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The efficiency of the management of top-class ground-based astronomical facilities supported by Adaptive Optics (AO) relies on our ability to forecast the optical turbulence (OT) and a set of relevant atmospheric parameters. Indeed, in spite of the fact that the AO is able to achieve, at present, excellent levels of wavefront corrections (a Strehl Ratio up to 90% in H band), its performances strongly depend on the atmospheric conditions. Knowing in advance the turbulence conditions allows an optimization of the AO use. It has already been proven that it is possible to provide reliable forecasts of the optical turbulence (CN2 profiles and integrated astroclimatic parameters such as seeing, isoplanantic angle, wavefront coherence time, ...) for the next night. In this paper we prove that it is possible to improve the forecast performances on shorter time scales (order of one or two hours) with consistent gains (order of 2 to 8) using filtering techniques. This has permitted us to achieve forecasts accuracies never obtained before and reach a fundamental milestone for the astronomical applications. The time scale of one or two hours is the most critical one for an efficient management of the ground-based telescopes supported by AO. Results shown here open, therefore, to an important revolution in the field. We implemented this method in the operational forecast system of the Large Binocular Telescope, named ALTA Center that is, at our knowledge, the first operational system providing forecasts of turbulence and atmospheric parameters at short time scales to support science operations.