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Pesticides Research No. 116 2008 of fungicide application in winter wheat

4 Model development

• 4.1 Regression model
• 4.2 Causal model
  • 4.2.1 Yield responses
  • 4.2.2 Disease responses
  • 4.2.3 Fungicide deposition
  • 4.2.4 Parameterisation of the causal model
• 4.3 Yield and economic benefits of applying the models
• 4.4 Spatial variation in soil and plant properties
• 4.5 Quality of sensor measurements
• 4.6 Fungicide treatment effects
  • 4.6.1 Disease and yield responses
  • 4.6.2 Fungicide deposition
• 4.7 Models for estimating yield response to fungicide
• 4.8 Evaluation of estimated spatial variation in fungicide rate

Two types of models were tested in the project; a regression model and a causal model. The regression model attempts to use the experimental results directly for establishing a link between yield increase from fungicide control and the sensor readings. The causal model establishes the underlying causal relations between the fungicide application and their effect on disease and thus on wheat grain yield, and how these processes relate to sensor measurements.

4.1 Regression model

The split-plot design allowed the response of yield and disease to fungicide application to be determined within each of the 40 sub-blocks in each experiment. The crop density within each subplot varied considerably less than between sub-blocks, since the N strategy was identical for all plots within a su-block and since most of the soil variation was partitioned between blocks and sub-blocks. This then allowed the responses to fungicide dose to be compared with crop characteristics measured at GS39. For spatially varied fungicide applications to be of any value, there must be a relationship between either the yield or fungicide response to fungicide dose and some of the measurable crop characteristics at time of fungicide spraying.

Table 16. Correlation coefficients between yield and disease response to fungicide and sensor measurements of leaf N concentration (SPAD), LAI (LAI2000) and RVI (VIScan) at GS39. The yield response was taken as the slope of a regression of grain yield (t DM ha^-1) on fungicide dose. The disease response was taken as either the slope of a regression of septoria coverage (%) on fungicide dose or the normalised disease response, which was calculated by the slope divided by the intercept of the regression of septoria on fungicide dose.

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

The yield and disease responses to fungicide dose were estimated for each sub-block by linear regression of the grain yield and the septoria coverage against fungicide dose. However, only sub-blocks with no missing data for yield or septoria coverage were used. The septoria coverage was estimated as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75. The responses were then taken as the slope of these regressions. As the disease response will to some extent depend on the disease level, a normalised disease index was calculated as the ratio of the slope to the intercept in the regression.

Figure 28. Relationship between yield and normalised disease response to fungicide rate and three selected crop characteristics at GS39; leaf N concentration measured with SPAD (a,b), leaf area index measured with LAI2000 (c,d) and ratio vegetation index measured with ViScan (f, g).

There were significant relationships between yield response to fungicide and the measurements of leaf N and RVI at GS39 for Dybvad only (Table 16). At this location higher leaf N concentrations or high RVI gave a higher yield response to fungicide application. The relationship between the yield response to fungicide and leaf N was also positive for the other locations, but not significant. Across locations there was a lot of scatter in the responses (Fig. 28).

There were significant negative correlations between disease response to fungicide and all sensor measurements, in particular at Schackenborg and Dybvad. Much of these relationships between disease response to fungicide and the sensor measurements are caused by differences in disease levels depending on crop density and N supply, since the significant relationships disappeared at most locations, when the disease responses were normalised for the disease level without fungicide application (Table 16).

However, there was a consistent relationship between normalised disease response to fungicide and leaf N for Nissumgård and Dybvad (Fig. 28b). Excluding the data from Schackenborg, which had consistently lower SPAD readings than the other sites, gave an overall correlation coefficient of 0.49 (P<0.0001) between normalised disease response to fungicide and the SPAD readings. This indicates that higher leaf N concentrations give a relatively flatter dose response curve thus reducing the efficacy of the fungicide application.

Table 17. Regression of yield response to fungicide (t DM L^-1) against Yara SPAD sensor readings (SPAD) and EM38 measurements with vertical polarisation (EM38v). The yield response was taken as the slope of a regression of grain yield (t DM ha^-1) on fungicide dose.

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

Table 18. Regression of yield response to fungicide (t DM L^-1) against ViScan reflectance measurements of ratio vegetation index (RVI) and EM38 measurements with vertical polarisation (EM38v). The yield response was taken as the slope of a regression of grain yield (t DM ha^-1) on fungicide dose.

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

The yield response to fungicide across all sites was significantly influenced by plant N concentration (SPAD readings) and by soil type as reflected by the EM38 value (Table 17). The yield response to fungicide was increased for crops with high N concentration and also for areas with higher clay content (higher EM38 values). Similar effects were seen for RVI, but RVI was not as good a predictor of yield response to fungicide as SPAD readings (compare Tables 17 and 18). This difference may partly be related the fact that RVI values were higher for Schackenborg in 2005 at GS39 due to infestation with grass weeds. These results show that SPAD, RVI and EM38 measurements significantly influence yield response to fungicide, and that therefore higher fungicide doses should be applied to areas in the field with higher leaf N concentrations, higher RVI or higher clay content.

An alternative method for estimating the possibilities for varying fungicide rate is to estimate the yield response to sensor measurements and to fungicide dose. Several regression models of grain yield on sensor measurements and fungicide dose are shown in Table 19. A sensor-based variation in fungicide dose will be possible, if the there is a significant interaction between one of the sensor measurements and fungicide dose. This was the case for the interaction between RVI and square root of fungicide dose (Table 19). The regression coefficient for this interaction was consistent at 0.023 t DM L^-1 for all regression equations involving several predictors. This value is close to the value of 0.018 t DM L^-1 estimated from the regression of the yield response on fungicide dose on RVI (Table 18).

