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IntroductionUnderstanding spatial variability in perennial crops, such as winegrapes, is important for farmers and those downstream of the crop, but in the absence of appropriate sensors, the cost of sample collection necessary to create maps of productivity constrains most operations (Bramley 2021). Vegetation indices, derived from remote or proximal sensors, are tools that can alleviate some of this burden by allowing practitioners of precision agriculture to collect strategic samples based on the assignment of management zones to areas considered to contain similarly productive plants (Acevedo‐Opazo et al. 2008, Tagarakis et al. 2013, Bonilla et al. 2015, Meyers et al. 2020, Oldoni et al. 2021, Sams et al. 2022b). Nevertheless, direct measurements may be necessary to characterise variability in regions where image collection is difficult due to atmospheric conditions, or where the variable of interest is not closely related to the spectral response of canopies (Sams et al. 2022a,b). In these cases, mapping support must meet some minimum criteria in order to be trustworthy. Kriging (e.g. Webster and Oliver 2007) is regarded as the optimal method for map interpolation in agriculture (Whelan et al. 1996), and relies on the function known as the ‘experimental variogram’ which describes the relationship between the variance among sample measurements as a function of the distance between the locations at which the samples were collected. This function is used in the kriging interpolation process to give appropriate weighting to neighbouring sampled locations in estimating the values of the variable of interest at unsampled locations. Robust estimation of the experimental variogram requires a minimum of 100 samples (Webster and Oliver 2007), though more statistically complex techniques such as the residual maximum likelihood (REML) variogram estimation have shown promise in reducing sample size requirements in soil science (Pardo‐Igúzquiza and Dowd 1998, Kerry and Oliver 2007). Additionally, at least 30 pairs of points per distance class, or lag, may be necessary to fully characterise this variability (Cressie 1993). Some published studies have included maps with a resolution far lower than the smallest distance between any two sample points (Cortell et al. 2005, 2007, Martínez‐Lüscher et al. 2019, Brillante et al. 2020, Yu et al. 2020), and/or with far fewer than 100 samples used for mapping, making both the maps and subsequent analysis potentially unreliable. A method for aggregating samples from many vineyards would therefore be useful to the grapegrowing community, as it could allow for a more robust estimation of the spatial structure of fruit composition and other indices of vineyard performance with low sampling requirements for individuals.Taylor et al. (2005) found similarities in several geostatistical metrics (effective range, Cambardella index, and opportunity index) related to yield variability between vineyards in Europe and Australia. Accordingly, they suggested that it would be useful to also develop an understanding as to how fruit composition varies across regions, cultivars and production. While McBratney and Pringle (1999) provided a basis for the estimation of ‘average’ and ‘proportional’ variograms, Bramley et al. (2017) pioneered the use of a ‘common’ or ‘across‐years’ variogram in vineyards to assess the spatial patterns of berry rotundone concentration over several years and to reduce the potential for artefacts of subjective variogram fitting to data from any single year on analysis of the temporal stability of patterns of spatial variability. Sams et al. (2019) used this common variogram approach in order to assess the effect of aggregating samples on the spatial patterns of anthocyanins in four vineyards in central California and found the method to add robustness to the variogram estimation as suggested by Cressie (1993) without compromising the characterisation of spatial patterns of variability when mapping each vineyard individually.The first objective of the current study was to expand the results presented by Sams et al. (2019) to include multiple years to determine the effect of the common variogram estimation on spatial patterns of variability over time. The second objective was to determine the effectiveness of this method to generate more robust and useful maps of fruit compositional attributes that Sams et al. (2022a) found to be somewhat spatially and temporally erratic—possibly due to artefacts of the variogram fitting process rather than due to annual variation in the pattern of spatial variation. Simulation studies were also conducted to assess and to demonstrate the ability of the common variogram method to produce maps suitable for characterising spatial variability in an unknown or unsampled vineyard.Materials and methodsVineyards and sample collectionImmediately