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”
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.
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.
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.
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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.
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.
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Miller, B.A. and R.J. Schaetzl. 2014. The historical role of base maps in soil geography. Geoderma 230-231:329-339. doi:10.1016/j.geoderma.2014.04.020. Continue reading “The historical role of base maps in soil geography”