Table 19. Regression of dry matter grain yield (t DM ha^-1) on RVI measured with ViScan (RVI), Yara SPAD sensor readings (SPAD), EM38 measurements with vertical polarisation (EM38v) and the interaction of RVI and square root of fungicide dose. The coefficients of the regression equations and the R² and RMSE of these equations are given.

4.2 Causal model

The causal model links the different responses of crop and disease to environmental conditions and fungicide application (e.g. Olesen et al., 2003a). The following relationship were initially assumed:

• A relationship between disease free yield (Y_p) and sensor measurements.
• A relationship between yield reduction and disease occurrence, possibly depending on yield level or sensor measurements.
• A relationship between disease and sensor measurements without fungicide application.
• A relationship between disease and fungicide concentration on the leaves.
• A relationship between fungicide dose, canopy structure and fungicide concentration on the leaves.

These relationships can, if quantified, be combined into a system of equations, which then allows the response function of yield and disease to fungicide application to be estimated at any given site in the field, provided sensor measurements are available.

4.2.1 Yield responses

The grain yield obtained for a non-diseased crop (disease free yield) was estimated for each sub-block as the intercept of a regression of yield on septoria coverage. However, only sub-blocks with no missing data for yield or septoria coverage were used. The septoria coverage was estimated as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75.

The disease free yield correlated well with crop canopy measurements at GS39, in particular LAI and possibly RVI seem to be good predictors of disease free yield (Table 20 and Fig. 29). The soil measurements showed a correlation with disease free yield at Nissumgård in 2005, but not at the other sites, which indicates that it may be more difficult to derive a generally applicable relationship between soil sensor measurements and disease free yield than between crop sensor measurements at GS39 and disease free yield.

Table 20. Correlation coefficients between disease free yield and yield response to septoria disease and sensor measurements of leaf N concentration (SPAD), LAI (LAI2000), RVI (VIScan), soil electrical conductance (EM38 with horizontal or vertical polarisation) and TDR measurements of soil water capacity or impedance. The crop sensor measurements were taken at GS39. The disease free yield was taken as the intercept of a regression of yield (t DM ha^-1) on septoria coverage (%), and the yield response was taken as the slope of the same regression.

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

Figure 29. Relationship between disease free yield and three selected crop characteristics at GS39; leaf N concentration measured with SPAD (a), leaf area index measured with LAI2000 (c) and ratio vegetation index measured with VIScan (e), and with soil characteristics; soil electrical conductivity (EM38) (b), soil water capacity (TDR) (d) and soil impedance (TDR) (f).

The yield response to septoria disease did not depend on crop characteristics at GS39 at most of the sites (Table 20 and Fig. 30). However, this may in part be due to large uncertainties in the estimated responses. Some of the very large yield responses (both positive and negative) at Schackenborg thus seem highly unlikely (Fig. 30). Dybvad was the only location, where significant relationships between sensor measurements and yield responses to disease were obtained, and even these responses were rather weak. Also there was very little variation in yield response to disease at Dybvad. Overall the yield response to disease can probably be considered to be constant across fields.

Figure 30. Relationship between yield response to disease and three selected crop characteristics at GS39; leaf N concentration measured with SPAD (a), leaf area index measured with LAI2000 (c) and ratio vegetation index measured with VIScan (f), and with soil characteristics; soil electrical conductivity (EM38) (b), soil water capacity (TDR) (d) and soil impedance (TDR) (e).

4.2.2 Disease responses

The septoria coverage was estimated as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75. This disease attack depended on fungicide application and analyses of the relationship with sensor measurements at GS39 were therefore performed separately for each fungicide rate. The highest correlation coefficients were obtained between septoria coverage and measurements of either leaf N or RVI (Table 21).

Figure 31. Relationship between septoria attack and three selected crop characteristics at GS39; leaf N concentration measured with SPAD (a, b), leaf area index measured with LAI2000 (c, d) and ratio vegetation index measured with VIScan (e, f) for untreated (a, c, e) and full fungicide treatments (b, d, f).

The highest correlation coefficients were obtained at Schackenborg and Dybvad across fungicide treatments. The weakest correlations were obtained for Nissumgård in 2006, which may reflect the large inhomogeneity of the crop stand at this particular location. The data from the different locations could not be fitted onto a joint relationship between septoria attack and sensor measurements, although there seems to be some relationship, in particular between septoria attack and leaf N (Fig. 31).

Table 21. Correlation coefficients between septoria coverage on the top two leaves and sensor measurements of leaf N concentration (SPAD), LAI (LAI2000), RVI (VIScan).

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

The slopes of the relationship between septoria coverage and the sensor measurements were estimated for the different fungicide rates using a common intercept. The slope declined with increasing fungicide rate (Fig. 32).

Figure 32. Response of disease to sensor measurements estimated as the slope of a regression of septoria coverage on either leaf N (SPAD) (a) or RVI (VIScan) (b) at GS39 for different fungicide rates. The vertical lines show the standard error.

4.2.3 Fungicide deposition

The deposition of fungicide was measured by addition of a tracer to the fungicide spray. The amount of tracer that was deposited on the soil surface depended on the leaf area index as expected (Fig. 33a). However, different relationships were obtained at the Schackenborg and the other sites, most likely because of the dense stand of Poa annua at Schackenborg. This large weed population is probably also the reason why the deposition of fungicide on the soil surface fits better to the measured RVI (Fig. 33b). The relationship between soil deposition of the fungicide and LAI or RVI fits an inverse exponential relationship, suggesting that the deposition efficiency is constant.

