Using Quantitative Flux Ecoregions to Determine the Extent of the NACP Mid-Continent Intensive
William W. Hargrove and Forrest M. Hoffman
William W. Hargrove and Forrest M. Hoffman
The first Intensive Campaign of the North American Carbon Program (NACP), the Mid-Continent Intensive, is scheduled to begin with the 2005 growing season. This campaign will emphasize a multi-state area of the upper Midwestern United States comprising eastern SD, eastern NE, eastern KS, northern MO, IA, southern MN, southern WI, and IL. The Mid-Continent area was selected for the first Intensive because of predominantly flat, relatively homogeneous terrain, prevalence of agriculture, and a high density of meteorological stations. The exact spatial extent of the Mid-Continent Intensive has not yet been identified, however.
Here we suggest an approach, based on a set of existing statistical products, which represents a way to pick logical and defensible borders for the extent of the area to be considered by the NACP Mid-Continent Intensive. This approach is based on a set of flux ecoregions that divide the continental United States into a set of areas that are homogeneous with respect to a set of flux-relevant environmental conditions. We offer an initial suggestion for a subset of these flux ecoregions for the extent of the Mid-Continent Intensive. Even if more or less area is desired, these flux ecoregions make it easy to see the consequences of deciding to include or exclude another statistically different "piece." Since the borders of the flux ecoregions are available in GIS format, the results of the decision can be immediately mapped.
When tasked with sampling an extensive area but having only limited resources, statisticians often pre-stratify the area to be sampled into groups that have similar properties, and then array the limited samples across these strata. Ecologists also use this directed sampling approach, but call their pre-existing spatial strata "ecoregions." Ecoregions are geographic regions that are relatively homogeneous with regard to particular environmental conditions.
We have developed a quantitative multivariate statistical method for delineating ecoregions in an objective and repeatable way. Using a supercomputer and a set of maps of quantitative ecological characteristics that have been selected as relevant for a particular question, our algorithm forms groups of map cells which have a similar multivariate mixture of the relevant characteristics. Since the spatial location of each map cell is not used in the process, the quantitative ecoregions that result are not necessarily geographically contiguous. The number of ecoregions that is produced is specified beforehand. All ecoregions that are produced contain about the same degree of environmental heterogeneity, and are created such that the within-ecoregion variance is minimized while the across-ecoregion variance is maximized. Both the data sets and the algorithm are open to inspection, and the method, if repeated, will produce the same ecoregions again.
We used this quantitative algorithm, along with maps of environmental characteristics relevant for carbon flux, to produce nine alternative sets of homogeneous carbon flux ecoregions. Increasingly inclusive subsets of up to 30 flux-relevant environmental characteristics mapped for the conterminous United States at 1 square kilometer resolution were used to produce the nine alternative flux-relevant ecoregions. Three sets represent a spectrum of flux ecoregions that, while ever more inclusive, are based on more highly derived, and therefore less certain data. Each of these three sets were, in turn, divided into growing season, non-growing season, and both seasons taken together. Characteristics were integrated over growing season based on the duration of the frost-free period within each 1 square kilometer cell. Integration over the complementary period formed the non-growing season. A third set of seasonal flux-relevant ecoregions included both seasonal integrations, while keeping the seasons separate. Each map breaks the conterminous United States into the 90 most-different flux ecoregions at 1 square kilometer resolution. A report describing the development of all input layers and the statistical methods used to produce the ecoregions can be found here. Each input map and set of flux ecoregions can be viewed, and digital versions of all flux ecoregions can be downloaded for use in GIS systems.
These custom-created, flux-relevant ecoregions are ideally suited to the problem of identifying an appropriate extent for the NACP Mid-Continent Intensive. Since they were created on the basis of characteristics deemed a priori as important and controlling for carbon flux, each flux ecoregion should be relatively homogeneous with respect to the amount and seasonal trend of carbon flux exchange with the atmosphere through time.
