Analyzing Toblers Hiking Function and Naismiths Rule Using

Analyzing Tobler’s Hiking Function and Naismith’s Rule Using Crowd-Sourced GPS Data Association of American Geographers Annual Meeting April 9, 2014 Erik Irtenkauf, Master’s Candidate The Pennsylvania State University

Background • Terrain has a big effect on human movement • Modeling movement is important o Helps explain how humans interact with our environment • Two common methods in Geography/GIS o Tobler’s Hiking Function o Naismith’s Rule

Tobler and Naismith • Both methods estimate walking speed/time based on slope Naismith-Langmuir Tobler 14 • • Dr. Waldo Tobler published his hiking function in 1993, based on empirical data from Imhof (1950) Naismith’s Rule developed by mountaineer William Naismith in 1892, amended by Langmuir Used for: • archaeology • recreation • resource management • public safety 12 Velocity (km / hr) • 10 8 6 4 2 0 -70 -50 -30 -10 10 Slope (Degrees) 30 50 70

Methodology Goal: Analyze both rules using hiking GPS tracks shared on the internet Methodology: • Download a sample of 120 GPS tracks from www. wikiloc. com • Model Tobler and Naismith in a GIS to calculate predicted hiking times for each track 14 • Analyze predicted vs. actual hiking times Velocity (Km/Hr) 12 10 8 6 4 2 0 -70 -50 -30 -10 10 Slope (Degrees) 30 50 70

Crowd-Sourced GPS Data • Offers the chance to quickly gather data from a diverse range of environments and conditions : Tracks by Season 55 37 20 8 Spring Summer Fall Winter Tracks by Land Cover Type 80 70 60 50 40 18 Marine 30 20 Hot Cont. nd 1 29 21 21 2012 15 4 ss la ub hr b/ S G ra t ru Sc ed Fo r es st re M ix Fo en re rg ou s. F Ev e D ec i du D or e re st n Temp. Steppe Ba r lo pe d 11 Warm Cont. 10 0 ev e Tracks by Year 2006 2007 2008 2009 2010 2013

Findings • Predicted times for each method are strongly correlated across ecoregion divisions: Marine Regime Mountains . 98 Temperate Steppe Regime Mountains Correlation Between Tobler and Naismith Predicted Hiking Times Warm Continental Regime Mountains Hot Continental Division Mountains . 99

Findings • Accuracy ranges can be determined o Predicted times are generally accurate 93% 70% 35% Tracks where predicted time is within 10% of actual time is within 25% of actual time is within 50% of actual time

Findings • Accuracy varies across ecoregion divisions o Available data does not fully explain these differences 28. 34 23. 52 Marine Regime Mountains Warm Continental Regime Mountains 16. 14 16. 84 22. 02 21. 34 Temperate Steppe Regime Mountains Tobler Naismith Average Difference (%) Between Predicted and Actual Times Hot Continental Division Mountains 17. 69 17. 18

Conclusions • Both models work well, with some caveats • Crowd-sourced GPS data is a rich data source • Lack of additional information limits usefulness • Questions remain about generalizing this sample to a larger population

Erik Irtenkauf, Master’s Candidate The Pennsylvania State University eji 107@psu. edu irtenkauf@gmail. com Project Advisor: Dr. Doug Miller Permission to use this project data was obtained from www. wikiloc. com, their contribution is gratefully acknowledged.