New, Mysterious USGS Gage Toggle: What Does It All Mean?

By Kim Buttleman and Jenny Thomas

Questions have been raised about a toggle switch for a "Linear" or "Log" (from "logarithmic") graph that has recently appeared on the new version of the USGS gage pages. Specifically, when do you use one or the other for graphing gaging data? And is one or the other more helpful for paddling trip planning purposes?

Spoiler alert:  The Linear/Log toggle can cause more confusion than benefit. The easiest thing to do is ignore the toggle completely. By default, it selects correctly the linear graph for gage height and log graph for discharge. However, if you want to understand the differences in the graphs and how discharge is measured and determined for stream flow, by all means read on.

River flow data is reported as either "gage height" or "stage" measured in feet, or "discharge" measured in cubic feet per second (cfs). On a graph, both gage height and discharge are plotted on the (vertical) y-axis. Time is plotted on the (horizontal) x-axis.

A stream gage is usually installed in a location that is easy to access and where the river or stream has a somewhat uniform depth. The gage height is simply a measure of the depth of water at a specific gage location in the river. Gage height is easy to measure but has limitations because it does not reflect the amount of flow (or discharge) of the river. In addition, gage height can vary over time if, for example, the stream bed is eroded in that location, making determinations of "runnability" more complicated. An example is the Kitzmiller section of the North Branch Potomac gage, whose American Whitewater minimum has dropped more than a foot in recent years.

Linear graphs are best used for gage height measurements because they are additive, meaning that the y-axis increases incrementally in a uniform manner and because the gage height data typically have a small range in the values of data points. For example, a linear graph may start at 0 on the y-axis and increase by adding one foot of elevation to each equally sized interval, so the numbers would increase from 0 to 1 foot to 2 feet to 3 feet and so on. 

Figure 1 is a linear graph of Gage Height for the Little Falls gage on the Potomac from Aug. 8 to 15, 2024. It shows a high precipitation event, where the maximum gage measurement was between 7 and 8 feet.

Alternatively, discharge measurements provide a more accurate view of the river flow but are more difficult to measure. The amount of flow (cfs) is determined by measuring the velocity of the water at several depths along a transect across the stream at the gage location. The measurements collected are then integrated to give a total discharge, which represents the total volume of water passing through a cross-section of the river (cubic feet) over time (second). As the river flow increases, so does the speed or velocity of the water and, if the banks allow, the river gets wider.

In the past these measurements were made by a technician who rode a trolley suspended on a cable across the river. The technician lowered a current meter to set depths across the river to determine the flow rate at each depth on the transect. Recently USGS technicians have been using small raft-mounted doppler sonar, which is moved across the river at the gage location. This method provides a profile of bottom topography and a better measurement of flow rates in the water column.

You might ask: how does the USGS correlate gage height to discharge? USGS staff collect data in the field at several different flows, or discharges, over a range of stages at a particular gage location. Like a good wine, the gage height measurements (y-axis) are then paired with the streamflow measurements (x-axis) by applying a mathematical rating curve (Figure 2) to produce a stage-discharge relation graph. (The graph shown in the figure is not associated with a specific gage; rather it serves as an example of the type of correlation used.)

The USGS explains that its computers "use these site-specific rating curves to convert the water level data into information about the flow of the river.... The stage-discharge relation depends on the shape, size, slope and roughness of the channel at each gage and is different for every stream gage. A rating curve often changes after a flood when the physical force of high water movement can change the dimensions of the streambed or stream channel." The USGS visits each gage every six weeks or so to measure the flow to recalibrate the rating curve if needed. Graphs such as this for specific gages are not readily available to the user.

If the discharge were proportional to river stage, this graph would be a straight line and these correlations would not be needed at all. Table 1 compares the gage height (using actual data as close to whole numbers in feet as possible) to the discharge at Little Falls for the same dates used in Figure 1. The amount of change in discharge from one foot of gage height to the next is presented in the column on the right. It shows that there is a disproportionate increase in discharge with each uniform increase in gage height. Minor variations in discharge occurred because not all the gage height measurements were collected at even foot values. 

Discharge data are plotted on log graphs. Rather than the linear "additive" intervals used for gage height, a log graph is based on multiplication. The intervals of a log graph on the y-axis are commonly multiples of 10, such as 1, 10, 100, 1,000, 10,000 and 100,000 cfs. Log graphs are used for discharge for several reasons. First, they allow for the expression of large ranges of numbers in a manageable way. They also provide greater detail in the lower values as there is more detail shown in the gaging information from 1,000 cfs to 10,000 cfs while still accommodating higher flows from 10,000 cfs to, in this case, 70,000 cfs. Finally, the lack of proportionality of the data alone also lends itself to being presented in log form. Figure 3 is a log graph of discharge at Little Falls for the same dates as Figure 1 and Table 1. 

An additional benefit of the log graph is the decline of the discharge graph following the peak frequently becomes a straight line (Aug. 14-15), which can be extended out to help predict water levels a day or two ahead.

Figure 4 is a combination graph that visually summarizes this discussion. It is drawn using the new version of the USGS gage comparing both the gage height (darker line) and the discharge (lighter line) for Aug. 8 to 15, 2024, for Little Falls. The "linear" y-axis for gage height is on the left, the "log" y-axis for discharge is shown on the right. The horizontal line at 5 feet represents an "action stage" established by the National Weather Service.