Precision Agriculture

, Volume 9, Issue 1, pp 101–113

A technical opportunity index based on mathematical morphology for site-specific management: an application to viticulture

Authors

    • UMR ITAPMontpellier SupAgro/Cemagref
  • A. B. McBratney
    • University of Sydney, Australian Centre for Precision Agriculture
Article

DOI: 10.1007/s11119-008-9053-5

Cite this article as:
Tisseyre, B. & McBratney, A.B. Precision Agric (2008) 9: 101. doi:10.1007/s11119-008-9053-5

Abstract

The aim of this paper is to provide a method that enables a farmer to: (i) decide whether or not the spatial variation of a field is suitable for a reliable variable-rate application, (ii) to determine if a particular threshold (field segmentation) based on the within-field data is technically feasible with respect to the equipment for application, and (iii) to produce an appropriate application map. Our method provides a Technical Opportunity index (TOi). The novelty of this approach is to process yield data (or other within-field sources of information) with a mathematical morphological filter based on erosions and dilations. This filter enables us to take into account how the machine operates in the field and especially the minimum area (kernel) within which it can operate reliably. Tests on theoretical fields obtained by a simulated annealing procedure and on a real vineyard showed that the TOi was appropriate for assessing whether the spatial variation in a field was technically manageable.

Keywords

Site-specific management (SSM)Opportunity indexViticultureMathematical morphology

Introduction

Over the last 5 years, many new services based on remotely sensed images have become available and have been adopted by farmers to characterize their production systems and within-field variation. These services are dedicated to both annual broadacre systems (Roudier et al. 2007) as well as high value perennial systems, such as viticulture (Bramley and Hamilton 2004; Tisseyre et al. 2007). The advantage of these images is that they can provide information on a field by field basis at the production stage on the level of within-field variability. This information is of interest to farmers as it can be provided at several critical growth stages which allows management decisions to be optimized at various stages during the growing period. For wheat for example, the Farmstar service (Infoterra company, Toulouse, France) provides farmers with within-field maps of nitrogen requirement at the stem elongation growth stage. These maps also provide information on the spatial variation and the degree of variability in nitrogen requirement observed at the within-field level. This service, which has been operational in France since 2001, was used by more than 10000 farmers in 2007. In viticulture, vegetative indices derived from canopy imagery at veraison, a few weeks before harvest, are used to identify areas of different vigour within blocks. The grape quality within these different vigour zones is tested using a targeted sampling scheme, and the results are used to formulate differential harvest strategies (Bramley et al. 2005; Best et al. 2005).

When maps are delivered, farmers receive a large amount of data which has to be analysed rapidly. This means that the decision as to whether or not it is appropriate to apply site-specific management (SSM) has to be taken in a few days. This step is even more critical in viticulture when the information is delivered and analysed at the cooperative level. In this case, more than a hundred blocks may have to be analysed by a viticulturist within a short timeframe of two to three days.

The development and adoption of these imagery services over large areas highlights the need to provide an automatic quantitative characterization of field variability as a decision-support tool for the adoption of SSM.

Whelan and McBratney (2000) suggested that assessing the opportunity for SSM implies the assessment of: (i) an economic component (E) where the benefit of SSM relative to uniform management has to be quantified, (ii) an environment component (V) where, depending on local policy or other environmental constraints, the environmental benefit of SSM has to be quantified, and (iii) a spatial variation component (T), where both the degree of variation and the suitability for management intervention have to be characterized. Therefore, the definition of the opportunity for SSM relies on the aggregation of several components that summarize this from different points of view. Whelan and McBratney (2000) proposed a preliminary approach based on a decision tree to aggregate these different components. This approach is interesting because it relies on the definition of separate indices (E, V and T) and their aggregation to provide an answer about the opportunity to manage a particular field in a site specific way. Ideally, to shift to SSM, the observed variation in a field should meet criteria associated with the above components.

Many authors have dealt with the problem of economic opportunity (E) (e.g. Tozer and Isbister 2007; Rider et al. 2006). Bullock et al. (2002) proposed an interesting approach based on the economic performance of variable-rate application (VRA) as a function of yield, vigour maps or other within field information to address the problem. The component V is usually derived from the reduction of inputs and an anticipated improvement in the use of pesticide and fertilizer (Korsaeth and Riley 2006).

