If you have Spatial Analyst extension
If you have access to the Spatial Analyst extension, you can use the Zonal tools to extract the value of the maximum fishing intensity value found within a given area (or many different areas).
For example, the Zonal Statistics As Table will give you a table as output with all the maximum values found in a raster layer based on zones defined on another raster or polygonal layer calleed the "zonal layer".
If you however need to find the exact location of the maximum pixel within a specified area you could (Spatial Analyst extension still needed):
- run the Zonal Statistics tool with a) the polygon shape deifning your area as the in_zone_data parameter and b. your fishing intensity raster as your in_value_raster
use the Raster Calculator to extract the exact maximum pixel within the specified zone with an expression like the following
Con("FISHING_RASTER" == "MAX_RASTER", "FISHING_RASTER")
This way you would extract only those pixels with the maximum value of fishing intensity from your original raster according to your area.
If you DON'T have Spatial Analyst extension
If your aim is only find the highest value on a pecified area and only once in a while, you could simply clip the raster with your polygon layer (Clip tool), and then have a look at the statistics of it to find the maximum (and other interesting statistics values). Try using the Calculate Statistics tool to calculate the statistics if they are not included in the clipped raster. You can see them in the layer properties, Source page.