In accordance with the Chesapeake 2000 Agreement, the Chesapeake Bay Program has recently implemented important modifications to (1) ambient water quality criteria for living resources and, (2) the procedures to determine attainment of those criteria. A novel statistical tool for attainment, termed the Cumulative Frequency Diagram (CFD) approach, was developed as a substantial revision of previous attainment procedures, which relied upon a simple statistical summary of observed samples. The approach was viewed as advantageous in its capacity to represent degrees of attainment in both time and space. In particular, it was recognized that the CFD could represent spatial data in a synoptic way: data that is extensively collected across diverse platforms by the Chesapeake Bay Program Water Quality Monitoring Program. Because the CFD approach is new to Bay Program applications, underlying statistical properties need to be fully established. Such properties are critical if the CFD approach is to be used to rigorously define regional attainments in the Chesapeake Bay.