19 | | == Clarification at start of section 7.3.3 (not needed if above is accepted) == |
| 20 | == 3. Addtional text for masks which vary over additional dimensions (e.g. time) .. form proposed by Karl == |
| 21 | |
| 22 | When the “where” construct is used, and when “area” is not the only “dimension” to which it applies, the interpretation more generally is that a “weighted” mean is reported. Specifically, the quantity of interest is integrated over the additional dimension(s) with weights proportional to the fraction of “type1” area_type that exists, and then this is divided by the integral over the same dimension(s) of the fraction of “type2” area_type that exists. [Note that certain variables might be undefined if the fraction of the area_type considered is 0; for example the temperature of sea ice is not defined if there is no sea ice. In this case, a time-mean value can still be computed for cells containing some sea ice during at least a portion of the averaging interval because no matter what the value assumed for temperature when sea ice is missing, those values are given zero weight in computing the time-mean.] |
| 23 | |
| 24 | Note that "`all_area_types” is one of the valid strings permitted for a variable with the standard_name area_type, so a cell_methods string of the form “area: mean over type1 where all_area_types” indicates the mean is calculated by integrating over the type1 portion of the grid cell and dividing by the entire area of the grid cell. |
| 25 | |
| 26 | The following three examples illustrate cases when one might want to use “where” or “where … over” in defining the cell_methods: |
| 27 | |
| 28 | 1. Suppose that in a grid cell the fractional sea ice varies over time, but there is interest in the time-mean surface temperature of the sea ice. The time-samples, each representing a spatially-averaged sea ice temperature can be summed and then divided by the number of samples to obtain an unweighted mean where sea ice exists. This would be indicated with: |
| 29 | cell_methods = “area: mean where sea_ice time: mean” |
| 30 | |
| 31 | 2. Suppose there is interest in recording the mean fractional area covered by sea ice and the mean sea ice thickness in such a way that their product would equal the time-mean volume of sea ice in each grid cell. In this case the sea ice area would be reported as an unweighted time-mean, while the mean sea ice thickness would be calculated with time samples weighted by the fractional area of sea ice. Thus, for sea ice thickness: |
| 32 | cell_methods = “area: time: mean where sea_ice” |
| 33 | |
| 34 | 3. Suppose the time-mean contributions to total heat flux from different portions of a grid cell (e.g., ice-free and ice-covered) are of interest, and there are reasons to report these in such a way that the total heat flux is the sum of the individual contributions. Then the cell_methods attribute would be defined: |
| 35 | cell_methods=”area: mean where sea_ice over all_area_types time: mean” |
| 36 | |
| 37 | In some cases a variable referencing a specific area_type will actually be defined even in the absence of that area_type (i.e., over the entire grid cell). Consider the surface_snow_thickness, which could sensibly be considered to be 0 in the absence of snow. In this case one might in some instances want to report “area: time: mean where snow” (giving a measure of the typical snow depth when snow exists) and in other instances “area: time: mean where snow over all_area_types” (which in this case would be identical to “area: time: mean”) or “area: time: mean where snow over land”. |
| 38 | |
| 39 | |
| 40 | == 4. Clarification at start of section 7.3.3 (not needed if above is accepted) == |