## Abstract

Pruning weights are a useful indication for growers of vine size within their production systems. However, pruning weights are rarely collected in commercial situations, as there is little information to help growers determine how many samples to measure. An intensive study of individual vine pruning weights was undertaken over three years in a Concord (*Vitis lambruscana* Bailey) block at the Lake Erie Research and Extension Laboratory, New York. The population variances associated with individual and aggregated neighboring vine measurements were used to determine random sampling schemes to assist growers. A sampling scheme based on 23 random interpost samples (3-vine sampling) is suggested as a good compromise to minimize the time associated with sampling and to maximize the accuracy of measurement and the value of the information. A spatial analysis of the variance indicates that the same sampling scheme could be extrapolated to block sizes larger than the survey area (0.93 ha), provided that the management and environmental conditions can be considered uniform over the larger block.

In cold climates, measuring the weight of pruned wood from a vine or section of the cordon is the preferred approach for measuring and quantifying vine size. While pruning weight is an effective estimate of vine size, it is not widely used in commercial production systems, mainly because of the time required per measurement and a lack of information on how and how many vines to sample. There are two issues that contribute to the time cost of measurement: (1) the separation of canes associated with individual vines, as a high degree of intertwining may occur between neighboring plants, and (2) the process of physically accumulating the pruned wood and then weighing and recording the values, a process that interrupts the natural flow of a pruning operation.

Vine size is important to juice grape (and winegrape) growers, as it is relates to vine balance and cropping potential (Shaulis and Steel 1969); however, the variability within pruning weight measurements in Concord vineyards has not been well quantified. The variability in vine size (pruning weight) needs to be understood if correct sampling protocols are to be developed and used in commercial vineyards. The data from an intensive survey of pruning weights are used here to determine the sampling size required for effective random sampling to estimate the mean vine size within vineyard blocks. The spatial relationship between vine pruning weights is modeled to provide insight into sampling at a whole vineyard, vineyard block (field), and sub-block level. Implications of estimating the mean pruning weight in a vineyard or a block are examined as are implications for sub-block (management unit) estimates in the context of a movement toward site-specific viticulture.

## Materials and Methods

### Data collection.

At the conclusion of the 2009, 2010, and 2011 growing seasons, the mass of pruned wood (g/vine) was measured for each individual vine within a 0.93 ha area of a single-wire trained Concord (*Vitis lambruscana* Bailey) juice grape block at the Lake Erie Research and Extension Laboratory, Portland, New York. The block is over 50 years old and was managed as a commercial system until 2007, when it was acquired by the research station. Since then, it has been managed using commercial best-management practices (Wolf 2008). In total, 1192 vines were measured in each year using the protocol of Jordan et al. (1981). The coordinates of each vine were derived from measurements of the end posts of rows and equidistant placement of the known number of vines along the row. On average, vines were spaced at 2.44 m within a row and rows were spaced at 2.74 m.

The individual vine data was subsequently aggregated to determine the response from 2, 3, 4, and 5 consecutive vines along the rows. Aggregation was done without replacement: that is, once a vine was used it was not used to determine the mean in another local neighborhood. Aggregation over missing or renewal vines was not permitted. The four aggregations (2-, 3-, 4-, and 5-vines) were run independently. The spacing along the rows was 4.88 m, 7.32 m, 9.66 m, and 12.20 m for the 2-, 3-, 4-, and 5-vine groupings, respectively, which produced 549, 353, 254, and 193 data points, respectively, in the vineyard. An alternative “cross”-sampling scheme was also generated, which consisted of sampling three vines within a row and the vines in the adjacent rows that neighbored the middle of the three interrow vines (forming a cross pattern of five vines, or 5-vines cross). This cross aggregation was not performed on the two edge rows (east and west sides of the block). The aggregation was restricted to every second row in the block and to an offset (1-vine) introduced in alternate rows to avoid repeat sampling of vines from the adjacent rows. This sampling scheme yielded 183 points in total in the block.

### Nonspatial approach.

For each sampling scheme the variance (*σ*^{2}) and mean (*μ*) were recorded and a mean *σ*^{2} (*σ̄*^{2}) calculated across the three years. The sample size required for a given level of confidence in estimating mean pruning weight (50 to 99%) and an acceptable level of error in estimating the mean (0.02 to 0.1 kg/m) was calculated using Equation 1 (Montgomery 1997),

where *σ̄*^{2} is the mean standard deviation from the three years of data collected. *z*_{α}_{/2} is the critical value derived from the table of standard normal distribution for a given level of confidence (*α*).

The range of the confidence level and the error were selected to encompass all possible reasonable scenarios for commercial application of the results. Sample sizes relative to the confidence and error level were displayed as contour plots. All nonspatial analysis was performed with JMP software (ver. 9; SAS Institute, Cary, NC).

