Definition of an `Annualized Mean' for the ERBE Period, February 1985 - April 1989

Computing an annual mean of the ERBE period (February 1985 - April 1989) radiation data presents somewhat of a conundrum because the data does not begin in January, nor does it end in December. Thus, a definition is in order that is used consistently throughout all of our work involving annual means derived from ERBE period monthly mean data.

First, an overall monthly mean - a monthly climatology if you will, is computed for each month January (m=1) through December (m=M=12). This is accomplished by computing a weighted sum where the weights w are a function of month (m) and year (y), and dividing by the sum of the weights. (The actual data values are indicated by .) Thus,

Here the number of years N(m) to sum over is a function of the given month. Thus, N(m)=5 for m=2,3,4, that is, February, March, and April. For all other months, N(m)=4. It is appropriate to equate the weights with the number of days in the month. An example is in order. Considering all the Februaries contained by 1985 to 1989, the overall monthly mean can be written as

From the overall monthly means it is then straight forward to compute a weighted annual mean, defined as

where Wm is given by

The Wm, m = 1, 2, ..., 12, are (31, 28.2, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31).

Back to `ERBE Period (February 1985 - April 1989) Radiation Products and Net Upward Surface Flux'.