While I'm unsure of your local regulations, some jurisdictions view stormwater differently depending on source. For example, in Washington State, runoff from vehicle space and chemically-treated landscaping is viewed as pollution-generating, which requires water quality treatment in addition to flow control; whereas runoff from other hard surfaces (e.g., rooftops) is considered non-pollution generating and requires only flow control.
Given the rooftop use as a dog park, that space would fall into the pollution-generating category, requiring water quality treatment. Perhaps you could do something like a "modular wetland", sand filter, or similar. And of course, source control in the form of signage, public outreach to tenants, and bag dispensers and trash receptacles couldn't hurt.
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Eric Pilcher P.E., M.ASCE
Bonney Lake, WA
eric.pilcher@...------------------------------