Osama Samawi Tobler's hiking function may be used to simulate how the expense of traversing a territory changes with slope. It is commonly used in geography and spatial analysis to anticipate how long someone will take to go across a particular area.

Tobler's hiking function in QGIS requires that you have QGIS installed on your computer, as well as access to a digital elevation model (DEM) of the area you want to analyze. To utilize Tobler's hiking feature in QGIS, follow these steps:

1. Load your DEM data into QGIS by heading to the "Layer" menu and selecting "Add Layer," followed by "Add Raster Layer."

2. After loading your DEM, go to the "Raster" menu and pick.

3. To compute the slope of the landscape, pick "Slope" from the Terrain Analysis menu. You may need to define the slope's unit of measurement (e.g., degrees or percent).

4. After calculating the slope, go to the "Raster" menu and pick "Cost Distance."

5. Select your beginning position as the "Source Layer" and the slope raster as the "Cost Layer" in the Cost Distance dialog.

6. To calculate the cost distance, press the "OK" button. This will add a new raster layer to QGIS that shows the cost of traversing the landscape.

7. To utilize Tobler's hiking feature, you must use the Raster Calculator. Select "Raster Calculator" from the "Raster" menu.

8. Enter the following formula in the Raster Calculator dialog: cost * exp(-3.5 * slope). This will apply Tobler's hiking function to the cost distance raster while accounting for terrain slope.

9. To compute the outcome, press the "OK" button. This will generate a new raster layer in QGIS that displays the cost of traversing the landscape using Tobler's hiking function.

I hope this was helpful! Please let me know if you have any queries or require any other support.

@Qamar Ul Islam First of all, thank you for this detailed explanation and for your time, I appreciate it a lot.

But you need to create the fraction surface immediately after you had the slope layer ready by using the Tobler function ( which the original formula does not fit with my research)

I managed to create the slope layer (in degrees) by using r.slop.aspect tool, my current problem is to use the formula in the raster Calculator, in which the exponential function is not valid

(your_res /1000)/(6 * Exp(-3.5 * Abs(Tan(("your_slope" * 3.14159)/180) + .05)))

Thank you again for your time and your help

Osama Samawi I understand you successfully built a slope layer using the r.slope.aspect tool and you're now attempting to construct a fraction of the surface layer using Tobler's hiking function, but you're having difficulties utilizing the calculation in the raster calculator since the exponential function is invalid.

One solution to this problem is to utilize the calculator's exp() function instead of standard exponential notation (e.g. "e" raised to a power). The exp() function raises e to a specified power, yielding the same result as the customary notation.

Here's an example of how the exp() function may be used in the calculation for Tobler's hiking function: (your_res /1000) / (6 * (exp(-3.5 * abs(tan(("your_slope" * 3.14159)/180) + .05)) ) )

It should be noted that various GIS software handles this type of activity in different ways. It could be a good idea to consult your program documentation or the support staff for the best method for your specific situation.

Please let me know if you have any more questions or if something is unclear.

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