Alpha Units:

    Fixed Locations
    Where Resources May Be      Changing

Robert H. Giles, Jr.


What if the Earth surface was divided into separately named units, each a column that was 10 meters by 10 meters wide and then extending1000 meters below the surface and 1000 meters above the surface? (e.g., the UTM map projection.) What if an enterprise existed to improve the way that natural resources and lands are used, and to make money for themselves and their posterity? (It does). What if all of the land and resources could be considered as existing within the column, each a uniquely-labeled map cell or unit, each 10 meters by 10 meters? (Some people can do so.) What if ecologists know that there are 200 large animal species on most Virginia mountains, 2000 plant species, and 20,000 insect and soil organisms? (They do.) But what if someone knew that only 20 factors (fewer for solving single-species problems) could give more that 80% control over the variations usually encountered in systems undisturbed for about 50 or more years? (Evidence now exists that this is likely for a variety of species.) What if the 20 factors can be put into a GIS? (They can, and many have been, and some are for sale.) What if each factor was broken into only 5 gross categories along a scale for each. The combinations are 5 20 or about

95,367,431,000,000 potentially unique land units. There are only 12,019,000,000 land units of the 10 x 10 meter variety in Virginia. (think of them as the 10-yard line on an American football field a few feet, or 3 such widths being within a basketball court).
Sample double-sided pocket card
Alpha Units (AU): Unique Spatial and Temporal Resource Units for the Future
  • Equivalent units: 1 alpha unit is:10 meters x 10 meters
  • 100.0 square meters
  • 154,999.7 square inches
  • 1074.87 square feet
  • 119.6 square yards
  • 0.1 hectare
  • 0.0247 acres
  • 0.0001square kilometers
  • 0.1111 of a 30x30 Landsat pixel
  • There are:100.0 alpha units (AU) in a hectare
  • 40.52 AU in an acre
  • 25,900 AU in a square mile
  • 10,000 AU in a square kilometer
  • 4.05 AU in a square chain (66 ft.) plot
  • About 1230 AU in a 30-acre "stand"
  • About 2000 AU in a 50-acre "stand"
Premise: every AU in the world is unique.
Rural System is ready to do modern land analysis and design for your land. Using Alpha Units is not a bad idea.
Call or email us at:

We have studied the major ecological factors and their variability. We have had experience with Landsat, videography, and GPS. We have worked with old land surveys; we've tried to re-locate randomly selected points. We've broken chain, paced distances, estimated crown coverage, and have watched peculiar numbers creep into basal area measurements as well as those of forage and wildlife sign. Based on these experiences, we have developed the rationale that the Alpha Unit is the most practical, smallest unit that has meaning in land analyses of any land ownership or area over 3 acres in size. Alpha Units are ecological units (including temporal and spatial concepts), also economic (e.g., expected yield and costs), also an esthetic unit. It is also analyzed as an energy-budgeting unit. It has costs of enforcement -- the constraints of laws and regulations as well as patrol costs. These words, all starting with E, comprise the 5 dimensions of the context within which Alpha Units make sense.
A simple example:
Landsat is very expensive and very difficult and very changing and always a victim of cloud cover. It can only give one major factor, land cover. Few other ideas can be consistently applied; detailed research is needed to make the images "talk" locally. Suggestion: avoid it or buy data sets from others.
Your staff notes where they see ginseng. Make a map of where all of the conditions are like those places; then where all but one factor, then all but 2 factors, etc. Logistic regression can be uses to make a complete map of the probability of occurrence based on the data in your computer, the GPS code and the GIS data associated with each GPS point... and revised for a price... or next year as more data become available. Then map the areas to be reserved and protected from harvest, trespass, etc.

The chances are that each unit is unique. We already have or can readily get information about each such unit for any land unit. We may no longer need to aggregate and synthesize and combine data into a set of statistics (information for decision making, or why else should we get it?) about a population of areas. What if we had great computer power and could prescribe in ways that are responsive to the unique set of conditions within each unit? (We have the computers; we do not have the prescriptions.) Prescriptions that experts can now formulate can be made site specific to increase production, avoid conflicts, reduce losses, reduce risks, increase statistical controls in experiments and the statistics of observations, and help assure future desirable future conditions for future people.

Radloff and Betters(1978) saw that their land classification grouped individual sites having relatively similar characteristics. Within the Alpha Unit process, we specify the characteristics a priori. We know the characteristics and ask for a display, not in groups, but in whatever patterns they emerge. We believe we have over-grouped and over generalized in the past and that the reason(s) for doing so are no longer as relevant as they were once. No statistics for grouping or discriminating are needed; we specify the known conditions and characteristics of each small unit of land or water.

