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Averaging/Integrating over Irregular Regions

Question:

How to integrate a variable within a surface/volume delimitated by an isoline/isosurface, or other complex regions ?

Example 1:

Integrate temperature only above the 20 degree isotherm

Solution:

Create a mask, apply it to the variable and then integrate.

     yes? LET iso20 = my_temperature[Z=@LOC:20]
     yes? LET mask = IF Z[g=my_temperature] .LT. iso20 THEN 1     ! else missing is implied
     yes? LET masked_temp = mask*my_temperature

Example 2:

Average over complex regions in 2-dimensional space.

Solution:

Averaging over complex regions in space may be achieved by masking the multi-dimensional variable in question and using the multi-dimensional form of @AVE.

     yes? LET salinity_where_temp_gt_15 = IF temp GT 15 THEN salt
     yes? LIST salinity_where_temp_gt_15[X=@AVE,Y=@AVE,Z=@AVE] 

Note:

This approach applies an all-or-nothing criterion to each grid cell, rather than including fractional grid cells in the integration. If necessary the accuracy of the integration or averaging can be improved by first regridding my_temperature to a finer grid.