Towards mapping soil carbon landscapes: Issues of sampling scale and transferability

Miller, B.A., S. Koszinski, W. Hierold, H. Rogasik, B. Schröder, K. Van Oost, M. Wehrhan, and M. Sommer. Towards mapping soil carbon landscapes: issues of sampling scale and transferability. Soil and Tillage Research 156:194-208. doi: 10.1016/j.still.2015.07.004. Continue reading “Towards mapping soil carbon landscapes: Issues of sampling scale and transferability”

History of soil geography in the context of scale

Miller, B.A. and R.J. Schaetzl. 2015. History of soil geography in the context of scale. Geoderma 264:284-300. doi: 10.1016/j.geoderma.2015.08.041. Continue reading “History of soil geography in the context of scale”

Impact of multi-scale predictor selection for modeling soil properties

Miller, B.A., S. Koszinski, M. Wehrhan, and M. Sommer. 2015. Impact of multiscale predictor selection for modeling soil properties. Geoderma 239-240:97-106. doi:10.1016/j.geoderma.2014.09.018. Continue reading “Impact of multi-scale predictor selection for modeling soil properties”

Types of Scale

When you read the phrases “large scale” or “small scale,” do you know what they mean? Sometimes “large scale” is describing a large area and sometimes it is describing a small area, depending on if the author was thinking about process scale or cartographic scale. This is a problem for communication. In this post I will describe the different types of scale used in geography, which will hopefully encourage others to be specific when they are discussing scale.

First, we have to recognize that the world “scale” has evolved. Its origin reaches back to Old French or Germanic terms for cup or shell. The use of similar looking objects to form the two sides of a weighing instrument likely explains the naming of that instrument as a scale. The verb “scale” primarily comes from the Latin “scala”, which describes a ladder or flight of stairs. From these various pathways in time, we are left with some central concept of measuring something in proportionality. As vague as that may sound, it does somewhat account for the wide range of uses we have for the word. Still today, our evolving understanding of spatial concepts continues to create more stems on the geographical branch of scale’s etymology tree. Therefore, even the traditional use of the word in geography now warrants clarification.

Abbeville, SC (1902)
This section of a soil map from 1902 of Abbeville County, South Carolina illustrates the interrelationship between attribute scale, analysis scale, and cartographic scale on paper maps. The soil mapper was limited in how much detail could be included on that sheet of paper. If more delineations were added, then more variations in the feature space would have been identified and the legend would have to expand. Similarly, if the attribute scale included more details in the feature space, then the map units would need to be subdivided to show where those differences in attribute classes were.

The most fundamental uses of “scale” in geography are the cartographic scale and the attribute scale. The cartographic scale (aka map scale) is the ratio between the size of objects in the real world and their representation on the map, making it a measure of proportionality in the most central idea of space, geographic space. The attribute scale (aka thematic scale) is equally important to cartographers because it is how the feature space is divided/measured for representation in the map legend.

As geography expanded from the design aspects of map making to more spatial analysis, geographers began to recognize connections between the cartographic scale of a map and the spatial patterns observed in that map. Because the map was only a representation of reality, they needed a term to distinguish between the spatial characteristics of the reality and the spatial characteristics of the map pattern. Although mostly a philosophical concept, geographers describe the extent over which the pattern is seen operating as phenomenon scale (aka process scale). For example, in climatology the influence of the jet stream can be seen at global scales, while influences of topography produce micro-climates observable at local scales. Similarly, international politics operate at a global scale, while interstate commerce mostly operates at a regional scale.

The last type of scale to be discussed here needed to be recognized as a separate form of scale after we gained more flexibility in how we map. Although past cartographers had some control over the sizes of delineations in their maps, this was largely constrained by what could legibly fit on the piece of paper at the cartographic scale being used. Now with geographic information systems (GIS), that restriction or link between cartographic scale and delineation sizes has been removed. Geographers can now analyze space using whatever size or shape of spatial units that they please. Hence, we now also recognize analysis scale as separate from cartographic scale. We can view or produce maps at whichever cartographic scale suits our needs, and independently from that we can adjust the analysis scale as we search for patterns in the real world’s phenomenon scale.