Few papers have dealt with the problem of T. The aim of this paper is to focus on the definition of an index for T called Technical Opportunity Index (TOi). Our aim is to use the data on within-field variation together with the technical aspects of VRA to develop a SSM technical opportunity index (TOi). Pringle et al. (2003) described an approach based on yield monitor data. They suggested that a pertinent opportunity index has to take into account both the magnitude of the yield variation and the arrangement in space of this variation. They proposed a SSM Opportunity Index (Oi). The Oi is interesting because it was shown to be reasonably successful in ranking the fields from the most suitable to the least suitable for SSM. Improvements in the calculation of Oi were proposed by De Oliveira et al. (2007), however, the principles underlying the index remain the same. The main difficulty in using the Oi is that it relies on a manual step that requires skill to compute and model variograms from the data. This step is not compatible with analysing large amounts of information, and it does not solve the practical and the technical considerations of the within-field variability. This means that once the spatial variation of a field is considered as significant, the Oi neither indicates whether it is useful and feasible to adopt SSM according to the application that is planned nor how the field needs to be segmented to optimise the VRA.

The technical opportunity index that we propose in the following section should bring solutions to these problems. Our approach aims at removing all manual steps during the computation. The input information used to determine the index has to be based on parameters that the average farmer can define easily (speed and width of the machine, time required to change the application rate, etc.). Our index should also bring a practical decision-support system to help the farmer to manage the within-field variability.

In the first part of this paper, we describe our Technical Opportunity index (TOi). In the second part, we present and discuss the results obtained from hypothetical fields with known variability in order to check the relevance of our approach, and also from a real example of a grape yield map. The latter was chosen because the vineyard block studied has additional data available on soil and vigour. It has been shown that the variation in grape yield shows considerable temporal stability (Bramley 2003), therefore, yield maps might provide relevant information to develop SSM in viticulture. Evidence of variation in soil and growth derived from airborne imagery might be good alternatives to yield data to develop SSM in viticulture.

Theory

From a practical point of view, site-specific management leads to at least two different management strategies (or two application rates) for the same field. If we consider P = {x1, x2, x3,..., xN} to be the set of data measured at the within field level on a particular field P, it is possible to consider at least two levels of treatment such as:
$$ SA_{\alpha}=\{x_{i} \in P/x_{i} < \alpha\} $$
(1)
$$ SB_{\alpha}=\{x_{ i} \in P/x_{i} \geq \alpha\}, $$
(2)
where SAα is the set of points in the field that should be managed to level A (strategy A), SBα is the set of points that should be managed to level B (strategy B) and α is a threshold for the data.
If the points associated with SAα and SBα form distinct patterns (Fig. 1c), it will be easy to apply the two strategies (even with an inaccurate machine). In this case, the technical opportunity for SSM will be high. Conversely, if SAα and SBα are intimately mixed in the field (Fig. 1a), it will be almost impossible to apply the two strategies and the technical opportunity for SSM will be low. Considering the examples in Fig. 1, the technical opportunity for SSM will also depend on the conditions under which specific management is performed. The possibility of managing the resulting patterns in SAα or SBα can vary dramatically according to the minimum area (k) within which the VRA is technically possible.
https://static-content.springer.com/image/art%3A10.1007%2Fs11119-008-9053-5/MediaObjects/11119_2008_9053_Fig1_HTML.jpg
Fig. 1

Three hypothetical fields after application of a threshold (α) to the within-field data. The white pixels belong to SAα where treatment A should be applied and the black ones belong to SBα where treatment B should be applied

Step 1:

Definition of the minimum area, k, within which VRA is technically possible.

The k can be considered as a kernel. A similar kernel was defined by Pringle et al. (2003), but we modify their definition to take into account the inaccuracy of the positioning system; for example, the innacuracy of the GPS receiver or the DGPS receiver depending on the system used to locate the machine within the field. The kernel k is defined as
$$ k=(\beta +d)(v\tau +d), $$
(3)
where β is the width of application by the machine in metres, ν is the speed of the vehicle in m s−1, τ is the time required to alter the application rate in seconds and d is the inaccuracy of the positioning system in metres.

