I try to calculate Stream Power Index (SPI) in ArcGIS. For this reason, i checked many videos or documents but there is no certainty about the formula in the raster calculator. So I wrote these formulas below to learn which one is right. Each one creates different results.
DEM Cell Size=10m
SPI_1 --> "flow_accumulation" * 10 * Tan("slope_degree" * 0.017453)
SPI_2 --> Ln("flow_accumulation" * 10 * Tan("slope_degree" * 0.017453))
SPI_3 --> Ln("flow_accumulation" + 0.001) * (("slope_percent" / 100) + 0.001)
SPI_4 --> Ln(((flow_accumulation+1)*10) * Tan("slope_degree"))
SPI_5 --> "flow_accumulation" * Tan("slope_degree")
Also, while creating a slope, am I need to choose which one? DEGREE or PERCENT_RISE
And the last question: When I calculate SPI with the formulas above, I get SPI map that included negative values. Is it true? Are negative values a problem or not?
Dear Kemal,
If you are panning to use 3rd equation, you have to create slope raster in percent. As I remember, 3rd formula is the most widespread one.
https://www.wrc.umn.edu/sites/wrc.umn.edu/files/terrain_analysis_workshop_exercises.pdf
https://www.leg.mn.gov/docs/2016/mandated/160722.pdf
Good luck.
Dear Mariam Tsitsagi,
Thank you for your reply.
I get SPI value as maximum=6,7 minimum -5,0 with 3rd equation and the map looks meaningful. But I'm not sure that negative values are correct. Do you have any ideas about these negative values?
Thanks in advance.
Dear Saurabh Gupta,
As theoretically, we know the information you write in. However, in practice, I am looking for answers to the questions I mentioned above.
i think the correct formula is SPI_2 where:
flow accumulation must be in square meters and then not multiplied for 10;
the slope degree must not be equal to 0, so add + 0.1 degrees
In this way, SPI should be a dimensionless positive value (more or less)
SPI is calculated using the following equation: SPIi = ln(DAi * tan(Gi)) where SPI is the stream power index at gridcell i, DA is the upstream drainage area (flow accumulation at gridcell i multiplied by gridcell area), and G is the slope at a grid cell i in radians.
- Badges
- Science topic
- Similar topics
- Mathematics