Stream Gradient Hacks Sl Calculator
Free Stream gradient hack’s sl Calculator for geomorphology & mapping. Enter variables to compute results with formulas and detailed steps.
Formula
SL = (dH/dL) x L
Where SL = Stream Length-Gradient Index, dH = elevation drop across the segment (m), dL = length of the stream segment (m), L = distance from the drainage divide to the segment midpoint (m). Higher SL values indicate steeper reaches relative to their position along the stream.
Worked Examples
Example 1: Detecting a Fault Zone Knickpoint
Problem: A stream segment crosses an active fault zone. The segment drops 50m over 2km length, at a distance of 10km from the source. The stream total length is 25km, dropping from 500m to 100m elevation.
Solution: Local gradient = 50/2000 = 0.025 (2.5%)\nSL Index = (50/2000) x 10000 = 250\nOverall gradient = (500-100)/25000 = 0.016 (1.6%)\nNormalized SL = 250 / (0.016 x 10000) = 1.56\nConcavity index = 0.025/0.016 = 1.56 (steepened reach)\nThe elevated SL suggests tectonic steepening at the fault zone.
Result: SL Index: 250 | Local gradient: 2.5% | Concavity: 1.56 | Steepened Reach
Example 2: Comparing Graded Stream Reach
Problem: A graded reach in the lower portion of the same stream drops 10m over 2km at 20km from source.
Solution: Local gradient = 10/2000 = 0.005 (0.5%)\nSL Index = (10/2000) x 20000 = 100\nOverall gradient = 0.016\nNormalized SL = 100 / (0.016 x 20000) = 0.313\nConcavity index = 0.005/0.016 = 0.313 (graded/flat reach)\nLow SL confirms this is a well-adjusted, graded reach.
Result: SL Index: 100 | Local gradient: 0.5% | Concavity: 0.31 | Graded/Flat Reach
Frequently Asked Questions
What is the Stream Length-Gradient Index (SL Index)?
The Stream Length-Gradient Index, commonly known as the SL Index or Hack SL Index, was developed by John Hack in 1973 as a quantitative measure of stream gradient that accounts for the typical downstream decrease in slope. It is calculated as SL = (dH/dL) x L, where dH is the elevation drop over a stream segment, dL is the length of that segment, and L is the total stream length from the drainage divide to the midpoint of the segment. The SL Index normalizes gradient by stream length, making it possible to compare slopes at different positions along a stream profile. Values that are anomalously high compared to adjacent reaches indicate zones of tectonic activity, resistant lithology, or recent base level change.
What does a concave-up stream profile indicate?
A concave-up longitudinal profile is the equilibrium shape of a graded stream, where the channel has adjusted its slope to efficiently transport the sediment supplied from upstream with the available discharge. The concavity arises because discharge increases downstream as tributaries add water, requiring less slope to transport sediment. In the headwaters, steep gradients compensate for low discharge, while in the lower reaches, gentle slopes suffice because of high discharge. The degree of concavity is quantified by the concavity index, typically ranging from 0.3 to 0.6 for graded streams. Deviations from the idealized concave profile indicate disequilibrium caused by tectonic activity, lithological changes, glaciation, base level changes, or large sediment inputs from tributaries or landslides.
How does base level change affect stream gradient?
Base level is the lowest elevation to which a stream can erode, typically sea level for streams draining to the ocean or lake level for inland streams. When base level drops, either due to sea level fall, lake drainage, or tectonic uplift at the mouth, streams respond by incising from the mouth upstream. This incision creates a knickpoint that migrates upstream over time, steepening the lower profile while the upper profile remains unchanged. The SL Index downstream of the knickpoint increases as the stream adjusts to the new base level, while upstream values remain at pre-change levels. Conversely, base level rise causes aggradation and gradient reduction in the lower reaches. The rate and pattern of stream adjustment to base level change depends on discharge, rock resistance, and the magnitude of the change.
Can I use Stream Gradient Hacks Sl Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
What formula does Stream Gradient Hacks Sl Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
How accurate are the results from Stream Gradient Hacks Sl Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.