Reflexionando para transformar: por Mary Isabel Villa Ramírez

In order to avoid confusion of terms related to scale in the subsequent chapters it is necessary to clarify the different conceptions of scale and scaling. The conceptualizations given below are linked to the meaning of scale and scaling in geographic information science, environmental and ecological studies. The terms and explanations are derived from more profound discussions on the issue by Lam et al. (2004) and Wu and Li (2006).

3.1.1 Scale

Based on earlier work by Lam and Quattrochi (1992) and Cao and Lam (1997), Lam et al. (2004) propose four major meanings of scale that address different aspects of the matter:

observational scale, operational scale, measurement scale and cartographic scale. All four are prevalent in the topics discussed in this thesis and shall provide a guideline to the issues related to scale. According to the authors, they apply to both the spatial and temporal domain as well as spatial-temporal domains.

Observational scale or geographic scale refers to the spatial extend or size of a geographic area under investigation. With this notion a large scale study encompasses a larger study area, a small-scale study focuses on a smaller area. In this study, the area under investigation is a subsection of the larger study area of the GLOWA-Danube catchment of the upper Danube (see section 2.1).

The operational scale is the scale at which processes or natural phenomena operate in the environment. It denotes the distance (or time span) at which spatial patterns exhibit maximum variability. Knowing the operational scale of a phenomenon is important for researchers as determining appropriate observational scale is dependent on the extend of the action of the object under study. Measuring and Modelling LAI requires some thought on the operational scale of LAI and is discussed in chapter 5.

Measurement scale refers to the size of sampling intervals and is commonly called resolution. In applications involving uniform raster data it is equivalent to grid size or pixel (proxel) size. Due to storage and computational capacities, measurement scale is often connected to observational scale: A large-scale study sets a limit to the number of individual samples that can be stored or processed. Usually, the smaller the observational scale, the finer a grid or resolution of samples can be deployed. Decreasing cost and increasing efficiency of computer facilities however, allow for an increase of measurement scale in relation to observational scale. Measurement scale is also related to the operational scale. In order to assess a phenomenon the sampling interval needs to be smaller than the operational scale of the phenomenon.

The cartographic scale or map scale refers to the size of objects on a map in relation to the real world size of the objects. A large-scale map usually covers a smaller area and exhibits more detail than a small-scale map. Other than the previous denotations of scale, which refer to data characteristics, cartographic scale is coupled to graphical data representations. It provides information on how data is displayed. Any depiction of spatial data should provide information on the cartographic scale it is presented at.

The four meanings of scale are closely related. In the context of a spatial or temporal study, they can be ordered: The observational scale is largest, so that it can cover the operational scale of the phenomenon under study. Data on the subject should be sampled at intervals with a smaller scale than the operational scale. Presentation of the data will finally be at some

cartographic scale, which people will rely on for interpretation, conclusion or policy making (Lam et al., 2004).

The above definitions stem from authors with a strictly geographical background. They appear to be focused on GIS and remote sensing applications with an emphasis on rastered information. A different notion of the issue of defining scale was presented by Wu and Li (2006). They propose a three-tiered conceptualization of scale that organizes scale definitions into a conceptual hierarchy that consists of the dimensions, kinds, and components of scale. It encompasses the four meanings given above, but emphasizes related terms and points out synonymically used perceptions of scale. From their perspective of ecological sciences, some additional meaningful concepts shall be presented here.

Figure 3.1: Physical and ecological phenomena tend to maintain a constant ratio in their spatial and temporal scale (Wu, 1999)

Scale is defined in terms of time and space. It is well understood, that the characteristic scales of many physical and ecological phenomena are related in space versus time. The ratio between temporal and spatial scales of phenomena tends to be invariant over a range of scales, which is illustrated for a number of different natural processes in Figure 3.1 (Wu, 1999). Together with an organizational level, time and space make up the three dimensions of scale (Wu and Li, 2006).

The kinds of scale encompass the observational and operational scales defined above. Wu and Li use the term intrinsic scale to address the scale at which a pattern or process actually operates. It expresses the same notion of a scale immanent to a phenomenon as operational

scale. Yet, they award intrinsic scale a broader notion than the term process scale. The two notations are used synonymical in this study.

Confusion arises with observational scale. Wu and Li use observational scale as a synonym of measurement scale and sampling scale. While sampling scale denotes the same as the measurement scale, the separation of observational scale and measurement scale as defined above seems more adequate and is pursued in the following.

More kinds of scale are given by the experimental scale referring to the extend of experimentation, the analysis or modeling scale which refers to statistical analysis and modeling and the policy scale which is influenced by economic, political and social factors. Policy scale arises in the context of management and planning and is dependent on regional and national legislation. Although important differentiations of the definition of scale, these scale terms are not relevant in the presented study. In the wake of general definitions, the author thinks that these latter scale terms are contained in the definitions above. Any experiments scale is encompassed by an observational scale; analysis and modeling depend on the data’s scale, which is defined by the above notions of scale. When policy scale plays a role in a research it will provide one notion of operational scale and set rules for observational or measurement scale as defined above.

The components of scale defined by Wu and Li (2006) are cartographic scale, grain, extend,

coverage and spacing. Their concept of cartographic scale agrees with the definition given above. Grain is what has been termed resolution or measurement scale earlier in this section. Extend is equivalent to the observational scale defined by Lam et al. (2004). Yet, coverage and spacing add two more terms in relation to scale. Coverage is the intensity of sampling in space and time. Spacing refers to the interval between two adjacent samples or lag (Wu and Li, 2006).

The four definitions by Lam et al. (2004) suffice for the conceptualizations of scale in this study. Important aspects and clarification of terms were added from the hierarchical definition by Wu and Li (2006). Still, other lexical meanings of scale and related terms may exist and be defined, yet it has been stressed repeatedly, that for a progress of a “science of scale” agreement on scale terms is a fundamental step (Quattrochi, 1993).

The dimension of a scale is often roughly classified by terms like micro, meso, macro, moderate, continental or the like. In the context of this study, the term micro scale is understood as a dimension smaller than 100m. The terms moderate and meso scale refer to scales of 100m to 1000m, which contains the three resolutions of the MODIS sensor (Table 3.1). The items are mainly used to describe the resolution of data.

Table 3.1: Scale terms used in this study and the dimensions attributed

Scale Dimension

micro < 100m

meso, moderate 100 to 1000m

macro > 1000m

3.1.2 Scaling

The item scaling is closely related to scale and just as the scale term may have different signification in different scientific disciplines. In the context of geographical information and earth science and in connection with the above definitions scaling is the translation of information between or across temporal or spatial scales (Turner et al. 1989, Blöschl and Sivapalan, 1995, Curran et al., 1997, Marceau 1999, Wu 1999, Wu and Li, 2006). A lot of research has been completed on the question of how scaling or the transfer across scales can be achieved. The question may apply to data on the one hand and to the description and definition of processes on the other. Scaling may be further distinguished by the direction the

transformation is performed in. In the GLOWA-Danube community agreement was achieved that upscaling or scaling-up is the process of moving from a small scale to a large scale. In connection with process descriptions, the term bottom-up is linked to the transfer from a small scale to a large scale. Upscaling of data usually goes along with aggregation and data reduction. Conversely, downscaling or scaling-down is associated with moving from a large scale to a small scale. Transferring a process in that direction is referred to as top-down. Downscaling of data will require disaggregation of parameters or data values and will increase data amounts.