Precision Agric (2010) 11:358–378 DOI 10.1007/s11119-010-9164-7

A model for the spatial prediction of water status in vines (Vitis vinifera L.) using high resolution ancillary information C. Acevedo-Opazo • B. Tisseyre • J. A. Taylor • H. Ojeda S. Guillaume

•

Published online: 25 March 2010  Springer Science+Business Media, LLC 2010

Abstract This paper establishes and tests a model to extrapolate vine water status spatially across a vineyard block. The proposed spatial model extrapolates predawn leaf water potential (PLWP), measured at a reference location, to other unsampled locations using a linear combination of spatial ancillary information sources (AIS) and the reference measurement. In the model, the reference value accounts for temporal variability and the AIS accounts for spatial variation of vine water status, which enables extrapolation over the whole domain (vine fields in this case) at any time when a reference measurement is made. The spatial model was validated for two fields planted with Syrah and Mourve`dre during the seasons 2003–2004 and 2005–2006, respectively, in the south of France. The proposed spatial model significantly improved the prediction of vine water status, especially under conditions of high water restriction (PLWP \ -0.4 MPa), compared with a non-spatial model. The model was robust to the choice of reference site. The results also highlighted that AIS pertaining to canopy growth are the most relevant variables for predicting PLWP under these experimental conditions. Preliminary results showed the potential to calibrate the model from a limited number of field measurements, making it a realistic option for adoption in commercial vineyards. The success of the spatial model in improving the

C. Acevedo-Opazo (&) Facultad de Ciencias Agrarias, Universidad de Talca, CITRA, Casilla 747, Talca, Chile e-mail: [email protected] B. Tisseyre Montpellier SupAgro, UMR ITAP, Baˆt. 21, 2 Pl. Pierre Viala, Montpellier 34060, France J. A. Taylor INRA, UMR LISAH, Baˆt. 24, 2 Pl. Pierre Viala, Montpellier 34060, France H. Ojeda INRA, Experimental Station of Pech Rouge, 11430 Gruissan, France S. Guillaume Cemagref UMR ITAP, Montpellier 34196, France

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quality of prediction of PLWP means it could be incorporated into a decision-support tool to improve irrigation management within a vineyard. Keywords Vine water status  Spatial prediction model  Spatial ancillary information sources  Vineyard spatial variability

Introduction In a recent review paper Acevedo-Opazo et al. (2008a) discussed the importance of methods for monitoring the water status of vines spatially. Furthermore, they proposed a conceptual spatial model to predict the water status of vines across a given domain (vineyard block, vineyard, region, etc). The proposed model predicts vine water status by combining local reference measurements to take into account the temporal variability, and ancillary information sources (AIS) to characterize the spatial variability of vine water status. Acevedo-Opazo et al. (2008a) hypothesized that with denser ancillary information it may be possible to model the relative difference in vine water status between a reference point and all other sites across the domain. They demonstrated subsequently (AcevedoOpazo et al. 2010) that this relative difference was linear and temporally stable. A spatial model of vine water status using AIS may be of interest to commercial vineyards as it can be calibrated easily (it does not rely on a full descriptive model of the vineyard environment) and spatial predictions can be generated easily from singular reference points. By coupling high quality, high cost punctual vine measurements with low cost medium-high density ancillary data sources, the model would provide rapid estimates of vine water status at spatial resolutions that are too costly to generate with punctual measurements. To illustrate the concept, Acevedo-Opazo et al. (2008a) presented a brief case study on the use of multi-spectral imagery and soil apparent electrical resistivity (ERa). However, Acevedo-Opazo et al. (2008b) only justified the hypothetical relevance of the model; there was no analysis of inputs or validation with a significant data set. They considered only data from what they termed ‘high resolution information sources’ (HRIS), whereas medium-density, manually-sampled spatial data might provide valuable information in the model. For this reason the term AIS is preferred here to describe potential model inputs. The goal of this paper is to present a formal solution to the proposed model and investigate its feasibility, the selection of suitable AIS and the efficacy of prediction both spatially and temporally. The model requires the measurement of a reference value of vine water status zre (sre, tj) at site sre and time tj. The goal is to extrapolate the reference value zre (sre, tj) using a function fD, which relates zre (sre, tj) to the AIS over a domain scale (D) at the same time (tj). The AIS are available at each location si across D, and sre is a site within D, where D can be either a block or a set of blocks or a whole vineyard. In this model, qk (si) corresponds to the value of AIS for K obtained at si. The number of available AIS on si is K. If several AIS are available, then si is characterized by a vector q, q ¼ ½q1 ðsi Þ; q2 ðsi Þ; . . .; qK ðsi Þ: So, the proposed conceptual model (Acevedo-Opazo et al. 2008a) is given in Eq. 1      ^z si ; tj ¼ fD q1 ðsi Þ; q2 ðsi Þ; . . .; qK ðsi Þ; zre sre ; tj ; 8 si 2 D with sre 2 D: ð1Þ Acevedo-Opazo et al. (2008a) modelled the function, fD, by a linear combination of AIS with the reference value zre (sre, tj). Such a model can then be expressed in Eq. 2 as

