This page describes in detail the analysis functions used by Giovanni. This information is provided so that the user has a full understanding of how Giovanni generates the output images and data.

## Interval Weighted Averaging (GrADS Function Name: ave)

This averaging is weighted by grid interval to account for the uneven grid spacing. Missing data values do not participate - the average is taken with fewer data points. The average in the latitude dimension is weighted by the difference between the sines of the latitude at the northern and southern edges of the grid box. The edges of the grid box are always defined as being the mid point between adjacent grid points.

In the above equation, Xave is the averaged data value for the user selected latitude, longitude, or time range. Here, n is the total number of data points with non missing data values. Xi is the data value for the data point i, and wi is the weighting factor for this data point as described below:

wi = (ti+1 - ti) |
(for averaging in time) |

wi = [Lonieast - Loniwest] |
(for averaging in longitude) |

wi = [sin(Latinorth) - sin(Latisouth)] |
(for averaging in latitude) |

## Areal Weighted Averaging (GrADS Function Name: aave)

This function takes an areal average over a user-selected latitude-longitude region. This average does weighting in the latitude dimension by the difference between the sines of the latitude at the northern and southern edges of the grid box and weighting in the longitude dimension by the interval between the two adjacent grid points as well. Missing data values do not participate in this average.

In the above equation, Xarea_ave is the averaged data value for the user selected area. Here, n is the total number of grids with non missing data values. Xi is the data value for grid i. The weighting factor for this grid is:

wi = [sin(Latinorth) - sin(Latisouth)] * [Lonieast - Loniwest]

Note that in Giovanni, after the user selects the area of interest, GrADS first finds the nearest grid points and the averaging is then performed over the range of grid points.