“…This is mathematically expressed as follows: where g is the gravity constant, t is the time, x defines the horizontal position, z represents the vertical coordinate, ρ ( x , z , t ) is the water density, and is the reference density in complete mixing conditions, both of which include the suspended sediment density; d is the total depth that is the sum of η ( x , t ), the elevation over mean sea level and h ( x ), the mean depth. From the time when it was first proposed in the mid 1970s (Simpson & Hunter, ), the potential energy anomaly has been widely used to identify physical processes that produce water exchanges in shelf seas (Hofmeister et al, ; Simpson et al, ; Yang et al, ), regions influenced by freshwater (De Boer et al, ; Simpson, ), estuaries (Garvine & Whitney, ; Rice et al, ; Sun et al, ), and lakes (Zhao et al, ).…”