While the HEC-EFM process can involve hydraulic modeling and GIS, statistical analyses of links between hydrology and ecology are the foundation of HEC-EFM applications.
The math performed by HEC-EFM during these statistical analyses is actually very basic. The challenge is in understanding how the parameters that define relationships (Season, Duration, Rate of change, and Percent exceedance) are used by HEC-EFM to compute the flow and stage that meet those criteria.