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1 Geographia Napocensis Anul VI, Nr. 2, 2012 DETERMINING MINIMUM HIKING TIME USING DEM ZSOLT MAGYARI-SÁSKA 1, ŞTEFAN DOMBAY 2 Abstract: - Determining minimum hiking time using DEM. Minimum hiking time calculus can be used to assess the maximum area where a lost person can be. Such area delimitation can help rescue teams to efficiently organize their missions. The two well known walking time rules was used to determine, compare and correlate the obtained result in a test area. The calculated times has a high correlation coefficient which makes possible a precise conversion between Naismith and Tobler walking times. For delimiting the rescue area a graph based modeling from a raster layer was implemented using R environment. The main challenge in such a modeling is the efficient memory management as the use of Dijkstra algorithm on directional costgraph requires high memory resources. Key-Words: hiking time, accessibility, R environment, Dijkstra algorithm 1 Introduction The definition of spatial accessibility has many definitions, and the study of accessibility has many application fields too. One of the basic formulations of spatial accessibility assumes the idea of defining the possibility of an individual with a give spatial location, to participate in different activities (Ulimwengu, 2004). If we want to apply the former definition for tourism, under the different activities we can understand the possibility of hiking. In the scientific literature we can find studies related to the degree of accessibility for different touristic attractions (Theobald, 2010). In these studies the accessibility is expressed in time, making the assumption that the fastest reachable areas (with the least time) will be the most frequently visited. The spatial accessibility expressed in time can be used not only for hikers but also for the rescue teams. In this case, two approaches are possible: - a person in trouble how fast can leave the danger zone, or a safe place where he can find assistance (Cinnamon, 2008; Wood, 2012) - how long it takes for the rescue teams to get to the distressed persons (Pingel, 2009). Pingel in is study indicates the possibility of such analysis and the usefulness of such approach. In this latter case, the essential problem is to determine how far can get a given person, saw for the last know time at a given spatial position. If we consider hiking, we can find a plenty of factors that influences the maximum reachable position in a give time period. Among these factors we can mention the relief, the existence of roads and paths, the psychical state and fitness of the person, the meteorological conditions, the land cover, and other blocking factors. The aim of this research is to determine the area were a lost person can be found taking account only the relief based on a Digital Elevation Model, his starting locations and the elapsed time. 2 Methodology and objectives For determining the time for field distances there are two well known and largely used 1 Babeş-Bolyai University, Faculty of Geography, Gheorgheni Extension, Gheorgheni, Grădina Csiky fn., Romania, zsmagyari@gmail.com 1 Babeş-Bolyai University, Faculty of Geography, Gheorgheni Extension, Gheorgheni, Grădina Csiky fn., Romania, dombay.istvan@gmail.com 124

