and 7 observation points (OP 1 to OP 7) plus OP 0 for planting, a maximum score of 71 is possible for a year. OP 0 is related to the desirability of a given DOY for planting. If its relative frequency of yields ≥ sgy is less than 0.5, that is to say, if more than half of the time the harvest is disappointing, this observation is assigned a value of 1. Thus, if planting is forced to a day (through weather-dependent trigger conditions) that has a relative frequency value less than 0.5, then OP 0 is assigned a value of 1 for that production year.

Results of future climate simulations.

The results of this investigation are displayed in a comparative static context in Table 3, in which the results are further refined into a mean-standard deviation approach.

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Table 3. Simulated yield statistics for over 20 years, 2014–2033, using 10 WETTREG future realizations for Eppingen weather station.

https://doi.org/10.1371/journal.pone.0181954.t003

The mean-standard deviation analysis provides an overview of how each of the ten future WETTREG weather realizations affects winter wheat production based on a standard production procedure. All ten realizations were used to avoid any bias in a single realization based on their statistical nature and to examine a range of possible outcomes using the sgy approach.

At a sgy level of 69.17 dt/ha, the results for the WETTREG-forced winter wheat production in the Kraichgau can be interpreted from a risk point of view as follows. Realizations 44 and 55 show the second lowest yield standard deviation (4.72 dt/ha, Table 3) for all future weather years. The standard deviation of ARS scores for the same realizations is noticeably higher than its counterparts. For realization 55, the standard deviation of all ARS scores is the third highest, although the yield standard deviation is the second lowest in the mean variance comparison. The relative frequency is also relatively favorable, at 0.85 (Table 3) for realizations 44 and 55. Thus, for 85% of the 20-year yield time series, a yield ≥ sgy of 69.17 dt/ha could be achieved. This finding represents favorable skewness for a decision-maker who sets his economic profitability yield threshold at this level. However, when taking a farmer´s mid-season assessment into account, those future production years are characterized by relatively large deviations from the modeled acceptance ranges. This result gives an indication that farmers often experience anomalous winter wheat performance sometime during the season, even in favorable years with a yield ≥ sgy.

The additional information provided here for the analysis is that a farmer’s mid-season observations are often ambiguous regarding what yield can be expected at a harvest [25, 45].

A different picture is drawn with realization 99. For such a projection of future climatic conditions, a mean-variance analysis at yield level illustrates the same issue as the ARS methodology, in which the highest mean of ARS scores corresponds to the highest standard deviation of ARS scores. The mean yield is among the lowest, and the standard deviation is the highest. Low yields that are traceable to a problematic climate at the 69.17 dt/ha sgy level show how mean-variance analysis at a yield level leads to the same conclusions as the ARS methodology. Farmers’ knowledge of crop-response patterns to climatic influences holds true and leads to accurate expectations regarding their yields.

The picture drawn with realization 11 in Table 3 is most interesting. The mean-variance analysis shows a completely different picture than the ARS methodology. This realization led to one of the highest standard deviations (16.26 dt/ha) in yields and a relatively low mean yield (68.61 dt/ha) (Table 3), close to the average sgy level for the Kraichgau region (69.17 dt/ha, Table 1). However, the mean ARS score is at 4.05 (Table 3), which is not among the highest scores achieved over all future climate realizations. This finding indicates that conditions were not unfavorable throughout the studied growing season but rather single events were responsible for the production outcomes in this time series of winter wheat yields.

How acceptance ranges can adapt.

As a consequence of evaluating inter-temporal production outcomes, the following implications are possible for the perception mechanism in the simulation model: (1) no consequence and (2) a shift in the acceptance range. These implications can be the consequence of three possible scenarios. First, an observation value is within the acceptance range and a yield higher than or equal to the sgy is achieved; then, the entire process can be assessed as having gone as expected for a given parameter value. The observed value from the now past production year is included in the distribution of observation points that constitute the observation parameters’ acceptance ranges for the upcoming year without causing a shift of the range. Second, if an observed value is outside the acceptance range and a yield lower than the sgy is achieved, the observation parameter range for the upcoming year is not affected since this was an expected yield loss considering the set loss threshold (sgy). The third consequence is that observational fluctuations lie outside the acceptance range but do not result in negative consequences for the acceptance ranges because a yield above the sgy threshold is achieved. In that case, the observation is collated as a non-downside-risk value for the distribution of observations for a given parameter. However, depending on the amplitude of the fluctuation, a shift in the acceptance range may occur. When such outliers accumulate, they will add to a shift in the acceptance range that changes the expected performance of a given crop in its response to climatic (and management) influences. The larger the amplitude of the deviating value is, the longer it will most likely remain among the outliers that are excluded during the initialization process for the acceptance ranges in the model. Many outliers over several years in a row—again, depending on the learning mechanism—may indicate that a crop is quite difficult to cultivate at a given location. This can occur even though the simulated farmer annually adapts production procedures while also responding to daily environmental conditions.

ARS scores in that context should be used as a constraint.

The constraint should be modeled as follows: (3) were f = field and c = crop;

ARS_0,c = the reference ARS score for the current year (the latest year for which observations are available) of all fields that have been allocated with a crop c [60].

= the expected ARS score for an activity (i.e., crop) as explained in the following. The ARS score for an activity should not be lower than the expected ARS score for an activity. Otherwise, certain fields should no longer be planted with a certain crop, or management options need to be evaluated in the model, which would provide an improvement in the production process.

The expected ARS score () of crop c in year t is the average ARS score of past production processes for a certain crop in a farmer’s fields. How the average ARS score is calculated is subject to how learning is modeled and thus past observations are weighted, a topic left for future research. Learning depends on the weighting of past observations and if-then rules [24], which lead to consequences for the farm agent´s decision-making in bio-economic models.

Overall, the sgy approach is designed to provide a more comprehensive understanding of the drivers of farm planning decisions by explicitly modeling how farmers monitor production. Only when such underlying processes are better represented in more up-scaled bio-economic simulation models [62, 63] can deterministic statements about the climatic impact on agricultural production and land-use decisions be improved, as stated by White et al. [16].

Future research should aim to attach different valuations and learning patterns to this suggested mechanism and thus gain a more realistic and less assumption-driven understanding of farmers’ climate change perceptions and adaptation responses in their land-use decisions [62]. This approach may even assist in diminishing over- and underestimations of the rate of adaptation, which many models show through strong behavioral assumptions despite the high degree of complexity and level of detail of the approach [13–16, 33].