Development and Evaluation of a Leaf Disease Damage Extension in Cropsim-CERES Wheat

Developing disease models to simulate and analyse yield losses for various pathogens is a challenge for the crop modelling community. In this study, we developed and tested a simple method to simulate septoria tritici blotch (STB) in the Cropsim-CERES Wheat model studying the impacts of damage on wheat (Triticum aestivum L.) yield. A model extension was developed by adding a pest damage module to the existing wheat model. The module simulates the impact of daily damage on photosynthesis and leaf area index. The approach was tested on a two-year dataset from Argentina with different wheat cultivars. The accuracy of the simulated yield and leaf area index (LAI) was improved to a great extent. The Root mean squared error (RMSE) values for yield (1144 kg ha−1) and LAI (1.19 m2 m−2) were reduced by half (499 kg ha−1) for yield and LAI (0.69 m2 m−2). In addition, a sensitivity analysis of different disease progress curves on leaf area index and yield was performed using a dataset from Germany. The sensitivity analysis demonstrated the ability of the model to reduce yield accurately in an exponential relationship with increasing infection levels (0–70%). The extended model is suitable for site specific simulations, coupled with for example, available remote sensing data on STB infection.


Introduction
Wheat (Triticum aestivum L.) is the second most important staple food crop for human nutrition.It is grown worldwide on approximately 220 million hectares under different climatic conditions.It is projected that wheat production must increase by 1.6% annually to meet the expected global demand by 2050 [1].However, increasing temperatures and changing global rainfall patterns will likely influence breeding, management, fertilization and crop protection strategies for wheat [2] and also influence disease patterns [3,4].Hence, crop protection measures will play an important role under future climate change, as rising temperatures and changes in rainfall pattern, will cause more favourable conditions for pests and diseases, especially in the warming north, where wheat production is predominant [2].
On a global scale, there are approximately 50 diseases and pests, which have the potential to damage wheat and reduce farmer's income [5][6][7].On a global level, the most widely adapted wheat fungal diseases are leaf rust caused by "Puccinia triticina E.," stripe rust caused by "Puccinia striiformis W.," stem or black rust caused by "Puccinia graminis E.," powdery mildew caused by "Blumeria graminis P." and septoria tritici blotch (STB) caused by "Zymoseptoria tritici D." [1].The infection by "Zymoseptoria tritici D." is the most economically damaging wheat disease worldwide [8].It can cause yield reductions of 50% to 60% [9] by creating leaf lesions resulting in defoliation and reduced photosynthesis.It has been estimated that 70% of the annual usage of fungicides in Europe is related to the treatment of this disease [10].
During the past decade, there has been an increasing resistance of STB to azole and strobilurin fungicides in Europe [9][10][11].Breeding for STB disease resistance is complicated, due to the variability of the pathogen reproduction cycle [12,13].Researchers have studied different strategies including tillage, crop rotation, delayed sowing, fungicide application and a proper level of fertilizer application to reduce or control the infection of STB [14].It appears that moderate fungicide application coupled with the right amount of fertilizer is a strategy that holds promise for environmentally friendly wheat production, while reducing at the same time STB infection.
Crop models are suitable for decision support and contribute to a better understanding in the development of new wheat production strategies.They can play a vital role in understanding plant growth processes, the impact of different weather scenarios as well as management strategies on disease outbreak, final yield and grain quality.Hence, crop models might help to spread the production of wheat in more economic and sustainable ways.
Crop models can also provide an insight into yield losses due to pests and diseases, including STB.Several mechanistic wheat crop growth models have been developed over the last several decades, including APSIM [15], WheatGrow [16], STICS [17], Sirius [18] and DSSAT [19].These models were developed to study crop-environment interaction and to evaluate optimum management strategies.
The Cropsim-CERES-Wheat (CCW) model [20][21][22] included in the DSSAT version 4.6 [23] was developed to study the impact of genetics, management, weather and climate change on wheat growth and yield.The model simulates daily plant development based on daily maximum and minimum temperature, daylength and vernalisation requirements.Growth is computed on a daily basis using a radiation use efficiency approach.Carbon is allocated daily to different plant parts based on the development stage.The CCW model has been linked with remote sensing data [24] and was successfully tested with different cultivars, soil characteristics as well as in different climatic conditions including Canada [25], Argentina [26], Southern Italy [27] and the United Kingdom [28].Currently the CCW model does not account for damage due to weeds, pests or diseases [29].As a consequence, inaccurate simulations of crop growth and yield result when simulating datasets that include pests and diseases [30,31].
Developing and incorporating a disease damage extension would expand the use of the CCW model to simulate and study the impact of disease damage on crop growth and yield.Batchelor et al. [32] incorporated a pest damage into the CROPGRO [33] family of models distributed with the DSSAT [34].In their approach, they defined pest coupling points as daily rate and state variable modifiers to simulate the impact of daily pest damage on leaf, stem, seed, shell and root state variables and daily photosynthesis rate based on daily inputs of pest damage.They tested this approach for different pest damage types for peanut and soybean crops.They evaluated this approach using a dataset to simulate the impact of velvetbean caterpillar on soybean.
Using the same approach, the purpose of this work was to: (i) develop a disease model extension for the simulation of STB in wheat, to (ii) evaluate the model performance using a dataset from Argentina; and (iii) to conduct a sensitivity analysis for the impact of different disease progress curves on leaf area index and yield using a dataset from Germany.