Every tree is a resource; so is every bird, every mammal, every stream-month, and every visitor opportunity. Each nominal resource exists in a place; each existence has a period. Each period has a transition (cf. ecological succession, tree growth, stand yields, erosion rate). Each resource (whatever it is or is named) exists in a place and has a change rate (that may be zero). The Alpha Unit emphasis is transitory. For today or for this project the named resource is number of trees. For tomorrow, or the next instant, the named resource might be number of species of birds probably present. Forest type, while of interest, is little more than an index to one or more such nominal resources.A tree map is not a bird or salamander map. Trying to relate everything to trees has great appeal because trees are so conspicuous. We may know the species, age, height, and stem density, but we may also know 50 other factors (other than tree facts) of equal or greater importance to a decision at some point on the land. These can help describe runoff, insect attacks, fire potentials, profits to be made, mushrooms for deer, allergens, deer antler size, rodents eating tree seed, r mosquitoes bearing the potential of encephalitis. Trees are important, but so is their value and their cost of removal. Either value or cost may change faster than biological or ecological factors. The thought processses needed for 1000 Alpha Units of walnut trees are different than those for 1000 units of scarlet oaks.

Alpha Units are not just potentially dynamic spatial units but also potentially dynamic economic units. A month is the smallest unit of time for an Alpha Unit. The year is often used. Much forestry work is done with 5-year classes of ages and growth and likely yields. The variation encountered in these 5-year groups of data further justify the 10 x 10 Alpha Unit size decision. Typically a 5-6 month growing period will be treated as the data for "a year," just as a single minimum temperature for one day in a year may be used as data for a year in some models.

It may be feasible for an enterprise to operate on the basis of these small land units (called Alpha Units) and because of having detailed and specific information about each unit, could do the following, for example:

Alpha Units provide maximum differentiation using the fewest GIS map layers (resource-related factors) and models (e.g., logistic regression, expert system, and heuristics). This is a principle of "minimum data, maximum information for decisions." The maps composed of the Units may be used as any maps are used, often in a variety of ways. Representative maps include:

The Alpha Unit and its related concepts are not theoretical or academic but a practical way to do precise, competitive, profitable wildland management and to escape the tight hold that "communities", "ecosystems", "watersheds", "stands", and "compartments" and "units" now exercise on planning and field work. It does not replace them, only allows analyses at a precise level, then allows grouping upward to meet other objectives. The phenomena within every unit may be modeled as a function of phenomena of the surrounding units...and that may be in any direction or distance (thereby including the mysterious, enigmatic "landscape ecology"). It, as now conceived, is not about all GIS, or about producing maps, or cartographic excellence. It is about how to make money from wildlands...forever, maybe even more than now made. It is wildland limited, regional, and incrementally improving. It is proprietary. Air pollution, geological and mineral, and groundwater GIS work are massive fields and avoided at the start. Depositions and surface geology need to be included soon within the Alpha Unit work. Both of these are mentioned here to attempt to introduce: The Alpha Unit is a valued volume that is changing. The mapped unit is a slice through the volume, a column 2 km above the land surface and 2 km beneath the land surface. (The legal dimension of this is recognized, i.e., Justice Dougles in the Causby opinion, 1946, that the landowner has control upward only as far as is necessary for reasonable use and enjoyment of the surface as adjudged on a case-by-case basis.)While most work and analyses are done at the surface, the volume includes the air, weather, and climate above the surface and beneath it - mining, solution channels and caves, groundwater, and so-called "parent-material" of the soil layer.

The concept of a valued volume includes the three factors (other that the nominal resource itself) (1) the probability of not encountering destruction or failure to achieve an objective, i.e., 1.0 minus the probability of flood, fire, storm, land subsidence, poaching, theft, tresspass, etc.; (2a) a planning horizon (years to a specific project date or for achieving a set of objectives and (2b) also 150 years (an observation requirement within the Alpha Unit analyses); (3) time since last major disturbance or time zero in primary succession; (4) 1.0 minus the probability of a suitable or better substitute being available locally for the resource within the planning horizon (2a);(5) three estimated likely interest rates for the nominal resource. It is evident that the Alpha Unit is not simply an ecological or timber-oriented unit, but a resource unit. It attempts to create conditions for unifying ecology and economics so that the results can be mapped and visualized by decision makers. The economic dimensions will be elaborated later as needed.

