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I created a map with locations plotted in Tableau and have utilized a background map from NOAA to show which locations are being impacted by excessive rainfall. How do I filter the data so only those that fall within the excessive rainfall areas appear on the map? Alternatively how do I get aggregate measures of the locations that fall within the excessive rainfall zone?

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A background map is delivered from the server to the client as some sort of raster (bitmap) image. The WMS server does not send the data that was used to construct the background image, it just sends the resulting image based on whatever options you selected.

If you want to use that image as a background layer behind your other data layers, that's all you need. If you want to do analysis that combines your other data with the spatial data for filtering or calculations, you'll need to get the actual underlying geospatial data and not just a raster image.

Tableau can work with spatial data, and then do spatial calculations and spatial joins. You'll need to get your rainfall data in a spatial data set, such as a shape file, GeoJSON file, KML file or at least a CSV file with coordinate locations included, and then learn to use Geometry datatypes. If your data is large or your calculations are complex, you may benefit from using a spatially aware database such as the spatial extensions to PostgreSQL (called PostGIS), Oracle or SQL Server.

Alex Blakemore
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It's not a perfect solution, but one method that I found success with is creating a filter action and then using the lasso selection tool on the dashboard to select all of the points within the desired area in order to filter the desired values. More info on the filter action can be found here.