Model Development
Currently the CCW model does not account for competition with weeds, pests or diseases.To solve this problem, modifications of the current CCW version are necessary to include the impact of leaf diseases on final crop yield.
Plant dry matter accumulation and yield can be expressed as a function of leaf area index (LAI), radiation use efficiency and the loss of assimilates due to respiration.Pathogens can modify both leaf area index and daily photosynthesis [35].
The primary damage resulting from STB is defoliation, which reduces both leaf area and leaf photosynthetic rate [36,37].
To apply the damage theory, it was necessary to integrate the pest damage module [32] structure into the current CCW wheat model (Figure 1).These changes included the adding and linkage of the following subroutines to the original version: PEST.for,LINDM.for,PESTCP.for,VEGDM.for and OPPEST.for.A pest damage definition file was created to define the coupling point "leaf area" for the leaf disease STB (Figure 1), where daily damage could be applied to state and rate variables in the model.Percent cumulative leaf area destroyed (PCLA) was chosen as major coupling point in the model.

Model Development
Currently the CCW model does not account for competition with weeds, pests or diseases.To solve this problem, modifications of the current CCW version are necessary to include the impact of leaf diseases on final crop yield.
Plant dry matter accumulation and yield can be expressed as a function of leaf area index (LAI), radiation use efficiency and the loss of assimilates due to respiration.Pathogens can modify both leaf area index and daily photosynthesis [35].
The primary damage resulting from STB is defoliation, which reduces both leaf area and leaf photosynthetic rate [36,37].
To apply the damage theory, it was necessary to integrate the pest damage module [32] structure into the current CCW wheat model (Figure 1).These changes included the adding and linkage of the following subroutines to the original version: PEST.for,LINDM.for,PESTCP.for,VEGDM.for and OPPEST.for.A pest damage definition file was created to define the coupling point "leaf area" for the leaf disease STB (Figure 1), where daily damage could be applied to state and rate variables in the model.Percent cumulative leaf area destroyed (PCLA) was chosen as major coupling point in the model.Field observed damage levels were entered in the time series file, referred to as File T in the DSSAT family of models.In this file, the year and day of year (DOY) are entered, along with STB infection in percent.Observed disease infection was linked to the percent cumulative leaf area destroyed (PCLA) coupling point.This damage type (i.e., PCLA) is defined in the pest damage definition model input file, which links field observed damage type and levels to the internal model pest damage coupling point.The model uses a linear interpolation to compute daily damage from periodic field observations.In this work, it was assumed that STB infection began ten days before the first infection symptoms were observed in the field.This assumption was made, based on Sánchez- Field observed damage levels were entered in the time series file, referred to as File T in the DSSAT family of models.In this file, the year and day of year (DOY) are entered, along with STB infection in percent.Observed disease infection was linked to the percent cumulative leaf area destroyed (PCLA) coupling point.This damage type (i.e., PCLA) is defined in the pest damage definition model input file, which links field observed damage type and levels to the internal model pest damage coupling point.The model uses a linear interpolation to compute daily damage from periodic field observations.In this work, it was assumed that STB infection began ten days before the first infection symptoms were observed in the field.This assumption was made, based on Sánchez-Vallet et al. [38] who reported a latent period for STB between day 8 and 14 after infection depending on the environmental conditions.The daily percentage of damage (N pt ) was calculated between field observations using N pt = daily reported damage for damage type p at time t; D pt = DOY of next field observation of damage (P rt ); D pt* = DOY of previous field observation of damage (P rt* ); D s = day of current simulation; P rt = damage level reported in the next field observation; P rt* = damage level reported in the previous field observation.The daily damage calculation, which was applied to the leaf area coupling point (P it ) is calculated in the PESTCP.for subroutine (Figure 1) by Equation (2): The pest coefficient (C ip ) allows the model to convert units of damage into units used for the model state or rate variable that is being damaged.
After calculating the daily damage to be applied to the diseased leaf area based on interpolations from field observations, the daily damage (D ipt ) to be applied to the leaf area state variable (defoliated leaf area) is calculated by the following equation:  The trial in Argentina was conducted in two consecutive years (2010 and 2011) and published by Castro and Simón [39].The objective of this trial was to test the tolerance of ten different Argentinean wheat cultivars (Triticum aestivum L.) for STB and to evaluate the disease impact on grain yield and grain quality.The sowing dates were on 15th of July in 2010 and 16th of June in 2011.The soil type was a silty loam.Nitrogen was applied as urea at 100 kg N ha −1 at sowing and 80 kg N ha −1 at the end of tillering.Three different inoculation levels with Zymoseptoria tritici D. were performed.The first level was the control treatment, the second was considered to be a low inoculation level (with 5 × 10 5 spores mL −1 suspension), while the third treatment was considered as high inoculation treatment (5 × 10 6 spores ml −1 suspension).All inoculations were performed at growth stage 22 (beginning of tillering) [40] and at growth stage 39 (flag leaf emergence).For model development weather data (daily temperature, rainfall, solar radiation) from the weather station La Plata (34 • 56' S, 57 • 57' W), disease severity ratings (%) from three growth stages (GS 39, 60, 82), leaf area index (LAI) which was calculated from the green leaf area (GLAI) plus non-green leaf area (NGLAI), yield, soil properties and management information were collected.
The second trial in Germany was conducted in 2006 using the cultivar Monopol with three inoculation levels (control treatment; low inoculation 50%; high inoculation 100%) of Zymoseptoria tritici.Inoculation was imposed by spraying 50% or 100% of a spore suspension (1 × 10 6 spores per mL, strain CBS 292.69) onto the plots at growth stage 32 [41].The sowing date was 22nd of October 2005 on a silty clay soil.Nitrogen in form of ammonium nitrate was applied at three growth stages: 100 kg N ha −1 at GS 30, 80 kg N ha −1 at GS 32 and 40 kg N ha −1 at GS 49.The objective of this field trial was to use different vegetation indices to determine the occurrence of plant diseases in winter wheat (Triticum aestivum L.).For model sensitivity analysis, data including temperature, rainfall and solar radiation from the weather station Ihinger Hof, as well as growth stages, yield monitoring data, disease severity ratings and the LAI at growth stages GS 31, 34 and 49 were collected.Further information on the trial layout can be found in Gröll [41].

