These are not ordinary tree boxes. Instead of draining into a standard storm sewer, these gutters drain into the tree boxes, where stormwater then naturally drains into the ground instead of into a storm sewer. This reduces the amount of water entering the combined storm and sanitary sewer, and thus can help reduce the number of combined sewer overflow (CSO) events. Since the combined sewer system mixes storm water and regular sewage, substantial rainfall will force the system to overflow into area rivers, dumping raw sewage mixed with stormwater directly into the Anacostia and Potomac.
From the street side:
Storm water will slowly absorb into the ground, aided by the various plants soils that can capture pollutants though the process of biofiltration. Look at other rain gardens and tree boxes under construction - note the drainage layers of soil and gravel to be added.
In this completed rain garden/tree box, note the grade of the soil in the box, below the grade of the curb:
Cross-posted at City Block.