Dear Jonathan, thanks for that detailed overview. I accept your justification for having the the key physical quantity of interest in the standard name.
In broad usage, I have the impression that a "histogram" can be expressed as either a count or a percentage, so we should be explicit in the convention if we want a narrower definition here. A narrower definition is probably needed, as there would otherwise be no way of distinguishing between the two. Would you support the addition of a paragraph in the convention to explain the usage you have described below. There are two further CMIP variables, both or which are bi-variate distributions, with bins of spectral bands and cloud top height ranges, which I'd like to bring into the discussion, but it might be useful to transfer the conclusions of the exchange so far into a ticket first. I think the two additional variables could be covered by a simple extension to "probability_density_function_of_X_and_Y" ... though you might want to insert "joint_" at the beginning of the term. regards, Martin Dear Martin and Alejandro (following off-list discussions) > The CF definitions say ''"histogram_of_X[_over_Z]" means histogram (i.e. > number of counts for each range of X) of variations (over Z) of X.' Yes, that's in the guidelines for construction of standard names, and there are only two of them at present, as you say. The simplest case is when you have some quantity Q depending on only one dimension, Q(Z). Then the histogram H(Q) is the number of values of Q which fall into each interval of Q, considering variation over Z. In general there could be more than one dimension retained, and more than one removed. If the original field was Q(P,Y,Z,T), we might construct a histogram H(Q,Z,T), for instance, containing the frequencies of values of Q falling into joint intervals of Q, Z and T, for variation over P and Y. Following the guideline above, we would call this a histogram of Q over P and Y, I think. It is not necessary to indicate in the standard name the dimensions which the histogram depends on (Z and T in my example) because the coordinate variables (of Z and T) make that clear. Martin suggests that by this argument we could also omit Q from the standard name, and just call it a histogram (or frequency distribution) rather than a histogram of Q, where Q is air temperature, precipitation amount, backscattering ratio, etc. I think there are two reasons why we include Q in the standard name, * I think a histogram of air temperature is not the same geophysical quantity as a histogram of precipitation amount, for instance, so they should be distinguished by standard name. * Although histograms are pure numbers, and so are probabilities, probability densities are not. Histograms, probability distributions and probability density functions are all related ways of expressing the same information. In the guidelines, we foresee that we might need names for all of them (though so far we have only histograms) and it would make sense to give them consistent names. The probability density function of air temperature has units of K-1, and of precipitation amount kg-1 m2, for instance. Because they have different canonical units, they must have different standard names, so Q needs to be included in the standard name. Cell methods describe how the values represent variation within the cells. The transformation from the values of a quantity to a histogram of the quantity makes the original quantity into a dimension. This seems more of a radical transformation than computing a mean or a standard deviation, which doesn't change the dimensions of the variable, but just reduces their size (to unity if completely collapsed). A frequency distribution of Q is regarded as a different geophysical quantity from Q itself, so we have not used cell methods to describe the relationship. Of course, this is a bit arbitrary (like everything else in the CF convention!). I agree with Martin that we could omit the "over" part of the standard name for histograms, probabilities and probability densities. It is useful to retain the collapsed dimensions as size-1 dimensions, so that their original range can be recorded. They could be assigned cell_method of "sum", the default for extensive quantities, because the histogram applies to their entire range. The same applies to the variable with has been histogrammed and is now a dimension; the histogram is a sum for each of its cells. For example, in the 1D case, suppose the original field is air_temperature as a function of time only. Then the histogram variable is float hair(tair); hair:standard_name="histogram_of_air_temperature"; hair:units="1"; hair:cell_methods="time: sum tair: sum"; hair:coordinates="time"; float time; // scalar coordinate variable with bounds float tair(tair); tair:units="K"; As a multidimensional example, suppose the original field is float tair(time,altitude,latitude,longitude); tair:units="K"; tair:standard_name="air_temperature"; tair:cell_methods="altitude: mean area: mean time: mean"; from which we might construct float pair(tair,time,altitude); pair:standard_name="probability_density_function_of_air_temperature"; pair:units="K-1"; pair:cell_methods="altitude: mean time: mean area: sum tair: mean"; pair:coordinates="latitude longitude"; // to record the ranges Here, I suggest that the cell_method for area is "sum", because the PDF applies to the whole area, which is an extensive quantity. For air temperature it seems more sense to interpret a PDF as a mean within cells, since a PDF is an intensive quantity - you can interpolate it, for example - but not a point quantity if it's calculated from a histogram with finite bin-widths. Best wishes Jonathan _______________________________________________ CF-metadata mailing list CF-metadata@cgd.ucar.edu http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata