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”

Comparison of spatial association approaches for landscape mapping of soil organic carbon stocks

Miller, B.A., S. Koszinski, M. Wehrhan, and M. Sommer. 2015. Comparison of spatial association approaches for landscape mapping of soil organic carbon stocks. SOIL 1(1):217-233. doi:10.5194/soil-1-217-2015. Continue reading “Comparison of spatial association approaches for landscape mapping of soil organic carbon stocks”

CLORPT: Spatial Association in Soil Geography

From as early as 500 BCE, humans have recognized that some things vary together in space. This is essentially correlation, but the spatial aspect sometimes adds a special twist. Also, correlation requires evaluation of quantitative data, while this concept is not limited to quantitative characteristics. For example, Diophanes of Bithynia observed that “you can judge whether land is fit for cultivation or not, either from the soil itself or from the vegetation growing on it.” Although used frequently in the history of science (e.g. Humboldtian science), the first naming of this principle that I have found appears in a book by F.D. Hole and J.B. Campbell, published in 1985. They referred to it as spatial association. Because I am not aware of another term that covers this concept, I will continue with their use of it. Unfortunately, in the 1990s some began to use this term to describe clustering. In order to be clear, I define spatial association as the degree to which phenomena are similarly arranged over space.

Eugene W. Hilgard
(Online Archive of California)

The first scientific application of spatial association to soil mapping that we know about was by E.W. Hilgard. In 1860, he published his report on the ‘geology and agriculture’ of the state of Mississippi, USA. Hilgard observed that knowledge of the geology and type of vegetation were useful indicators for predicting soil type. In 1883, V.V. Dokuchaev added climate, relief, organisms (both plants and animals), and time to that list of useful spatial predictors. Because these spatial covariates are connected to processes, thinking about their geography enabled Dokuchaev to formulate ideas about soil formation. His descriptions of these factors of soil formation were key in the establishment of modern soil science.

Coinciding with the ‘quantitative revolution,’ H. Jenny wrote a landmark book entitled Factors of Soil Formation (1941). In this book, Jenny accomplished two main things. First, he coined an acronym for the soil formation factors: CLORPT (CL=climate, O=organisms, R=relief, P=parent material, and T=time). This easy to remember abbreviation popularized the concept and became the standard framework for teaching about soil formation. Second, Jenny proposed a system to experimentally control geographic variables so that a single variable could be better studied. He advocated for research to be designed so that soils that formed under similar factors, except for one, could be quantitatively compared. This way, differences between the soils compared could be directly attributed to the one factor that had changed. In practice this is a bit harder than it sounds because the different factors influence one another, but this was a greatly improved strategy for advancing soil science.

Before the factors of soil formation were assigned an acronym, soil mappers were regularly using them to design their maps. Notably, Hilgard’s application of geology and vegetation as predictors was primarily focused on producing a better spatial description of where different soils were. Dokuchaev’s work prior to and after writing the list of five factors was driven by the Russian government’s desire for better soil maps. Most of the soil maps made at that time were at the continental or national scale and the limited information available led to a heavy reliance on large scale climate. However, later work – particularly more detailed soil maps – began to utilize the other factors as predictors of soil variation. As T.M. Bushnell synthesized these concepts – along with G. Milne’s catena concept – in the 1940s, he applied them to what he could see in aerial photographs. Those images provided more spatial information about vegetation and relief than had been previously available.

Recognizable by changes in the image’s tone and texture, shifts in vegetation helped the soil mapper decide where to delineate different soils.

Soil mapping in the 20th century continued to build on field experience to better understand the local variations of CLORPT. It was still difficult to quantify many of the indicators for soil formation factors, so soil mappers tended to develop unique mental models of the soil landscape. These models were based on their experience in a region for key indicators that marked shifts from one soil series to another, usually in connection with one of the soil formation factors. However, within those mental models, certain factors tended to become emphasized due to the limited spatial information available, map scale, purpose of the map, and the particular conditions of the area.

Today in digital soil mapping, we still utilize these concepts. Because we use much more quantitative variables – still primarily related to CLORPT – we typically describe our method as spatial regression, or something related to that. However, the geographic principle for why spatial regression works remains rooted in the idea of spatial association.

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:

Fundamentals of Spatial Prediction

In the process of creating a map, geographers often have to engage in the activity of spatial prediction. Although there are many tools we use to accomplish this task, they generally boil down to the use of one or two fundamental concepts.

Waldo Tobler is credited for identifying the ‘first law of geography’, stating “Everything is related to everything else, but near things are more related than distant things.” This concept is essentially synonymous with spatial dependence and spatial autocorrelation. Spatial interpolation methods rely on this principle to make predictions about the attributes of areas between sampled locations. For example, kriging utilizes an observed spatial lag relationship to determine the range of autocorrelation. In other words, it quantifies the degree to which locations are similar with respect to their distance from each other (i.e. semivariogram). Kriging then uses that information to optimize predictions for the unobserved locations.

If spatial autocorrelation is the first law of geography, then spatial association should be the second. Actually, spatial association has arguably been in use longer, so maybe it should be the first law. In any case, spatial association describes how phenomena are similarly distributed. To put it in a phrase parallel to Tobler’s law, “Everything is related to everything else, but things sharing similar conditions are more related than things under dissimilar conditions.” A quantitative form of spatial association is spatial correlation or regression. A more focused use of spatial association is often called environmental correlation, which uses environmental covariates as predictors. Soil science has heavily relied on this concept. Although vegetation was recognized as an indicator of soil quality by the ancient Greeks, E.W. Hilgard formally described the relationship of soil properties with the more readily observable characteristics of vegetation in 1860. V.V. Dokuchaev went further in 1883 by recognizing that soil characteristics could be predicted by considering the factors of climate, organisms, relief, parent material, and time. The guiding principle that where these five factors are the same, similar soil will be found remains the primary strategy for mapping soils today.

This colorized version of a diagram from the USDA-NRCS illustrates spatial association by identifying similar soils on similar landscape positions. It is also true that adjacent soils are more likely to be more similar than non-adjacent soils, but with the exception of distant soils that have the same formation factors.
This colorized version of a diagram from the USDA-NRCS illustrates spatial association by identifying similar soils on similar landscape positions. It is also true that adjacent soils are more likely to be more similar than non-adjacent soils, but with the exception of distant soils that have the same processes of soil formation.

The concept of spatial association has also been referred to as regionalization, but that term is easily confused with different forms of spatial analysis. The term ‘regionalization’ has also been used to describe the process of identifying regions based on clusters and it has been used to describe spatial interpolation methods, such as kriging. To add to the confusion, spatial association has also been used to describe statistics that evaluate the existence of clusters. To make things worse, spatial autocorrelation has been sometimes described as a type of spatial association. For these reasons, I think it is important that we establish spatial autocorrelation and spatial association as independent, fundamental concepts in spatial prediction.

Recognizing these two separate concepts in geography makes it easier to explain the variety of spatial prediction methods that attempt to utilize some blend of both. For example, co-kriging adds information from covariates with similar spatial distributions to improve upon interpolations based on spatial autocorrelation. Conversely, geographically weighted regression identifies spatial association relationships within different spatial units, which can be based on cluster analysis or some other form of analysis that recognizes similarity by spatial autocorrelation.

The importance and utility of spatial autocorrelation and spatial association, as defined here, is clear. However, the consistent use of these terms, especially for spatial association, has clouded the recognition of their widespread use. Regardless, these are fundamental and unifying concepts in geography.

Why Geography?

System of Geography (full page)The scientific discipline of geography has taken on many important topics over the course of its history. From locating natural resources, to understanding the intricacies of human cultures in diverse locations, to predicting climate change and its impacts on society, geography has helped us better understand our world.

Students in grade schools are taught basic geographic facts such as the location of countries, because knowing where things are, is the first step to figuring out why those things are there. Geography began in a similar way; geographers documented where things were and developed better ways to measure and communicate that information. Eventually though, geographers expanded onto questions of ‘why’ are things where they are. The description on the title page of Emanuel Bowen’s 1747 book (image to the right) may reflect a beginning of geography’s transition from cataloging spatial information to trying to make sense of it (understanding the system). Today, geography continues to document where things are (hence, a strong relationship with GPS), but spends most of its time studying the interactions between spatial phenomena. Because addressing modern problems require system approaches, understanding the time and space components of the processes involved is more important than ever.