Model Calibration and Evaluation
The modified CCW model extension was incorporated into the DSSAT 4.6 software.Model inputs were created for both datasets from Argentina and Germany.The dataset from La Plata of 2010, which included phenological, yield, soil data (Table 1) and weather data, was used for calibration to test the ability of the model to simulate the impact of STB on wheat growth and yield.Genetic coefficients for growth and development were calibrated using the 2010 dataset and the control treatment for each cultivar.Calibration was performed by sequentially adjusting the genetic coefficients (Table 2) to minimize the error between measured and simulated values [19].The existing species file was set as default and the existing ecotype UKWH01 as well as the cultivar file were modified.Coefficients for phenological development (P1V, P1D, P1-P5 and PHINT) were calibrated in the first step, followed by crop growth coefficients (G1, G2 and G3).The RMSE, index of agreement (d-Index) and modelling efficiency (EF) statistics were used to assess the quality of the calibration (see section statistical evaluation).After calibration of individual cultivars, the percentage infection with STB of the low and high inoculation was applied to test the model response.The dataset from La Plata of 2011 was used for model validation.The second dataset from Ihinger Hof was used for sensitivity analysis to test the model on a different location to proof the concept and to test the responsiveness of the model of different STB infection levels.The calibration was performed in the same way as in La Plata with the control treatment by modifying the necessary cultivar coefficients (Table 2).We applied 0%, 10%, 20%, 30%, 50% and 70% damage rates at maximum LAI (GS 39) and started the damage application at growth stage GS 31 to estimate the corresponding yield loss.The different damage rates were used to test the model responsiveness on a broad disease range, which typically starts to impact yield after growth stage 31 [42].

Statistical Evaluation
The statistical model evaluation was conducted by comparing the simulated and observed LAI and yield of the different inoculation treatments (dataset from La Plata).
For statistical analysis, the root mean squared error (RMSE.Equation ( 5)), the index of agreement (d-Index, Equation ( 6)) [43] and the modelling efficiency (EF, Equation ( 7)) were used.The RMSE was used to quantify the amount of variation between simulated and measured values on a metric scale.The d-Index shows if the model is under -or over-estimating the measurements.The EF parameter compares simulated values with the average of the measurements.For a perfect fit between simulated and observed data, the RMSE should be at 0 and the d-Index and EF parameter should have a value of 1.0.
The statistical evaluation was done for simulation runs of the original CCW version and the modified CCW for LAI and yield from both years (2010; 2011) on the location La Plata over all cultivars and inoculation treatments.
Root mean square error (RMSE): Index of agreement (d): Modelling efficiency (EF): where: O i = observed values; S i = simulated values; n = numbers of samples; O = mean of observed data

