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With the advances of new proximal soil sensing technologies, soil properties can be inferred by a variety of sensors, each having its distinct level of accuracy. This measurement error affects subsequent modelling and therefore must be integrated when calibrating a spatial prediction model. This paper introduces a deep learning model for contextual Digital Soil Mapping (DSM) using uncertain measurements of the soil property. The deep learning model, called Convolutional Neural Network (CNN), has the advantage that it uses as input a local representation of environmental covariates to leverage the spatial information contained in the vicinity of a location. Spatial non-linear relationships between covariate pixel values and measured soil properties are found by optimizing an objective function, which can be weighted with respect to a measurement error of soil observations. In addition, a single model can be trained to predict a soil property at different soil depths. This method is tested in mapping top- and subsoil organic carbon using laboratory analyzed and spectroscopically inferred measurements. Results show that CNNs significantly increased prediction accuracy as indicated by the coefficient of determination and concordance correlation coefficient, when compared to a conventional DSM technique. Deeper soil layer prediction error decreased, while preserving the interrelation between soil property and depths. The tests conducted using different window size of input covariates matrix to predict organic carbon suggest that CNN benefits from using local contextual information up to 260 to 360 metres. We conclude that CNN is a flexible, effective and promising model to predict soil properties at multiple depths while accounting for contextual covariates information and measurement error.