Step 2:

Determination of the field area over which it is possible to manage according to threshold α and application kernel k.

This step can be viewed as a filter applied to the patterns of SAα and SBα (Fig. 1) where all spatial structures fulfilling the kernel condition are stored. This operation can be summarised by the following relations for SAα and SBα:
$$ \begin{aligned} A_\alpha^k\,=\,&F^{k}\left( {SA_\alpha}\right)\\ B_\alpha^k\,=\,&F^{k}\left( {SB_\alpha}\right), \end{aligned} $$
(4)
where \(A_\alpha^k\) and \(B_\alpha^k\) are the sets of points in field P managed by strategy A and B, respectively, according to k and α, k is the kernel corresponding to the conditions of VRA, α is the data threshold considered for the field and Fk is the filter applied to the patterns of SAα and SBα.
We reasonably assume that the machine which does the VRA cannot apply treatments A and B simultaneously at the same location, and that all locations in the field have to be treated as A or B. This leads to the following conditions that the filter Fkmust satisfy:
$$ \begin{aligned} A_\alpha^k\cap B_\alpha^k=\emptyset \\ A_\alpha^k\cup B_\alpha^k=\hbox{P} \end{aligned} $$
(5)
The aim of the filter Fk, is to eliminate all patterns that do not fulfil the kernel condition, i.e. field patterns that are too intricate to be managed reliably by the machine. Many operators could be used for Fk; in this study we applied two successive morphological filters on the resulting patterns of SAα. First, an opening (Serra 1982) that performs erosion and then a dilation. Erosion eliminates all structures that do not fulfil the kernel condition. Dilation reconstructs the image structures to the original size, but without the eliminated structures. Secondly, a closing that performs first a dilation and then an erosion is carried out. The effect of the dilation is to fill holes smaller than the kernel. Erosion reconstructs the image structures to their original size, but without the holes that have been eliminated.
Figure 2 shows that the size of the areas removed increases with the size of the kernel. As defined above, Fk provides a good assessment of the ability of the machine to be accurate and to account for more or less small patterns. When the machine can change the application rate rapidly over a small area (small kernel) the areas that can be managed effectively are also small (Fig. 2b). Conversely, when the machine operates over a large area and needs time to change the application rate (large kernel) then the areas that can be managed are also large (Fig. 2d).
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Fig. 2

The effect of the filter Fk and different values of k applied to (a) the thresholded map (SAα); (b), (c) and (d) represent examples of resulting maps with k = 2 m2, k = 9 m2 and k = 16 m2, respectively. The white pixels correspond to \(A_\alpha^k\) and the black ones correspond to \(B_\alpha^k\)

Step 3:

Determination of the set of points managed correctly.

After step 2, it is possible to determine the set of points that have not been managed correctly. This set is called \(E_\alpha^k\) and is computed as follows:
$$ E_\alpha^k=\left({A_\alpha^k \cap SB_\alpha}\right)\cup \left({B_\alpha^k \cap SA_\alpha}\right) $$
(6)
Figure 3 shows the resulting \(E_\alpha^k\) for the three examples shown in Fig. 2. Note that the number of points managed incorrectly increases as one would expect with the size of the kernel.
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Fig. 3

The set \(E_\alpha^k\) of points managed incorrectly (white pixels) for different sizes of kernel (k)

Knowing \(E_\alpha^k,\) it is possible to determine the set of points correctly managed, it corresponds to the complementary set \(^{c}\left({E_\alpha^k}\right).\) It is then possible to determine the set of points that have been managed correctly according to the strategies A \((ScA_\alpha^k)\) and B \((ScB_\alpha^k)\) and also the number of points belonging to each of them:
$$ \begin{aligned} ScA_\alpha^k=SA_\alpha \cap\;{}^c\left({E_\alpha^k}\right) \Rightarrow N_{A,\alpha}^k=card\left({ScA_\alpha^k}\right) \\ ScB_\alpha^k=SB_\alpha \cap\;{}^c\left({E_\alpha^k}\right) \Rightarrow N_{B,\alpha}^k=card\left({ScB_\alpha^k}\right) \end{aligned}, $$
(7)
where card\((ScA_\alpha^k)\) and card\((ScB_\alpha^k)\) are the cardinal (counts of the elements) of the set \(ScA_\alpha^k\) and \(ScB_\alpha^k,\) respectively.