### Spatial approach.

A spatial analysis was performed with variogram analysis. For the aggregated sampling schemes there was sufficient data (>100) to perform variography (Webster and Oliver 1992). Variograms permit the spatial structure of the variance in the data to be modeled. The experimental variogram calculates the variance between points separated by a predetermined distance (lag). In data with a spatial structure, pairs of data points that are closer together (smaller lag) will be more similar (that is, have a lower variance) than pairs that are farther apart. By calculating the variance at multiple lags, the spatial relationship in the data, termed a *variogram cloud*, can be plotted as a function of variance versus lag distance. If the data have no spatial relationship (akin to white noise), then the variance at small and large lags will be the same. Once the experimental variogram data (or cloud) has been generated, a theoretical variogram model can be fitted to the data to mathematically describe the relationship between variance and lag. Many different models may be fitted, but they generally have at least three parameters: (1) a nugget variance (c_{0}) that estimates the amount of variance at a lag distance of 0 m and is a function of stochastic effects and measurement error; (2) an estimate of autocorrelated variance in the data, c_{1}, that together with c_{0} defines the sample population’s estimated “sill” variance (c_{0} + c_{1}); and (3) a range (*a*) that defines the distance over which data are autocorrelated (the distance where the sill variance is reached).

Since data were available for three years, the average variogram approach of McBratney and Pringle (1999) was used in this analysis. The experimental variogram was generated and saved for each year and sampling scheme using VESPER software (Minasny et al. 2005). These values were fourth root transformed to normalize the response (McBratney and Pringle 1999). For each sampling scheme, the mean-transformed variance across the three years was calculated for each lag distance before the mean values were raised to the fourth power to put the data back on scale. A theoretical variogram was fitted to the data to generate the parameters of the average variogram in JMP (ver. 9). An exponential model (Equation 2) was used for the theoretical variogram fitting. For the discussion, the range value in Equation 2 (*r*) was multiplied by 3 to approximate the real-world range (*a*) (McBratney and Pringle 1999),

where *c*_{0} is the nugget variance, *c*_{0} + *c*_{1} is the sill, and *r* is the exponential model range (*a* = 3r).

## Results

### Nonspatial.

The annual mean and variance for the pruning weight and the mean variance across the three years were determined for the individual vine data (1-vine) and the different levels of aggregation (Table 1). The mean response in 2010 was lower than in 2009 and 2011 due to a dry season. However, the variance was similar across all three years: that is, the variance does not appear to be proportional to the mean on this limited data. The range in pruning weight in a given year was on average 1.15 kg/m, bearing in mind that the target pruning weight for optimum production is approximately half this value (0.46 to 0.56 kg/m) (Shaulis and Steel 1969).

Contour plots to determine the required sampling size for random sampling to achieve a given level of confidence and error in the prediction of the mean pruning weight for each sampling scheme in the survey area are shown (Figure 1). For a 90% confidence in the prediction with an acceptable error of ±0.046 kg/m, the required random sample size (*n*) was 64, 32, 23, 19, and 17 for the 1-, 2-, 3-, 4-, and 5-vine sampling schemes. For the 5-vines cross sampling scheme, *n* = 18. The choice of a 90% confidence (rather than 95%) and an error of 0.046 kg/m were based on values that industry personnel would use. (An error of ±0.046 kg/m equates to an estimation of vine size to within 0.5 lbs/vine.) The contour plots (Figure 1) and the data (Table 1) provide the means to calculate other desirable combinations of confidence and error.

### Spatial.

The average variograms from the data are shown (Figure 2). The variograms are labeled with the sampling (aggregation) method applied to the data. Aggregation has the effect of reducing both the nugget (c_{0}) and sill (c_{0} + c_{1}) variance. The adjusted range (*a*) of the average variograms varied from 31 m (5-vines) to 58 m (1-vine), with a mean *a* of 41.4 m.

The vine-to-vine variation was high, particularly in the individual vine measurements where 89% of the observed variation was c_{0}. Aggregation decreased the variance in the data set considerably, with aggregation to a 2-vine sample halving the estimated population variance (Table 1, Figure 2). The autocorrelated component of the variance (c_{1}) was between 40 and 60% for the aggregated sampling schemes compared to 11% for the individual vine sampling. Consideration of the neighboring rows in the sampling (via the 5-vines cross) did not provide any benefit compared with the 5-vine in row aggregation scheme, and the cross-sampling approach was not considered in the discussion.

## Discussion

The principal objective of this research note is to provide information to assist with vine size estimates of commercial production systems. The results showed that there was a high variability among individual vines. If individual vine sampling is required (or preferred), then ~64 measurements need to be taken to estimate the mean response to ±0.046 kg/m with a 90% confidence. (This value increases to ~91 measurements for a 95% confidence.) While 95% is a more common statistical preference, a confidence of 90% has been preferred in this analysis. In commercial situations, growers are likely to act on information at a lower (but still high) level of confidence. The contour plots (Figure 1) provide visual estimates of the sample size required if information at a higher or lower level of confidence and/or error is required. Alternatively, the information in Table 1 can be used with Equation 1 to determine the required random sample size (*n*) for a particular confidence and error level.

