Exposure to human influence – a geographical field approximating intensity of human influence on landscape structure

ABSTRACT A new spatial variable for the land use and land cover change modelling is introduced, approximating the intensity of human influence on the landscape. The ‘exposure’ simulates the dilution of human activity from settlements (source points with information about population size or other human activity quantification) to landscape, based on the accessibility. Exposure to a settlement is directly proportional to its population size and inversely proportional to the cost distance from the settlement. Cost distance uses the sine of the slope angle as a cost raster to simulate a barrier effect of the terrain. Overall exposure to human influence summates exposure to all individual settlements in a region. The resultant raster field created for Slovakia achieves observable resemblance to the actual intensity of land use derived from Corine Land Cover map. The ArcGIS tool developed for the exposure calculation is supplemented.

There is a wide spectrum of the variables used in the studies, representing both environmental and socioeconomic characteristics of the landscape (Bürgi, Hersperger, & Schneeberger, 2004;van Vliet, de Groot, Rietveld, & Verburg, 2015). Variables representing the intensity of human activity belong to the most important ones. There is a wide variety of their definitions, focusing on demographic, economic, agricultural and other indicators. Population size (Figure 1) may be considered as a basic indicator, used for example by Millington, Perry, and Romero-Calcerrada (2007) and Calvo-Iglesias, Fra-Paleo, and Diaz-Varela (2009), its change by Gellrich, Baur, Koch, and Zimmermann (2007). Wang et al. (2016) used GDP and other economic variables, while various agricultural variables were used by Hietel, Waldhardt, and Otte (2005), Van Doorn and Bakker (2007), Martínez (2011), or Smaliychuk et al. (2016. However, the use of these indicators is restricted by the fact that they are usually assigned to an administrative area. Population density is an efficient example. It is widely used to depict the distribution of population in landscape (e.g. Demek, Mackovčin, & Slavík, 2012;Inouye, de Sousa, de Freitas, & Simões, 2015;Ku, 2016;Martínez, 2011;Newman, McLaren, & Wilson, 2014) but the resulting picture is strongly dependent on the administrative borders, which do not always adequately approximate the actual spread of the human activity in the landscape (Figure 2).
Accessibility is a further key factor commonly used to approximate the intensity of human influence in the landscape (e.g. Eiter & Potthoff, 2016;Martínez, 2011;Shu, Zhang, Li, Qu, & Chen, 2014). Most of the studies use Euclidean distance to human settlement or road network for its determination (Baumann et al., 2011;Łowicki, 2008;Rutherford & Bebi, 2008;Xu, McNamara, Wu, & Dong, 2013). Although this approach offers simplicity, we consider the use of cost distance much more appropriate, because barrier effects of the terrain, land cover and other factors shaping transportation routes can then be taken into account (e.g. Etter, McAlpine, Pullar, & Possingham, 2006;Martínez, 2011;Müller & Munroe, 2008;Pazúr, Lieskovský, Feranec, & Oťaheľ, 2014;Schirpke, Leitinger, Tappeiner, & Tasser, 2012). Accessibility from human settlement may be considered as one of the most important predictors of the land use formation, reflecting 'how far' is human activity concentrated. However, it does not distinguish among settlements with a different intensity of human activity (quantified by population size, for example) and therefore it cannot adequately assess the intensity of human activity in the landscape. This paper proposes the concept of variable 'exposure to human influence'. Its main goal is to combine the intensity of human activity and accessibility in one spatial variable for the purposes of land cover and land use change modelling. While developing the concept, we tried to balance its ability to approximate the human influence in sufficient detail on the one side, and its simplicity on the other side. Under simplicity, we understand both relying on easily obtainable data and using the smallest possible number of calibration coefficients.
We are aware that there are many ways to define both source variableshuman activity and accessibility. For the purpose of this initial concept, we simply use population size as the measure of human activity and terrain slope as the sole variable in accessibility calculation. However, population can be easily replaced by any other relevant point-assigned measure of human activity without any change of this concept. A small change in the equation allows to implement other determinants of accessibility.
We produced the 'exposure to human influence map of Slovakia' to demonstrate this concept's ability to approximate the human influence on the landscape, especially in the hilly areas. The resultant raster field of exposure is available for detailed examination as an attachment of this article, as well as the ArcGIS tool used for the calculation.

