Well from the current developments Ive passed for thought.
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When she was on the bench and it was cold that night so in wondering if he offered if she wanted to sit in his car rather than out in the cold, possibly said can we go for a drive. If your upset sometimes this helps calm down.
During the drive something was said or done she panicked, he made an advance, I'm thinking is there are traffic lights near the park? She wanted to get away from him and the best option to evade someone in a car is the park. Snow was still on the ground then. This is the assumption the reported screams were her, but going by police presence it points towards this.
He ran after her, either with bad intentions or maybe just to sort out the misunderstanding. If she was attacked and murdered in the park I would think this would leave substantial trace evidence and be alot quicker than 30 minutes. Another possibility he ran after her in a chasing and hiding senerio and could of fell in the river.
I guess he could use the excuse she needed the loo and took her to a park, but are they even open at night? Seems very odd, put plausible and he mentioned that he had a ciggerettte on the bench they were examining.