What is this upside-down transparent funnel-shaped item on a weather monitoring station?
The upside down funnel-shaped attachment is used to prevent rain-water getting inside the inlet of instruments which analyse ambient air. Usually, these instruments are air pollution monitoring instruments like ozone analyser, carbon monoxide analyser, particle concentration analyser, etc.

One may think why can't just use U-shaped tube (inlet). In case of U-shaped inlet, rainwater falling on inlet will eventually roll down near the entrance and will be pulled in with air due to strong flow. Funnel shape will have smaller flow near the wider opening and prevents water from getting into the air stream.