It's usually a good idea to consider a poem's speaker separately from the poet. However, in this case, there is no reason to believe the speaker is anyone other than the Roethke himself. Roethke was a teacher and one of his students, Jane Bannick, died in an equestrian accident.
It is clear that this poem's speaker has strong feelings about Jane's death. After all, he wrote an elegy for her. The speaker "speak[s] the words of [his] love" at Jane's graveside, but the nature similes and metaphors don't praise or idealize Jane's grace or beauty as we would expect, and he tells us that his relationship with Jane is "neither father nor lover." We are left to consider the nature of the speaker's love for Jane, why he feels it, and how we feel about such a strong emotion attached a platonic, teacher/student relationship, a relationship we usually perceive as relatively casual.
A good place to start looking for the answers to these questions is in the speaker's gaze. We know that the elegy is for Jane. Roethke tells us it is right there in the title. He also tells us that he loves Jane. But paying attention to what the speaker notices, what he sees and how he describes it, can give us some real insight into what his love for Jane is all about.
Every description of Jane becomes a description of nature. Jane is never just Jane. She's a bird or a fish or a plant. When the speaker declares his love for Jane, he's really declaring his love for the natural world. His love seems to be less for Jane the girl and more for what Jane represents to him: the embodiment of youthful vigor, curiosity, and vulnerability—many of the things Roethke himself seems drawn to in nature. Sorry Jane.