How are 〜上, 〜上は and 〜上に different?

Question

I'm wondering about these, mainly because I don't see how they change the meaning.

これほど確かな証拠がある上は、Ａが犯人だと認めないわけにはいかない。
Since there's such solid evidence, there's no denying that A's the culprit. [?]

Could I replace 上は with 上 or 上に, if so how would the meaning change?

How about in these cases?

彼の姉は成績優秀な上、スポーツもよくできる。
彼の姉は美人の上に性格も良い。

In reading them I think "in addition to" but if I were to use them I might stutter because I don't get how they differ.

Thank you!

Answer 1

1. Simple Adverbial

上(に) means 'on top of'.

これほど確かな証拠がある上(に)、Ａが犯人だと認めないわけにはいかない。
(1) 'On top of having such solid evidence, there is no denying that A is the culprit.'

彼の姉は成績優秀な上(に)、スポーツもよくできる。
'On top of having high academic achievements, his sister plays sports well.'

彼の姉は美人の上(に)性格も良い。
'On top of being beautiful, his sister also has good personality.'

2. Topicalization

When you topicalize the 上(に) phrase using は,　it will be interpreted as contrastive topic. That is, while:

これほど確かな証拠がある上は、Ａが犯人だと認めないわけにはいかない

denotes the same (1) as with the non-topicalized sentence, it further implies the converse:

(2) 'If it were not on top of having such solid evidence, it would not have been the case that there is no denying that A is the culprit.'

So, by combining the denotation (1) and the implicature (2), the actual (informal) meaning of the topicalized sentence becomes:

(1) and (2), that is:
'Since I have such solid evidence, there is no denying that A is the culprit.'

By the way, the combination 上は is a bit archaic or formal. You can use 以上(は) to avoid that and mean the same thing.