2 DETERMINING MINIMUM HIKING TIME USING DEM methods: the Naismith and the Tobler rules. The Naismith rules and its later corrections (Langmuir and Tranter), consider the slope in the direction of walking and obstacle (for upslope and down-slopes higher than 12 degrees) but also as a supporting component (for downslopes between 5-12 degrees). At the same time it considers the fitness of the person (Tranter correction), based on which the necessary time can be reduced or grown up. The original formulation of William Naismith, a Scottish mountaineer, rule for hiking distances is to consider 1 hour for 5 km, and for every 600 ascent to consider another hour. Later Langmuir makes the following correction: he considers just 4 km for every hour, and for down-slopes between 5-12 degrees every 300m of descent reduces the necessary time with 10 minutes, while in case of downslopes higher than 12 degrees, every 300 m of descent grows the necessary time with 10 minutes (Langmuir, 1984). The Tranter correction is in fact a correspondence table between the calculated time based on the (corrected) Naismith rule and the fitness class of a given person. The fitness class is measured as the necessary time to walk upslope having a baseline of 800 m and an ascent of 300m. Based on Tranter s table the corrected time can be higher or lower than the originally calculated time. The Tobler rule is in fact a formulae (equation 1) determines the hiking speed based on exponential function which takes account the slope. The dissymmetry effect of slope direction in walking speed is marked with a shift of 0.05 in the exponent (Tobler, 1993). dh dx V = 6 e (1), where, - V walking velocity (km/h) - dh slope high - dx slope base Pingel s study warns against the direct use for persons of Tobler s formulae. Among its argument are the slow down effect of high descent slopes, and also the proved fact that persons estimates incorrectly the field distances, the gradient of the terrain and the necessary hiking time. Due to this they face with considerably higher hiking time the optimal one s. The mentioned arguments showes that in reality the hiking time is increased, so the safely of localization for lost tourists will not suffer using this formulae. One of the aims of our study was to compare the result given by using the two mentioned rules in a given territory. For application area we have choose the operational area of the local mountain rescue team, because the good relationship with them can provide field based control data. In the next phase of our research we will use that rule which gives a higher safety for determining lost person s possible location area, that will give s the larger area. Due to the fact that Tobler s rule doesn t account the fitness level of a person we considered just the Langmuir correction of Naismith rule, without the Tranter s correction. For the comparison of two methods we have selected five random points, and then we analyzed the hiking time for the resulted ten bidirectional paths. The problem in defining the maximum spatial distance was that we didn t know the direction in which a person passes an area. Therefore another aim of our research was to study the practical usefulness of modeling the study area with a directional cost-graph. In this case every cell of the raster layer becomes a graph node, while between the adjacent cells a connection will be formed having the travel time as cost. In the scientific literature there are three well known adjacency versions: the Rook, the Queen and the Knight connections (Pingel, 2009). In our study we use the Queen connection, in which case a center cell has 8 adjacency cells [Fig.1]. 125

3 Zsolt Magyari-Sáska, Ştefan Dombay Fig.1 Queen adjacency connection (a) its decomposition (b) and graph based representation (c) Several studies use the graph based terrain modeling, but only on test or small-scale areas (Collischonn, 2000, Fritz, 2000). That s why we think that is necessary to investigate it on larger scales. For our research we used R the free, open source, programmable statistical environment and the IDRISI GIS environment. As for many research is necessary to involve several software is optimal to choose that ones that provide programming capabilities (Magyari-Sáska, 2010) 1 3 Analyses and results Our research area was the operation area of the local mountain rescue team. Firstly we analyzed the hiking time for the ten bidirectional paths formed with the five random points [Fig. 2]. The paths profile is realized with IDRISI s Profile command and they are presented in figure 2 [Fig. 3] Fig.2 Study area and the used paths 126

4 DETERMINING MINIMUM HIKING TIME USING DEM Fig.3 Paths profile For determining the hiking times we created special functions in R for modeling each rule. These functions are created to read and analyze data from IDRISI s ipf files, optionally create by the Profile command. In case of Naismith rule the created function can determine the hiking time based on original rule (N time) or using the Langmuir correction (NL time) [Table 1]. Table 1 Hiking times paths N time NL time T time 1_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Comparing the hiking times we found that in majority of cases the NL time is higher that the hiking time based on Tobler s rule (T time) Based on the pair wise correlation values we found that the correlation between N and NL times (both based on Naismith rule) is 0.999, suggesting that Langmuir correction in our study area increases the hiking time, but in general terms does not change the basic rule [Fig. 4]. The correlation between T time and N and NL time respectively is also very high (0.97), Fig. 4 Hiking time correlation which proves the compatibility of the two methods, even if they use different approaches. Our next step was to determine the access time for different locations of the study area. For this we had to transform the elevation raster layer into a directional cost-graph. In general the GIS software cannot make such a transformation, that s why we used again the R statistical environment. In this case a plenty of external packages are developed for different application areas by a wide number of contributors. There are also packages which 127

