Sharing with research team about being affected by a natural disaster Is it professional enough to share personal worries with your research team and your supervisor where you are pursuing doctoral studies away from home and your hometown has been affected by a natural disaster like a tornado or a super cyclone in the context of your reduced productivity and lesser focus? What would be the recommended mode of sharing such information - in person or over emails?
If they do not react to your statement, does that mean that they see such a case as an excuse only and fail to understand the effect it has had on the doctoral student?
I would call it not only professional but close to mandatory. A supervisor has to be informed of special circumstances or reasons for specific behaviour in order to manage the team effectively, set realistic goals, assure the people are comfortable and to show basic human decency. You do not have to share something that makes you feel uncomfortable, and do not have to provide a lot of detail on personal circumstances. I think it is best to do so at an early stage, saying there is issue X and you would appreciate some consideration, rather than have to explain possible poor performance later after frictions have appeared. 

Suffice to say that many academics have friends and family outside their country of work and are personally aware of what it means to be away from them in a time of need. I cannot imagine many supervisors who would not be sympathetic to such a discussion, or would not appreciate the honesty. In practice this may not mean more than a pat on the shoulder and some more relaxed time, but even that can be important. If the conditions allow, a leave or temporary interruption of studies can also be warranted.