I assume you mean "surmise". And I surmise you think it means the same as "assume"... They do, in your examples. But a surmise would have some small, albeit scanty amount evidence for the supposition, whereas an assumption may have none. Also note that "assume" has other meanings, as in assuming responsibility for something.

I think you mean surmise. As far as I'm aware the principal difference is one of usage. Assume is used far more often, whilst surmise is more formal and would be used in written and academic language.

Are you sure it is sumrise ? I've never seen that word before....