prior to commercial harvest, 125 samples per year were collected in 2017, 2018 and 2019 from each of four Vitis vinifera L. cv. Cabernet Sauvignon vineyards in the Lodi American Viticultural Area in central California (38° 7′ 44″ N, 121° 16′ 51″ W). The vineyards and samples were the same as those presented in Sams et al. (2022a,b). Briefly, all four vineyards were drip‐irrigated, spur‐pruned, and machine harvested. Vineyard A, planted in 2010 on the rootstock 039‐16 and to clone FPS 08, was pruned to a single bilateral sprawling training system and had no inter‐row cover crop. Vineyard B, planted in 2013 on SO4 rootstock and to clone 7, and Vineyard C, planted 1998 on 1103P and to clone 7, were trained to quadrilateral sprawling systems with a perennial inter‐row grass cover crop. Vineyard D, planted in 2012 on rootstock 039‐16 and to clone 15, was a mechanised high‐wire sprawling canopy with the same inter‐row cover crop as Vineyards B and C. Elevation in Vineyards A and C varied by less than 2 m, Vineyard B sloped about 20 m downward from north to south, and Vineyard D was characterised by rolling hills with an elevation range of about 8 m.As outlined in Sams et al. (2022a), the sampling scheme was designed and intended for spatial analysis of fruit chemistry using modified regular grids based on row and vine distance (i.e. Vineyard A had a spacing of 2.1 m between vines and 3.1 m between rows, so the grid was 2.1 × 3.1 m), but with random offsets assigned to each data vine location. This method allowed for the characterisation of spatial dependence and variability at short, uneven distances for robust variogram generation at low sample separation of ‘lags’. Commercial harvest for the four vineyards occurred within 10 days of one another in all 3 years, with the entire 2019 sample collection occurring over just 5 calendar days. In most cases, the vineyards were sampled either the day before or on the day of commercial harvest. Fruit from each data vine was completely removed and yield for each vine recorded. Twenty bunches, sampled at random from each vine, were then set aside for laboratory analysis.Laboratory analysisTotal anthocyanins were measured using the UV‐Vis method of Iland et al. (2000). Malic acid was analysed by Fourier‐transform infrared spectroscopy using a WineScan FT‐120 (FOSS North America, Eden Prairie, MN, USA) using a calibration created in WinISI II (FOSS, Hillerød, Denmark) using the reference chemistry quality standards of E&J Gallo Winery. Quantification of bound form β‐damascenone was completed following a method of solid phase extraction derived from Whiton and Zoecklein (2002), fast acid hydrolysis, and headspace solid‐phase microextraction (SPME) coupled to GC/MS (Kotseridis et al. 1999, Ibarz et al. 2006, Canuti et al. 2009).Variogram analysisExperimental variograms for individual constituents of fruit composition in each year were estimated as part of Sams et al. (2022a). Building on this work, and that of Bramley et al. (2017) and of Sams et al. (2019), the focus of the current study was to explore the application of the common variogram to multiple sites, seasons, and an expanded number of variables. The choice of the variables used in this study followed Sams et al. (2019) with the addition of 2018 and 2019 anthocyanins, but malic acid (2017 to 2019) and β‐damascenone (2017 to 2019) were chosen as they showed high vine to vine variability where higher sample numbers may be necessary to generate zonal maps with high confidence and may be aided by the use of a common variogram. Bramley et al. (2017) used 1000 m offsets, applied sequentially to data from additional seasons to both the x and y coordinates, to combine data from multiple years from a 6.1 ha vineyard. These offsets enabled the derivation of a common variogram from multiple years by incorporating the semivariance from multiple years into the same spatial model. A larger number of point pairs in each lag class was achieved and any artefacts of variogram fitting in a single season were removed from the overall analysis. The larger set of point pairs is especially important at short distances as these are typically those at which the fewest pairs exist, yet characterising spatial dependence at short distances is critical to robust definition of the variogram and of the range of spatial dependence—the distance beyond which, samples can be regarded as independent. In the present context with multiple vineyards in multiple seasons, a much larger offset was required to ensure that the data contribution from any single vineyard/season was spatially discrete in relation to the others. Given that the four vineyards lie within approximately 40 km of each other, common variograms were generated by adding a 100 km offset to the eastings and northings of each vineyard to combine data from 2017 to 2019 such that the original coordinates were used for the 2017 data, +100 