The vegetation in most Eastern-US forests is a diverse mixture of natural groups of plants and animals which respond differently to environmental and biological conditions. Unlike in the western US, there is inconspicuous zonal variation. (We believe that the variations are real but that the zones are not conspicuous because the differences are less and the consequences of knowing the differences are less.) Technology is needed to separate and see the differences. However, more than technology is needed. Herein we develop an approach to differentiating land units on the basis of a set of factors:

Daubenmire and Daubenmire (1968) devised a scheme for "land classification." We are attempting to suggest using the concepts that they developed but to take an alternative path to classification, that of disaggregating and discriminating. Past efforts to classify land resulted in a few classes, inadequate to identify the evident types (pointed out by Williamson (unpub PhD dissertation) and to respond to the many different demands impossible for a single system.

The types of classes are used by some managers (after training) for:

  1. planning
  2. making decisions
  3. making ecological studies. (As Alexander et al. said, "Not all readers will find each category of information of equal value.")
  4. mapping vegetation for many reasons
  5. evaluating for sale or purchase
  6. explaining and predicting forest growth
  7. explaining and predicting susceptibility to diseases
  8. explaining browse for game
  9. understanding natural succession
  10. providing a framework within which to relate additional basic or applied biological studies
  11. selecting sites for a variety of reason (see below).

Mueggler(1988) observed that "intensive management of these wildlands requires an ability to recognize the units of land and vegetation with similar production capabilities and similar response to management activities."

Research may be sponsored but results must be couched in proprietary form or end use. Studies and verifications are badly needed and need to be viewed as one of the costs. Massive databases (very large n) defy classical efforts to express "significant differences." Running after new, faster, specialized software can increase costs over the long run and make the system operator specific (destroying the system if the operator departs). Personnel backup (limited, but with a system designed so that another person can operate it if needed) is essential.

Hundreds of factors may be used but a few powerful factors to which most wildland phenomena respond and that can be well mapped are used first. (Air pollution and geological and mineral GIS work are massive fields and we have avoided them at the startup.Deposition and surface geology need to be included early on.) Not to include economic factors (powerful factors, far exceding the role of ecological factors in decison-making about wildland processes and programs and land-use development)to which wildland phenomena respond seems narrowly silly. The factor-screening process is critical and linked to knowledge of ecosystems, forest and wildlife production, economics, and the statistical concepts within stepwise regression and sensitivity analyses. The factor list is long (and an ancillary is similar)

  1. Slope
  2. Elevation
  3. Aspect (2 types)
  4. Transformed Aspect
  5. Slope/aspect unification
  6. Landform or relief
  7. Slope position
  8. Distance from Stream
  9. Stream or Pond
  10. Watershed Boundary (600 acres +)
  11. Wetland (several classes)
  12. Pseudo-soil units
  13. Soil texture class
  14. Age since wildfire
  15. Surface geology
  16. Land Cover (landuse)
  17. Administration: state, county, planning district, river basin, wildlife agency and natural resource regions
  18. Temperature (Mean, max, min, range, total annual, degree days)
  19. Growing-season days (frost-free days)
  20. Total precipitation within the growing season
  21. Adjusted probable precipitation available in soil
  22. Mean growing season degree days (Temperature summations)
  23. Hours in topographic shadows in the growing season
  24. Phenology Index (Hopkins' Bioclimatic Relationship)
  25. Presence of springs and seeps; distance from such places
  26. Major disturbances (roads, structures, quarries)
  27. Canopy coverage(%) classes

(In select areas, correlations and relations may likely be found among fire maps, basal area, last-10-year tree growth, stem density, canopy coverage, percent soil cover, elevation range, occurrence of broken tree tops (storm damage), grouse flushes, and deer sign abundance.)

There are many other maps for the GIS (maps of any type are also called layers or may be conceived as "spectral bands" in the sense of classical remote sensing) but we need to think of them as factor maps since using them as layers will be rare. Use of the layers is likely to be made in the following pattern:

Resource Map = a + b (Map Factor P) + c (Map Factor Q) - d (Map Factor RKZ) + e

These factor maps also include cemeteries, mines, and quarries. Each is a separate map or layer in the system and can be combined in any way desired. Others layers or maps: 2000 separate plant maps, 60 species-specific tree species suitability maps, 200 animals, monthly temperatures (maximum, minimum, mean), monthly precipitation (mean, maximum, minimum), fog drip, monthly prevailing wind directions, probably stumpage, fire risk, wildfire loss probability, lunar light and shadows, sampling intensity, prescribed harvest per acre in a year or 5 year period, hunters per acre, anglers per stream reach, stream side zones...may be developed for clients or for sale to potential users.

