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# 6.2 Slopes and moments

The tracer mass is (kg) and the air mass is (kg) The mixing ratio is then (kg tracer/kg air).

A tracer field is defined by 1, 4, or 10 three-dimensional arrays:

array unit description
rm kg toal tracer mass in cell
rxm, rym, rzm kg/(half grid cel) first order moments (slopes)
rxxm, ryym, rzzm
rxym, rxzm, ryzm
kg/(half grid cel) second order moments

The slopes and moments are properties of the concentration gradient inside the cell.

Consider a cell volumne . The convention for the length scales is that a half cell has lenght , thus . We would like to know the concentration in a point in the cell. From equations (7) and (9) in [Prather, 1986] we find that the tracer mass mixing ratio (kg tracer/kg air) is given by:   (6.1) (6.2) (6.3) (6.4) Coding of slopes and second moments

The best way to implement slopes/second moments is to have them compiled only if certain preprocessor macro's are defined.

In cy3, at least macro 'slopes' should be defined; in addition, 'secmom' might be defined to.

      ! at least slopes should be defined:
#ifndef slopes
stop 'slopes not defined'
#endif

! second moments as extension of slopes:
#ifdef slopes
rxm = 0.0
#ifdef secmom
rxxm = 0.0
#endif
#endif

! different codes:
#ifdef slopes
#ifndef secmom   