Figure 33. Deposition of tracer on the soil surface (% of applied tracer) in relation to measured LAI (a) and RVI (b).

The deposition on the leaves was measured as concentration of the tracer per unit leaf area. These measurements were compared with measurements of LAI and mean leaf angle derived from the LAI2000 and with RVI from the VIScan. There was a tendency for slightly higher concentrations on the upper leaves at higher LAI and RVI (Table 22 and Fig. 34). However, this was probably caused by the correlation between LAI and leaf angle. More horizontal leaves, which are associated with a higher leaf area, were thus found to give a higher concentration on the upper leaves. The opposite trends were found for the lower leaves (Table 22).

Table 22. Correlation coefficients between concentration of tracer (mg cm^-2) on each of the top three leaves and measured LAI (LAI2000), leaf angle (LAI2000) and RVI (VIScan).

Significance levels: ^*: 0.05<P<0.01, ^** 0.01<P<0.001, ^*** 0.001<P.

Figure 34. Deposition of tracer on leaf 1 (a, b), 2 (c, d), 3 (e, f) in relation to measured LAI (a, c, e) and RVI (b, d, f).

4.2.4 Parameterisation of the causal model

The causal model attempts to estimate the effect of disease and fungicide application on grain yield based on sensor measurements. It was originally anticipated that this estimation would be based on the following assumed equations:

Yield = Pot.Yield x f₁(Disease)                                           (3)

Pot.Yield = f₂(Sensor)                                                       (4)

Disease = f₃(LAI,N-conc,Variety) x f₄(FungicideConc)        (5)

FungicideConc = FungicidDose x f₅(LAI)                           (6)

LAI = f₆(Sensor)                                                              (7)

N-Conc = f₇(Sensor)                                                        (8)

The study of fungicide deposition on leaves has not shown any major effects of leaf area index or canopy structure on fungicide concentration on the top two leaves (section 4.2.3), whereas there were clear effects of canopy structure on the fungicide concentration on the third leaf level. However, the protection of disease on the third leaf is not considered as important as for the top two leaves. The effects of fungicide concentration in eqns (5) and (6) were therefore ignored, when developing the causal model.

The potential yield (Pot.Yield) in eqn (4) can be estimated using the measurements of RVI, SPAD and EM38 as shown for the regression equations in Table 20. RVI appears to be just as good a predictor of yield as the other measurements, and as RVI is the simplest measurement, this measure is used here for estimating potential yield. Data from all plots in the experiments with highest fungicide rate (0.8 L ha^-1 Opus) were used for this estimation to avoid effects of large disease attacks on the potential yield estimation.

Figure 35. Relationship between dry matter grain yield and (a) RVI at GS39 or (b) EM38 with vertical polarisation for all plots with the highest dose of fungicide (0.8 L ha^-1 Opus).

There was clear relationship between RVI at GS39 and grain yield (Fig. 35), resulting in the following estimated regression equation (R² = 0.34, RMSE = 1.01):

Y_max = 3.38 + 0.124 RVI     (9)

where Y_max is a surrogate for potential yield and taken as the observed yield at the highest fungicide rate (t DM ha^-1), and RVI is the ratio vegetation index at GS39.

The regression equation was slightly improved by also introducing the EM38 measurements as an explanatory variable (R² = 0.39, RMSE = 0.97):

Y_max = 2.74 + 0.119 RVI + 0.059 EM38v     (10)

where EM38v is the EM38 measurement with vertical polarisation.

Here only effects of septoria are considered, since this disease was the primary disease in the experiments and generally the major disease affecting yields in winter wheat. The septoria coverage was estimated as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75.

Figure 36. Relative yield response taken as the change in dry matter yield between fungicide treated and non-treated plots in percent of yield of treated plots versus the difference in septoria coverage of the two sets of treatments. Data from the treatments with full fungicide rate in the experiments described in this report (a) and fungicide trials in winter wheat from 2000 to 2006 (b). The line shows a linear regression of yield response on septoria coverage.

The response of grain yield to septoria disease was considered using two different data sources (Fig. 36). Firstly the data from the four field experiments conducted in this project were used (Fig. 36a). These data showed only a moderate yield response to septoria, which may be related to the climatic conditions (relatively dry summers) during these years. In fact only the data from Dybvad indicated a lower yields at higher septoria coverage (Fig. 36a). Therefore additional data were included from fungicide trials in winter wheat carried out at different locations during 2000 to 2006 (Fig. 36b). A total of 29 different experiments were included. The relative yield response was taken from the experiments as the grain dry matter yield difference between fungicide treated and non-treated plots. This relative yield response was regressed on the difference between septoria coverage between fungicide treated and non-treated plots.

The regression equation included a response to septoris coverage (%) (Sep) and a response to fungicide dose (L ha^-1 Opus) (Dose). The estimation had to consider that the septoria coverage was based on uncertain assessments, which potentially influences the parameter estimation. Therefore a structural regression approach was used for the parameter estimation using the CALIS procedure of SAS. The parameter estimation was based on the observation that the standard deviation of the septoria coverage was 1.5 times the standard error of the relative yield. The following regression equation was obtained for the data from the fungicide trials carried out during 2000 to 2006 (R² = 0.31, RMSE = 6.9):

      (11)

All parameters were significant at the 99.9% confidence level.

The regression equation and Fig. 36 show that average response of grain yield to septoria disease is generally considerably larger than what was observed in the experiments conducted in this experiment. Also there appears to be a 7% yield increase from fungicide application, which is unrelated to control of the septoria disease.