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^zðsi ; tj Þ ¼ ðb0 þ b1  q1 ðsi Þ þ b2  q2 ðsi Þ þ    þ bK  qK ðsi ÞÞ  zre ðsre ; tj Þ;

ð2Þ

where sre 2 D; 8si 2 D; qk ðsi Þ; k ¼ 1; . . .; K 2 < and bk ; k ¼ 0; . . .; K 2 -0.4 MPa -0.6 to -1,0 MPa < -1.0 MPa

(c)

0

1:30.0000 10 20 30

1:60.0000 0

20

40

60

(d)

0.66

1.01

0.79

0.79

0.6 6

0.6

6

1.01

01

1.

0.66

0.6

6

1 1.0

1:60.0000 0

20

40

60

1:30.0000 0

10

20

30

Fig. 5 Maps of PLWP for date t7 in 2003 for Syrah and date t5 in 2005 for Mourve`dre. The maps in (a) and (b) are interpolated from physical measurements, whereas maps (c) and (d) are interpolated from point predictions using the spatial model. PLWP sampling sites shown as points on the maps

data sets were not available and all subsequent AIS after the first two variables were nonsignificant. The stepwise selection of the same two AIS (ELA and TC) on two independent data sets indicates strongly that vine vigour is of particular significance for modelling PLWP. This result concurs with previous work on zoning vineyards according to vine water status (Acevedo-Opazo et al. 2008b). These two properties provide a seasonal (ELA) and historical (TC) indication of vine vigour. Vine vigour integrates genotype, environmental and interaction effects at the site and will be related to water availability and soil fertility among other things. However, the effect of soil properties on vine vigour appears to be more relevant to model prediction than direct measurements of soil properties (such as the ERa measurements used here). One reason for the lack of fit of the ERa data, in the particular conditions of this study, may be due to the depth of measurement of the ERa (1 m), which does not necessarily correspond to the depth of exploration by vine roots (here about 3 m). The two selected properties are both medium density measurements. Analysis of the quality of the spatial model prediction Standard error of prediction over time (SEPtj) The SEPtj never exceeded 0.15 MPa (Table 5) for either domain. These results fit with management application requirements, which require an accuracy of ±0.2 MPa. However,

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Mean PLWP

-0.17

0.05

t1

Time

0.06

10 Jun

Date

SEPtj

2005

Mourve`dre

SD PLWP

-0.18

0.06

Mean PLWP

0.06

t1

Time

SEPtj

18 Jun

Date

SD PLWP

2003

Syrah

t3

-0.12

0.03

-0.25

0.06

0.06

06 Jul

0.06

0.17

0.10

16 Jul t4

-0.54

t2

-0.52

0.16

23 Jun

-0.34

0.07

0.10

t2

0.06

08 Jul

t3

26 Jun

0.10

0.07 -0.41

t4

19 Jul

-0.73

0.21

0.13

23 Jul t5

0.18

0.14 -0.75

t5

05 Aug

-0.84

0.22

0.12

30 Jul t6

0.15

0.14 -0.78

t6

25 Aug

-0.92

0.26

0.11

12 Aug t7 0.05

0.06

0.11

0.08 -0.42

t1

13 Jul

2006

-0.11

t1

09 Jun

2004

0.11

0.10

0.11

0.09 -0.46

t2

27 Jul

-0.34

t2

05 Jul

0.08

0.08

-0.59

0.08

0.12 -0.38

t3

0.15

0.12

18 Aug t4

22 Aug

-0.28

t3

05 Aug

0.15

0.12 -0.61

t5

23 Aug

Table 5 Summary of different measurement dates, standard error of prediction at different times (SEPtj) and mean PLWP for the Syrah and Mourve`dre fields