Methods
Derivation of the final exposure concept consisted of three steps: (1) Defining the general exposure equation; (2) Replacing Euclidean distance by cost distance; (3) Specifying the barrier raster for cost distance calculation.

Exposure
Our exposure definition is based on the following simple principle: exposure to human influence from a settlement ('source point') is directly proportional to its population size (or other quantification of human activitygenerally termed 'source intensity') and inversely proportional to the distance from this point. It is an analogy to widespread urban gravity models, which model spatial interaction of cities, urban growth and development (Chen, 2009;Paulov, 2004). This principle is further analogous to Newton's law of universal gravitation, Coulomb's law of electrostatics and other inverse square laws modelling any point-source radiation in three-dimensional space: Quadratic influence of distance can be explained by geometric dilution corresponding to point-source radiation into a three-dimensional space. However, because we are modelling the spread of the intensity into a two-dimensional space of landscape, we suggest the simple value of distance instead of its squared value. The reason is that the density of flux lines is inversely proportional to the square of the distance in 3D, but it is inversely proportional to the simple distance in 2D space. Since exposure value in the source point (settlement) should equal source intensity, we applied the addition of the number '1' in the equation denominator. Then, if the population size of the source point centre c1 is the measure of its influence, the exposure to the centre c1 (Ex c1 ) is: Exposure to human activity from n centres is then defined as: The resultant exposure values are dependent on the unit of distance; for example, exposure equals one half of the original population in the distance of one meter, one-third in two metres, etc. Therefore, we introduced distance one (d1) calibration coefficient to eliminate dependence on distance units. It is defined as the distance, in which exposure to human influence is one half of the exposure in the centre:

Cost distance
The previous concept alone would probably not yield very original results, as it would produce a raster field with circularly shaped isolines, which would probably be relatively similar to some other concepts using for example kernel density ( Figure 2). Precision is obtained by replacing simple Euclidean distance with cost distance, using the barrier effect of landscape as the cost raster. We used ArcGIS tool Cost distance for this purpose. The cost distance algorithm automatically searches for the smallest cost distance path between the raster cell and the centre. The cost distance is calculated as (5) where j is an individual raster cell on the least-cost path and m is the set of all cells on the path. Distance j represents a distance travelled across the cell j. It equals the cell size if the path crosses the cell perpendicularly to its side, or 1.414214 (square root of 2) of the cell size if it crosses the cell diagonally. The cost distance raster can be used as a representation of the accessibility. The barrier effect is the key variable affecting the shape of this raster.

Barrier effect
Slope gradient was used as the main measure of the barrier effect of landscape. We did not consider other factors affecting accessibility, such as land cover and road network, in order to keep simplicity of the concept. Sine of the slope was utilised because it was physically well interpretable: It was derived from the decomposition of the gravitational force on the slope, with sine representing the component of the force needed to overcome the barrier. The sine transformation of the slope was suggested for the accessibility modelling also in the work of Minár, Tremboš, and Vajlíková (1992). Regarding Equation (5), the barrier effect should have value '1' in zero-slope areas so that the cost distance on the plain surface is equal to the Euclidean distance. The value should then increase to '2' in the areas where the costs needed to ensure a bi-directional transportation double the costs in the flat areas. Similarly, it should increase to '3' in the areas where the costs triple. A wide range of transportation costs needs to be considered. Under 'ensuring the transportation', we therefore do not understand only the energy needed for physical transport of persons or goods, but also the energy for building a sufficient infrastructure and other related costs.
Two components of the barrier raster calculation were introduced to implement these requirements: the constant '1' ensured the equality of cost distance to Euclidean distance in the zero-slope areas and the coefficient 'k' enabled calibration of the original sinslope raster. The resulting equation is Barrier effect = 1 + k * sin slope.
Calibration of the barrier effect by the coefficient k enables change in the cost distance isolines shape. Setting the coefficient higher strengthens the barrier effect. Transport along the areas of lower slope is then preferred, even if it involves longer distance. This produces more lobed shape of the cost distance isolines. Setting the coefficient to lower values weakens the barrier effect of the slope. Transport along paths with shorter distance is preferred, even if it involves steeper slopes. This results in more compact cost distance isolines shape. Changing the 'k' coefficient, however, also changes the cost distance raster scale with a change in the overall value level and therefore re-consideration of 'd1 (4)' is required.

Final definition of the exposure to human influence
Embedding cost distance calculation in the exposure equation gives Calculation in ArcGIS requires two data inputs: (1) slope raster and (2) point layer of centres with numeric field providing the intensity of human influence, for example, population size. The tool works in the following steps: (1) Calculation of the barrier raster (2) Iterative calculation of the exposure: (a) Calculation of the cost distance raster of a centre i (b) Calculation of the exposure to the influence from the centre i, (c) Addition of 'Ex i ' to the total exposure: 'Ex 1 ' is added to a zero raster and each following 'Ex i ' is added to the previous total exposure raster. This approach is chosen to avoid a memory demanding process where exposure rasters of all centres required summation in one step and increased hard-disk space.
The threshold value of the exposurethe minimum 'Ex i ' value calculated for the centre i was introduced to enable faster calculation of the exposure for the tasks with many centres. The calculation of the cost distance ceases when exposure shrinks to the threshold value, so cost distance is calculated only for the area where resultant exposure is higher than the threshold, rather than for the complete working extent. This provides less time-consuming cost distance computation for every centre; however, the threshold should not be set too high as this would bias the final result, especially in rural areas where small impacts from many villages become important.

Production of the exposure to human influence map of Slovakia
The exposure concept was tested with the use of real data (Figure 1) from the 2001 Slovak population census for 2935 municipalities and town parts (Tomášiková, 2010) and slope gradient derived from EUDEM elevation model with the resolution 25 m (European Environment Agency, 2013). The exposure computation resolution was set to 100 m. Several combinations of the k and d1 coefficients were tested in order to find the combination yielding a raster image that would satisfactorily approximate the intensity of human activity.
Decisions were based on the visual comparison with the Corine Land Cover 2012 data (European Environment Agency, 2016) because statistical testing of suitability of different model design requires more complex research. Level of hemeroby was assigned to each land cover class to estimate the actual human influence intensity (Table 1). Hemeroby can be understood as an integrative measure of the impact of all human intervention on ecosystems (Walz & Stein, 2014). A slightly modified version of Walz and Stein's (2014) Corine Land Cover to hemeroby classification was applied. Data generalisation was then performed by focal statistics with 100-m radius of five cells raster resolution to improve the hemeroby map interpretation.
The final model design of this study employs k = 25 and d1 = 100, which are also set as the default values of the attached ArcGIS tool. The resultant map was designed in ArcGIS 10.3.1. A non-linear stretch of the colour ramp was used for the resulting raster.

Conclusions
Although approximation of human influence intensity depicted in the Main Map's resultant exposure raster was developed solely from two spatial sourcesslope angle raster and population size point layerit Table 1. Classification of the land cover hemeroby, originally published by Walz and Stein (2014) for Germany and modified for land cover in Slovakia.