Leaf Area Index
The calibration was performed on the 2010 dataset by fitting the relevant genetic coefficients (Table 2) for phenology and growth.One essential prerequisite for model development is an accurate simulation of growth stages.In this study, growth stages (GS 39; GS 60; GS 82) were predicted by the model conclusively: For all ten cultivars the flowering date (GS 65) was documented approximately 110 days after sowing (DAS), the model simulated this growth stage 115 DAS.A similar result was obtained by comparing observed and simulated DAS of the early dough stage (GS 82) (observed approximately at 131 DAS, simulated 132 DAS).
The main focus of this model calibration was on the adjustment of leaf area as a major coupling point for disease damage.Figures 2 and 3 illustrate the simulated and the observed values for leaf area index and grain yield across different inoculation treatments along with the statistics (Table 3).For demonstration of the overall model behaviour in regard to LAI changes induced by three different STB inoculation treatments over time, the wheat cultivar K. Chaja was selected.This cultivar was considered to be highly susceptible to STB infection [39].Figure 4a shows the impact of disease infestation on LAI according to different inoculation treatments 90 days after sowing.All three simulation runs reached the maximum LAI at day 100.For the control treatment a maximum LAI of 3.5 was simulated.A difference of 0.5 LAI was found between the control and the high-inoculation treatment.Comparing simulated and observed LAI values, the model predicted the LAI over the vegetation period in an accurate manner (RMSE 0.47, d-Index 0.9).
Similar results are displayed in Figure 2a-c, which illustrates the simulated versus observed LAI across three different inoculation treatments for different cultivars.Regardless of susceptibility, in GS 39 all ten cultivars showed a homogenous distribution of all data points around the 1:1 line with no strong outliers.A slight tendency for an overestimation of LAI was given at GS 39 in the low and high inoculation treatments, whereas for the control treatment a slight underestimation was shown over all cultivars.In GS 60 and GS 82, a slight overestimation of LAI was found for all inoculation treatments.
Finally, the modified CCW model (RSME 0.69; d-Index 0.51) performed better compared to the original CCW model (RSME 1.19; d-Index 0.33), as indicated by the corresponding statistics.Outliers in Figure 2a-c can be explained by the LSD ranging from 0.4 to 1.0 depending on the sampling date, reported from Castro and Simón [39].
Nevertheless, the model was able to account for all ten cultivars representing different tolerance levels to STB at different growth stages and disease severities accurately.For demonstration of the overall model behaviour in regard to LAI changes induced by three different STB inoculation treatments over time, the wheat cultivar K. Chaja was selected.This cultivar was considered to be highly susceptible to STB infection [39].Figure 4a shows the impact of disease infestation on LAI according to different inoculation treatments 90 days after sowing.All three simulation runs reached the maximum LAI at day 100.For the control treatment a maximum LAI of 3.5 was simulated.A difference of 0.5 LAI was found between the control and the high-inoculation treatment.Comparing simulated and observed LAI values, the model predicted the LAI over the vegetation period in an accurate manner (RMSE 0.47, d-Index 0.9).
Similar results are displayed in Figure 2a-c, which illustrates the simulated versus observed LAI across three different inoculation treatments for different cultivars.Regardless of susceptibility, in GS 39 all ten cultivars showed a homogenous distribution of all data points around the 1:1 line with no strong outliers.A slight tendency for an overestimation of LAI was given at GS 39 in the low and high inoculation treatments, whereas for the control treatment a slight underestimation was shown over all cultivars.In GS 60 and GS 82, a slight overestimation of LAI was found for all inoculation treatments.

Yield
A reduction in LAI after infection with STB also leads to a reduction in yield (Figure 5a).Yield formation started for the cultivar K. Chaja (Figure 5a) on day 122 and was negatively correlated with the inoculation treatment.Yield of the control treatment (3800 kg ha −1 ) was slightly underestimated and the high inoculation treatment (3400 kg ha −1 ) showed a slight overestimation.Figure 3a represents the observed versus the simulated yield for all ten cultivars and showed a dense clustering of the different inoculation treatments around the 1:1 line.Overall, it indicated the highest simulated yield for the control and the lowest yield for the high inoculation treatment.The results illustrated the capability of the modified CCW model to account for disease damage.This is expressed in the statistical evaluation (Table 3), where a reduction of the RMSE from 1144 (original version) to 499 (modified version) was observed.The d-Index also underlined these findings, which increased from 0.47 (original version) to 0.81 (modified version).Finally, the modified CCW model (RSME 0.69; d-Index 0.51) performed better compared to the original CCW model (RSME 1.19; d-Index 0.33), as indicated by the corresponding statistics.Outliers in Figure 2a-c can be explained by the LSD ranging from 0.4 to 1.0 depending on the sampling date, reported from Castro and Simón [39].
Nevertheless, the model was able to account for all ten cultivars representing different tolerance levels to STB at different growth stages and disease severities accurately.