Regression and correlation analyses showed that the major determinants of septoria coverage as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75 was septoria coverage at GS39, fungicide rate and RVI at GS39. A multiple linear regression was made on the product of septoria and RVI at GS39 with separate regression coefficients for each fungicide rate (R² = 0.81, RMSE = 5.1). These regressions coefficients were subsequently fitted to an exponential equation, resulting in the following equation for estimation of septoria coverage:

where Sep is the septoria coverage (%) taken as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75, Sep₃₉ is the septoria coverage at GS39, RVI is the ratio vegetation index at GS39, and Dose is the dose of fungicide applied at GS39 (L ha^-1 Opus). The predicted versus the observed septoria coverage is shown in Fig. 37.

Figure 37. Predicted versus observed septoria coverage taken as the mean cover of septoria on leaf 2 at GS65 and septoria on leaf 1 at GS75. The predictions were made using eqn (12). The 1:1 line is shown.

4.3 Yield and economic benefits of applying the models

The effect of spatially varying the fungicide rate was estimated using two types of models, either an empirical regression model (section 4.1) or a causal model (section 4.2). Both types of models estimate the yield response to sensor measurements and fungicide application.

The empirical regression model was selected from Table 19 as the model including responses to RVI, EM38v and fungicide dose:

    (13)

where Y is grain dry matter yield (t ha^-1), RVI  is ratio vegetation index, EM38v is EM38 measurement with vertical polarisation, and Dose is fungicide dose (L ha^-1 Opus).

The causal model was based on eqns (10), (11) and (12).

All plot based data with normal N fertiliser rate (N treatments 1 and 4) were selected from the four experiments. The data obtained from these plots were used as input to the yield prediction models, which were applied to fungicide doses varying from 0 to 1 L ha^-1 Opus in steps of 0.01 L ha^-1. The net grain yield was calculated under the assumption of a grain price of 1000 DKK per ton DM and a fungicide price of 373 DKK L^-1. The optimal fungicide rate was calculated by finding the fungicide dose giving the highest net grain yield. These calculations did not include application costs, and the fungicide dose was thus calculated under the assumption that at least some part of the field would need to be sprayed and that driving would be needed also to obtain the sensor measurements.

Table 23. Mean and standard deviation (in brackets) of estimated fungicide dose for each site estimated using either the empirical or causal model. The causal model was applied with either observed septoria at GS39 for each plot (causal 1) or for the location as an average (causal 2).

The average estimated fungicide rates were generally higher for the empirical compared with the causal model (Table 23), except for Nissumgård in 2006, where similar results were obtained (Fig. 38). This difference may partly be explained by the fact that the causal model also requires information on septoria coverage at GS39, which in the model regulates for different disease pressures between sites and years. There was little difference between using measured septoria coverage at plot or location level (Table 23), primarily because most of the variation in septoria at GS39 was site and year dependent.

The estimated effect of using a spatially variable fungicide rate compared with a fixed fungicide rate was estimated by calculating the net grain yield (grain yield minus fungicide costs) for the spatially variable fungicide rates and for a standard fungicide rate of 0.4 L ha^-1 Opus. The causal model was used for estimating the grain yield response. The effect on soil deposition was also estimated by deriving the following relationship between soil deposition and RVI using the data shown in Figure 33b:

Dep = 49 exp(-RVI / 26)       (14)

where Dep is soil deposition of the fungicide (%), and RVI is the ratio vegetation index at time of fungicide application.

Figure 38. Estimated fungicide dose calculated using the causal model versus fungicide dose calculated using the empirical model. The causal model was applied with either observed septoria at GS39 for each plot (a) or for the location as an average (b). The 1:1 line is shown.

Table 24. Net dry matter grain yield (estimated grain yield using the empirical model minus fungicide costs) and soil fungicide deposition for either variable fungicide rates using the empirical model or using as standard fungicide rate of 0.4 L ha^-1.

Table 25. Net dry matter grain yield (estimated grain yield using the causal model minus fungicide costs) and soil fungicide deposition for either variable fungicide rates using the causal model (Causal 2 in Table 23) or using as standard fungicide rate of 0.4 L ha^-1.

The application of the empirical model for estimating the spatial variation in fungicide rate resulted in very small yield differences compared with a fixed fungicide rate (Table 24), except for Schackenborg where there was a net yield reduction of about 0.1 t DM ha^-1 for varying fungicide rate spatially. On average grain yields were 1% lower for the spatially varied fungicide rate compared with fixed fungicide rate. There was in most cases an increase in fungicide deposition on the soil for the spatially variable compared with the fixed fungicide rate. On average the fungicide deposition increased by 24%.

Application of the causal model for spatial variation in fungicide rate gave small increases in mean net grain yield of -0.01 to 0.27 t DM ha^-1 compared with the fixed fungicide rate (Table 25). On average grain yields were 1% lower for the spatially varied fungicide rate compared with fixed fungicide rate. There was on average a reduction of 43% in the deposition of fungicide on the soil surface with the use of spatially varying compared with the fixed fungicide rate.

Discussion

4.4 Spatial variation in soil and plant properties

There was a considerable spatial variation in soil properties at the four experimental sites, which also resulted in a large yield variation, in particular at Nissumgård in both years. The use of four different N-strategies gave additional variation in crop density and N-status. There was also some unintended variation in plant cover, caused by weeds, plant stand, molehills and manganese deficiency. Most of this unintended variation does not appear to have influenced the applicability of the data for analyses of the relationships between sensor measurements and crop performance.

