AnalyzingTobler’s Hiking Function and Naismith’s

RuleUsing

Crowd-Sourced GPS Data

Erik Irtenkauf, Master’s CandidateThe Pennsylvania State University

Association of American Geographers Annual MeetingApril 9, 2014

Background• Terrain has a big effect on human movement

• Modeling movement is importanto Helps explain how humans interact with our environment

• Two common methods in Geography/GISo Tobler’s Hiking Functiono Naismith’s Rule

Tobler and Naismith

-70 -50 -30 -10 10 30 50 700

1

2

3

4

5

6

7

Naismith-Langmuir Tobler

Slope (Degrees)

Velo

cit

y (k

m /

hr)

• Both methods estimate walking speed/time based on slope

• 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

MethodologyGoal: 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

• Analyze predicted vs. actual hiking times

-70 -50 -30 -10 10 30 50 70

0

2

4

6

8

10

12

14

Slope (Degrees)

Velo

city

(K

m/H

r)

Crowd-Sourced GPS Data• Offers the chance to quickly

gather data from a diverse range of environments and conditions :

Spring Summer Fall Winter

20

55

37

8

Tracks by Season

2006 2007 2008 2009 2010 2011 2012 2013

14

11

1815

21 21

29Tracks by Year

Developed

Barren

Deciduous F

orest

Evergr

een Fo

rest

Mixed Fo

rest

Scrub/Sh

rub

Grassla

nd0

10

20

30

40

50

60

70

80Tracks by Land Cover Type

Marine

Warm Cont.

Hot Cont.

Temp. Steppe

• Predicted times for each method are strongly correlated across ecoregion divisions:

MarineRegime

Mountains

TemperateSteppeRegime

MountainsHot

ContinentalDivision

Mountains

WarmContinentalRegime

Mountains

.98.98

.99

.99

Correlation BetweenTobler and Naismith

Predicted Hiking Times

Findings

• Accuracy ranges can be determinedo Predicted times are generally accurate

Findings

35%

70%93%

• Accuracy varies across ecoregion divisionso Available data does not fully explain these differences

MarineRegime

Mountains

TemperateSteppeRegime

MountainsHot

ContinentalDivision

Mountains

WarmContinentalRegime

Mountains

28.3423.52

Average Difference (%)Between Predicted and Actual Times

Findings

22.0221.34

17.6917.18

16.1416.84

ToblerNaismith

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 CandidateThe Pennsylvania State University

eji107@psu.eduirtenkauf@gmail.com

Project Advisor: Dr. Doug Miller

Permission to use this project datawas obtained from www.wikiloc.com,

their contribution is gratefully acknowledged.