We have developed a list of about 20 factors and made paired comparisons of importance (a contingency table; identical columns and rows). Then we assigned importance to each pair...the value (if any) of maps made of only 2 factors. We produce triplet maps, interesting 3-factor combinations.

The classical map resulting from the Alpha Unit presentation or other GIS applications may not be important. The summary data that accompany maps are often the primary payoffs. The information from the maps (means, percentages, counts, etc.) become the inputs to a range of decisions (e.g., percent of the total ownership in forests with slopes greater than 15% on north facing slopes within 10 chains of existing roads, a map which requires the joint use of slope, aspect, roads, cover, and property boundary factor maps (all previously mentally integrated splendidly with perfection by every land advisor who may not have even had an aerial photograph of the tract?!)).

Site selection is one key function or use of the mapping system and the Units. Examples include:

Two Dog , the forest survey software, use provides the field analyses that few other systems have. For example, with 30 sample points (locations registered with GPS) that say that sourwood is present, it is then possible to say "make a map of where the conditions now present on those 30 sites also exist." You have a potential sourwood map! (at least for the property...and then for the region that you define with your available data.) This is a remote sensing concept of "supervised classification" that is typically applied with 4 or more spectral bands. The same procedures can and need to be used with the factor "bands", the map layers.


The Alpha Unit concept may be viewed as just another form of vegetation or ecological classification, another one created over years of research such as reviewed in Wirsing and Alexander (1975), Paysen et al. (1980), Brown et al. (1980), Ecoregions Working Group (Canada) (1989), National Vegetation Working Group (NVWG)(1990). These classification systems have been asserted to be valuable in making a variety of decisions, discussing the processes of the land, and communicating to people the common elements of land and the changes likely to occur with treatments or due to natural trends. They are said to be of value in understanding and management in almost every area of resource management (NVWG 1990). Mueggler (1988) said that habitat types, in his work, were based on potential natural vegetation, with understory used to clarify series within each type. Classification reduces data to information much as statistical analyses convert data into statistics. If too few statistics are used, then information useful for analyses and decisions can be lost. An average without its variance, for example, may supply inadequate, even erroneous information about a population. The data were present and needed to compute the average and failing to compute the variance might result in faulty diagnoses or prescriptions. Similarly, gross classifications (e.g., into SAF Forest Types) can result in great loss of information, especially when such types are used or intended for use by different resource groups. Alpha Units have been difficult to describe because they seem to be excessively small, as if they are the units that need to be classified. They are new, unique classifications for very precisely defined resources (as mentioned above). They are the result of classification. Their difference is in the procedure of their use and display. Maps are costly, difficult to produce, and (realized by few people) limited to about 20 colors that can be readily discerned by normal people. There may be the need to display 53 different classes of resources but they must be regrouped (not for ecological or other reasons, but because only 20 can be effectively be mapped!).

Alpha Units are of known size (square, UTM map projection) and of known characteristics. A unit, for example, may have one, each, of 10 slope classes, 10 elevation classes, and 8 aspect classes. There are known, by definition, 800 unique classes for these 10 x 10 map cells and in some areas of the world there may be at least one pixel or map-cell unit having the characteristics of one of the 800 "classes." In some area of interest there may be only 326 different units. There may be thousands of units on a single mappable area with the characteristic of: slope of class 3, elevation in class 4, and the compass direction downhill from a point (aspect)...class 7. The special character of the computer mapping capability is that a map may be made of only places having the specified set of characters (for example, the 3 mentioned above). The map will have only 2 "colors", one symbolizing places that have exactly those characteristics, and the other, places having all other characteristics. If there are, by design, 10 levels of magnitude assigned for each factor and there are 20 factors, then the number of potentially distinctive classes is merely 1 x 10 20. (There are 1.26 x 10 11 acres of Earth surface, water and land, 5.1 x 1012 surface units the size of an Alpha Unit. The number of potential classes that might be created with only 20 factors exceeds the potential area within which to fit them.)

