Stream Power Index Calculator
Compute stream power index using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
SPI = As * tan(slope); Omega = rho * g * Q * S; omega = Omega / W
Where SPI is the Stream Power Index, As is specific catchment area, Omega is total stream power, rho is water density, g is gravity, Q is discharge, S is channel slope, W is channel width.
Worked Examples
Example 1: Mountain Catchment
Problem:Specific catchment area 800 m2/m, slope 12 deg, discharge 50 m3/s, channel slope 0.008, width 12 m.
Solution:SPI = 800 x tan(12) = 800 x 0.2126 = 170.1\nOmega = 1000 x 9.81 x 50 x 0.008 = 3924 W/m\nUnit = 3924/12 = 327 W/m2
Result:SPI: 170.1 | Power: 3924 W/m | Unit: 327 W/m2
Example 2: Low-Gradient Floodplain
Problem:Specific catchment area 2000 m2/m, slope 1 deg, discharge 100 m3/s, slope 0.0005, width 30 m.
Solution:SPI = 2000 x tan(1) = 34.9\nOmega = 1000 x 9.81 x 100 x 0.0005 = 490.5 W/m\nUnit = 490.5/30 = 16.35 W/m2
Result:SPI: 34.9 | Power: 490.5 W/m | Unit: 16.35 W/m2
Frequently Asked Questions
What is the Stream Power Index and what does it measure?
The Stream Power Index (SPI) estimates the erosive power of flow at any landscape point, calculated as As times tan(slope) where As is specific catchment area. Higher SPI values indicate locations where large water volumes concentrate on steep terrain, creating conditions for erosion and channel incision. It is widely used in geomorphology and GIS terrain analysis to map erosion risk. It serves as a proxy for hydraulic stream power when discharge measurements are unavailable.
How is stream power different from the Stream Power Index?
Stream power (omega) is a physically-based measure of energy expenditure by flowing water, calculated as omega = rho * g * Q * S in watts per meter. The SPI is a topographic surrogate using specific catchment area as a discharge proxy multiplied by slope tangent as an energy gradient proxy. Total stream power has physical units while SPI is dimensionless. Stream power is used in hydraulic engineering while SPI is common in GIS-based landscape modeling.
What is unit stream power and how is it used?
Unit stream power equals total stream power divided by channel width: omega_sp = rho * g * Q * S / W, in watts per square meter. It represents power available per unit bed area for geomorphic work. Channels below 10 W/m2 tend to be stable and meandering, while those above 100 W/m2 are typically braided or incising. Geomorphologists use unit stream power thresholds to classify river behavior and design restoration projects.
What factors influence stream power magnitude?
Stream power is controlled by discharge, channel slope, geometry, and flow resistance. Discharge is dominant and determined by catchment area, rainfall, and runoff. Slope decreases downstream as rivers mature. Width and depth determine power distribution across the bed. Flow resistance from roughness, vegetation, and bedforms reduces energy available for transport. During floods, discharge increases dramatically producing orders-of-magnitude power increases.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy