Even something as simple as "tomorrow" can be ambiguous. I often ask my phone to set a reminder for tomorrow. If I'm asking after midnight, what I really mean is "today" since I haven't gone to sleep yet. Google seems to get this right, thankfully.
Gets it right for you. If I mean today, I say today. This is especially true when I'm talking to a computer.
Sometimes we need to use non-human language to communicate intent correctly to a computer, but we shouldn't let that redefine perfectly good and well established human language.
Your definition has the same issue that mine does, just with sunrise being the time around which the meaning of tomorrow is unclear. How high does the sun have to be before "today" becomes defined and the meaning of "noon tomorrow" shifts by 24 hours? If I wake up before sunrise, does tonight refer to now or to after the next sunset?
There's a certain amount of ambiguity inherent to the English language.
I think using midnight as the anchor for the today/tomorrow distinction is a lot less confusing and ambiguous than having today/tomorrow not tied to the current date.
Just print the date and time.
/folks up north