MMD2 shows an "ordering-attribute" element for a series, but no such thing is deserialized by the current server code.

Series does have an ordering_type property that is not currently serialized by the webservice (whether for XML or JSON).

Perhaps it makes sense to adjust MMD2 accordingly, and have

<ordering-type id="$ordering_type->gid">$ordering_type->name</ordering-type>

for XML and

ordering-type: $ordering_type->name,
ordering-type-id: $ordering_type->gid,

for JSON.