Because they are relatively uniform and internally similar throughout, whole flux ecoregions should be selected for inclusion or exclusion in the Mid-Continent Intensive. Including only part of any flux ecoregion makes little sense, since the remaining parts, with which it is classified as similar, would be left out. Thus, collections or subsets of flux ecoregions, selected in their entirety, will comprise a logical extent for the Mid-Continent Intensive.
To obtain even finer spatial resolution, we could break the conterminous United States into more homogeneous flux regions. Requesting the 120 most-different flux ecoregions (instead of the 90 most-different) would result in smaller, more tightly defined, more homogeneous regions for use as "building blocks." Note that we have not made predictions about the amount or direction of carbon flux that is expected -- we have only grouped map cells that have similar combinations of flux-relevant environmental characteristics.
Only two of the nine alternative ecoregion sets, the most inclusive using both seasons and using the growing season only (IIIA and IIIB, respectively), will be considered here. Click on any of the images at the left to enlarge them.
Because they reflect actual attributes at 1 square kilometer resolution, quantitative flux ecoregions look complex, especially when compared to the highly generalized ecoregions subjectively drawn by experts. Flux ecoregions are shown here colored randomly, to distinguish different regions from each other. Borders between adjacent ecoregions are gradual and feathery in this part of the country, and geographically isolated pieces of adjacent ecoregions may be contained on each side of the line. River courses are often visible, since they may be classified as a bordering ecoregion type. Despite this complexity, each part of the map is predominated by a single underlying flux ecoregion classification.
The full level of detail is not useful in this design exercise. Here we have produced a generalized version of the flux ecoregions by passing a 13 km x 13 km mode filter across the map to eliminate small details and simplify the quantitative flux ecoregions. Speckles are removed, and the borders between adjacent flux ecoregions are straightened and simplified. AmeriFlux tower locations that are either currently reporting data or are under construction are also shown.
Each of the flux ecoregions discussed below can be found in the flux ecoregion report by their identifying numbers. The synoptic or mean conditions within each flux ecoregion in terms of each of the 30 flux-relevant environmental characteristics is also given (Table 3.13, pg 113-114).
Centered on IA, one can identify three flux ecoregions in a north-south transect that should probably be included in a Mid-Continent Intensive. The northernmost of these is a turquoise region comprising parts of MN, ND, and SD. Although the flux ecoregion numbers are not shown on the map, this is flux ecoregion #39. Below it we see a brown ecoregion, #89, which comprises most of IA and parts of IL, SD, and NE. Finally, a pink ecoregion, #86, comprises northern MO, southern IL, and western KS, and completely surrounds the Ozarks. This flux ecoregion also contains the Mississippi valley, and extends southward to southern LA. Any Mid-Continent Intensive should minimally include these three flux ecoregions.
In addition to these "backbone" flux ecoregions, it is possible to identify additional groups to the west and the east which could also be included in the Mid-Continent Intensive. In the west, a blue-green ecoregion, #76, forms the northern half of MT and part of ND. Below this, there is a green ecoregion, #17, which forms the southern part of MT, western SD, and parts of WY and NE. Below this, there is a dark gray ecoregion, #62, which forms central NE, eastern CO, and western KS. We recommend also including the black flux ecoregion, #56, that constitutes central KS and OK. We do not include the magenta flux ecoregion #37, which extends from central OK south into west TX, since this area is outside what is normally thought of as mid-continent. Nor do we include the chocolate-brown ecoregion #19, which comprises eastern and southern TX.
To the east of the central "backbone," we add the leaf-green ecoregion, #7, which forms northern IN, southern MI, and northern OH. The purple-colored ecoregion #46, which is spread through WI, northern MI, southern IN, KY, TN, and GA, could be added, although we have not done so here. We have also not included the golden yellow ecoregion #8, which is the Ozark mountains, since environmental conditions there are substantially different from the rest of the mid-continent plains. Nor have we included the blue flux ecoregion #78 in southern AR, since this ecoregion also represents the piedmont of AL and GA.