Hemeroby
Corine land cover provides great detail. Relatively higher values of the exposure can simulate the shape of the meta-and polyhemerobic areas (settlements), a bit lower values can indicate localisation of α-euhemerobic areas (arable land), and to some extent also β-euhemerobic areas (pastures), while the lowest values point to oligo-and ahemerobic areas (forests and other natural areas). The model is also able to meaningfully approximate the exposure in the areas further from the settlements by indicating the spread of human influence along less steeply sloped areas. This portrayal often conformed to the actual land cover pattern. The exposure to human influence is the result of a cumulative effect of the influence from all the settlements. This effect is especially observed in the flat areas with low barrier effect and large settlements (e.g. southwestern Slovakia). The average exposure value here is significantly higher than in the hilly areas, where the spread of the human influence disappears over much smaller distances. We consider this effect to be one of the most important benefits of the concept, as it allows to depict the pressure of human activity on the environment. On the other hand, this effect probably reduces the overall correlation between the exposure and the actual land use intensity, because the same values of exposure may indicate forest in flat or densely populated regions, while they may also point to urban areas in hilly or sparsely populated regions. However, we suggest that this fact should not be considered a disadvantage for land cover modelling, because we suppose that exposure can be used in combination with other variables such as accessibility, which can balance the resulting prediction. This effect can also be reduced by different calibration of the exposure calculation.
Quality of the exposure raster is directly dependent on the quality of the input slope raster and population point layer. The use of more precise DEM, or setting smaller cell size, would therefore result in a more detailed structure of the resultant exposure raster. The use of separate points for wards of large towns or municipalities with more centres would be the most significant improvement of the population point layer.
Population size is used as a proxy for human activity to demonstrate the potential of the concept. This way, the resultant raster may also be interpreted as the 'probability of the human occurrence in the landscape', which can be secondary considered as the measure of human activity. However, the overall quality of the information carried by the exposure raster would be largely improved by the use of more sophisticated quantification of the source intensity of human activity. The concept and the supplemented computation tool are adjusted to the use of any other measure of human activity. The exposure concept has a potential to improve the spatial resolution of many socio-economic variables (e.g. number of employees in primary sector, amount of investment and agricultural subsidies), which are traditionally measured at the administrative unit level.
There are many other options to improve this concept. While we used slope as the sole factor in landscape barrier effect (6), there is usually other information available to detail modelling of human influence spread in geographic space. The greatest issue in central Europe may be incorporation of barrier effect of water bodies and other wet areas and areas with high risk of flooding. Here, DEM-derived characteristics, such as the topological wetness index and possibly other more advanced characteristics, can provide compromise between information suitability and ease of data obtaining.
A further challenge is implementation of the land cover 'friction' data and corridor effects of road and rail networks introduced in research by authors such as Lieskovský et al. (2015). It is even possible that employing a network-based measure instead of cost distance would lead to results, which would be visually slightly similar to the exposure. However, it would require detailed data about the network and incorporation of network analysis, both decreasing the simplicity of the model. Besides that, these data are timedependent and therefore the resultant exposure might be considered as time limited and unstable. Incorporation of land cover barrier effect and network-based analyses therefore seems to be promising, but it would require complex redevelopment of the model.
Alternatives also exist for the main exposure Equation (4). While we used simple distance value to preserve the principle of geometric dilution and maintain equation simplicity, other studies employed squared values (e.g. Chen, 2009;Paulov, 2004). It is difficult to determine the more appropriate approach. However, the exponent of the distance may also be made a parameter of the equation, further expanding calibration possibilities.
Questions remain in deciding the most appropriate and precise exposure calculation calibration and its further improvements. Statistical analysis comparing the predictive power of the exposure and commonly used variables is required to answer these questions and to assess the benefits of the exposure to human influence concept. This kind of assessment should be a part of a more extensive study.

Software
ArcGIS 10.3.1 for Desktop was used to develop the tool for the exposure computation, as well as for the graphic design of all maps. Accordingly, the tool was tested in this ArcGIS version. The tool is supplemented to this article. Please contact us in a need to run it under other ArcGIS versions as well as in case of malfunction. ArcGIS tool used for the calculation of the exposure raster is supplemented to this article, as well as the exposure raster itself.