Step 4:

Index definition

It is then possible to consider the following probabilities:
$$ P\left(A\right)_\alpha^k=\frac{N_{A,\alpha}^k}{N_T}, \quad P\left(B\right)_\alpha^k=\frac{N_{B,\alpha}^k}{N_T}, \quad P\left(E\right)_\alpha^k=\frac{N_{E,\alpha}^k}{N_T}, $$
(8)
where \(P\left(A\right)_\alpha^k\) and \(P\left(B\right)_\alpha^k\) are the probabilities of managing the field correctly according to strategies A and B, resepctively, \(P\left(A\right)_\alpha^k\) and \(P\left(B\right)_\alpha^k)\) can also be regarded as the proportions of the field managed correctly according to strategies A and B, respectively, \(P\left(E\right)_\alpha^k\) is the probability of managing the points within the field with the wrong strategy or the proportion of the field managed as such and NT is the total number of points within the field. Considering Eqs. 5 and 6, it is possible to show that:
$$ \begin{aligned} &P\left(A\right)_\alpha^k+P\left(B\right)_\alpha^k+P\left(E\right) _\alpha^k =1,\forall \alpha,k \\ &\hbox{and} \\ &P\left(A\right)_\alpha^k \times P\left(B\right)_\alpha^k \leq 0.25=M,\forall \alpha,k \end{aligned}, $$
(9)
where M is the maximum possible value for the product, M standardizes TOi by M = (1/2)2 for two strategies, M = (1/3)2 for three strategies, etc.

Our approach is based on the test of different thresholds, α, on field data {x1, x2, x3, ..., xN} to determine if two different management strategies are possible and if there is an optimal threshold. The approach is based on a simulation of the footprint of the machine to determine the error in VRA for each possible threshold. If α is very small (i.e. close to the minimum x value) then \(P\left(A\right)_\alpha^k\,{\approx}\,0, P\left(B\right)_\alpha^k\,\approx\,1\) and \(P\left(E\right)_\alpha^k\,{\approx}\,0.\) This means that the machine makes almost no error when only one strategy has to be applied in the field. This particular example shows that the proportion of field managed with the wrong strategy (\(P\left(E\right)_\alpha^k)\) cannot be considered alone to define an index aiming at testing whether the field can be managed site-specifically. Considering our approach, whatever the field, an index designed to minimise \(P\left(E\right)_\alpha^k\) alone would then lead to applying only one strategy. Therefore, to be relevant, the TOi must take into account simultaneously the proportion of field area managed specifically and how properly the machine operates. For a given field, we assume that the opportunity index for SSM increases when the proportion of the field area treated site-specifically and correctly increases. Therefore, our index has to take into account this first proposition.

Both \(P\left(A\right)_\alpha^k\) and \(P\left(B\right)_\alpha^k\) should be maximal, then:
$$ P\left(A\right)_\alpha^k\,\times\,P\left(B\right)_\alpha^k \; \hbox{should be maximal}. $$
(10)
We also want the probability of making an error to be minimal, that means we want our index to take into account this second proposition:
$$ P\left(E\right)_\alpha^k \; \hbox{to be minimal} \Leftrightarrow 1-P(E)_\alpha^k\; \hbox{to be maximal}. $$
(11)
The index \((P_\alpha^k)\) is then defined to be maximal when the proportion of field site-specifically managed is maximal and when the error of application is minimal according to (i) different threshold values (α), and (ii) kernel k:
$$ P_\alpha^k=\frac{1}{M}\,\times\,\left[{\left({P\left(A\right)_\alpha^k\,\times\,P\left(B\right)_\alpha^k}\right)}\times \left({1-P\left(E\right)_\alpha^k}\right)\right]. $$
(12)
The technical opportunity index needs \(P_\alpha^k\) to be maximal for a given value of k and all the possible values of threshold α. It is then defined as follows:
$$ \hbox{TO}_{\rm i}=\frac{1}{M}\,\times\,\mathop{\hbox{sup}}\limits_\alpha\left[{\left({P\left(A\right)_\alpha^k\,\times\,P\left(B\right)_\alpha^k}\right)}\times\left({1-P \left(E\right)_\alpha^k}\right)\right]=\mathop{\hbox{sup}}\limits_\alpha\left[{P_\alpha^k} \right], $$
(13)
where \(\mathop{\hbox{sup}}\limits_\alpha\) means the value α that maximises \(P_\alpha^k.\)