5 Zsolt Magyari-Sáska, Ştefan Dombay allow the read/write and manipulation of raster data. Such external packages are important because they gives the possibility of accessing individual cells of a raster layer and offers high processing speed as their functions are written using low level instruction. The R environment has a special advantage processing vector and matrix like data. Complex operations can be symbolized with relative simple instructions, offering a good formalization for such operations. The constructed graph from the raster layer has an equal number of nodes with the number of cells. Every cell has eight bi-directional connection with the adjacent cell (excepting outside cells), resulting 16 values per cell. For determining the access time for every cell we used the Dijkstra algorithm, which offers the possibility to analyze every possible route to the target cell and calculates the minimum cost (time) to reach it. This algorithm can be used to get the maximum area coverage where a lost person can be. The Dijkstra algorithm contained in igraph package for R offers the possibility to get the least cost path for every node pairs. This means that after generating such a correlated table, from every location we directly can select all the other locations reachable in a given time period. In reality this approach cannot be used as for our study area, having 1151 columns and 861 rows at the resolution of 31 meter uses cells (nodes). To model the pair wise hiking time it would be necessary x values, which reach at 914GB, practically impossible even if every cost is modeled at byte limits. In practical terms remains the version in which for every location the minimum cost should be generated for determining the maximal coverage area where a lost person could get [Fig. 5]. Fig. 5 Maximum spatial distance where a person could get at hourly resolution from test points 1,2,3 and 5 128

6 DETERMINING MINIMUM HIKING TIME USING DEM 4 Conclusion The aim of our primary study was to get methods based on digital elevation models which can help to determine the possible location of lost tourist. We considered the Naismith rule with its Langmuir and Tobler corrections and the Tobler rule. Testing twenty paths we concluded that the resulted hiking times of different methods are strongly correlated, having a correlation coefficient of This doesn t mean that hay have has very close values, but the possibility to calculate one based on the other very precisely. This also means that the Tranter s correction on Naismith time is also usable on Tobler s time. We also consider that the strong correlation validates both rules modeling capacity. After that we analyzed the performance of Dijkstra algorithm (and its implementation) on a relatively broad raster layer, with a high number of cells, in order to get the shortest time-cost paths. We concluded that for a realistic modeling this algorithm could not be used to determined the pair wise shortest time-cost paths, but a generating the access paths just from an initial location offers a real possibility of getting lost persons possible location area. Acknowledgment. This research and paper has been created within a project funded by the Domus Program of Hungarian Academy of Sciences. References [1] CINNAMON, J., SCHUURMAN, N., CROOKS, V.A., (2008), A method to determine spatial access to specialized palliative care services using GIS BMC Health Service Research, Open Access Journal [2] COLLISCHONN, W., PILAR, J.V., (2000), A direction dependent cost path algorithm for roads and canals International Journal of Geographical Information Systems [3] FRITZ, S., CARVER, S., (2000), Modeling remoteness in roadless areas using GIS, [4] LANGMUIR, E., (1984), Mountaincraft and leadership The Scottish Sports Council/MLTB [5] MAGYARI-SÁSKA, ZSOLT (2010), Algoritmi S.I.G. pentru calculul riscurilor naturale în Bazinul Superior al Mureşului, Presa Universitară Clujeană [6] PINGEL, T.J., (2009), Modeling slope as a contributor to route selection in mountainous areas, UCGIS 2009 Summer Assembly [7] THEOBALD, D.M., NORMAN J.B, NEWMAN, P. (2010), Estimating visitor use of protected areas by modeling accessibility: A case study in Rocky Mountain National Park, Colorado, Journal of Conservation Planning, vol. 6 [8] TOBLER, W., (1993), Non-isotropic geographic modeling, Technical Report No. 93-1, Santa Barbara, CA: National Center for Geographic Information and Analysis [9] ULIMWENGU, J.M., GUO, X., (2004), Modeling spatial accessibility within discrete choice framework, Selected paper for the presentation at the American Agricultural Economics Association Annual Meeting, Denver, Colorado, August 1-4, 2004 [10] WOOD, N.J., SCHMIDTLEIN, M.C., (2012), Anisotropic path modeling to assess pedestrian-evacuation potential from Cascadia-related tsunamis in the US Pacific Northwest, Natural Hazards, vol. 62, Springer 129