The large stand of weeds (Poa annua) at Schackenborg was most likely the cause of the very high RVI measured at Schackenborg at GS39. Because of this large weed stand, measurements of LAI using the LAI2000 sensor were underestimated because the measurements were not taken at the soil surface but above the weed stand. The large weed stand also influenced the measurements of soil fungicide deposition on the soil surface, since much of the tracer that was not deposited on the wheat was deposited on the weeds.

There were large intra-block variations in soil and plant properties and therefore also a large coefficient of variation for grain yield measurements at all sites, except Dybvad (Table 4). This made it difficult to directly determine the relationship between the yield response to fungicide and sensor measurements (Table 16), and these relationships were only significant at Dybvad.

There was generally a good correlation between the different types of soil measurements (TDR and EM38), so that a high conductance was linked with a high water holding capacity. However, parts of the field at Schackenborg did not follow this general trend. In general a high conductance is linked with a high clay content (Greve et al., 2002), which also has a large water holding capacity. However, this relationship often breaks down where the soil has a large soil organic matter content, and measurements of soil texture showed that a high variation in soil organic matter content at Schackenborg may indeed be the reason the discrepancies between EM38 measurements and soil water content (compare Figs. 9 and 10).

4.5 Quality of sensor measurements

The comparisons of manual sensor measurements and destructive plant samplings showed that the LAI2000 measurements could be used as good estimates of canopy leaf area index (LAI) (Fig. 19), although there was a tendency for underestimation at high LAI. Similar results have been found in other studies (e.g. Stroppiana et al., 2006). There was a small underestimation of LAI using LAI2000 at Schackenborg, which most likely was caused by the need to raise the sensor above the grass weeds in the lower crop canopy at this location.

There was in general a good relationship between SPAD measurements and leaf and plant N concentration (Fig. 20), so that these sensor measurements can be used as reasonably accurate indicators of leaf N concentration. However, two different varieties were used in the experiments. The variety was Grommit at Schackenborg and Deben at all other locations. There appear to have been variety differences in some of the plant characteristics. The specific leaf weight was higher at Schackenborg compared with the other locations (Table 10), and the leaf N concentrations were also slightly lower at Schackenborg compared to the other locations (Fig. 20). However, the SPAD measurements of leaf N generally underestimated leaf and plant N concentrations at Schackenborg compared with the other location (Fig. 20), which may be caused by the higher specific leaf weight at Schackenborg reducing light transmission. It is therefore likely that accurate measurements of leaf N using the SPAD method will require variety specific calibrations.

The manual sensors are, however, much too laborious to use operationally for spatially varying fungicide applications. The recordings of the manual sensors were therefore compared with results of the tractor-mounted MobilLas sensor system, which both measures spectral reflectance (RVI) and uses an infrared laser to estimate LAI. There was good agreement between the tractor-mounted measurements of RVI and the measurements of RVI based on the manual VIScan measurements (Fig. 26).

It is technically very demanding to measure leaf area index (LAI) reliably from a mobile platform, and the MobilLas instrument is the only known remote sensing instrument capable of doing this (Thomsen and Schelde, 2007). It was known from a previous study comparing different approaches that dense canopies with LAI values exceeding 2.5-3.0 is a challenge for any indirect measurement of LAI. As shown in Fig. 22, the MobilLas laser range measurements are used to first calculate the accumulated height of hit distribution. From this distribution, the canopy gap fraction can be directly obtained for any height within the canopy. From the canopy gap fraction LAI is then calculated using eqn. (1). Because of the non-infinite diameter (0.5 mm) of the laser beam and the resulting underestimation of gap fractions, the initial estimates of canopy gap fractions have to be corrected using eqn. (2). The denser the canopy, the greater is the underestimation of gap fraction. For canopies with LAI values exceeding 2.5-3.0, the ground surface can no longer be consistently detected and LAI values become seriously underestimated. Fig. 23 shows the considerable scatter observed in both manual and mobile measurements of LAI. Fig. 23 also shows a generally good relationship between mobile and reference measurements for LAI values below approximately 2.7 and the underestimation of higher LAI values by the mobile instrument.

The software calculating total canopy LAI also calculates profiles of LAI starting at the top of the canopy. Information on the LAI profiles may potentially be useful for optimising crop protection, but this aspect has not been investigated in the present project. The LAI profiles are expected to be reliably estimated for accumulated LAI values not exceeding 2.5-3.0 as for total canopy measurements. Mobile measurements of LAI to a depth of 30 cm are compared in Fig. 24 with reference measurements of total canopy LAI at GS 32 and 39. At GS32 the plant height is typically less than the 40 cm required for calculating LAI at a depth of 30 cm with a ground reference distance of 10 cm (Fig. 22), and the data are thus not comparable. At GS39, where the height is typically more than 40 cm, there is a fair relationship between mobile and reference measurements. The mobile measurements are approximately 1.5 LAI units lower than the reference measurements because only the top 30 cm of the canopy is included. The challenge is thus to develop better algorithms for estimating LAI in dense canopy stands such as for winter wheat at GS39. There may be some prospects for looking at profiles of gap fractions and empirically relate this to observed LAI. However, such approaches are likely to be sensitive to variety and management effects.