Yield
A reduction in LAI after infection with STB also leads to a reduction in yield (Figure 5a).Yield formation started for the cultivar K. Chaja (Figure 5a) on day 122 and was negatively correlated with the inoculation treatment.Yield of the control treatment (3800 kg ha −1 ) was slightly underestimated and the high inoculation treatment (3400 kg ha −1 ) showed a slight overestimation.

Yield
A reduction in LAI after infection with STB also leads to a reduction in yield (Figure 5a).Yield formation started for the cultivar K. Chaja (Figure 5a) on day 122 and was negatively correlated with the inoculation treatment.Yield of the control treatment (3800 kg ha −1 ) was slightly underestimated and the high inoculation treatment (3400 kg ha −1 ) showed a slight overestimation.Figure 3a represents the observed versus the simulated yield for all ten cultivars and showed a dense clustering of the different inoculation treatments around the 1:1 line.Overall, it indicated the highest simulated yield for the control and the lowest yield for the high inoculation treatment.The results illustrated the capability of the modified CCW model to account for disease damage.This is expressed in the statistical evaluation (Table 3), where a reduction of the RMSE from 1144 (original version) to 499 (modified version) was observed.The d-Index also underlined these findings, which Figure 3a represents the observed versus the simulated yield for all ten cultivars and showed a dense clustering of the different inoculation treatments around the 1:1 line.Overall, it indicated the highest simulated yield for the control and the lowest yield for the high inoculation treatment.The results illustrated the capability of the modified CCW model to account for disease damage.This is expressed in the statistical evaluation (Table 3), where a reduction of the RMSE from 1144 (original version) to 499 (modified version) was observed.The d-Index also underlined these findings, which increased from 0.47 (original version) to 0.81 (modified version).
The modification of the existing CCW showed very good results in LAI and yield simulation (Table 3).It indicated a clear improvement for all statistical parameters compared with the existing CCW included in the current DSSAT version.The calibration successfully minimized the error between measured and simulated data for both, LAI and yield.

LAI
Illustrating LAI (Figure 2d-f) and yield (Figure 3b) for the cultivar K. Chaja and all cultivars in the validation year 2011.
In 2011, a maximum LAI of 6.3 was observed in the control treatment for K. Chaja (Figure 4b) at day 120.The model simulated a maximum LAI of 6.2 for the control treatment on the same day.For the low-inoculation treatment, a maximum LAI of 4.7 was observed, whereas the model simulated a maximum LAI of 5.8.Regarding the highest inoculation treatment, a LAI of 4.6 was observed in the field experiment.The model simulated for the same treatment a maximum LAI of 5.7.The model was capable to simulate the maximum LAI for the control treatment exactly but it slightly overestimated the maximum LAI both for the lowest and highest inoculation treatment.
In general LAI was higher in 2011 than in 2010 independent of cultivars, growth stages and inoculation treatments (Figure 2).For 2011 and GS 39, the 1:1 plot showed no strong outliers and a slight overestimation for the control treatment and a slight underestimation for the highest inoculation treatment.This can be caused by an earlier onset of disease in the inoculated treatments which was not reported and cause a slightly underestimation in the model.For GS 60 and GS 82 the model predicted the observed LAI values accurately.

