National Oceanic and
Atmospheric Administration
United States Department of Commerce

Averaging/Integrating over Irregular Regions

Averaging/Integrating over Irregular Regions


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


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

Now integrate masked_temp instead of my_temp.

Example 2:

Average over complex regions in 2-dimensional space.


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] 


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