The RVI/LAI ratio is in principle closely related to the nitrogen status of the entire canopy, and the MobilLas sensor was primarily developed for precision nitrogen management making use of this ratio. The RVI/LAI ratio is only applicable to green developing canopies for growth stages less than GS32. Thomsen and Schelde (2007) showed that mobile and manual measurements of the RVI/LAI ratio compared favourably to each other and to SPAD readings. Mobile measurements of the RVI/LAI ratio were compared to plant N concentration (Fig. 27a) and to SPAD readings (Fig. 27b). The poor correlations obtained in Fig. 27 are in part due to the late development stage (GS39) and the problems associated with estimating high LAI values. However, some of the scatter in Fig. 27 is also due to observations from Schackenborg differing from the response obtained from the other sites. This is caused both by deviations in RVI and SPAD measurements at Schackenborg compared with the other sites due to effects of both weeds and differences in variety. Therefore, in practice the applicability of the RVI/LAI ratio as a measure of plant N status, will also depend on how sensitive this index is to such influences, and this needs to be further investigated.

4.6 Fungicide treatment effects

4.6.1 Disease and yield responses

The underlying assumption in the project is that there is a yield gain for fungicide application in winter wheat and that this yield gain can be related to one or more sensor measurements that can be made before fungicide application. Septoria was the major disease occurring in both experimental years, and this disease is generally known to cause considerable yield reductions (Shaw and Royle, 1993; Jørgensen and Nielsen, 2003; Olesen et al., 2003a). However, only small yield gains from fungicide application were obtained in the experiments reported here (0.1 to 0.9 t DM ha^-1), possibly because of the dry weather conditions during much of the summer in both years. Under conditions more conducive for disease development, yield responses of 1 to 2 t DM ha^-1 can be expected (Ørum et al., 2006; Jørgensen et al., 2007).

The small yield increases from fungicide application in this project could not cover the costs of fungicide application in 2005, and it is therefore not surprising that no significant relationship between yield increases from fungicide application and sensor measurements could be found in this year (Table 16). The disease pressure was considerably higher at Dybvad in 2006, and this did indeed result in significant interactions between N strategy and fungicide rate on grain yield (Fig. 13) and a significant relationship between yield response to fungicide application and sensor measurements (Table 16). There was, however, a tendency in all experiments for the response of grain yield to fungicide application to be larger at the highest compared with the lowest N rate.

The results clearly confirm previous findings that increasing N fertiliser rates increases attack of Septoria tritici (Olesen et al., 2003ab; Simon et al., 2003). This pattern was present at both GS65 and GS75 (Fig. 14). There was no clear effect of single or split N application on septoria attack. Olesen et al. (2003a) also found little difference in septoria attack between single and split N application strategies.

4.6.2 Fungicide deposition

The fungicide treatments were applied with conventional hydraulic flat fan nozzles at a driving speed of 3.6 km h^-1. This is a typical speed used with manually driven experimental plot sprayers. The nozzle type used and the volume rate of 230 l ha^-1 is within the normally recommended and used by farmers. However the driving speed used is much lower than the normal practice where the typical driving speed lies in the interval from 6 to 9 km h^-1. The driving speed influences the distribution of the droplets in the canopy in combination with other spray technical factors. Reducing the driving speed increases penetration into the canopy (Göhlich et al., 1976). The driving speed used in the experiment is therefore supposed to give a deeper penetration into the canopy and thus less deposition on the upper part of the canopy compared to the deposition pattern obtained using a driving speed closer to the situation in practical agriculture.

The supplementary experiment (section 3.6) showed that increasing driving speed caused a steeper deposition gradient in the crop canopy. At 4 km h^-1 deposition of spray liquid per area unit leaf was only slightly reduced for the 2^nd leaf and the value for the 3^rd leaf was close to 75% of the deposition on the flag leaf. At 8 km h^-1 a much steeper gradient in deposit was found, with a value for the 3rd leaf close to 40% of the per area unit deposit on the flag leaf. What influence such a difference in deposition pattern in the canopy has on disease control and crop yield probably depends on mobility of the fungicides used and interval between fungicide applications. No published investigations on this topic can be found in literature.

The effect of driving speed on fungicide deposition was greatest for the third leaf, which will result in poorer control of septoria on the lower leaves in the crop canopy at realistic driving speeds compared with the driving speed used in the experiment. However, the control of septoria on the lower leaves probably has little effect on grain yield, because the upper leaves are the primary sources of assimilates for grain growth (Dimmock and Gooding, 2002).

Loss of spray liquid to the soil was not significantly affected by the sprayer speed used and this is in accordance with a previous study by Jensen and Spliid (2005).

4.7 Models for estimating yield response to fungicide

The response of grain yield and septoria disease to fungicide application was estimated for each sub-block using regression analysis. For spatially variable fungicide application to be valuable, there must be a relationship between grain yield response to fungicide and one or more of the sensor measurements. This was only the case at Dybvad (Table 16), where the coefficient of variation in yield was small and where there was a substantial septoria infestation.

There was for all experiments significant negative relationships between disease response to fungicide and sensor measurements, in particular for SPAD and RVI (Table 16). This could be attributed to the relationship between disease level and the sensor measurements of crop characteristics at GS39. However, when a correction was made for this effect there were significant positive relationships between disease response to fungicide and sensor measurements for the sites in 2006, which points to higher disease prevalence with higher leaf N concentrations, higher leaf area index and RVI. It also indicates that higher leaf N concentrations give a relatively flatter dose response curve thus reducing the efficacy of the fungicide application. There is little literature on the effect of crop N supply on fungicide efficacy (Jørgensen et al., 1997; Olesen et al., 2003a), and these results indicate that a deeper understanding of the causes of such responses is called for.