The TOi proposed in Eq. 13 determines only the maximal ability (and the related threshold) of the machinery to manage the field site-specifically and correctly according to the observed within-field variation and the footprint of the machine. It is designed as a decision-support tool to allow fields to be ranked from the most suitable to the least suitable for SSM. The decision to change to site-specific management also has to take into account economic, environmental and plant response model considerations. According to these other considerations another threshold α might be chosen. In this particular case, our approach enables \(P\left(A\right)_\alpha^k,\)\(P\left(B\right)_\alpha^k\) and \(P\left(E\right)_\alpha^k\) to be calculated. This information can be used as a decision-support tool to check if the considered threshold is relevant for the machine characteristics. Comparing \(P\left(A\right)_\alpha^k\) and \(P\left(B\right)_\alpha^k\) to \(P\left(E\right)_\alpha^k\) enables one to check if the proportion of the field managed correctly is significant compared to the error and to decide whether or not uniform management will remain the best option.

Material and methods

Data

The simulated data were used to test our TOi on hypothetical fields of known variability to verify the relevance of the index and to test the possibility of using the TOi as a decision-support tool. Tests were also performed on grape yield data because of the availability of such data and because of our experience with their within-field variation. As a result of the perennial nature of the vines, grape yield patterns tend to be quite stable over time. However, the tests could have been performed on the soil’s apparent resistivity, airborne imagery or other information because yield maps might not be the best information to develop SSM in all cases. Two types of data were then used to test the TOi:
  1. (1)

    Yield monitor data (Fig. 7a) obtained from a sensor mounted on a grape-harvesting machine (Pellenc S.A). The field is 1.4 ha and planted with the Bourboulenc variety and was harvested in 2001 in Provence (France). The average sampling rate is about 2400 measurements per ha. Yield data were kriged on to a grid of 1-m resolution.

     
  2. (2)

    Hypothetical fields of known spatial variation were obtained from a simulated annealing procedure (Goovaerts 1997). For all the vineyard blocks in our database, the theoretical variogram is an exponential function with a nugget effect of approximately one third of the sill. We used a nugget effect of 5 and a sill of 16 (arbitrary units) for the simulations, therefore the different fields differ only in their variogram ranges. The simulation was run with a Gaussian data distribution centered on 100 with a variance of 16 (arbitrary units). To simplify the tests, data were standardised so that they belong to [0;1]. Five fields were generated with effective ranges for the variogram model of 9, 18, 27, 36 and 45 m. The variogram parameters used to create the hypothetical fields were chosen to correspond with those from vineyards harvested previously with real-time yield monitors (Taylor et al. 2005).

     
In addition, we had one field with no spatial structure to examine a pure nugget effect. All of the hypothetical fields have an area of 1 ha (100 × 100 m) and a grid resolution of 1 m; so each virtual field can be considered as an image of 100 pixels × 100 pixels where 1 pixel = 1 m2. The data are available at the following web address (www.precisionviticulture.org). Figure 4 shows the theoretical fields obtained at the end of the annealing procedure. Note that for all fields the distribution of pixel values is the same (normally distributed) and the only attribute that changes from one field to another is the spatial arrangement of these values. The fields are ranked according to the increasing range of the theoretical variogram used for the annealing procedure. The patches of dark or light pixels become larger as the range increases. This is clear when comparing field (b) where the average size of the light patches is around 10 m2 to field (e) where only 3–4 light patches of more than 1000 m2 remained after the annealing procedure.
https://static-content.springer.com/image/art%3A10.1007%2Fs11119-008-9053-5/MediaObjects/11119_2008_9053_Fig4_HTML.jpg
Fig. 4