Yield
Yield formation started 140 days after sowing for K. Chaja (Figure 5b), while full maturity was reached on day 165.A maximum yield of 6000 kg ha −1 was reached in the control treatment compared with the lowest yield of 5400 kg ha −1 in the high inoculation treatment.The corresponding error bars of the measured values were met by the simulated curves, which indicated a high accuracy of the simulation.Under consideration of all cultivars and inoculation treatments (Figure 3b) data points scattered around the 1:1 line on a broader range compared to the calibration (Figure 3a).An inverse relationship between inoculation level and yield was shown (Figure 5).
Overall, the developed model extension was able to account for STB disease damage.This is also shown by the statistics (Table 3), where a 30% improvement of the RMSE in the modified CCW version was achieved compared with the original model.This improvement was also shown by the d-Index and EF values.Further, the calibration showed a higher model accuracy when compared with the validation.Jing et al. [44] and Attia et al. [45] also reported a slightly weaker simulation accuracy regarding the validation dataset.
For 2010, a 20 days shorter growing period due to a 30 days later sowing date and a 130 mm lower precipitation compared to 2011 [39] was reported.Both factors resulted in a reduction of LAI and yield in 2010.Despite these differences the model performed very well for each inoculation treatment and showed its robustness when growing conditions differ between years.Measured yields in the inoculation treatments were simulated quite accurately, while the measured mean value of the control showed a 5% off-set.An explanation for this offset might be given in the way the disease ratings were performed and represented in the model.The model used the mean values from the disease ratings of all repetitions and did not represent each individual plot.It is also possible that the trials had a slight infection of other diseases, which were not measured and caused a slight model offset.Another conceivable reason is the defined onset of disease ten days before disease rating was reported.This assumption was made because of the reported latent period for STB between day 8 and 14 after infection from Sánchez-Vallet et al. [38].
For 2010 and 2011, the d-Index values of the original CCW version are in a similar range for both LAI and yield.In the developed model extension, the d-Index, which represents the model accuracy, increased strongly even though in different intensities for each year.This may point to one possible shortcoming of the current model extension, as it does not account for spore disposal [46].Spore disposal model use different leaf layers, rain intensity thresholds, droplets, sporulation and concentrations of starting spore pools and can therefore extend the simulation accuracy further.
Nevertheless, other STB models show a strong performance, if a minimum dataset is provided, in which more inputs like leaf wetness are included [47] or in which the initial state of infection of the first leaves is known [46].Magarey et al. [47] also reported the necessity of hourly weather data for many disease models.In previous datasets this information is not given [48] and they cannot be used for disease modelling, which is literally a loss of information for agricultural decision making.This clearly shows the advantage of the developed CCW extension, in which only the percentage of disease rating, weather-and soil data is needed as a minimum dataset.This leads to a more accurate simulation as shown in Table 3 and makes the CCW applicable for a broader use.

Sensitivity Analysis
In order to test the general responsiveness of the developed model extension, a sensitivity analysis was carried out by comparing different inoculation treatments with the corresponding disease infections [41].The model was calibrated by using an independent dataset with disease infections from Germany [41].The disease infections varied between 4%, 13% and 15%.Disease infection started in GS 31 (DAS 200).Figure 6a  increased strongly even though in different intensities for each year.This may point to one possible shortcoming of the current model extension, as it does not account for spore disposal [46].Spore disposal model use different leaf layers, rain intensity thresholds, droplets, sporulation and concentrations of starting spore pools and can therefore extend the simulation accuracy further.Nevertheless, other STB models show a strong performance, if a minimum dataset is provided, in which more inputs like leaf wetness are included [47] or in which the initial state of infection of the first leaves is known [46].Magarey et al. [47] also reported the necessity of hourly weather data for many disease models.In previous datasets this information is not given [48] and they cannot be used for disease modelling, which is literally a loss of information for agricultural decision making.This clearly shows the advantage of the developed CCW extension, in which only the percentage of disease rating, weather-and soil data is needed as a minimum dataset.This leads to a more accurate simulation as shown in Table 3 and makes the CCW applicable for a broader use.