We have assumed that one intention of a Mid-Continent Intensive is to emphasize the study of carbon flux from agricultural systems. For this reason, we have not included flux ecoregions in northern MN, WI, and MI, which are predominantly forested. If, on the other hand, the intent is to study all land cover types in the Mid-Continent, these flux ecoregions could be included as well. Urban areas are readily apparent within the map. Northern cities are within flux ecoregion #19, while southern cities are within flux ecoregion #82.
This map shows the two tiers of flux ecoregions selected above as two levels of gray. The central "backbone" is darker gray, and the additional flux ecoregions added to the west and east are a lighter gray. Perhaps these areas could be studied with lower intensity, or at a lower resolution than the "backbone." In any case, these regions form logical edges for the extent of a Mid-Continent intensive. Borders between flux ecoregions are shown as gray lines, and reporting AmeriFlux stations are shown in red.
Because they are quantitative, we can depict the flux ecoregions using colors that reflect their calculated degree of similarity. Such similarity colors are created by performing a Principal Component Analysis on all 30 input characteristics, and taking the top three PCA axes, and assigning them to the red, green, and blue color guns. Exact loadings for each of the 30 factors on each PCA axis are shown in the flux ecoregion report (Table 3.14, pg 118). The two levels of flux ecoregions proposed above for the Mid-Continent Intensive are shown as white outlines. Reporting AmeriFlux towers are shown in white.
When shown in Similarity Colors, the degree of similarity of the mix of flux-relevant conditions within adjacent flux ecoregions is apparent by the similarity of their colors. Such flux similarity depiction reinforces choices made for the proposed Mid-Continent Intensive regions. The entire central "backbone" and the eastern addition are all a very similar shade of green. The added western components are darker green, changing to brown at their southern extent. The Ozarks, not included, are a light purple color, and the northern MN/WI/northern MI forested areas are blue rather than the green shown by most of the Mid-Continent region.
Because carbon flux patterns change with seasons, we generated multiple sets of flux-relevant ecoregions reflecting differences in seasonality. This map shows quantitative flux ecoregions generated from flux-relevant conditions during the growing season within the same area. While the random colors and the ecoregion numbers are not constant between the previous map and this one, it is nevertheless possible to identify the same flux ecoregions in each map, and see how they have shifted during the growing season.
The white outline added in this map shows the extent of the two gray zones proposed for the Mid-Continent Intensive above. Inspection shows that, while particular flux ecoregions have shifted, and at least one extra flux ecoregion has appeared in the northernmost "backbone," the spatial extent of the region proposed to be considered has altered only slightly within the growing season. This is further evidence that the proposed "edges" of our Mid-Continent study region represent locations of definite ecoregion shifts, and are reasonably "hard" borders. GIS-compatible digital coverages of these flux ecoregions can be downloaded from http://geobabble.ornl.gov/flux-ecoregions.
We prepared these flux ecoregions for the purpose of guiding design exercises such as this. In addition to helping define the logical extent of NACP Intensives, quantitative flux ecoregions can also be used to locate places where a fixed number of samples should be taken in order to maximize how well those samples represent a particular region of the map. Statistically guided design and growth of such sampling networks, based on a set of specialized quantitative ecoregions, can maximize the degree to which a particular number of samples represents a particular region of the map.
We believe that quantitative flux ecoregions may have additional uses as well. A quantitative degree of similarity can be calculated between the flux-relevant environments in any two homogeneous flux ecoregions. Such quantified similarities might be used as a statistical basis to adjust flux measurements made in one flux ecoregion such that they represent the flux environment in another, unmeasured flux ecoregion. Thus, flux ecoregions might form a statistical basis for extrapolating a limited set of flux measurements across a region or continent.
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