Судя по высоте волны, штормовое предупреждение верно.

Судя по means judging by or to judge from.

So:

• Судя по высоте волны = Judging by the wave height

Grammatically, судя comes from the verb судить (to judge), but in modern Russian судя по + dative is very often treated as a set expression.

Because Судя по высоте волны is an introductory phrase, similar to English judging by the wave height.

Russian normally separates this kind of phrase with a comma:

• Судя по высоте волны, ...

It sets up the basis for the conclusion in the main clause.

Because the preposition по here requires the dative case.

The base form is:

• высота = height

Its dative singular form is:

• высоте

So:

• по высоте = by/from the height

This is part of the standard pattern судя по + dative.

Here волны is genitive singular.

The phrase is:

• высота волны = the height of the wave / wave height

Russian often uses the genitive after a noun to show of relationships:

• высота чего? = the height of what?
• волны = of the wave

So this is not the subject of the sentence. It depends on высота.

In this sentence it is singular, but it can still refer to wave height as a general measure, not necessarily one specific wave.

Russian often uses the singular in technical or descriptive phrases like this:

• высота волны = wave height

If you wanted to emphasize many waves, you might also see:

• высота волн = height of the waves / wave height

Both are possible depending on context, but the singular here is perfectly natural.

Штормовое предупреждение means storm warning.

It consists of:

• штормовый = storm-related
• предупреждение = warning

Предупреждение is a neuter noun, so the adjective must agree with it:

• masculine: штормовый
• feminine: штормовая
• neuter: штормовое

That is why it is штормовое предупреждение.

Russian usually omits to be in the present tense.

So:

• штормовое предупреждение верно

literally looks like:

• storm warning correct

but it means:

• the storm warning is correct

This is completely normal Russian. You do not usually add a present-tense есть here.

Because верно is being used as the predicate: is correct.

Compare:

• верное предупреждение = a correct warning

  • here верное is a full adjective before the noun

• предупреждение верно = the warning is correct

  • here верно is the predicative form used after the noun

So in this sentence, верно is the normal form for saying that the warning is correct.

In this sentence, it is best understood as a short-form adjective/predicative form meaning correct.

That is why it can describe the whole noun phrase:

• штормовое предупреждение верно

For learners, the important point is this:

• верный / верная / верное = full adjective forms
• верен / верна / верно / верны = short predicate forms

Here the neuter subject предупреждение matches верно.

That is a very good question. Normally, Russian деепричастия (gerund-like forms) do tend to refer to the same subject as the main clause.

But судя по is a common exception because it behaves much like an introductory expression meaning:

• judging by
• to judge from

In practice, it often refers to the speaker's conclusion rather than to the grammatical subject of the sentence. So this sentence is natural even though the subject of the main clause is штормовое предупреждение.

No, Russian word order is fairly flexible.

The given version is natural:

• Судя по высоте волны, штормовое предупреждение верно.

But you could also say:

• Штормовое предупреждение, судя по высоте волны, верно.

The difference is mostly about emphasis and style. The original sentence is clear and neutral: first the evidence, then the conclusion.

The sentence is grammatical and understandable.

However, in real-life weather or official language, Russians might also use words that mean justified or well-founded, for example:

• штормовое предупреждение оправданно
• штормовое предупреждение обоснованно

That is because a warning is often described as justified, not just correct.

So the given sentence is fine, but depending on context, another adjective may sound more idiomatic.