ADVERBIAL PARTICIPLES

Adverbial phrases with present participles

Modifying the verb is only one of the three prototypical uses of adverbs or adverbial phrases:

1. Attributing the verb: He walked slowly back home.
2. Attributing an adjective: He was a surprisingly good chess player.
3. Attributing the entire sentence: Yesterday, he came home late.

The last of these three is the relevant prototype here.

* Not being able to govern events, I govern myself. Michel de Montaigne 
* Life is what happens while you are busy making other plans. John Lennon



adverbial participle (plural adverbial participles)

1. (linguistics) A participle that modifies a verb in same sentence and which is equivalent to an adverbial clause in English. Adverbial participles may denote time, condition, cause, concession, manner, means, purpose, or attendant circumstance.

 I agree with you that those are participles but there is nothing wrong with the analysis of the use as adverbial. The comma should already be enough to convince you that crying in Crying, he sat there cannot be attributing he. It becomes even clearer, if you replace he by the man:
The man sat there crying = Crying, the man sat there. <-- Adverb
The crying man sat there. <-- Adjective

Adverbial phrases with present participles

1. We can use an adverbial phrase beginning with the ‘ing’ (present participles) when describing an action done by or an event caused by the same subject in the main clause.

Example;

The tornado swept through the town, leaving a trail of destruction.

(leaving a trail of destruction):-

adverbial phrase showing result.

2. We put the adverbial phrase after the main clause if the action or event is the result of the action in the main clause.

Example:

                     (Main clause)

They were at loggerheads with each other, (Comma) creating a tense atmosphere.

(adverbial phrase showing result)

We can place the adverbial phrase before the main clause if the action or event takes place before the action in the main clause.

Example:

Sensing her growing displeasure, I quickly changed the conversation topic.

Sensing her growing displeasure – adverbial phrase

Remember:

• A comma is usually placed between the main clause and the adverbial phrase beginning with an ‘ing’ form.

Example:

He often makes sarcastic remarks without thinking, (comma) hurting other people’s feelings as a result.

• Hence, therefore or thus can be added immediately before an adverbial phrase showing result.

However, they should not be added before words like causing or resulting in, which already indicate very clearly that the phrase shows result.

Example:

1. They introduced certain rulers, complicating things. (right)

2. They introduced certain rulers, hence / therefore or thus complicating things. (right)

3. They introduced certain rulers, causing complications. (right)

4. They introduced certain rulers, hence / therefore or thus causing complications. (wrong)