Do we have a unit to measure turbulence?
Turbulence can be quantitatively expressed as Eddy Dissipation Rate (EDR). EDR can be calculated from available onboard measurements, however it is not yet common for aircraft to have software to calculate the EDR. 

Originally it was thought to have EDR reported over ADS-B, but it did not become a part of the current specifications. It might be in the next ADS-B version. 

NASA Langley paper

World Meteorological Organization (WMO) presentation