Hypothetical fields produced by an annealing procedure with: (a) a pure nugget variogram, and an exponential variogram with effective ranges of: (b) 9 m, (c) 18 m, (d) 27 m, (e) 36 m and (f) 45 m. Each field has an area of 1 ha and each pixel is 1 m2. The pixel values follow a normal distribution with a mean of 100 and variance of 16 (arbitrary units)

Standard vineyard operations considered and resulting kernels

The kernels were chosen according to standard operations that could be used for SSM in a vineyard. A plantation density of 4000 stocks per ha. was considered. The resulting kernels are given in Table 1.
Table 1

Standard vineyard operations considered and resulting kernels

Operation

Speed (m s−1)

Width (m)

Time rate (s)

Location inaccuracy (m)

Kernel (m2)

Winter pruning

0.1

2 (1 row)

1

1

k1 = 3

Summer pruning

1

2 (1 row)

1

1

k2 = 6

Harvesting

1

2 (1 row)

3

1

k3 = 12

Spraying

2

4 (2 rows)

2

1

k4 = 25

Fertilizer application

2

8 (4 rows)

2

1

k5 = 45

Results

Results for theoretical fields

Figure 5 shows how the index Pαk of managing site-specifically and correctly varies with the different threshold values (α) for the theoretical data. It also shows the evolution of the probability of the error P(E)αk.
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Fig. 5

The index \(P_\alpha^k\) of managing the field site-specifically and correctly, and the probability \(P(E)_\alpha^k\) of making an error as a function of α (threshold on the normalized within-field data). The TOi value and optimal threshold α correspond to the maximal value of \(P_\alpha^k.\) These results were obtained from a theoretical field with an effective variogram range of 36 m and a kernel of 2 m2

Figure 5 shows that for a given range of α values, the index Pαk becomes larger than the probability of making an error. That means this range of values indicates that SSM should be considered. Among these values, the one that simultaneously minimizes the error and maximizes the probability corresponds to the best possible threshold. This value gives the TOi. For the case presented in Fig. 5, the optimal threshold is α = 0.48 (standardized data value) and the corresponding TOi is 0.7. The symmetric shape of the curves is logical since the data are normally distributed.

To verify that our TOi is useful for assessing that SSM is a technical possibility, it was applied to all theoretical fields with different ranges of spatial dependence and with different values for the kernels (see Table 1). Figure 6 shows the results. Regardless of the extent of spatial dependence in the field, the smaller is the kernel, the larger is the index. Whatever the kernel size, the larger is the range of spatial dependence in the field, the larger is the index. These results correspond to what we would expect from a SSM Technical Opportunity Index. The index enables us to assess whether it is possible to manage the field according to the observed spatial variation and the characteristics of the machine which does the operations. Our results show that our TOi is relevant because it can identify fields which are more-or-less manageable technically. The results obtained with this index are similar to those obtained with the Opportunity Index (Oi) which are also shown in Fig. 6.
https://static-content.springer.com/image/art%3A10.1007%2Fs11119-008-9053-5/MediaObjects/11119_2008_9053_Fig6_HTML.gif
Fig. 6

Results of the TOi tested with five different kernels (Table 1) on six theoretical fields with different variogram ranges (Fig. 4) and compared with the Oi index proposed by Pringle et al. (2003)

The TOi increases dramatically from a spatial range of zero to one that corresponds roughly to the size of the kernel. This is clear for the kernels k1, k2 and k3 in Fig. 6. For these three kernels, the index remains roughly the same for spatial ranges that exceed the size of the kernels (10 m). A similar tendency is obtained for a range of about 30 m for k4. This result is logical if you consider that once the range of variation within the field is larger than the kernel, it means that patterns in the field have a greater average extent than the kernel. Then, whatever the range of spatial variation in the field, the patterns are all technically manageable in the same way. This was not the case for Oi because its computation takes into account the spatial structure of the field, therefore, it increases continuously with the range.

Results for the real data

The application of our approach to a real field aims to verify that the additional information provided by our TOi is significant compared to the use of Oi.