km to each coordinate in 2018, and +200 km to each coordinate in 2019. Data from each vineyard and year were standardised [mean (μ) = 0, SD (σ) = 1] to eliminate issues related to site or season specificity such as inherent differences in the absolute values of compositional metrics, or differences due to seasonal weather. Common settings of lag size (20), lag tolerance (10%), and maximum distance (250 m) were applied to the variogram estimation of each dataset in VESPER (Minasny et al. 2005) with the maximum distance of 250 m being appropriate both in terms of expected patterns of variation (Sams et al. 2022a) and as a means of ensuring data from the different vineyards remained discrete. As in Sams et al. (2022a), a spherical model was found to be suitable for the spatial characterisation of fruit composition, and spatial statistics were produced for each variable and associated variogram. Each variable from each vineyard was then interpolated using each set of variogram parameters derived from the single and combined datasets [single vineyard–single year (SVSY), n = 125; single vineyard–multiple year (SVMY), n = 375; multiple vineyard–single year (MVSY), n = 500, multiple vineyard–multiple year (MVMY), n = 1500] to assess differences in map products. Variogram statistics were calculated for all four classes of variograms listed above. These include the nugget [measurement and sampling error (c0)], partial sill [spatially dependent variance (c1)], effective range [distance at which samples are no longer spatially dependent (a1) (Webster and Oliver 2007)], and root‐mean‐squared‐error (RMSE). Cambardella index was calculated as the nugget divided by the sum of the nugget plus the sill and multiplied by 100 and was used as a descriptor of the spatial structure of variability (Cambardella and Karlen 1999, Sams et al. 2019). Low values of Cambardella index indicate high spatial structure and can be used to assess the potential suitability of a farm for variable rate management (Han et al. 1994).To further demonstrate the utility and application of the approach, two case study simulations were carried out for an ‘unknown’ vineyard and analyte. The first was conducted in order to simulate how a common variogram could be used for a practical purpose. For this, the 2019 anthocyanin concentration in the ‘unknown’ vineyard (Anth2019D in Vineyard D) was predicted based on different numbers of sample points (n = 10 to 120 with intervals of 10) and common variograms using Monte Carlo simulations (100 iterations per n). To ensure that selected sample points (n) in each simulation were uniformly spread out in the ‘unknown’ vineyard, a ten‐cell grid of five rows and two columns was used to label all 125 points (Figure 1). The grid labelling system mimicked a sampling strategy where samples were spread across the vineyard but also that each section of the vineyard would be represented in each simulation. In each Monte Carlo simulation, three steps were defined as selection, prediction, and evaluation. In the selection step, n/10 points were randomly selected from each grid cell and used as inputs for the kriging model. Next, Anth2019D was predicted using three different models: a common variogram produced from using data from 2017 to 2019 in Vineyards A, B, and C (CV); a common variogram produced using data from 2017 to 2019 in Vineyards A, B and C with the (n) points from the ‘unknown’ vineyard (CV+); and the SVSY variogram of the ‘unknown’ vineyard with the (n) points (SVSYn, where n represents the increasing number of included points from 10 to 120). Finally, Anth2019D maps produced from three different variograms were classified by histogram analysis into 33rd percentiles (low, medium and high) and compared to the classified 2019 anthocyanin map in Vineyard D using the SVSY of Vineyard D with all 125 points. Kriging estimates from simulated maps of each model were compared against the SVSY using the ‘accuracy’ metric from a confusion matrix, where accuracy is equal to the proportion of predictions the model was able to classify correctly (Fawcett 2006). Average kriging variance and average variance of estimated anthocyanins were also calculated from the resulting layers.1FigureSample points labelled by grid cell for the Monte Carlo simulation to ensure whole vineyard coverage in the ‘unknown’ vineyard. Each iteration of single vineyard–single year (SVSYn), from 10 to 120 sample points included, consisted of increasing numbers of sample points coming from each grid cell.The second simulation study was conducted to illustrate how a grower might take advantage of the common variogram and the reduced annual sampling requirement that it enables. Using the same target vineyard (Vineyard D) as in the first simulation, 35 sample points were randomly selected from each of the four vineyards and each year (2017–2019), with no repeated samples, and were standardised (μ = 