1. The quality of being hard to endure, uninviting or formidable
   "the rigorousness of northern winters";
   - asperity, grimness, hardship, rigor [US], rigour [Brit, Cdn], severity, severeness [rare]
    
2. Excessive or stern strictness in attitude, judgment, or treatment
   "The rigorousness of their discipline";
   - severity, severeness [rare], harshness, rigor [US], rigour [Brit, Cdn], inclemency [archaic], stiffness

Type of: difficultness, difficulty, sternness, strictness