If you have NDVI and rainfall at only three common points, you are relying almost entirely on the interpolation, Alan. My first choice would be to get the NDVI at the other rainfall measurement locations. If that's truly difficult, at least consider a sensitivity analysis: vary the interpolation as radically as you can. (This can be done well with stochastic simulation; but if you don't want to get into that, use some sharply different interpolators, such as nearest-neighbor, IDW with several different powers, and cubic splines.) The results that hold up regardless of the interpolation method have some claim to being real.

As far as the mechanics of translating formulas to raster operations go, it's really simple. Consider first a textbook formula for standardizing data. Let the data be (x_1, x_2, ..., x_n). Call their mean m and their standard deviation s. The formula for the standardized values xi_i, i = 1, 2, ..., n, would readxi_i = (x_i - m)/s.

On a raster the indexes i represent individual cells. Therefore the mean and standard deviation are summaries of the data over the grid: they are numbers. I'll get to that in a moment, to show how to create two new grids whose values *everywhere* are equal to m and s, respectively. With map algebra you don't have to reference the indexes, because all local operations are automatically done cell-by-cell. So the map algebra syntax just drops the i's and puts brackets [] around the names of *existing *raster datasets to indicate they are grids, as inxi = ([x] - [m])/[s]

(Notice the lack of brackets around the name of the new grid. Also, the new name "xi" refers to the Greek letter corresponding to "x"; it has nothing to do with "x" and the index "i" mashed together!)

Next consider a formula involving a summation. The mean is a good example, where a textbook formula ism = Sum{x_i, i = 1 to n} / n

You obtain such summaries with zonal statistics. The zonal average of an entire grid does the following:

- For each category in the zone grid, it locates the cells having that category.
- For each such cell in the category, it obtains the value in the corresponding cell of the
*value* grid.
- It computes the desired statistical summary, such as the mean, sum, standard deviation, or whatever.
- It copies that summary value into
*every* corresponding cell of the zone grid.

Thus, this textbook formula is implemented in two steps:

- Create a zone grid having one constant value at every cell of the [x] grid.
- Compute the zonal average grid for [x] based on this zone and call it m.

A zonal standard deviation will compute the s grid for you.

Zonal summaries are available from the SA menu, as ArcTools, and via the Raster Calculator, Command Line, SOMA tool, and Model Builder.

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