Every cell is potentially unique, given that there are far more than 20 factors at work in each unit and permutations (related to the sequence of effects of factors) add greatly to the potential number. Not needing to map one point, a request may be made to list the coordinates of all sites having a set of factors (e.g., 12). It is likely that only 2 to 3 places would be listed that have those factors in exact combination. Thousands of spots, however, might be mapped having a range of factors (e.g., between r and s, above g, less than h, etc).

Data may not be estimated for each Unit. For example, Klopfer (1998) estimated mean temperatures (and other temperature, precipitation, and evapotranspiration data) for every 300 x 300-m block of Virginia. This is a far superior estimate that ever available. Each Alpha Unit, all 900 within these blocks, would be loaded with the estimated temperature. As algorithms, data, time, and funds become more available (if ever) then the models may be improved and Unit-specific estimates made. We hypothesize that the following relations will be readily modeled:

Depth ot bedrock = f( distance to water, distance to ridge, geologic type, and slope position


age of forest stands (constrained by Landsat reflectance as non-sappling class) = f (major timber type, distance from roads, slope, and maximum age

These relations can be estimated in the field but in order to map large areas before going to the field (as needed within The Trevey procedures,) a map showing such approximations can be useful. Field work with GPS can improve the estimates. Animals respond more to tree age than to type, and more to type than to factors of edge or interspersion. Difficulties persist in stating the age of an uneven age hardwood stand but this suggests the reasonable limits on the approximations and estimates. Since vegetative weight is related to tree species and weight is related to the known specific gravity of each type of wood, then maps of weight can probably be made. It may be that the site characteristics produce total weight (actual or potential tree phytomass) and site ecological equivalencies and tradeoffs can be estimated based on tree weight.

A sample application:

Great difficulties and past errors have attended use of aspect measures, estimates, and analyses. The appendix presents alternative transformations of aspect in to 2 types, one being easy-west, the other north-south. A solar-related aspect transformation is suggested as a third map alternative. These may be project or site-specific data or they may be computed for storage and later retrieval (without further computations).

An underlying assumption with the Units is that factors are (or may be) non-linear. In most cases simple logistic relations are sought. In some cases, thresholds are used (e.g., the biological effects after water freezes). Strong regressions are likely within ecosystems, therefore using the most easily gotten and least costly factor maps as independent variables is a common strategy.

Alpha Units do not have to have names. Numbers or codes are sufficient. If names are needed, a likely translation may eventually be developed (e.g., hypothetically, number 1245 to 1578 and 2323 are called SAF Type x; soil type 321 is equivalent to the Hillvill Silt Loam (which can then be linked to probable-soil-use types in the data base from the former SCS, Natural Resource Conservation Service).

Users of Alpha Units typically will identify a vegetation type or dominant plants or observation such as presence of animal sign, then seek characteristics of that site...and similar ones. Often the map can become more accurate as observations are accumulated. Unlike vegetation mapping which uses the vegetation (e.g., plant associations) as the integrated expression of all of the factors at work on such sites, (e.g., Carleton and Maycock 1980) the Unit uses the vegetation, animals, etc. to point to factors operative in the past and present on observable conditions. Of course we seek high accuracy and to progressively improve, but the standard is not what is possible but what data we have (or know) now. Often that criterion suggests statistical alpha levels of 0.51 may be suitable, temporarily. Few people realize that many things in nature have very high variability; it is natural. Achieving a good "fit" is unnatural. Carleton (above) found a site moisture-nutrient gradient and a general fertility-productivity gradient affected understory vegetation. Understory-overstory coincidence is related to site factors and many abundant herbs seem indifferent to dramatic canopy change. Consistently observers study the adult plant, rarely the conditions likely at the time of seed rain or germination.

Stand and Similar Land Unit Analyses

Alpha Units provide an alternative to stand analyses. A stand was defined by the SAF in 1950 as: aggregation of trees or other growth occupying a specific area and sufficiently uniform in composition (species), age arrangement, and condition as to be distinguishable from the forest or other growth on adjoining areas.

These stands have been mapped for many years. They generally have been the smallest unit of land in a manager's or company's analytical processes. These are the relatively uniform areas that look significantly different from their neighbors. They once "made sense"; they were the units to which wood and growth of wood could be attached and with which planning was done. That was BC, before computers.

The Alpha Unit allows land managers and owners to get excellent expressions of potential site quality (where site index is limited by the absence of dominant and co-dominant trees upon which the index is based. The unit exploits the convergence of:

  1. being able to know your position in the field (the exact Alpha Unit by using GPS equipment)
  2. past research in forestry
  3. computer hardware advances
  4. advances in GIS and mapping
  5. new, continuously revised software.