There are several indicators from the experiments pointing towards the need for increasing fungicide application rate with increasing crop canopy size and N concentration. These two variables are in practice closely correlated, since increasing N supply will cause winter wheat to increase its leaf area index (Olesen et al., 2002). Firstly, yield gains from fungicide application increased with increasing N fertiliser rate (Fig. 13). Secondly, grain yield and disease response to fungicide rate were at least for some sites significantly positively correlated with sensor measurements of canopy size and leaf N content (Table 16). This suggests that it should be possible to use sensor measurements for determining the optimal spatial variation in fungicide rate.

The results of the correlation analyses in Table 16 and the regressions in Table 17 and 18 indicate that leaf N and RVI measurements are the best candidates for sensor measurements to determine yield response to fungicide rate. This is in line with previous experience indicating that septoria incidence increases with increasing leaf N (Olesen et al., 2003b), and leaf N is generally positively correlated with RVI thus making both these sensor measurements suitable for estimating crop susceptibility to septoria disease.

The results of regression of yield response to fungicide application on SPAD, RVI and EM38v in Tables 17 and 18 could not be used directly for determining the spatially optimal fungicide rate. The reason is that this analysis did not include the diminishing yield response with increasing fungicide rate, which is fundamental for determining the optimal fungicide rate. Instead an empirical regression equation that included the interaction between RVI and the square root of fungicide rate was used (Table 19). The selected empirical regression equation (eqn. 13) included RVI and EM38v measurements, which are operationally available measurements. The EM38v measurement describes the soil characteristics, in particular the soil clay content. Increasing soil clay content means higher soil water availability and therefore a higher yield potential as also reflected in a positive effect of EM38v on disease free yield (Fig. 29). The EM38 measurement can be made only once and used subsequently, whereas the RVI measurement needs to be taken at GS39 at the time of fungicide application.

The empirical regression equation (eqn. 13) implies a higher yield response of fungicide application with increasing RVI. Since high RVI is associated with high yields, this should lead to a higher profitability of applying fungicide for high yielding crops, as also indicated in the data for the varying fertiliser rates (Fig. 13).

As an alternative to the simple regression model, a causal model was developed, which is based on a number of verified relationships between crop yield, disease occurrence and sensor measurements. There were initially four basic assumptions for these relationships:

1.    The maximum (potential) yield can be determined from sensor measurements taken before or at GS39.

2.    The yield effect of fungicide application is related to the control effect of septoria, and thus yield reduction from disease is directly related to septoria severity.

3.    The septoria disease without fungicide can be predicted from sensor measurements.

4.    The disease control effect of depends on leaf fungicide concentration and this concentration declines with increasing leaf area index.

The first three assumptions were verified in the experiments, and the analyses of leaf fungicide concentration based on tracer measurements also showed a relationship to leaf area index. However, this effect was strongest for leaf 3 and there were only weak relationships for leaf 1 and 2 (Table 22). It is the disease control on the upper two leaves that provides the main effect on yield gain from disease control (Gooding et al., 2000). This relationship between fungicide concentration and leaf area index was therefore ignored in the development of the causal model.

The actual yield is described as a product of a potential (disease free) yield and an effect of disease. The potential yield was related to both RVI and EM38v measurements (eqn. 10). Similar relationships have previously been reported for Danish winter wheat crops and used for determining the spatial variation in N fertiliser (Berntsen et al., 2002, 2006). The positive relationship between yield and RVI shows that a well-established crop with a high RVI and thus a high biomass and leaf area index at GS39 will generally result in high grain yields. However, the likelihood of high yields is improved under good soil conditions, which is indicated by the positive effect of EM38v on grain yield. A high EM38v measurement is generally associated with high soil clay content and high soil water availability (Fig. 10) (Greve et al., 2002).

Septoria was assumed to influence the ratio of actual to potential yield. The data from the four field experiments gave only a small effect of disease on grain yield (Fig. 36). This may be related to the relatively low infestation level with septoria in the experiments and the warm and dry conditions during both summer seasons, which reduced the effects of septoria on grain yield. Data from fungicide trials in Denmark from 2000 to 2006 were therefore used to develop this relationship, resulting in a stronger grain yield response to disease compared with the response from the present experiments only (Fig. 36). The regression analyses showed a significant additional yield increase from fungicide application, which was unrelated to control of the septoria disease. This effect was estimated to be related to fungicide dose. This is a substantial effect, which should be further investigated. The effect may be related to control of other diseases or to uncertainties in determining the proper effects of disease control on septoria disease levels.

There was no consistent relationship between the yield response to disease and any of the sensor measurements (Table 20), and this was also not hypothesised. The disease free yield was best related to crop characteristics at GS39, whereas soil characteristics were less good predictors of yield (Table 20). The inadequacy of the soil sensor measurements for estimating crop yield may be related to the fact that more factors than soil water supply affect crop establishment and growth and these effects are integrated in the sensor measurements of crop characteristics at GS39. However, soil water availability will affect crop growth and production after this measurement resulting in positive effects of EM38 measurements on disease free yield in addition to the effect of the RVI measurements (eqn. 10).

There was a clear relationship between both RVI and leaf N concentration at GS39 and septoria attack during the following two months (Table 21 and Fig. 31). These relationships were significant at all locations and for all fungicide dosages for leaf N and in most situations for RVI (Table 21). This confirms previous studies of Leitch and Jenkins (1995) and Olesen et al. (2003b), but it contradicts the usual concepts of septoria primarily being influenced by the effects of spore dispersal on disease prevalence. Several studies have thus found that septoria is most dominating in open stands (Jørgensen et al., 1997; Bjerre et al., 2006). However, the good relationship obtained strongly indicates new opportunities for predicting occurrence of septoria in winter wheat.