As described in the introduction, the time cost of collecting pruning weight data is a function of the need to separate (untangle) individual vines and to weigh the pruned wood. By aggregating vines together, the variance in the data is decreased, decreasing the number of (aggregated) samples required to predict the mean response with a given confidence and error. The use of trellising with regularly spaced posts provides a systematic structure in vineyards. In the Lake Erie juice grape industry, posts are recommended to be (and usually are) spaced at 7.32 m, with three vines between posts. Aggregating to an interpost area provides a simple way to reduce the time associated with disentangling individual vines. The posts provide a rigid structure to frame the sampling area. The aggregation to three vines also means that fewer aggregated samples are required (~23). This strategy actually measures slightly more vines (3 * 23 = 69) than the 64 vines required for individual vine sampling. However, the sampling time will be considerably less due to lower demands in separating vines, less weighing, and less travel time between fewer sites.

This analysis is premised on the measurement of random samples. Using posts as markers makes randomization simple, and if rows and posts are numbered, then the *n* sample sites can be randomly selected using these numbers before beginning the sampling. In this way, no bias is introduced into the sampling.

The *a* values from the average variograms had a mean of 41 m. Therefore, on average, data within a 0.17 ha area exhibit some level of autocorrelation. Beyond a lag distance of 41 m (or 58 m for the highest-case scenario), the variance between pruning weight measurements is distance invariant. Estimating the mean pruning weight value in areas <0.17 ha would be possible with a smaller sample size, as the population variance is expected to be lower. However, from the variogram analysis, the population variance for areas ranging from 0.17 to 0.93 ha (the limit of this study) was constant, thus the same *n* is required to predict the mean pruning weight at the same confidence and error level for any area within this range. The individual and average variograms do not indicate a trend in the data at lag distances >58 m, and the range observed in the survey area (~1.15 kg/m) is at the upper end of the expected range in these juice grape systems. It is therefore likely that the same population variance can be inferred over larger areas, provided that the management system (such as trellis, interrow management, vine management) and environmental conditions (such as soil type, mesoclimate) can be considered uniform over the target area. This area may be a single block (>0.93 ha) or cover several blocks. If any aspect of management or environment differs significantly between blocks, then a mean pruning weight (and sampling density) should not be estimated across blocks.

Similarly, if a single vineyard block is managed differentially (such as different sub-block management units), then the sample size recommendations above may not be sufficient even if the area is <1 ha. For an existing uniformly managed block that is to be stratified into management units, the determination of the mean pruning weight within each management unit will (probably) still require approximately the same sampling size as for the whole block estimate. In the best-case scenario, where the stratification into management units accounts for all the spatially structured (autocorrelated) variance in the data, the nugget variance can be used as an estimate of the population variance. Use of the nugget variance in Equation 1 (again with a 90% confidence in estimation and an error of 0.046 kg/m) generates *n* values of 61, 22, 18, 11, and 7 for the 1-, 2-, 3-, 4-, and 5-vine sampling schemes. For the preferred 3-vine approach, the difference is five fewer sites. However, this determination assumes the stratified management units account for all the structured variation in the data, which is unlikely. If the stratification explains only 50% of the autocorrelated variance, then the corresponding decrease in sample size is only one or two samples. Moving to management units will therefore increase random sampling requirements by a factor approximately equivalent to the number of management units chosen (provided the management units are >0.17 ha).

In this short analysis only random sampling has been considered. Under a management unit approach other sampling schemes, such as stratified sampling, may be more relevant and more practical. It is also important to stipulate that this analysis is intended to estimate the mean pruning weight in a block(s). It is not designed to consider how pruning weight data could be used to validate alternative methods of vine size estimation, such as remotely sensed canopy images.

## Conclusion

Pruning weight measurements showed high vine-to-vine variation. Aggregating data from neighboring vines decreased the variance and lowered the sampling density required to obtain a mean estimate of pruning weight in a vineyard block. Aggregation to an interpost length (typically three vines) will mean that 23 or 33 random samples are required to estimate the mean block pruning weight to within an accuracy of ±0.046 kg/m with a 90 or 95% confidence level, respectively. The use of the interpost distance provides a fixed frame within which to sample that should help minimize the time needed to collect the sample.

Spatial analysis of the data indicated that the population variance did not increase as block size increased from 0.17 to 0.93 ha (the limit of the study). It is likely that the population variances provided here can be extrapolated to larger blocks and/or over multiple blocks, provided that management and environmental conditions are relatively uniform over the area to be surveyed. Separate sampling schemes should be performed for different soil types and mesoclimates.

## Acknowledgments

Acknowledgments: This project work and J.A. Taylor’s position were financed through funding from the National Grape and Wine Initiative, Lake Erie Regional Grape Research and Extension Program, New York Grape and Wine Foundation, and the Viticulture Consortium–East.

The authors acknowledge the diligence and efforts of the technical staff at CLEREL during the collection of the NDVI and pruning weight data.

- Received May 2012.
- Revision received June 2012.
- Accepted July 2012.

- ©2012 by the American Society for Enology and Viticulture