The Alpha Units can be used in research, inventory, impact analysis and evaluation, planning and management. The persistent debate over what is an ecosystem (and laws that require some public land to be managed as if it were an ecosystem) suggest the need for more explicit units in which ecological principles may be applied. The Alpha Unit is not unlike the ecological unit of the US Forest Service defined as "a mapped landscape unit designed to meet management objectives, comprised of one or more ecological types." The units are not hierarchical since many combinations of factors can produce (or exclude) equaal quantities of tree growth or suitable conditions for plants and animals.

Increasingly it become more evident that every unit of land is likely to be unique. We now have the computer capability for analyzing and designing productive land use systems in keeping with this view. Not the old stand, but the new Alpha Unit is likely to become the new unit of measure and the unit for land use management for the future.

If you know that plots in a stand are highly variable, why are you satisfied with using an average plot value and with saying that such a number describes a stand?

If you know that the gypsy moth hits 3 adjacent tree species or types equally, why do you want to separate stands with these species?

If you know a viewscape from a park, trail, or vantage point makes a large unit of land beautiful or ugly -- no matter what its biological character -- why emphasize the stand?

If the upper edge of the stand is far from the road and hauldistance is uneconomical, why stick with a tree-species-based stand? Why not a land unit with a financial base?

If a rare plant is only found in a quarter-acre part of a stand, what will be preserved -- the unit or the stand...or?

Do birds, salamanders, or bears "see" and respond to stands?

Isn't discriminating (drawing the line between two populations) one of the most difficult statistical problems? What foresters have not been perplexed with where to drive the survey stake mark_ng a stand or watershed boundary?

Where do recent studies of forest patch dynamics and gap analyses in Eastern US forests fit into stand analyses?

Developers of the Alpha Unit have faced the answers to the above questions and in the maps that make it practical.

It is very expensive to characterize and map all stands in the field. These are typically 20-40 acres in size in mountainous terrain! By skillful computer use, all areas that cannot be harvested or that are very unlikely to be harvested because they are too steep (or for other reasons) can be omitted from the usual requirements for "stand mapping." For a "land-unsuitable-for-commercialwood-harvest" category (our "inoperable"), type can be estimated and the old or ancient forest class assigned. Inventory efforts can then be directed to the lands where cost-effective harvests may be feasible and knowledge is needed for profitable, sensitive forest conservation and management. This strategy of exclusion can be applied to areas proposed for industry, ponds, etc. Roads, viewscapes, and rare plant areas may be excluded to allow intensive analyses of the residual forest lands. (At lease removal can be simulated, then later decisions may be made when the consequences of doing so are clear.)


The following might become part of the text about an area for a customer. Alpha Units are used:

Elevation is the height of the land surface above or below sea level. "Altitude" is sometimes used, but usually this denotes a location in the atmosphere such as achieved by aircraft. The maximum elevation in the US is xxxxxx. The minimum isvvvvvvv. In the state, the maximum and minumum are zzzzz and cccccccc.The maximum or highest point on your property is kkkkk feet above sea level. The minimum is and thus the range is hhhhh feet. Some people think that the range strongly influences the potential biodiversity of the area, perhaps even moreso than the total area. The greater the range, the greater tend to be the richness or number of species.

Elevation data are critical to many ecological, watershed, and other features of the land and it sets limits to potential... but they open opportunities.

Maps to be displayed or studied:

DEM with boundary.

3-d elevation with boundary draped.

Elevation to the 1.5 or 2 power to accentuate the topography.

Elevation to other powers to represent the influence of elevation in other models.

From elevation we can calculate slope, landform (slope position, slope, ridge, saddle, etc.) and several types of aspect (the direction that the slope faces). Elevation is a key factor in models estimating monthly temperatures in each map. Slopes based on elevations, are critical in solar energy models and thus affect stream temperature. In addition they are useful in computing solar energy and shadows on areas. "Proportionally less high area" may be a useful study.

Elevation influences barometric pressure and a relative barometric pressure map may be created, useful in computing a map of relative evaporation and evapotranspiration (see Klopfer 1998).

Elevation is a major variable in determining potential forest vegetation in western Virginia.

