Figure 8 . Two-dimensional histogram of mixing length coordinated by tracer variability (horizontal) and inversed tracer gradient (vertical), indicating relative dependency of mixing length on the two variables. Rows correspond to the methods (spiciness and thickness) and layers (ASW and CDW), whereas columns correspond to the three frontal zones. Color shade is normalized to unity, and yellower indicates a larger data population. The axes are also normalized to illustrate their functional dependency. White cross denotes the averaged value of tracer variability and inversed tracer gradient, and white contours are the mixing length of 20 and 100 km. The diagonal dotted line indicates where controls by the two variables become comparable.