Contamination of a water supply can happen locally or at a large scale; for instance, if the Mackenzie River is contaminated, the impacts will be felt across much of Canadas north and have the potential to cross international political boundaries; however, if a subsystem of a watershed is contaminated (such as Beaver Creek along the South Saskatchewan River), the impact will be felt over a much more limited and local area. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as counting rods, carpenter's square's, plumb lines, compasses for drawing circles, and sighting tubes for measuring inclination. 
sec Map scales may be expressed in words (a lexical scale), as a ratio, or as a fraction. ) As an example, one possible secant Mercator projection is defined by. sec The only true representation of a sphere at constant scale is another sphere such as a globe. For a given phenomenon or process it is important to define its existence, or how it functions, across different scales, and whether an optimal scale (or range of scales) exists. and {\displaystyle \alpha } Cartographic scale is convenient for many reasons, not the least of which is that for any two scales we have an immediate understanding of the quantitative spatial relationship between them. Lay definitions of scale are also employed that are related and unrelated to the more strict definitions of the term employed in research-related endeavours. a is in the range The other plots show the meridian scale factor for the Equirectangular projection (h=1) and for the Lambert equal area projection. Examples are. {\displaystyle \beta } Since (Hardly surprising since this is the relation used to derive Mercator). and longitude This can be a cause of confusion. = y and substituting Let Q be a neighbouring point and let Since the point scale varies with position and direction the projection of the circle on the projection will be distorted. Want to adapt books like this? Such maps are good for countries aligned nearly north-south (like Great Britain) and a set of 60 such maps is used for the Universal Transverse Mercator (UTM). In a larger space, perhaps a university campus, one would be compelled to walk around the space in order to place him/herself in a position to see hidden objects that are obscured by other (likely immovable) objects such as buildings. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected. Geographers study phenomena at various scales and often use the term scale to help define their research interests. The scale is true (k=1) on the equator so that multiplying its length on a printed map by the inverse of the RF (or principal scale) gives the actual circumference of the Earth. However, the specific implementation of a climate change action plan is multi-scaled and does not equitably administer resources. Normal cylindrical projections of the sphere have {\displaystyle y'=a} {\displaystyle \varphi } ( {\displaystyle \varphi } We say that these coordinates define the projection map which must be distinguished logically from the actual printed (or viewed) maps. ) , However, we cannot assume that a provincial policy in Canada will necessarily impact a smaller space than a federal decision elsewhere. Therefore, this application of scale results in an infinite number of scales (for example, 1:24,000 or 1:50,000 for standard US and Canadian topographic sheets). In this case 'scale' means the scale factor (= point scale = particular scale). Data Models: Representing Reality as Simply as Possible. It has been suggested that global climate variability is effectively mitigated through the harmonization and coordination of all levels of government (DeMarco, Routliffe, and Ladymore, 2004). . is the longitude from the central meridian of the projection (here taken as the Greenwich meridian at In the English language, the word large-scale is often used to mean "extensive". Scale varies across the map, and the stated map scale is only an approximation. = are as in the previous example. The ratio of the Earth's size to the generating globe's size is called the nominal scale (= principal scale = representative fraction). Since {\displaystyle \varphi } 1.62 {\displaystyle (a\cos \varphi )\delta \lambda } Such narrow zones of high accuracy are used in the UTM and the British OSGB projection, both of which are secant, transverse Mercator on the ellipsoid with the scale on the central meridian constant at {\displaystyle \lambda =0} sec and {\displaystyle \varphi +\delta \varphi } An example of a socially constructed scale would be a distinctive community within a city that is made up of culturally defined groups, and not necessarily related to a specific boundary or physical geographic space within the citiys limits. {\displaystyle \lambda } In maps covering larger areas, or the whole Earth, the map's scale may be less useful or even useless in measuring distances. (See Snyder[1] pages 203206. ( : angles are preserved. The size is equivalent to scale relationship works nicely for internal classification schemes, or when a common process or feature can be used to determine how size and phenomena interact. {\displaystyle \pi } so it is the same for all normal cylindrical projections. ( Since k x {\displaystyle \lambda \,} There are many situations in which the relationship between scale and the terms to which it is appended do not have easily described relationships with changes in spatial extent. Comment: this precise distinction between azimuth (on the Earth's surface) and bearing (on the map) is not universally observed, many writers using the terms almost interchangeably. What is critical, however, is that within any scale a hierarchy of component scales or entities can be identified and declared (Brenner 2001; Purcell 2003). so that. For normal cylindrical projections the geometry of the infinitesimal elements gives, The relationship between the angles are as in the previous example. For example, a scale of one inch to a furlong (1:7920) will be understood by many older people in countries where Imperial units used to be taught in schools. ) y If we consider a line of constant slope The point Q is at latitude {\displaystyle \alpha } In order for this definition to exist (urban scale), non-urban scales must exist, but these are not necessarily tied to changes in spatial extent or spatial properties of any kind (location, distance, area, etc.). {\displaystyle k=\sec \varphi } As suggested above, the term scale can be used in a variety of ways, only some of which are related to spatial extent. and Many policies surrounding environmental issues such as climate change and variability are designed to change the behaviour of local communities in ways that will positively impact a problem that occurs or functions at a much larger scale; in the case of global climate variability, the problem is global and will not be effectively addressed unless collective global action is taken. Maps that show an extensive area are "small scale" maps. {\displaystyle \lambda } Reducing the amount of open land required for waste can reduce a communitys infrastructure costs. 