0, σ = 1) by vineyard and year. The standardised data from Vineyard D, obtained over 3 years, were combined into a single dataset and a SVMY variogram was fitted and a combined map of total anthocyanins from 2017 to 2019 was produced. To simulate how a group of growers may cooperate for the derivation of a common variogram, samples from the other three vineyards (Vineyards A, B and C) were added to the combined Vineyard D dataset and a MVMY variogram was fitted and applied to the combined Vineyard D sample points for interpolation.ResultsSpatial variabilityMaps produced from different variogram models were similar, with small deviations among the maps derived from the different variograms (Figures 2–4). The spatial variability of anthocyanin concentration did not change dramatically with different variogram settings in Vineyards B and D in 2018 (Figure 2) and the same was true for β‐damascenone in Vineyards A and C in 2017 (Figure 3). The variability of malic acid in Vineyard C changed little from 2017 to 2019 using the SVSY compared with the MVMY (Figure 4). In general, patterns of spatial variability could be characterised as ‘smoother’ as the number of vineyards or years included in each variogram model increased from 125 points in the SVSY variograms to the MVMY variograms with 1500 points used to determine spatial structure (Figures 2–4).2FigureMaps showing spatial variability of standardised (μ = 0, σ = 1) anthocyanin concentration in 2018 in (a–d) Vineyard B and in (e–h) Vineyard D derived from experimental variograms derived from (a, e) single vineyard–single year (SVSY) n = 125; (b, f) single vineyard–multiple year (SVMY) n = 375; (c, g) multiple vineyard–single year (MVSY) n = 500; (d, h) multiple vineyard–multiple year (MVMY) n = 1500.3FigureMaps showing spatial variability of standardised (μ = 0, σ = 1) β‐damascenone concentration in 2017 in (a–d) Vineyard A and in (e–h) Vineyard C derived from experimental variograms derived from (a, e) single vineyard–single year (SVSY) n = 125; (b, f) single vineyard–multiple year (SVMY) n = 375; (c, g) multiple vineyard–single year (MVSY) n = 500; (d, h) multiple vineyard–multiple year (MVMY) n = 1500.4FigureMaps showing spatial variability of standardised (μ = 0, σ = 1) malic acid concentration in Vineyard C derived from experimental variograms derived from (a) single vineyard–single year (SVSY) in 2017, (b) SVSY in 2018, (c) SVSY in 2019, (d) multiple vineyard–multiple year (MVMY) in 2017, (e) MVMY in 2018, (f) and MVMY in 2019. All SVSY n = 125; and all MVMY n = 150.VariogramsSpatial statistics showed that although there were differences between SVMY variograms and those from SVSY variograms, differences between them in terms of RMSE were small, with those for multiple years (SVMY) typically lower than the highest error of any single year (SVSY) (Table 1). Results from multiple vineyard variograms showed that RMSE was also similar between any MVSY and the MVMY (Table 2). In general, the nugget, sill, and Cambardella index of each SVMY variogram were somewhere between those of the highest and lowest values of the SVSYs, though anthocyanin concentration in Vineyard A was an exception (Table 1). Nugget (c0) and partial sill (c1) variance, along with effective range (a1), were more consistently similar among multiple vineyard variograms (Table 2) as compared with single vineyard variograms (Table 1). Since 3 years were included in the SVMY, the number of pairs of points in each lag class increased exactly threefold (Table 1), with the largest number of point pairs per distance class (lag) occurring in the MVMY variogram (Table 2)—as would be expected. Variograms derived from total anthocyanins were similar in shape and in ranges of spatial dependence (Figure 5), though the 2017 effective range in Vineyard B separated from the others in Vineyard B (Figure 5b). Variograms derived from β‐damascenone data and malic acid (not shown) exhibited some differences between vineyards, and variogram settings were similar to those found for anthocyanins, but these did not result in any major changes in mapped outputs.1TableSpatial statistics from each single vineyard–single year variogram and from each single vineyard–multiple year variogram incorporating data from 2017 to 2019.Vineyard AVineyard BVineyard CVineyard D20172018201917/18/1920172018201917/18/1920172018201917/18/1920172018201917/18/19AnalyteStatisticn = 125n = 125n = 125n = 375n = 125n = 125n = 125n = 375n = 125n = 125n = 125n = 375n = 125n = 125n = 125n = 375AnthocyaninsNugget (c0)0.4184.108.40.2060.030.590.380.450.430.480.200.370.730.150.040.46Sill (c1)0.550.880.840.470.880.440.650.540.550.520.820.630.230.760.850.46Range (a1) (m)481305115365106868712810712512088583884CAM441813553573745444820377616450RMSE0.080.130.100.080.130.060.100.050.080.150.070.070.100.100.110.10β‐DamascenoneNugget (c0)0.740.020.490.560.460.450.60.560.540.110.570.380.650.540.250.49Sill (c1)0.270.980.620.440.570.550.420.470.440.790.490.570.300.440.590.43Range (a1) (m)8021215769814910312668124259111178293202216CAM7324456454559545512544068553053RMSE0.070.070.140.080.070.090.500.190.100.150.080.090.110.080.070.06Malic acidNugget (c0)0.520.140.410.390.470.320.120.340.150.230.050.220.340.110.060.17Sill (c1)0.480.900.560.620.680.830.900.850.850.760.980.790.590.860.720.74Range (a1) (m)837380803413885030515417411714745624151CAM521342394128122915235223711819RMSE0.090.100.060.070.110.140.230.120.100.110.070.060.160.120.140.07Lag minimum2424247210101030181818543535351052TableStatistics from common variograms that include all four vineyards in each year (multiple vineyard–single year) and an aggregated common variogram (multiple vineyard–multiple year) with all four vineyards across all 3 years (2017–2019).20172018201917/18/19AnalyteStatisticn = 500n = 500n = 500n = 1500AnthocyaninsNugget (c0)0.650.510.380.79Sill (c1)0.340.510.600.21Range (a1) (m)10911094159CAM66503979RMSE0.050.050.070.05β‐DamascenoneNugget (c0)0.580.450.490.78Sill (c1)0.420.470.510.27Range (a1) (m)82105184269CAM59494974RMSE0.060.090.050.03Malic acidNugget (c0)0.600.330.440.67Sill (c1)0.440.620.540.33Range (a1) (m)21211995139CAM58354567RMSE0.080.060.100.04Lag minimum1111111116755FigureCommon (n = 1500) () and single year (n = 125), 2017 (), 2018 () and 2019 (), variogram models of standardised (μ = 0, σ = 1) anthocyanin concentration in Vineyards (a) A, (b) B, (c) C and (d) D.Simulation studyMonte Carlo simulations to predict Anth2019D were completed using two common variogram approaches, one derived from the 2017–2019 data in Vineyards A, B and C, that is, without data from Vineyard D (CV) included for variogram modelling, and one with data from Vineyard D included (CV+) (Figure 6). Both CV and CV+ produced maps with a tighter range of accuracy than that of the SVSY from 2019 anthocyanins in Vineyard D alone (Figure 6), regardless of the number of points included. This indicated that the common variogram approach provided a more confident set of maps than single vineyard data alone, and that information from regional vineyards without data from the unknown vineyard produced a similar result. Ranges of accuracies between each method overlapped until the number of points used to derive the local variogram exceeded 100 sample points (Figure 6), equivalent to the number recommended by Webster and Oliver (2007). The predictive capability, however, of the local variogram (SVSYn) with more than 100 samples reached nearly 90% of the accuracy of standard (SVSY) as compared with a top‐level prediction of about 70% for the common variograms (Figure 6). The addition of data from Vineyard D into the CV+ variogram method was slightly better than the common variogram without Vineyard D data (CV), though the difference was small (Figure 6).6FigureChange in the accuracy of predictions of two common variogram methods (common variogram without Vineyard D, CV; and common variogram with Vineyard D, CV+) and the site specific single vineyard–single year variogram with increasing numbers of points (SVSYn), compared against the anthocyanin maps produced with the site specific variogram from all 125 points in Vineyard D (SVSY). () SVSY versus SVSYn, () SVSY versus CV, () SVSY versus CV+. Note that sample points were selected from the locations shown in Figure 1 using Monte Carlo simulation. n = 100 simulations.Figure 7 provides a comparison of the variance in mapped (i.e. estimated) anthocyanin concentration and the average kriging variance (i.e. confidence of prediction) between the three variogram approaches over 100 simulations using 120 sample points. The average variance of kriged anthocyanin values was lower in the common variogram approaches (CV in Figure 7a; and CV+ in Figure 7b) compared with the SVSY (Figure 7c) as few pixels in the common variogram maps showed values above 0.05 mg/g compared with those in the SVSY map. While the two common variograms (CV in Figure 7d; and CV+ in Figure 7e) produced maps with only a few pixels with average kriging variances in the lowest class of prediction confidence (<0.014), they showed no pixels in the highest two classes (>0.022). Conversely, average kriging variances in the SVSY (Figure 7f) showed many pixels to be in the highest class (>0.026) reflecting increased uncertainty when only one vineyard was included in the variogram estimation. In summary, the SVSY approach resulted in higher anthocyanin variance by pixel (Figure 7c) and in a large portion of pixels in the bottom two classes of kriging variance (Figure 7f), indicating that both the confidence in prediction and the variance of predicted anthocyanins was improved with the use of a common variogram. Note here that Figure 7a–c show the variance of the predicted anthocyanin values and Figure 7d–f shows the kriging variance following 100 iterations of kriging, not the variances obtained from single