A technical opportunity index based on mathematical morphology for site-specific management: an application to viticulture
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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
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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 (TO_{i}). 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 TO_{i} was appropriate for assessing whether the spatial variation in a field was technically manageable.
Keywords
Site-specific management (SSM)Opportunity indexViticultureMathematical morphologyIntroduction
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 (TO_{i}). 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 (TO_{i}). 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 (O_{i}). The O_{i} 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 O_{i} were proposed by De Oliveira et al. (2007), however, the principles underlying the index remain the same. The main difficulty in using the O_{i} 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 O_{i} 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 (TO_{i}). 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
Step 1:
Definition of the minimum area, k, within which VRA is technically possible.
Step 2:
Determination of the field area over which it is possible to manage according to threshold α and application kernel k.
Step 3:
Determination of the set of points managed correctly.
Step 4:
Index definition
Our approach is based on the test of different thresholds, α, on field data {x_{1}, x_{2}, x_{3}, ..., x_{N}} 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 TO_{i} 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.
The TO_{i} 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
- (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)
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).
Standard vineyard operations considered and resulting kernels
Standard vineyard operations considered and resulting kernels
Operation | Speed (m s^{−1}) | Width (m) | Time rate (s) | Location inaccuracy (m) | Kernel (m^{2}) |
---|---|---|---|---|---|
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 that for a given range of α values, the index P_{α}^{k} 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 TO_{i}. For the case presented in Fig. 5, the optimal threshold is α = 0.48 (standardized data value) and the corresponding TO_{i} is 0.7. The symmetric shape of the curves is logical since the data are normally distributed.
The TO_{i} 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 O_{i} 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 TO_{i} is significant compared to the use of O_{i}.
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 TO_{i} 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 TO_{i} 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 (TO_{i}) and a threshold value (or a range of threshold values) to minimize application errors arising from the machine’s footprint. A TO_{i} 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.