Scaling for understanding spatial pattern 22

1.4.1. The meaning of scale

Owing to the scale multiplicity in pattern and processes, scale holds the key to

understanding the pattern-process relationships. Both scale and scaling are inevitably related to landscape ecology (Wu 1999; Wu and Qi 2000) and have been prominent in characterizing spatial patterns over multiple scales. The notion of scale refers to size in space and time; size is a matter of measurement (Allen and Hoekstra 1992). Scale is also often understood as

expressing dimensions of time and space (Linke et al. 2007); consequently it has been used to describe both spatial and temporal scales. Spatial scale is usually considered as the product of grain and extent (Wiens 1989), which in remote sensing, relate to the spatial resolution (length of a pixel’s edge in one dimension) and area coverage, respectively (Gustafson 1998; Allen and

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Hoekstra 1992). The effect of scale on diverse spatial phenomena (e.g., patterns of post-fire landscape structure) can be studied using these two components of a scale (Wu and Qi 2000).

1.4.2. Scaling and scale effects

Apart from the concept of scale, attention has been given to the concepts of scaling and scale effects. Scaling focuses on what happens to the patterns and characteristics of an object when its scale (size or dimensionality) is changed; therefore, it is defined as is the process of information transformation or extrapolation over multiple scales (Marceau and Hay 1999; Wu 1999; Wu and Li 2006). However, scaling is a challenge in both theory and practice (He and Mladenoff 1999; Wu et al. 2000) because of the non-linearity relationship between processes and variables, and landscape heterogeneity that determines the process (Wiens 1989; De’ath and Fabricius 2000). The first step in designing a scale-dependent experiment is to identify the factors operational at a given scale of observation (i.e., the spatial scale of the focal question) (Marceau and Hay 1999), which depends on the processes, organism, or responses of interest (Wiens 1989). In order to understand the scaling theory, three levels of analysis can be

formulated: 1) the focal level in question (L0), 2) the level below that (L-1), and 3) the level above

that (L+1) (Allen and Hoekstra 1992). Defining the focal level of a hierarchy is the most important

factor in the theory because focal level determines the resolution of the observations (O’Neill et al. 1991). The scaling theory suggests that when one studies a phenomenon at a particular

hierarchical level (L0), the mechanistic understanding comes from L-1 whereas the significance or

context of that phenomenon can be revealed at L+1 (O’Neill et al. 1991; Allen and Hoekstra 1992;

Wu 1999). The three levels can be described as micro (L-1), focal (L0) and macro (L+1) scales

respectively.

The process of information transformation or assessing the scale-dependency experiment can be accomplished by changing grain, extent, or both (Wu 1999). While working with scaling, one must distinguish between two forms of scaling: up-scaling and down-scaling. Up-scaling refers to a process that transfers information from local scale to derive processes at macro scale (Wu et al. 2000). Up-scaling can be achieved using is a resampling techniques, which are designed to transform an image data set acquired at finer spatial resolution to a coarser spatial resolution representation of the same image. Conversely, down-scaling is a method of

transforming information from macro scale to local scale; decomposing information at one scale into its constituents at smaller scales (Marceau and Hay 1999). In general, up-scaling and down- scaling can also be described as aggregation and disaggregation methods respectively (Figure 1.13).

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Figure 1.13. Scaling techniques: aggregation and disaggregation methods for implementing multi- scale analysis.

Remote sensing provides the desired data for up-scaling and down-scaling and the possibility of undertaking studies to understand the behaviour of variables when changing scale and derive appropriate rules for scaling (Marceau and Hay 1999). This study was provided with multiple spatial resolution data: 4, 8, 16, 32, and 64 m spatial resolutions, hereafter referred to by R4, R8, R16, R32, and R64 (Remmel and Perera 2009); hence a multi-scale analysis approach for

characterizing spatial patterns across a gradient of scales would be performed.

While examining the issue of scale and scale effect in various aspects of spatial analysis, it is important to mention the concept of Modifiable Areal Unit Problem (MAUP). MAUP is a problem that occurs in spatial analysis of aggregated data in which the same basic data

generates different results when aggregated in different ways (Wong 2009). For example, if the sizes of the pixels are changed or shift in location of the grid relative to the real scene on ground, it can then lead to a numerous datasets which will provide different results. An object (e.g., a residual patch) might have also different shape and size when derived from different images at different spatial resolutions; this problem is referred to as the MAUP (Openshaw 1984). There are two issues of concern related to the MAUP: scale and zonation; the MAUP involves both the effects of altered pixel size and the way of its alternation in a spatial context (Openshaw 1984). For example, in order to understand the spatial patterns of residual patches at landscape level, aggregation of fine resolution data (R4) to coarser resolution data (R64) is performed. This leads

to a problem in spatial analysis where areal units are aggregated to different sizes; this is known as the aggregation effect of MAUP. The process in which the number of pixels kept constant or unchanged, but their arrangement changes is a zonal process which gives rise to various zonation or zoning effect; this involves a change in zones or grouping scheme (Wong 2009).

Up-scaling Down-scaling

Fine spatial resolution Coarse spatial resolution

Down-scaling

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1.4.3. Scaling for characterizing spatial patterns

Understanding the effect of scale on detecting the patterns of spatial objects is an important step in landscape ecology or in assessing the relationship between patterns and processes, but there is no single all-encompassing scale at which all measurements can be made (Wiens 1989). It has been argued that geographic phenomena tend to have characteristic spatial and temporal scales or spatiotemporal domains (Allen and Hoesktsra 1992). Moreover, the amount of information available, variables that can be measured and the scale at which the process operate would not be the same across multiple scales. Thus, scaling theory becomes an important approach for characterizing the patterns over multiple scales; as variables and

processes important at one scale may not be useful at another scale. If one changes the scale of reference, the phenomena of interest change, and information is often lost as observational scale changes (Riitters et al. 1995). For example, at the scale of a sub-event scale, it might be

reasonable to ignore coarser-scale variability in temperature. Conversely, if the extent of our observational scale increases, the variability in temperature may also become important and should be accounted.

Moreover, spatial patterns and processes often occur over multiple scales (He and Mladenoff 1999) and there are hierarchical linkages among the scales; so information

transformation among the scales is an essential component of landscape ecology (Wu and Li 2006). A central theme of landscape ecology is that particular phenomena should be addressed at their characteristic scales (Turner 1989), and hence a scaling rule should be established to understand the patterns across gradient of scales. However, a successful scaling strategy must address the complex aspects of ecological systems: scale-dependence process and spatial nonlinearities (Wu 1999). Observations made on a single scale can capture only those patterns and process pertinent to that scale of observation, but the complexity arises when an analysis involves multiple scales (Wu 1999). Scaling is also important when a prediction is desired to capture patterns at a certain scale (e.g., coarse scale or spatial resolution), based on information obtained at another scale (e.g., finer scale) (Wiens 1989; Wu and Li 2006).