How do the calculation and expression of a stream gradient compare with those of a slope gradient?

How do the calculation and expression of a stream gradient compare with those of a slope gradient?

• A. They are calculated the same way, but expressed differently
• B. They are calculated differently and expressed the same
• C. They are unrelated
• D. They are identical in both

Answer: (A)

Both stream gradient and slope gradient are rates of vertical change per distance, so the basic calculation is the same: how much elevation changes (rise) divided by how far you move (run). The difference lies in what you use for the run and how you express the result.

For a stream, the run is the distance along the channel itself. That’s why stream gradients are often written as meters of drop per kilometer of stream (m/km) or feet per mile of channel. For a slope on a map or the landscape, the run is the horizontal distance in plan view, so the gradient is commonly expressed as a percent grade, a decimal, or an angle.

Example helps: if a stream drops 20 meters over 2,000 meters of channel length, the gradient is 20/2,000 = 0.01, or 1%, in terms of percentage. If the same 20-meter drop occurs over a horizontal distance of 2,000 meters, that would be 20/2,000 = 0.01, but expressed as 1% slope as a percent grade, and the angle would be about 0.6 degrees. The numbers reflect the different definitions of run and the different ways we express the result, even though the underlying idea is the same.