Figure 7a shows the yield map of grapes used for this study. The map shows a considerable change in yield from north to south. Other observations (vigour, resistivity, soil depth, etc.) on this particular field have shown that the variation in yield was due mainly to variation in the soil and soil–water availability (Tisseyre 2003). The southern end of the field has strong growth of the vines, a large yield and deep soil, whereas the northern end has a small yield, plants with weak growth (low vigour) and light soil. The perennial parts of the vine are also affected strongly by the different conditions, which means that this phenomenon results in temporal stability. For this particular field, yield maps should be a good indication of whether or not site-specific management should be adopted. In this particular case, one of the management strategies could be to grass some parts of the field to decrease the water availability to the vine. This would reduce the yield and the vigour of the plants, consequently, this would increase the quality (sugar content, flavour compounds, etc.). The TOi would be a good tool to decide whether or not this SSM approach should be adopted to improve the quality of the harvest. The TOi was computed with a kernel of 12 m2 corresponding to the characteristics of the machine (speed, width of application, estimated time to change the application rate, etc.) used by the grower. The TOi for this field with k  =  12 m2 is large (TOi = 0.85). This shows a great opportunity to manage this field site-specifically. The best threshold yield value was found to be α = 2650 kg ha−1. This threshold was determined according to Eq. 13. It corresponds to the maximal ability of the machine to manage the field site-specifically and correctly according to the observed within-field variation and the footprint of the machine. This threshold leads to the two management strategies shown in Fig. 7b and c in white. The two management zones identified by our approach correspond to two large patches in the field; one in the north and one in the south. This explains why a large technical opportunity index was observed. As shown in Fig. 7, these two strategies are easy to put into practice in the field, even with a large kernel. This example for a real field shows that our TOi can be used for decision-support to: (i) assess the opportunity to manage the field site-specifically with the machine under consideration, (ii) discover the threshold (on yield values in this particular case) which minimizes errors of application, (iii) make an appropriate application map and (iv) visualize the field as it could be treated by the operation under consideration.
https://static-content.springer.com/image/art%3A10.1007%2Fs11119-008-9053-5/MediaObjects/11119_2008_9053_Fig7_HTML.gif
Fig. 7

(a) Kriged map of yield of the Bourboulenc variety and two management strategies proposed for the field according to the threshold α on the yield values, (b) the result for strategy A where grass is placed between rows (yield of 4950 kg ha−1, std = 740 kg) and (c) the result for strategy B with no grass (2250 kg ha−1, std = 500 kg). Application maps were computed with a kernel k = 12 m2. As stated in Eq. 5, the machine cannot apply treatments A and B simultaneously at the same location, this condition leads logically to two application maps that are the inverse of one another

Conclusions

We have defined and implemented a technical opportunity index that will enable decision-makers to decide whether the observed variation within a field is manageable for some proposed field operation. The TOi index, which is based on mathematical morphological filters of interpolated data on a grid, may be viewed as a useful tool to rank the fields according to their opportunity for SSM. Compared to existing Opportunity Indices, the main advantage of our index is to be able to process the data automatically without any manual help. Our approach requires no skill to compute and model variograms from the data. The input data required to run the TOi calculation are based only on knowledge of the machine’s characteristics, such as the speed, the width of application, the time required to change the rate of application, etc. These characteristics are well known either by the viticulturists or by the growers. In the future, this approach could be implemented by simple software. Only one interface should be necessary to choose the machine or the parameters describing the way that the machines operate on the fields. The software will be able to process large amounts of data without the need for any manual intervention. It will then compute, for each field in the data base, the technical opportunity index (TOi) and a threshold value (or a range of threshold values) to minimize application errors arising from the machine’s footprint. A TOi of about 0.5 could be the minimum for considering SSM. Such a value means that it is possible to treat correctly 40% of the field area with respect to one treatment and 40% of the field area with respect to another treatment with an error of 20%.

Confidence in the index proposed here was obtained by showing that it increased with increasing variogram range for the simulated random fields. The results from observed grape yields also appeared to be intuitively correct. In the future we intend to improve the index by recognising that: there might be more than two possible decisions at any location, the grid interpolation required to apply the mathematical morphology operator might mask the problem of missing information and over estimate our technical opportunity index and finally, the real-time footprint for a particular within-field operation is not crisp but somewhat fuzzy. These points will be investigated further.

Acknowledgments

This work forms part of the project VI-TIS, project Eureka, funded by the French Ministry for Research.

Copyright information

© Springer Science+Business Media, LLC 2008