Sensitivity Analysis
In order to test the general responsiveness of the developed model extension, a sensitivity analysis was carried out by comparing different inoculation treatments with the corresponding disease infections [41].The model was calibrated by using an independent dataset with disease infections from Germany [41].The disease infections varied between 4%, 13% and 15%.Disease infection started in GS 31 (DAS 200).Figure 6a   In the next step an artificial disease infection level of up to 70% was applied (Figure 6b) to test the general responsiveness and the boundaries of the developed model and to test the leaf damage theory on the leaf area coupling point (PCLA).
In Figure 6a   In the next step an artificial disease infection level of up to 70% was applied (Figure 6b) to test the general responsiveness and the boundaries of the developed model and to test the leaf damage theory on the leaf area coupling point (PCLA).
In Figure 6a a maximum LAI of 7.3 was reached 40 days after GS 31 in the control treatment.LAI increased almost linearly from day 200 to day 240 before the onset of senescence led to a constant decrease in LAI up to final harvest date.For the depicted disease infection scenarios of 10%, 20%, 30% and 50 % a maximum LAI of 7.3, 6.2, 5.4, 4.6, 2.9 and 1.3 was reached at day 240 (Figure 6b).The 70% disease infection scenario showed that a maximum LAI of 2.0 was reached earlier at 220 DAS (Figure 6b).Due to the massive destruction of leaf area, a shortage of assimilate production occurred, which affected in a next step the growth of new leaves.Simulated LAI reduction for maximum LAI in the different disease levels followed the magnitude of 12.5 % (10% diseased LAI), 24.8% (20% diseased LAI), 37.1% (30% diseased LAI), 60.3% (50% diseased LAI) and 82.4% (70% diseased LAI) (Table 4).Table 4 shows the corresponding yields of the applied and measured disease infection levels.The maximum observed yield obtained with the disease infection level of 4% was 4409 kg ha −1 .Higher disease infection levels (13%; 15%) resulted in lower yield (3934 kg ha −1 ; 3965 kg ha −1 ).Simulated yield decreased gradually with higher infection levels.The control treatment resulted in a maximum yield of 4384 kg ha −1 , while the 70% disease infection level resulted in a total grain yield of 2380 kg ha −1 which corresponded to a 45.7% yield reduction.Over all tested disease infection levels, the simulated yield reduction followed an exponential shape, indicating that yield reductions became more severe and are more than doubled at higher disease infection levels.An exponential relationship between yield loss and disease infection was also shown by King et al. [49].
Comparing simulated and measured yield, the model showed a slightly underestimation for the 4% level and a slight overestimation for the 13% and 15% disease infection level.These variations are in an acceptable range.
Regarding the accuracy of the current simulation, similar results for yield reduction based on the occurrence of leaf diseases are reported by Ziv and Eyal [50].Ziv and Eyal [50] tested different inoculation treatments in different spring wheat cultivars and reported yield losses of up to 53% at a disease infection of 73%.The developed CCW model extension gave comparable results to a previous study of Bhathal et al. [51] also at lower infection level scenarios.Bhathal et al. [51] tested different inoculation treatments in wheat to evaluate the relationship between disease infection and yield.Notably, they showed an onset of the disease as it was used in the sensitivity analysis of this study, at GS 31 and demonstrated a 10% yield loss due to a natural disease infection of 26%.King et al. [49], also confirmed this model theory on an independent dataset from the United Kingdom carried out at four different locations.Similar observations and an exponential yield loss curve due to STB disease were obtained.In addition, a yield loss of 30% by a disease infection of 55.1% as well as a yield reduction of 8% by a disease infection of 14.5% occurred.This confirmed the model theory and clearly showed the capability to simulate leaf disease infection with STB by using the coupling point leaf area (PCLA).

Future Model Applications
Despite the good simulation results, the developed model concept can currently only be used for STB.The concept was not tested on other wheat diseases like stripe rust caused by "Puccinia striiformis W.," stem or black rust caused by "Puccinia graminis E." or powdery mildew caused by "Blumeria graminis P." It can be assumed that this concept will also work for other diseases, by changing the pest coefficient in the pest file to account for different damage types.Bastiaans [52] showed a ß-value for STB, which represents the correlation between visible affected leaf area and the affected photosynthetic rate.A ß-value > 1 indicates a stronger effect on photosynthetic rate as it visually appears.For STB this value is close to 1 wherefore the pest coefficient in the CCW model extension was set to 1. Bastiaans [52] reported a ß-value of 8.7 for "Erisyhe graminis" or 1.3 for "Puccinia recondita" in winter wheat.It is assumed, that the pest coefficient has to be increased in a similar manner but it has to be proven by real data.However, the structure of the model extension is set up in a flexible way and has the possibility to be transferred to other leaf diseases.
Further, the disease extension routine can suite as a gateway between crop models and remote sensing data, like it was published by Thorp et al. [53].Thorp et al. [53] showed an improvement of simulation results by updating the plant leaf area state variable with green LAI generated by remote sensing.This offers the opportunity to simulate a given field on a site-specific scale, which means the CCW model extension can be updated by the percentage diseased leaf area detected by for example, remote sensing.In this way, the model could serve as decision support tool to give farmers an economic advise on a field level as Ficke et al. [54] proposed.

Conclusions
In this study a disease extension for the CCW model was developed to simulate the damage effect of STB disease on LAI and yield in wheat.The model was tested successfully in a sensitivity analysis on a German dataset and on a dataset obtained from La Plata, Argentina.Results of the study clearly showed the effect of the implementation of the coupling point "PCLA" and on the corresponding LAI and yield for different locations.For the location La Plata, the obtained simulation results of the modified CCW model indicated a higher model accuracy which almost doubled and clearly showed an improved model behaviour.Especially for the cultivar K. Chaja, the CCW model extension showed a high modelling accuracy.The LAI and yield were simulated very accurate in both years.Furthermore the sensitivity analysis also displayed the flexibility of the CCW model extension to account for disease damage over a broad range between 0 and 70% of STB disease infection.
Nevertheless, further research is needed to test the developed model on other leaf diseases like leaf rust, powdery mildew or stripe rust in wheat.The model extension could be used in future studies as decision support system for example, coupled with remote sensing technologies to obtain the necessary disease ratings for the model input files.

Figure 1 .
Figure 1.A simplified diagram of the Cropsim-CERES-Wheat (CCW) model with the pest damage module incorporated.