1 = {\displaystyle \lambda } ) These situations often arise when the term scale is used to differentiate between place-based differences in geographic phenomena. In situations where a process or function varies as spatial extent (or scale) varies, and scale is used to define that variability, functional scale is the relevant concept for describing the spatial component of that relationship. is the radius of the sphere and Definition: the point scale at P is the ratio of the two distances P'Q' and PQ in the limit that Q approaches P. We write this as. be the angle between the element PQ and the meridian at P: this angle is the azimuth angle of the element PQ. {\displaystyle \varphi } {\displaystyle \alpha } Each of these classifications has subdivided space based on human interactions (physical, cognitive, and perceptual) with spaces of difference size. It is for this reason that representational and cartographic are used above, to allow for representations, or models, that are larger than that which they represent. A one size (scale) fits all approach will not work. {\displaystyle a\,\delta \varphi } While a local problem, as defined by problem scale, is obviously a problem occurring in a smaller space than a regional or global problem, it is difficult to calculate a ratio between the two because discrete boundaries are likely unavailable (as they are on a map sheet). -direction) by the equations[1][2][4]. On the other hand, recycling programs are considered substantially smaller scale problems that have both impacts and solutions that meet at a common scale. {\displaystyle k(\lambda ,\varphi )} ) In deriving a point property of the projection at P it suffices to take an infinitesimal element PMQK of the surface: in the limit of Q approaching P such an element tends to an infinitesimally small planar rectangle. {\displaystyle |k-1|<0.0004} ] . Furthermore, scale can be a useful tool for examining the extent to which a single policy will have its intended impact on the environment. [4] Thus a plan of New York City accurate to one metre or a building site plan accurate to one millimetre would both satisfy the above conditions for the neglect of curvature. . (Other examples[5][6]). {\displaystyle \varphi } ) y These internally structured scaled relationships result in a subset of the functional scale that could be termed internal functional scale. is about 1.1 so Mercator is accurate to within 10% in a strip of width 50 degrees centred on the equator. , the meridian scale is denoted by are slightly curved lines approximately 180km east and west of the central meridian. {\displaystyle \mu _{\alpha }} As one changes cartographic scale, a direct relationship between the representation and the actual space is explicit and known; space and scale are dependent on one another. An example of government attempting to address a large scale environmental issue is the Act passed by the Saskatchewan government in December 2009 titled, An Act Respecting the Management and Reduction of Green House Gases and Adaptation to Climate Change. {\displaystyle \delta \varphi } These types of scales are often said to be socially constructed, and while they have important spatial characteristics, they are not defined by their spatial nature. , Representations of Space and Spatial Representations, 8. {\displaystyle \delta y} 0 sec {\displaystyle \varphi =1.62} In addition, the range of problems that can be described is so broad that for a single environmental issue there might be instances where the problem impacts a relatively small space and other instances where the space is vast. {\displaystyle \sec \varphi } Since ) , the parallel scale is denoted by where the previous section gives. so the scale is isotropic (same in all directions), its magnitude increasing with latitude as = Poiani et al. When comparing the relative size of two cartographic scales we compare the size of the number calculated by the ratio of the size on the map (numerator) and the size on Earth (denominator). This gives rise to the gross distortion of shape in the Gall-Peters projection. and Introduction and Perceptual Elements of Colour, 11. For example, a map reader whose work refers solely to large-scale maps (as tabulated above) might refer to a map at 1:500,000 as small-scale. When cartographic scale increases (like from 1:1,000,000 to 1:50,000) the area on Earth that can be displayed decreases, while the detail of the geography being represented can increase (for the area displayed). Cartesian/Projected Coordinate Systems, UTM, 16. The Mercator point scale is unity on the equator because it is such that the auxiliary cylinder used in its construction is tangential to the Earth at the equator. While the classification of scale based on spatial dimensions, social institutions and practices, phenomena, and mathematics exist and have flourished within and beyond geography, there have been few attempts to categorize the nature of these different definitions and provide a systematic understanding of scale across disciplines. For a given cartographic scale, very little can be said about the phenomena being represented, in essence the square, or rectangle (or other shape), that is doing the representing can represent a space on the Earths surface, or any space, for that matter. {\displaystyle \alpha } 1.0004 The numeric multipliers do not alter the shape of the projection but it does mean that the scale factors are modified: This is illustrated by the lower (green) curve in the figure of the previous section. ) By comparing the elements on sphere and projection we can immediately deduce expressions for the scale factors on parallels and meridians. . These last two projections have a parallel scale identical to that of the Mercator plot. The Mercator projection maps the sphere to a rectangle (of infinite extent in the a Ratio of distance on a map to the corresponding distance on the ground, This article is about scale, nominal scale, principal scale, representative fraction, and scale factor of a map. The first way is the ratio of the size of the generating globe to the size of the Earth. If measured only to the nearest metre, then curvature of the earth is undetectable over a meridian distance of about 100 kilometres (62mi) and over an east-west line of about 80km (at a latitude of 45 degrees). Certainly this is a likely outcome in a province like Saskatchewan that has distinct urban/rural communities that have quite different needs and exhibit different day-to-day behaviours.
what is scale in geography and its types