simulations.7FigureVariance in predicted anthocyanin concentration and the average kriging variance (prediction confidence) from simulations of each variogram class using (a, d) common variogram without Vineyard D (CV), (b, e) common variogram with Vineyard D (CV+), and (c–f) single vineyard–single year from vineyard D in 2019 (SVSY) with 120 points included in the interpolations. n = 100 simulations.In order to provide a use case scenario for practitioners interested in deploying a common variogram without the large sampling (n > 100) required for variogram estimation in a single year, two additional maps were created using common variograms to simulate how this may be achieved. Figure 8 shows two maps of anthocyanin concentration derived from a dataset (n = 105) comprised of 35 samples randomly selected and normalised by year in each of 2017–2019 from a single vineyard. In Figure 8a, the map was interpolated using a variogram obtained from the 105 samples. The map in Figure 8b was produced using the same 35 normalised random samples per season, but with the inclusion of 35 additional random samples, normalised by year and vineyard, obtained from three other vineyards in the region each year and included for variogram estimation (n = 420). A strong resemblance is evident between the map derived from the common variogram fitted with 420 points (Figure 8) and those found in Figure 2e–h, which used a larger statistical support.8FigureMaps of anthocyanin concentration derived from 35 samples collected each year for 3 years (2017–2019) in a single vineyard and standardised (μ = 0, σ = 1) on an annual basis. In (a), the map was produced using a single vineyard–multiple year variogram derived from the 105 multi‐year combined samples, whilst in (b) the data used to derive the multiple vineyard–multiple year variogram were supplemented by an additional 35 randomly selected samples per year for 3 years (2017–2019) from four different vineyards in the same region (n = 420). In the latter case, the data were again standardised (μ = 0, σ = 1) by vineyard and year.DiscussionThe practical utility of a common variogram was assessed for a vineyard and analyte (2019 anthocyanins in Vineyard D) to simulate mapping done for a vineyard manager with interest in combining their data with that of others in the region to characterise within‐vineyard spatial variability. Results show that the predictive capability of the common variograms could correctly classify nearly 50% of input points with relatively high confidence compared to SVSY, and with as few as 30 samples (Figure 6). Compared against the results from SVSY, which reached only a mean prediction above 70% similar with 90 points, this simulation showed that the common variogram could be a useful tool in describing the spatial variability of anthocyanins even in a vineyard where high density sampling has not occurred, providing sufficient samples are available from nearby vineyards over several years to support creation of the common variogram. In the absence of further study, caution should be taken in determining the appropriate spatial extent within which to group vineyards for data aggregation. For example, samples from vineyards in the Lodi region should probably not be included for common variogram generation with those from vineyards in Napa Valley. Examining this issue presents an interesting opportunity for future study. In situations where a vineyard manager does have more than 100 samples and can estimate a local variogram with some confidence, results presented here indicate they would have higher confidence in maps produced using the common variogram approach (Figures 6–8) if data were available from other nearby vineyards. Additionally, the inclusion of those points into a regional variogram could help others to generate maps with more confidence. To take advantage of this technique, groups of growers, vineyard managers, or wineries could target samples in a subset of vineyards over a few years in such a way as to provide the group with at least a baseline common variogram from which predictions and maps could be generated to the benefit of all participants, as the example in Figure 8 illustrates. Importantly, this may be achieved with a reduced annual sampling requirement, though care should be taken regarding the size of the region within which vineyard data are pooled. Thus, 35 samples per year from each vineyard could be collected over the course of 3 years to collect the minimum 100 samples for variogram estimation (Figure 8a), but the robustness of the maps could be improved by a cooperative effort from other growers/vineyards (Figure 8b). Both maps illustrate how an individual grower might take advantage of the common variogram approach, coupled with a more manageable annual sampling requirement of 35 samples per year compared to more than 100. The fact that Figure 8b delivers a smoother map with