Figure 1 .
Figure 1.A simplified diagram of the Cropsim-CERES-Wheat (CCW) model with the pest damage module incorporated.

Agronomy 2018, 8 , 17 Figure 2 .
Figure 2. Simulated vs. measured leaf area index (LAI) for calibration (year 2010 a-c) and validation (year 2011 d-f) for all ten cultivars on the location La Plata.Different symbols represent the different inoculation treatments where × = No Inoculation; ∆ = Low Inoculation and O = High Inoculation.

Figure 2 .
Figure 2. Simulated vs. measured leaf area index (LAI) for calibration (year 2010 a-c) and validation (year 2011 d-f) for all ten cultivars on the location La Plata.Different symbols represent the different inoculation treatments where × = No Inoculation; ∆ = Low Inoculation and O = High Inoculation.

Figure 3 .
Figure 3. Simulated vs. measured yield (kg DM ha −1 ) for calibration and validation for all ten cultivars on the location La 2010 (a) and La Plata 2011 (b).

Figure 3 .
Figure 3. Simulated vs. measured yield (kg DM ha −1 ) for calibration and validation for all ten cultivars on the location La Plata 2010 (a) and La Plata 2011 (b).

Figure 4 .
Figure 4. Simulated and measured leaf area index values for cultivar K. Chaja, year 2010 (a) and 2011 (b) including different inoculation treatments with septoria tritici blotch (STB).The error bars demonstrate the LSD of the leaf area index.

Figure 5 .
Figure 5. Simulated and measured grain yield values for cultivar K. Chaja year 2010 (a) and 2011 (b) including different inoculation treatments with STB.The error bars demonstrate the LSD of the yield.

Figure 4 .
Figure 4. Simulated and measured leaf area index values for cultivar K. Chaja, year 2010 (a) and 2011 (b) including different inoculation treatments with septoria tritici blotch (STB).The error bars demonstrate the LSD of the leaf area index.

Figure 4 .
Figure 4. Simulated and measured leaf area index values for cultivar K. Chaja, year 2010 (a) and 2011 (b) including different inoculation treatments with septoria tritici blotch (STB).The error bars demonstrate the LSD of the leaf area index.

Figure 5 .
Figure 5. Simulated and measured grain yield values for cultivar K. Chaja year 2010 (a) and 2011 (b) including different inoculation treatments with STB.The error bars demonstrate the LSD of the yield.

Figure 5 .
Figure 5. Simulated and measured grain yield values for cultivar K. Chaja year 2010 (a) and 2011 (b) including different inoculation treatments with STB.The error bars demonstrate the LSD of the yield.
depicts the simulated curves for the three different inoculation treatments.A maximum LAI of 7.3 was reached 40 days after GS 31.Simulated curves illustrate a clear separation between the 4%, 13% and the 15% disease infection.A maximum LAI of 7.2, 6.3, 6.1 was reached at day 240 at 4%, 13% and the 15% disease infection rating.Comparing simulated infection scenarios with measured values, the model simulated the LAIs of the three different disease infection levels accurately.Agronomy 2018, 8, x FOR PEER REVIEW 12 of 17 depicts the simulated curves for the three different inoculation treatments.A maximum LAI of 7.3 was reached 40 days after GS 31.Simulated curves illustrate a clear separation between the 4%, 13% and the 15% disease infection.A maximum LAI of 7.2, 6.3, 6.1 was reached at day 240 at 4%, 13% and the 15% disease infection rating.Comparing simulated infection scenarios with measured values, the model simulated the LAIs of the three different disease infection levels accurately.
a maximum LAI of 7.3 was reached 40 days after GS 31 in the control treatment.LAI increased almost linearly from day 200 to day 240 before the onset of senescence led to a constant

Table 1 .
Soil properties for experiments in La Plata and Ihinger Hof used in the simulation.

Table 2 .
Cultivar coefficients in Cropsim-CERES-Wheat (CCW) model used to simulate crop development, crop growth and crop yield for different cultivars.
* various wheat cultivars with the same cultivar coefficients.

Table 3 .
Statistical evaluation of the simulation of leaf area index and grain yield of the original CCW model and the developed CCW model extension for diseases using root mean square error (RMSE), Willmott's d statistic (d-Index) and modelling efficiency (EF).

Table 3 .
Statistical evaluation of the simulation of leaf area index and grain yield of the original CCW model and the developed CCW model extension for diseases using root mean square error (RMSE), Willmott's d statistic (d-Index) and modelling efficiency (EF).

Table 4 .
Yield evaluation of the sensitivity analysis from the Ihinger Hof dataset, by comparing the percentage disease infection with STB and the corresponding simulated percentage yield reduction in kg DM ha −1 for the cultivar Monopol.