That's a good amount of water. My guess is that's it's either vent boots on the roof....check the furnace and water heater exhaust vents if you have gas units. If they weren't renailed properly and sealed after the new roof....melting snow could be the source....it will melt against the exhaust pipe and run underneath. It's best to nail these with serrated roofing nails with a rubber grommet at the top to seal them. We then seal all edges of the boot and the tops of the nails with Thru-the-Roof sealant....best long term fix I know of. This product is ususally available at Ace Hardware and the big boxes usually don't carry it. DAP also makes a clear elastromeric sealant that is available at the big boxes which can be used in a pinch.....we just prefer the other.
Don't let roofers use plastic boots....you have to check them on this....use the aluminum based boots for a longer solution and run a bead of sealant around the upper edge of the rubber grommet that seals against the vent pipe. These boots are used to seal vent pipes for plumbing stacks.
Check your bathtubs and showers. Most folks forget to seal around the flange rings at the tub/shower valves, divertors and spouts. You can use a clear siicone for this. Someone in the shower with the right stomach or body shape will shed water right into the gap around the rings....and it will send a good amount of water into the wall cavity..where gravity takes it where it will. We had an odd leak sometime back that was exactly this problem. Short, chubby guy took long hot showers and caused a leak into our basement unit. It's a property we've had for about a decade and for some reason, we had never caulked the rings....all caulked now and no more leak.
In more modern baths, check the joint at the tub/shower and tile. Most contractors grout these area and they split open pretty quickly....we prefer a color matched sanded caulk in these areas and it holds up much better. Just look for the "black" in the grount...will indicate a split, gap or hole.