So what about the original question of the difference between “large scale” and “small scale”? Well, usually larger means larger in size and for most uses of the word “scale” that is true. However, the wrench in the works is the common expression of the cartographic scale in terms of a representative fraction. Because smaller fractions mean a greater difference between the size of objects in reality and the size of their representation on the map, a map with a smaller representative fraction can actually cover a larger area of reality. For example, a global map would probably have a small cartographic scale (e.g. 1:800,000) and a city map would probably have a large cartographic scale (e.g. 1:20,000). That is why it is a problem to only state the size of the scale. To avoid confusion one should either specify the type of scale or use terms that don’t have multiple meanings such as “extent” or “regional” versus “local.”

The cartographic scale of this city map is large because its representative fraction is large (originally about 1:4,000).
The cartographic scale of this global map is small because its representative fraction is small (originally 1:35,000,000).









For more, take a look at:

Semantic calibration of digital terrain analysis scale

Miller, B.A. 2014. Semantic calibration of digital terrain analysis scale. Cartography and Geographic Information Science Journal 41(2):166-176. doi:10.1080/15230406.2014.883488. Continue reading “Semantic calibration of digital terrain analysis scale”

Is It a Scientific Theory or Hypothesis?

This is a common question addressing a popular misconception about how science classifies the knowledge that it has accumulated. The levels of hypothesis to theory to law often get interpreted as classes of confidence. However, this is not really right. The missing piece here is spatial scale!

It isn’t easy to draw the line for what is scientifically known and what is not. A major reason this line is so blurry is that knowledge can be applicable at different spatial scales. The three categories of scientific understanding (hypothesis, theory, and law) are often defined in introductory science courses as describing how thoroughly a concept has been tested. Although theories do need more testing than hypothesis and laws more testing than theories, the amount of testing required is only a consequence of the real definitions. These three classes are actually describing the extent over which we know an idea to be true. The larger the extent, the more testing that will be required to know that the concept is applicable across the entire extent.

science scalesBecause we encounter phenomena at a very local scale, this is usually the beginning of our ideas about how the world works. Based on these few observations, or anecdotes, we form a hypothesis about what is happening and why. In popular culture, this idea might be called a ‘theory’, but science would require proof that the concept applies in more situations before elevating it to a theory.

As we gather more data and test the idea more, we can start to explain connections between several phenomena. When we have evidence that a concept has greater applicability than to just a few anecdotes, then we can upgrade it to a theory. Although more testing was required to make this change in knowledge classification, the important part is that we now have confidence in a wider applicability of the idea.

At the top of this hierarchy of scales are scientific laws. These are concepts that have proven to be universally true. Clearly, to be confident that something is universal requires a lot of testing, which is why there is sometimes confusion about the meaning of these categories of scientific knowledge. Being universally applicable does not mean that laws cannot have defined conditions under which they apply. In fact, many are limited to certain conditions, but even with those conditions, scientific laws are expected to be reliable no matter where you go in space.

The clarifications I provide here do not contradict popular definitions, but they point out that oversimplified definitions focus on the wrong part of the scientific knowledge classification, which leads to misconceptions. At a single site, one can make millions of observations of the same thing happening the same way. However, the tested explanation for this one location will never be considered a law, despite a high confidence in that explanation being able to predict the same event occurring again. This is key to understanding why some scientific explanations with a high level of confidence will never get promoted to a higher category of scientific understanding.

To give a specific example, we have observed on the planet Earth that the acceleration due to gravity is between 9.76 and 9.84 m/s2. Despite the high level of confidence in the truth and predictability of this fact, it alone could never be promoted to a law. It cannot be considered a law because it lacks universal applicability. Observations of this phenomenon (plus celestial bodies) did lead to Newton’s Law of Universal Gravitation, which identifies a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other:

[latex]F = G \left ( \frac{m_1m_2}{r^{2}} \right )[/latex]
where, m1 and m2 are the two masses, G is the gravitational constant, and r is the distance between the two masses.

This equation is capable of being a scientific law because it has been generalized to be universally applicable. Of course, rates of gravitational acceleration on Earth are still useful and reliable. The same can be said for many other pieces of scientific information that cannot be or have not yet been established for greater extents.

For more, check out: Berkeley’s webpage on “Science at multiple levels”

Multi-scale Parameter Selection for Predicting Soil Organic Carbon (2014 Digital Soil Mapping Workshop)

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