The analyses of septoria response to sensor measurements showed large variations between years (Fig. 31). This could effectively be accounted for by taking the observed septoria coverage at GS39 as a covariate in the analyses. The best predictor of septoria severity using this approach was the product of RVI and septoria coverage at GS39 (eqn. 12). The fungicide response was accounted for by assuming an exponential dose response curve. In effect this gave a very good description of the observed septoria severity (Fig. 37). However, this is partly based on the assumption that septoria coverage at GS39 can be used as a reliable predictor of conditions for septoria proliferation in the given crop. In practice, more factors are likely to influence septoria, including variety and weather conditions, and there is therefore a need to further improve the basis for predicting septoria under different climatic and management conditions to supplement sensor measurements.

The models developed here only make use of EM38 measurements of soil conditions and of RVI at GS39. In fact these measurements proved to be the most reliable predictors of yield and disease occurrence. However, they are also the measurements, which can most readily be obtained on an operational basis. Analyses of the individual experiments indicated that in particular the leaf N concentrations would be good candidate for a sensor measurement to predict disease development. However, reliable measurements of leaf N concentrations can currently not be obtained on an operational scale at GS39.

4.8 Evaluation of estimated spatial variation in fungicide rate

The applicability of the sensor based models for spatially varying fungicide application was evaluated using data from the four experiments. However, only plots that had received the normal N fertiliser rate were used for this purpose. This included N treatments 1 and 4, where treatment 1 had received the N fertiliser in a split application, whereas the N fertiliser was applied in a single treatment in treatment 4. In practice both fertiliser application strategies may be used, and it is therefore relevant to evaluate the sensor-based models for both N treatments, whereas the two other N treatments would be outside the N fertiliser rate normally applied in practice.

Two types of sensor-based models were used in the evaluation, the empirical regression model (eqn. 13) and the causal model (eqns. 10, 11 and 12). Both models were developed on the data from the same four experiments as used for deriving the spatial variation in input variables for the evaluation. However, the causal model assumed a stronger yield response to disease than was obtained in the experiments (Fig. 36). This higher yield response is in better agreement with other experimental results (Olesen et al., 2003a; Jørgensen et al., 2007).

Since the causal model also includes septoria infestation at GS39 as an input variable this value was either taken for each plot individually or as the average for the experimental site. In practice it will not be possible to obtain spatially varying estimates of this input variable, and maybe not even field level estimates. There was, however, little difference in estimated fungicide rates depending on whether whole field or plot level septoria infestation was used as input to the causal model (Table 23, Fig. 38). It may therefore also be possible to substitute observations of this input variable with proxy estimates using variety information, cropping history and weather data to get an indication of general infection level at a given site in a given year.

The estimated variation in fungicide rate within the field varied between experimental sites, but the standard deviation was generally in the order of 0.1 to 0.2 L ha^-1 Opus. This is a higher variation than used in previous experiments with spatial variation in fungicide rate, where Secher et al. (1998) varied fungicide rate +/- 20% depending on RVI measurements.

There was a large discrepancy between the fungicide rates predicted by the two types of models for Schackenborg. The causal model in most cases did not estimate a need for fungicide application. This was primarily due to the low level of septoria disease observed at GS39. On the other hand high fungicide rates were estimated with the empirical model, which relies heavily on RVI measurements for estimating fungicide rate. The RVI values were particular and unrealistically high at Schackenborg due to a large infestation with grass weeds, and this indicates that these models, which rely heavily on one type of sensor measurement, may be vulnerable to other factors affecting these measurements.

The profitability of using the algorithms outlined in the two models were analysed by comparing net grain yield from application of the algorithms with grain yield from a fixed uniform application of 0.4 L ha^-1 Opus. This fixed rate application can be considered a typical fungicide treatment in winter wheat in Denmark. The yield results of using the fixed rate application were evaluated by using the yield predictions of the causal model, since no observed data could be provided in this respect that would compare with the other modelled results.

The results for the empirical model mostly showed no differences in net yield between the uniform and the variable fungicide rate. However, net negative yields were obtained at Schackenborg from using the variable fungicide rate, which primarily was due to much larger yield gains from fungicide application predicted by the empirical compared with the causal model due to the reasons described above. There was also a general increase in fungicide deposition on the soil due to generally higher fungicide rates applied with the variable fungicide rate compared with the uniform application.

For the causal model there was either no difference or a small increase in net yield from using the variable compared with the uniform fungicide rate. The variable fungicide rate gave in most cases a reduction in fungicide deposition on the soil, indicating possible positive environmental effects of using sensor-based variable fungicide rates in winter wheat.

The primary reasons for the small yield gains obtained from applying the sensor-based algorithms for varying fungicide rate is the generally rather small yield gains from disease control obtained in the experiment conducted in this project (Table 7). The largest predicted yield gains from spatially variable fungicide application was obtained at Schackenborg (Table 25), and this is only because the model predicted that no fungicide application would be needed here, largely in accordance with observed results (Table 7). The second largest predicted yield gains from spatially variable fungicide application were obtained at Dybvad, which had the highest septoria infestation observed in this project. There may therefore be scope for using these algorithms for improving farm economy and optimising (and reducing) fungicide use in winter wheat. However, this will require further testing of the algorithms under field conditions.

The analyses do not provide definite experimental conclusions on which of the empirical or the causal model is best suited for application in practice. However, the causal model is based on a stronger theoretical foundation of the effects of crop and soil characteristics on disease and the resulting effects on grain yield. The causal model should therefore be preferred. However, this model requires information on the general septoria infestation level at GS39, which may be estimated either by visual assessments or from general surveys and information on variety susceptibility.

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Version 1.0 January 2008, © Danish Environmental Protection Agency