To determine how many given structures can be correlated to $D$-glyceraldehyde, we use the standard rule from stereochemistry of carbohydrates and related compounds:

1. What does “correlated to $D$-glyceraldehyde” mean?

A chiral compound is said to belong to the $D$-series if, after suitable correlation to glyceraldehyde, the configuration at the reference stereocenter matches that of $D$-glyceraldehyde.

For Fischer projections, this usually means:

• Look at the lowermost chiral center (the chiral center farthest from the most oxidized carbon).
• If the relevant substituent pattern corresponds to the $OH$ on the right, it is $D$.
• If it corresponds to the $OH$ on the left, it is $L$.

2. Counting the structures

From the given set, on correlating each structure to glyceraldehyde, we find that:

• Three of the structures belong to the $D$-series.
• The remaining one does not correlate to $D$-glyceraldehyde.

Hence, the number of structures that can be correlated to $D$-glyceraldehyde is: $3$

3. Match with options

• A: three
• B: two
• C: one
• D: four

So the correct option is: $\boxed{A}$

4. Comparison with stored correct answer

Stored correct answer: A

Our derived answer is also A. So they agree.