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Electrical imaging of soil water availability to grapevine: a benchmark experiment of several machine-learning techniques

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Abstract

Electrical resistivity (ER) can be used to assess soil water in the field. This study investigated the possibility of extending the use of ER to measure plant available soil water variables, i.e. available soil water (ASW), total transpirable SW (TTSW), and fraction of transpirable SW (FTSW) using a pedotransfer approach. In a vineyard, 224 electrical resistivity tomography (ERT) transects and 672 time domain reflectometry (TDR) soil water profiles were acquired over 2 years. Soil physical–chemical properties were measured on 73 soil samples from eight different sites. To estimate the amount of soil water available to plants, grapevine (Vitis vinifera L.) water status was monitored by means of leaf water potentials. A benchmark experiment was carried out to compare four machine-learning techniques: multivariate adaptive regression splines (MARS), k-nearest neighbours (KNN), random forest (RF), and gradient boosting machine (GBM). Model interpretation led to a deeper understanding of the relationships between electrical resistivity and soil properties when predicting soil water availability for the plant. The models assessed had good predictive performance and were therefore used to map ASW, TTSW and FTSW in the vineyard. ER coupled to machine-learning algorithms was shown to be a good proxy for quantification and visualisation of plant available soil water with low disturbance.

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Abbreviations

Ψpd :

Pre-dawn leaf water potential

ASW:

Available soil water

ERV:

Electrical resistivity variation

FERV:

Fraction of electrical resistivity variation

FTSW:

Fraction of transpirable soil water

GBM:

Gradient boosting machine

KNN:

K-Nearest neighbours

MARS:

Multiple adaptive regression splines

RF:

Random forest

SWHC:

Soil water holding capacity

TTSW:

Total transpirable soil water

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Acknowledgments

This work was funded by the Conseil Régional de Bourgogne and the Bureau Interprofessionnel des Vins de Bourgogne (BIVB). The authors wish to thank Ing. Boris Champy and the Domaine Latour for access to the vineyard; Dr. Carmela Chateau Smith for assistance in English; students Sarah De Ciantis, Celine Faivre-Primot, Thomas Marchal and Basile Pauthier for help in laboratory analysis and/or field-data acquisition. Authors wish to thank anonymous reviewers for useful comments that improved the quality of the manuscript.

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Appendix: Short description of applied algorithms

Appendix: Short description of applied algorithms

KNN

The KNN approach predicts new samples using the mean (or other summary statistics, such as the median) of the k-closest samples from the training test. Different metrics can be used to calculate the distance between the samples. The most common is the Euclidean distance, which was also used here. The predictive performance of this method depend on the dimension of k, which is the parameter to tune, and must be large enough to avoid overfitting but not so large as to underfit data; the model is also sensitive to irrelevant predictors.

MARS

The MARS model predicts the outcome by creating the best subset of piecewise linear models for each predictor; interaction between predictors can also be included (Friedman 1991). A piecewise linear model is a function composed of linear regressions having different slopes, joined together at knots or cutting points, to allow continuity of the function. The algorithm evaluates all the data as a possible knot, to split the overall model into groups over which a linear model is fitted. A knot is then retained only if the addition of a different group and its corresponding linear regression significantly reduces the overall error (classically, the RMSE). The tuning parameters for MARS are the degree of interaction between predictors and the number of terms (i.e. the number of linear models) in the final model. MARS is implemented in R through the earth package.

Random forest

Random forest (Breiman 2001) is an ensemble of decision trees. Trees are a rule modelling technique, where data are split into sub-samples and different relationships are used for each sub-sample to predict the outcome. Full grown trees have low bias but high variance, because small variations in the data can completely change the splitting rules. Variance reduction can be achieved by using an ensemble of unpruned trees, a forest, on bootstrap resamples of the original data set. Resampling is used to perturb the structure of data and then diversify the trees in the ensemble; the final prediction will be the average of all single tree predictions. To diversify even more the trees in the ensemble, random forest (Breiman 2001) limits the search of the best split to a random sample of the possible predictors. The dimensions of this sample (mtry) have to be tuned, together with the number of data in the final leaves of the trees and the number of trees in the forest.

Gradient boosting machine

The gradient boosting machine (Friedman 2001) also uses an ensemble of trees for prediction, but the building of each successive tree depends on the previous ones. Indeed, in order to minimise a loss function (here the squared error), successive trees are fitted to the gradient (the residuals) of the previous trees, and the new ones are added to the ensemble. The process continues for a number of iterations, which is a tuning parameter (the number of trees). Each iteration, however, does not use the total training dataset, but only a random fraction of it. And, unlike random forest, trees are not full grown, and the number of splits has to be tuned. To limit overfitting, the participation of each tree in the ensemble can be regularised through shrinkage: for each new tree, only a fraction of the newly predicted values is added to the ensemble.

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Brillante, L., Bois, B., Mathieu, O. et al. Electrical imaging of soil water availability to grapevine: a benchmark experiment of several machine-learning techniques. Precision Agric 17, 637–658 (2016). https://doi.org/10.1007/s11119-016-9441-1

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