-0.72

0.21

0.14

10 Sep t6

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Table 4 shows that SEPtj was not constant over time, it increased as the standard deviation, r, of PLWP increased. For Syrah in 2003, SEPtj varied from 0.06 MPa on the first date of measurement to 0.13 MPa for the last measurement date, which corresponded to the greatest water restriction. For the same domain and during the same period of time, r of the PLWP values varied from 0.06 to 0.26 MPa. Similar results were observed in both years for the Mourve`dre field. At greater water restriction levels (PLWP \ -0.4 MPa), Table 5 shows that SEPtj values are always less than r. This confirms the advantage of taking the spatial variation of PLWP into account and the relevance of the proposed model. Spatial error of prediction (SEPsi) The spatial error of prediction (SEPsi) was computed to determine if there was any residual spatial pattern in the model. A perfect spatial model would produce a random spatial distribution of the error. Maps of SEPsi for the Syrah and Mourve`dre fields are shown in Fig. 6. The error is small (\0.1 MPa) for approximately 70% of the sites of both domains. Larger errors (SEPsi [ 0.15) occur at only three locations in the Syrah field and only one has a very large error (SEPsi [ 0.2). For Mourve`dre, the spatial error never exceeds 0.15 MPa. The white and light grey zones represent locations where the confidence of prediction is low. Figure 6 also indirectly validates the choice of reference sites. The spatial error shows no pattern associated with the reference sites, which suggests that the model can predict over the entire domain and not only in the area around the reference sites. Although the SEPsi is generally low, some spatial patterns remain in the SEPsi maps. These patterns indicate that information to characterize the spatial variation in PLWP properly is still missing. This missing spatial information may involve more sophisticated properties than AIS based on simple observations or measurements, for example, interaction with the nearby forest might explain the pattern along the northern edge of the Syrah field. In the Syrah field, one site has a large error (SEPsi [ 0.2); it is not an outlier caused by measurement error because the SEPsi takes into account all available dates. This site has a very high water restriction (less than -1.6 MPa at date t7 in 2003). Its ELA and TC values

(a)

(b)

0.24 0.20

0.15

0.10

0

1:60.0000 20 40

60

0.04

1:30.0000 0 10 20 30

Fig. 6 Maps of standard spatial error of prediction (SEPsi) for (a) Syrah and (b) Mouve`dre, respectively. Small errors (0.04–0.1 MPa) are black, medium errors (0.1–0.15 MPa) are dark grey, large errors (0.15– 0.2 MPa) are light grey and very large errors ([0.2 MPa) are white

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are also low, but not extremely so when compared to other sites with medium to high water restriction. This site may be considered as the limit at which the linear relationship between the AIS values and PLWP is no longer valid. Sensitivity analysis of the choice of reference site A sensitivity analysis of the choice of reference site was conducted for both fields across all the measurement dates. The distribution of the standard errors of calibration (SEC) from each possible model is shown in Fig. 7 for both domains. The median SEC remains less than 0.15 MPa for all dates. As expected, the median SEC and range of SEC values increases as the mean water restriction of the field increased, indicating that a poor choice of reference site could have an impact on the quality of prediction as water restriction increases (in a vineyard with considerable variation in PLWP within the field). This result is obvious for Syrah, where there are SECs greater than 0.3 MPa on dates t5, t7 in 2003 and t3, t6 in 2004. It is less significant for Mourve`dre, which might be due to the lower water restrictions observed for this field in 2005 and 2006. However, a considerable range of

(a)

t1

t2

t3

t4

t5

t6

2003

t7

t1

t2

t3

t4

t5

t6

2004

Date

(b)

t1

t2

t3

t4

t5

2005

t6

t1

t2

t3

2006 Date

Fig. 7 Effect of the choice of reference site on the calibration (SEC) of the model for (a) Syrah and (b) Mouve`dre for all dates. The limits of the box correspond to the quartiles and the horizontal line to the median

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Precision Agric (2010) 11:358–378 Fig. 8 Site maps showing the effect of the choice of reference site on the calibration error (SEC) of the model for (a) Syrah at t7 and (b) Mourve`dre at t5

375

(a)

S49 S48 S47

S41

S46

S40

S45

S39

S34

S44

S38

S33

S29

S26

S24

0.39

S35

S30

S27

SEC (MPa)

S42

S36

S31

S28

S43

S37

S32

S19

S25

S23

S20

S15

S22

0.15

S14

S8

S2

0.20

S18

S13

S7

S1

S17

S12

S6

S21

S16

S11

S9

S3

0.10 S10

S4

1:40.0000

S5

0

10

20

30

40

(b) S23 S17 S3 S2 S1

S6 S5 S4

S9 S8 S7

S16 S12 S11 S10

S15 S14 S13

S22 S21 S20 S19 S18

SEC (MPa)