Unfortunately, geography education has not progressed with the advancement of geography as a science. For many people the study of geography ended with location facts and they have never been exposed to the fruitful endeavor of scientific geography. The opportunities to increase scientific knowledge from geographic research are so immense that the discipline of geography has struggled to define a focused mission.

In addition to limited exposure to spatial science, people’s perception of geography is also confused by the diversity of issues that geographers work on. For example, what do topics in geomorphology have in common with topics in geopolitics (both topics regularly studied by geographers)? I think the answer is that the spatial component of these topics is crucial to understanding why phenomena occurred, are occurring, or will occur. Can these topics be studied by separate disciplines, focusing on the issues by subject (e.g. Geology, Political Science)? Of course, but what geographers bring to the table is a unique perspective on the complications of studying spatial phenomenon. And these complications are only beginning to be understood.

The complications of geographic research are regularly underestimated. For example, the basic concept of the modifiable areal unit problem was identified in the 1930s, but too often research is conducted oblivious to the dependency of the results on analysis scale. This concept is the primary concept behind gerrymandering, yet its potential to bias research (especially in the natural sciences) is rarely acknowledged.

As further evidence that the details of geographic concepts are often not fully appreciated, I point to the fact that fundamental terms for describing spatial concepts are ill-defined. The loose use of geographic terms leads to confusion in the scientific literature about what is actually being studied. One of the clearest examples of this is use of the term “scale.” Confusion about this term has been exasperated by the transition from paper to digital maps. Because of the constraints of drawing a map on paper, extent and map unit size were essentially bound together. Under those circumstances, map scale described both spatial concepts at once. However, on digital maps, resolution, map unit size (~analysis scale), representative fraction (cartographic scale), and extent are independent of one another. Digital methods provide a great deal more freedom to study spatial phenomena, but we must be careful to define our methods (i.e. by ‘scale’, is one describing resolution, extent, or analysis scale).

Geography needs to continue to work on the ‘applied’ topics that it has been working on, but in the process, geography should use the information gathered to further illuminate and define the characteristics of spatial phenomena (e.g. establishing standards for describing the different aspects of spatial structure). Progress in fundamental laws of geography will be difficult and slow going. Nonetheless, it is an endeavor with immense benefits for sorting out the complex world we live in.

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”

Relief Analysis Toolbox

The central purpose of this toolbox is to provide ArcGIS users a convenient way to calculate hillslope position from elevation grids. However, the Relief Analysis Toolbox also includes some other ArcGIS models that may be of interest to anyone working with landscape and landform segmentation. The main features of this toolbox are:

  • hillslope position (calibrated to the U.S. Soil Survey),
  • relative elevation (a moving-window approach as described in Miller, 2014; middle elevation used for reference),
  • topographic position index (modified from Weiss, 2001; mean elevation used for reference),
    • TPI slope position,
    • TPI landform class,
  • plus a couple of data classification tools that might come in handy.

Includes instructions and a suggested color scheme for displaying hillslope position.

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More about the Digital Classification of Hillslope Position

Hillslope Position

Classification of hillslope position has a long history in soil geomorphology. However, its roots in tacit field knowledge has prevented its use in GIS. The model provided here has been calibrated and validated on soil scientists’ observations in the field. The resulting maps of hillslope position represent base maps that can be used to (1) improve research on toposequences by providing explicit definitions of each hillslope element’s location, (2) facilitate the disaggregation of soils currently mapped as complexes, and (3) identify map unit inclusions that exist due to subtle topographic variation. The base maps developed by the model can also help identify areas of possible mismapping, especially where soil boundaries cross topographic breaks. This information can enable the mapper to redefine many existing soil map unit boundaries, placing them more correctly at locations where defendable landscape breaks exist.

Supplemental Materials

Development of the hillslope position classification tool is documented in the following publications and dissertation, and should be used for citation as appropriate:

Miller, B.A. and R.J. Schaetzl, 2015. Digital classification of hillslope position. Soil Science Society of America Journal 79(1):132-145. doi:10.2136/sssaj2014.07.0287.

Miller, B.A., 2014. Semantic calibration of digital terrain analysis. Cartography and Geographic Information Science Journal 41:166-176. doi:10.1080/15230406.2014.883488.

Miller, B.A. 2013. Incorporating tacit knowledge of soil-landscape relationships for digital soil and landscape mapping applications. Dissertation, Department of Geography, Michigan State University, USA.