strong similarities to Figure 2e–h, indicates how a cooperative sampling strategy could provide robust results, which represent the variability of this vineyard over the course of 3 years, but without the requirement for a large sample number in a single year. Given that the typical capital cycle of a vineyard is of the order of 30 years, we think this approach may be both attractive and useful. This sample number could potentially be reduced even further using techniques like REML variogram estimation (Kerry and Oliver 2007), but the present objective was to provide a practical method for understanding vineyard variability using simple techniques and software available to growers. This pragmatic approach is important given the results from recent conversations with growers about field experimentation in Australian vineyards (Song et al. 2022). Nonetheless, the use of more advanced techniques is of interest, especially since there are few, if any, studies incorporating these methods into the characterisation of spatial variability of vineyard productivity.The small differences in mapped patterns of spatial variability between each of the common variogram methods used to interpolate each fruit compositional analyte are important for the characterisation of spatial variability in vineyards. First, the increase in pairs of points per distance class means that the sample density to meet minimum variogram robustness requirements (Cressie 1993) can be met in large commercial vineyards without more excessive sampling campaigns. Those interested in variability maps need collect only the number of samples necessary to provide the accuracy desired. Some may choose to sample less densely and still achieve a zonal classification of at least 50% accuracy (Figure 6). The minimum number of pairs of points per lag class doubled with the addition of a second year and tripled when all 3 years were included, either when all four vineyards were included in the variogram estimation or from an estimation composed from a single vineyard (Tables 1, 2). In a study from the same four vineyards shown in this study, Sams et al. (2019) found that differences between anthocyanin maps derived from a single vineyard variogram and one from a common variogram of all four vineyards in a single year were primarily located on the edges of classified zones and would not have altered zonal prescriptions such as those used to underpin selective harvesting. Second, the common settings applied to each analyte or vineyard assessed in this study helped to reduce the effect of any potential subjective variogram fitting (Bramley et al. 2017, Sams et al. 2019). Since information from multiple vineyards (MVSY and MVMY) and/or years (SVMY and MVMY) was included in the analysis, there was less reliance on the fit of a single variogram (SVSY) for the characterisation of spatial variability of compounds found to have short ranges of spatial dependence (Bramley 2005, Sams et al. 2022a). These results suggest that pooling data into common variograms could be beneficial to those interested in characterising spatial variability by adding the geostatistical support necessary for robust variogram estimation. As suggested by Taylor et al. (2005) for yield mapping, the advantages of building a database for variability of regional fruit composition are numerous. Individual vineyard managers would be less reliant on small numbers of samples to characterise variability while at the same time achieving a more robust idea of the variability of local and regional fruit composition. Additionally, regional information about the range of spatial dependence of certain compounds would be beneficial even when only a few samples were collected by acting as a guide to how far apart samples should be in order to be considered independent.Given the requirements established by Cressie (1993) and Webster and Oliver (2007), of a minimum 100 samples per variogram and at least 30 pairs of points per lag class, maps describing spatial variability of grape composition must be based on sample numbers which are likely to be financially prohibitive to most winegrowing businesses. This is especially true in large commercial vineyards, since the sample number of 125 geolocated samples per vineyard in this study amounted to 9–17 vines/ha, which is somewhat lower than the 26 samples/ha used by Bramley (2005) or 28 samples/ha by Scarlett et al. (2014). Although these studies did not consider this density to be the absolute minimum number of samples required per hectare, they have been viewed as something of a guide for the geospatial analysis of fruit composition in vineyards. While the sample density per hectare used for this and related studies (Sams et al. 2022a, b) was similar to those collected by others in California (Santos et al. 2012, Martínez‐Lüscher et al. 2019, Yu et al. 2020), though nearly double in the case of Vineyard A, this