We are aware that elevations vary greatly and that using a single elevation to represent the average for a 10 x 10 meter area may not be sufficiently accurate for some purposes. The issues of map scale and cell-size are many and varied, but the first that must be faced is the cost of data collection, verification, storage, and retrieval. Analyzing average-sized areas requires hundreds of thousands of map cell. Even for small areas. The collection costs are high, the accuracy of recorders (eye-strain, care, etc.) always a concern, and storage space for data (including backups) a continuing problem.

Sampling of elevation across a map may lead to inaccuracies. Grid points are a systematic sample of the elevations of a surface. Acceptable confidence levels and risk of error must be addressed in the context of natural variance, bias, and the conventional topics of rational statistical sampling.

At the practical level, it must be realized that the map sources, though excellent, are made by humans from aerial photo interpretations and field surveys. In some areas, radar-based instrument and satellite images are used. Experience will suggest there are dimensions of art as well as science in using any procedure for map making. Maps shrink and swell; overlays shrink and swell; the printing process changes some map scales (thus the actual location of a point on the ground represented on paper). Of course elevations themselves change in some areas from roads, land subsidence, and development. Gullies, upthrown tree roots, large rocks, mud or rock slides, and general surface and rill erosion can readily redult in differences of a few inches to over 10 feet. Such differences are (a) typically irrelevant, (b) variable, unique, and/or unpredictable, (c) dynamic (tomorrow's events), and (d) can be, and are fairly readily "smoothed out" or made extreme (e.g., road cuts) by any activity in an area (i.e., made irrelevant).

No apology is made for the current elevation data base. It is too gross for some work, too precise for other work. It has been excellent in wildland work. Other sampling and data collection is underway. The present data cannot be made more precise but it can be aggregated.

We use DEMs or digital elevation models, data purchased from the U.S. Geologic Service, Washington, DC. DEMs are point elevations arranged in a grid pattern. Slopes, for example, are determined from them by comparing changes in the x and y axes in neighboring grid cells (e.g., Ritter 1987). Within 30 m DEMs, one point, the average elevation, is represented.

General knowledge about elevations (compare to general observations about latitude and longitude):

The higher the elevation, the more northerly the conditions.

Barometric pressure decreases ddddd units for every 100 feet increase in elevation.

Evaporation decreases about rrr% for every 100 feet increase in elevation.

Solar radiation is reduced www for every 100 feet of atmosphere through which it passes (close to Earth).

The higher the elevations, the steeper the slopes.

The greater the change in elevation (called by some "the range"), the greater the richness.

The more coarse the resolution of the elevation data, the lesser become the slopes. Ecologically important places (e.g., rock faces, waterfalls, hiding places) become obscure. [Expert systems related work is likely to be able to locate and map such probable sites. RHG]

Mueggler (1988) noted that occurrence of elevation limit to trees and shrubs generally increased with declining latitude. He discussed aspen (Populus tremuloides Mich.) and noted upper elevation limit seems primarily determined by the length of the growing season, the lower limit by evapotranspiration.

All of these can be qualified and maps made. The understanding within the use of and concept of Alpha Units is that elevation itself is not important. It is not an ecological factor. It is something that we can observe but has no functional bearing or meaning. It is a locator, like latitude and longitude, specifying a point within the three dimensional thick zone around Earth. Temperatures change in relationship to it. Temperature is the key variable. Barometric pressure changes in relation to it. Pressure is the variable, not the correlated height above the sea. Factors are clustered into and easily analyzed under the elevation concept. How much water there is all of the time and how nutrients are supplied to plants in that heat-laden moisture are the key factors. They operate at different rates when at different elevations because there, temperature, pressure, and other basic factors differ. We have to include these factors in the maps, not their non-linear correlatives.

Stand Age

A stand age map might be created (Arno et al. 1993) using trees of known age from cross-section study, borings, wind damage, etc. The classes often used for age are seedling (less than 4.5 ft) saplings (less than 4 inches dbh), mature , advanced age, etc. Each, a distinctive category, has a different number of (e.g., 0-15, 15-50, 50-110, 110-160, 160-250 plus) years making some analyses inappropriate. Trees are aged (at high cost) to the year, then observations are thrown into 5 or 10-year classes. It seems likely that very close approximations of diameter to age can be created, given site characteristic values (within the Alpha Unit files) and attention to putting trees accurately within 5-year age classes. Nearness to roads, Landsat cover, operability, forest type...are likely ancillary factors that would allow estimating the acreage that is likely to be changing within a county within a 5-year period...and the likely quail abundance (for example only), and...the potentials are numerous. This however, is a low priority map and age is best estimated from regressions related to tree diameter and height (with GIS variables thrown in where needed as independent variables for improved accuracy). Historically, stands have resulted from harvests and approximate ages of trees over large areas can be estimated. Recent fire history can be gotten from state records.


