The development of parameterizations is a major task in the development of weather and climate models. Model improvement has been slow in the past decades, due to the difficulty of encompassing key physical processes into parameterizations, but also of calibrating or â\euro˜tuningâ\euro™ the many free parameters involved in their formulation. Machine learning techniques have been recently used for speeding up the development process. While some studies propose to replace parameterizations by data-driven neural networks, we rather advocate that keeping physical parameterizations is key for the reliability of climate projections. In this paper we propose to harness machine learning to improve physical parameterizations. In particular we use Gaussian process-based methods from uncertainty quantification to calibrate the model free parameters at a process level. To achieve this, we focus on the comparison of single-column simulations and reference large-eddy simulations over multiple boundary-layer cases. Our method returns all values of the free parameters consistent with the references and any structural uncertainties, allowing a reduced domain of acceptable values to be considered when tuning the 3D global model. This tool allows to disentangle deficiencies due to poor parameter calibration from intrinsic limits rooted in the parameterization formulations. This paper describes the tool and the philosophy of tuning in single-column mode. Part 2 shows how the results from our process-based tuning can help in the 3D global model tuning.