study is, so far, the only one conducted in California which meets the100‐sample threshold (Webster and Oliver 2007). Another study in North America used a high sample number but in a small vineyard (Reynolds et al. 2007) not representative of commercial conditions in the California Central Valley. Our study sought a compromise to these sampling issues by pooling data into common variograms in order to satisfy the large sample number requirements necessary for the characterisation of spatial variability, but without the need for even more intensive and expensive ground sampling. The variograms produced from this exercise, or other similar studies in other regions of the world, could be considered the typical variograms for those analytes and regions with which others in these areas could compare against their own degrees of spatial variability. Additionally, if suitable covariates such as soil electrical conductivity surveys, high‐density yield maps from a yield monitor, or remotely sensed imagery (Sams et al. 2022b) exist for their sites, they could be used to further increase confidence that patterns of spatial variability are stable.While Sams et al. (2022a) found that NDVI and canopy temperature measurements made from a fixed wing aircraft were sufficient to describe differences in variability of fruit composition in vineyards with highly structured and temporally stable zones, many samples had to be collected at great expense to demonstrate this. Thus, the development of fruit composition sensors may be increasingly necessary in vineyards with less distinct patterns and/or where imagery is difficult to acquire as a means of reducing the cost of sampling and analysis. Since the labour cost and complexity of sample collection involved in such a strategy may not decrease at the level needed to add value for smaller producers, either an advancement in the capabilities of remote sensing instruments or a high throughput proximal sensor may be necessary to accommodate the needs of characterising variability in fruit composition. The examples shown in Figure 8 could be produced with even less effort from collaborating entities, if they used sensor‐based estimates of fruit composition rather than being reliant on sampling and laboratory analysis.The simulations presented here show that additional vineyards could be added to a regional variogram without large sample numbers and could aid smaller operations in understanding spatial variability with higher confidence than from a single vineyard alone. Compounds with high nugget variance, either from measurement error, high local variation, or low concentration in the fruit, and no defined range of spatial dependence, may require either additional sampling or a separate approach to destructive sampling completely, that is, remote or proximal sensing. One potential remedy is to increase the sampling density to account for this variability, but results shown here point to the application of a common variogram to aid in the statistical support necessary for the description of vineyard spatial variability. As Sams et al. (2022a) pointed out, fruit compositional variability is largely influenced by a small number of key attributes such as anthocyanins, making it potentially unnecessary to map less important compounds unless a specific flavour or aroma is desired for winemaking.ConclusionsSimulations were used to demonstrate how a common variogram could be applied to the mapping of fruit composition in a vineyard. It was found that such an approach led to an increase in the confidence that could be attached to the resulting maps. While a higher number of point pairs per lag class enabled the most robust variogram fits in this study, the impact on maps of spatial variability was small. Along with comparison between the various forms of common variogram explored here, this indicates that data from multiple vineyards and years can add to the statistical support of map interpolation without changing the patterns of variation in individual vineyards. In turn, this may lead to an enhanced understanding of longer‐term patterns of spatial variability as the inclusion of multiple years lends weight to these patterns. Vineyard managers and wineries could have increased confidence in zonal management with the added statistical weight provided by a common variogram where patterns of variability continue to hold over several years. This is an especially important finding given the errors found in maps derived from the data collected from a single year, even with the relatively large sample size shown in this study. 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Australian Journal of Grape and Wine Research – Wiley
Published: Oct 1, 2022
Keywords: common variogram; kriging; map interpolation; precision viticulture; vineyard variability; Vitis vinifera Cabernet Sauvignon
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