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Is measuring water in a well like measuring a stream?
No, it isn't. To study groundwater, the USGS often uses wells to measaure track groundwater levels. Since water levels in underground aquifers can change (for a variety of reasons), we need to keep accurate records of these changes and what factors affect them, including climate and rainfall variability, drought, pumping characteristics of the well and of nearby wells.
Water levels in wells can be affected by water withdrawals nearby — sometimes far away. Water levels underground respond much more slowly to precipitation than do rivers, so the need to run out to a well and take a water-level measurement at 2:00 AM during a storm is not as timely as measuring a river about to flood and wash out some houses in the watershed.
One way to keep a record of the water levels in a well is to place a float at the end of a wire and lower it into a well. The float will go up and down as the water in the well goes up and down. The other end of the wire is attached to a machine that has a pen-like instrument attached, and the pen point moves up and down according to the action of the float. A roll of paper slowly rolls past the pen, so a record of water level is plotted continuously on the paper. With the advent of electronics over the last decades, more levels are being recorded electronically, where they are logged straight into a computer's memory. The USGS even has "real-time" groundwater monitoring sites, where continuous records of water levels are recorded and posted to the Web in near real time.