There are many tools for that, and you can compare the results in your images:
* Sen2Cor Software of @ESA: http://step.esa.int/main/third-party-plugins-2/sen2cor/
(Software easy to use in college, University context or work).
* Maja Software (ancient MACCS) of @CNES and @CESBIO: http://www.cesbio.ups-tlse.fr/multitemp/?p=14980
A little difficult to use, but strong in their results. (Personal advice).
... in my opinion, Maja is better for cloud detection and atmospheric corrections in my study Area (Latin America). But, it is better to take a little area and test the 2 software in your case.
On the other hand, there are images in level 2A corrections now, delivered by ESA (atmospheric corrections included) for Europe and Africa. They have plans to do the same for the entire world.
If you want to know more about Sentinel-2 work, corrections, time series analysis, there is an interesting Cesbio blog that explains many topics about that (agriculture included).
Dear Karel, in this link you can find a recent paper about atmospheric correction and cloud detection for Sentinel-2 using Sen2Cor or Maja tools.
Review: "Remote Sensing in Agriculture and Vegetation"
Paper: Validation of Copernicus Sentinel-2 Cloud Masks Obtained from MAJA, Sen2Cor, and FMask Processors Using Reference Cloud Masks Generated with a Supervised Active Learning Procedure.
By Louis Baetens, Camille Desjardins and Olivier Hagolle.
You also can correct Sentinel 2 imagens using the Semiautomatic Classification Pluguin (SCP) for QGIS, by the DOS1 method. DOS1 is a great and simple method to atmospheric correction ( Article Atmospheric and Radiometric Correction Algorithms for the Mu...
).
SCP is a very good, free and intuitive tool, and tutorials to learn SCP management are available in https://www.researchgate.net/project/Semi-Automatic-Classification-Plugin.
We are pleased to share our new method “A Simplified and Robust Surface Reflectance Estimation Method (SREM) for Use over Diverse Land Surfaces Using Multi-Sensor Data” published in MDPI #Remote Sensing Journal.