S34 S28

S33

S27 S26

S32 S31

S25 S24

S39 S38 S37

0.22 S43

0.20

S42

S36 S46

S30 S29

S41 S35

S40

S45 S44

S48 S47 S49

1:80.0000 0

20

40

60

80

0.15

0.12

variation in SEC values (Fig. 7) is noticeable for larger water restrictions corresponding to dates t5 and t6 in 2005 and t3 in 2006. To visualize the effect of reference site on prediction quality, a specific analysis was conducted at t7 for Syrah and t5 for Mourve`dre. The standard error of calibration (SEC) associated with each point considered as a reference site is shown in Fig. 8. For Syrah (Fig. 8a), the SEC for the majority of the sites ranges from 0.10 to 0.18 MPa indicating that vine water status can be predicted with reasonable accuracy for management. However, five sites have a large SEC and can be considered as outliers. Four of them (s1, s2, s5, s34) are along the border of the field leading to a possible ‘interaction’ with the nearby pine forest that adjoins the block. The other outlier (s15) is adjacent to the internal track that bisects the field, again indicating an edge-effect. For Mourve`dre, the SEC of the models is less than 0.2 MPa for almost all the sites (Fig. 8b). Only two sites (s49 and s28) have a median SEC close to 0.2 MPa. Again one of these (s49) is close to the pine forest on the eastern border of the field. The reason for the high response at the second site s28 is unclear. Practical implementation of the approach From a practical point of view, this analysis has shown that the model was not very sensitive to the choice of reference site. Small differences in accuracy may occur but,

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except in rare cases, the choice of the reference site did not affect the quality of prediction. More detailed investigations into the choice and number of reference sites should provide a better understanding of these effects on prediction quality. However, the results of this study provide some simple recommendations to ensure the selection of an appropriate reference site, such as to avoid field borders and unhealthy vines. The choice of AIS information was also important; properties relating to seasonal (ELA) and historical (TC) indications of vine vigour were the most relevant. These two properties are both medium density measurements. Soil information (ERa) was not relevant in this case study. However, in other situations soil and elevation data might be relevant and should not be immediately discarded. Further investigations at other experimental sites are needed to answer this question. Vine vigour was dominant in this study, but this might not be so in other regions. Before implementing this model in another vineyard, the local factors that affect vine water status most strongly need to be considered. Expert analysis from a pedologist and/or a viticulturist should assist in choosing relevant AIS given the local characteristics and practical constraints of AIS acquisition, such as cost, spatial resolution and timeliness. The amount of PLWP data used to calibrate this model was large and not realistic for commercial vineyards. However, the selected model has only three unknown values (b0, b1 and b2). Therefore, theoretically only 3 measurements of PLWP are necessary to calibrate the model together with the reference site. To illustrate this, the combined PLWP data for the Syrah domain were stratified into low, medium and high groups and a value selected randomly from each group. The location and date of the selected values are shown in Fig. 9. The model was then calibrated using these three PLWP measurements and the original value of the reference site. The plot of actual versus predicted values together with the model parameters are shown in Fig. 9b. This shows that with three sites and two dates, it is possible to calibrate the spatial model with an accuracy (r2 = 0.87, SEC = 0.08) that

Fig. 9 (a) Location and dates of the PLWP dataset used to recalibrate the spatial model for the Syrah field and (b) predictions of PLWP from the spatial model computed with vine ancillary information (q1: exposed leaf area, q2: trunk circumference) for Syrah; r2 and SEC are computed for the full model

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is as good as that with the full dataset (49 sites and 13 dates). The potential to validate the model from a limited number of sampling dates will reduce the time required considerably for acquiring measurements. This is only a quick illustration of the concept. A more detailed analysis is required to determine how to choose the sites and dates for sampling that generate the most robust prediction model, while minimising the time and cost of data acquisition. From the spatial perspective, high resolution information such as NDVI or ERa might be good alternatives for determining the best sites at which to sample. This aspect will be investigated further in future work.

Conclusions This work has shown that it is possible to extrapolate vine water status (PLWP) to unsampled locations from a measurement at a reference site and from AIS at the unsampled locations. The proposed spatial model is based on a function that uses a linear combination of AIS with the reference value. In the model the reference value accounts for temporal variation and the AIS account for spatial variation in vine water status, which enables extrapolation over the whole domain (vine fields in this case). This model was validated on two fields planted with Syrah and Mourve`dre during the seasons 2003–2004 and 2005–2006, respectively. The proposed spatial model significantly improved the prediction of the vine water status, especially under conditions of high water restriction (PLWP \ -0.4 MPa), compared with a non-spatial model. The model was robust to the choice of reference site. The results also highlighted relevant AIS for predicting PLWP under these experimental conditions. The success of the spatial model in improving the quality of prediction of PLWP means it could be incorporated into a decision-support tool to improve irrigation management within a vineyard. Calibration of the model, however, still needs some simplification to be fully operational on commercial vineyards. The main issue is a need to decrease significantly the number of samples required to calibrate the model. We intend to improve our approach by proposing decision rules using high resolution auxiliary information (i.e. airborne imagery, soil apparent electrical conductivity, etc.) and other information sources to design the best sampling scheme. Acknowledgements This work was funded by the Vinnotec project (Qualimed Pole of Languedoc Roussillon region—France) and the Agropolis Foundation.

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