Résumé
Detecting Zones of Abrupt Change (ZACs), i.e. detecting ruptures in the plane, is a challenge in sparse and irregularly sampled spatial data.We propose a two-steps method :• After interpolating the variable by kriging, we estimate, i.e. detect, potential ZACs. We first define a test statistic, T(·), as a quadratic form of the interpolated gradient compared to its variance. Under a gaussian assumption for the variable of interest and under mild conditions about the regularity of its covariance function, T(·) has a non stationary χ 2 distribution. Potential ZACs are then defined as the excursion set of T(·) above the (1 − α)-quantile of the χ 2 distribution.• In the second step, we test the statistical significance of the detected potential ZACs. We establish new results about the curvature at local maxima of the non stationary χ 2 field and give the asymptotic distribution of the size of a potential ZAC. The associated p-value is compared to a global level η. A significant potential ZAC define a ZAC.The method requires two levels of significance : a fixed global level, η, and a local level, α, that we determine.The power of the method being related to the local density of the samples, we assess the local power of the detection test, i.e. the probability to detect at a given point a discontinuity that passes through this point. Mapping the power allows to visualize the zones where the local sample density is not adapted to the ZACs detection.We discuss the issues arised by the practical implementation of the method. The validation of the method on simulations and its application on soil data in a precision agriculture context brings to light a powerful method which is robust with respect to several parameters.