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Given a data set which consists of pairs of longitudes and latitudes, is it possible to determine an estimate of the ocean bottom depth at that point?

I can find maps of estimated sea depths online (e.g. https://maps.ngdc.noaa.gov/viewers/bathymetry/), but I am not sure how to go about it extracting the data.

I could look at every single point, and look at the map and find the depth level, but I have > 1000 points so ....

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    $\begingroup$ It sounds like the underlying question here may be "I found a way to click one point at a time, but I need a thousand, how do I automate this?". The answer to that is probably too broad to be in scope here, but you're probably going to need to download a dataset (rather than viewing it online) and then either do some light programming or possibly do something sophisticated with a GIS system. $\endgroup$ – Semidiurnal Simon Mar 28 '17 at 22:03
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The easiest products that provides ocean bathymetry (bottom depth) is the one you mentioned: https://maps.ngdc.noaa.gov/viewers/bathymetry/. It provides bathymetry data from a plethora of surveys. If you click in the map at any location, you will get a decent estimate of the depth at that point. You can also extract the surveys and data that are available for any given location. You also get DEMs and Lidar data. You can define a bounding box or a polygon (Identify tab) and it will provide the links to the original data. The original data in areas where no recent surveys are available is usually either from ETOPO or GEBCO.

If you are interested in a specific area you can also use a region selector directly from GEBCO (pick a box around all your points and extract the data that way).

You can also try NOAA electronic navigational charts.

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