This section is being developed based largely on Wajda , Anderson, and Klopfer. See Klopfer. Mueggler (1988) noted the ameliorating effect of topography on evapotranspiration.

Precipitation per unit area is normally assumed. The area is that of the map. The physical surface of impact and the forest floor is the surface of adsorption. It may be useful to compute the actual estimated surface area of each Alpha Unit and study the differences (if any) in equations using this factor or those using the map area only. Available moisture in the growing season within the estimated root zone is the quest.

Fog drip needs emphasis including a map of probable volumes by month.

Moisture intake by leaves and stems needs study and inclusion of findings from the literature.

An index to probable longterm (30-year) available median soil moisture is the quest, not actual precipitation. Tree-meaningful precipitation, evapotranspiration, runoff, probable adsorption by litter, and fog drip need to be unified for the growing season of each Alpha Unit.

Probable conditions for seedlings needs to be mapped by Units. What trees start and persist in areas (thus the proportion Designated by "type") is a function of the seedling or 0-5 year class conditions, not the adult conditions.

Soil Texture

Soil texture is suggested as a major factor in some analyses of forest growth. It relates to rooting structures, potentials for soil compaction (harvesting, recreation, etc.), and the matrix of the nutrient broth delivered to the trees. Texture is an expression of the proportionate amounts of sand, silt, and clay. If the forester knows any 2 of these, they know the third. Concentrating on 2, and the most easily measured, seems reasonable. Many word gradations for texture are used in agriculture. It is likely that variations within forests over time, only a few texture classes need to be estimated. It seems likely that by knowing bedrock (limestone, silt, sandstone, granite, etc.) and knowing slope position, (then including N-S aspect for refinement) the texture can be approximated well within the region of meaningful interpretation for most wildland decision making. Probable soil texture, a map of interest in some forest growth and yield models...which affects harvest rates... and thus early succession for quail and other fauna...may be a useful map layer.

Landscape Pattern Expressions

Landscape maps may be of value. Trani-Griep (1997) provides useful literature review and insight to over 26 indices, most of which can be collapsed into 9 units of measure since they are correlated or a function of other measures (Giles, R.H., Jr. and Margaret K. Trani. 1999. Key elements of landscape pattern measures. Env. Management 23(4): 477-481. ) In 1972 F.G. Goff was working on the concept of cover diversity. Diversity of structural types seems to "promote stability of functional output by redundancy of functional performance." Other system properties implied in the diversity-stability relationship are (a) differential susceptibility, among the types to inference in processing and (b) mutual limitation (competition). Whole system stability (i.e., stability of both structure and process output) is achieved through organizational complexity of the system. The complexity of co-evolution, which leads to stability of diverse natural systems, is replaced in agricultural and intensive forestry systems by the persistent economic, technological, legal, and enterprise systems underlying such production. "Buffers" is a word used in some GIS systems to indicate a mapped zone on one side or both sides of a map line. Since stream zone width varies with slope, a new map can be created if slope maps, stream or channel maps, and stream zone buffer widths are mapped. A riparian zone, streamside zone, and total map zone may be mapped. The total area and proportions of the total should be a major part of such analyses. Stream order is significant and estimates of the stream order should be attempted. The following are horizontal measures from the high water mark in feet.

  1 - 10 11 - 20 21 -30 31 - 40 41%
Riparian Zone 25 25 25 25 25
Streamside 75 100 150 200 250
Total 100 125 175 225 275


As with the above topics as they expand, a separate file may be come available.

Site Index

Monserud (1984) analyzed the problems with site index growing from work on the topic begun before 1913 and used for over a century in Europe. The problems notes are the major reasons why the alpha unit is needed.

  1. Height of dominant trees may not be (and probably is not) the best (consistent, etc.) indicator of site potential.
  2. Height is influenced by non-site factors such as stocking (stem density) and site preparation.
  3. Some stands stagnate at high densities (and site indices need a crown competition factor adjustment); space stands grow shorter.
  4. Site preparation and prior land use influences site index curve shapes.
  5. Brush competition, insects, and small mammals influence growth.
  6. It may not be (and probably is not) constant over time. (It is highly variable over time.)
  7. Plantations and long-term use can for the same practices result in site index change (degradation). Irrigation and fertilization can increase the index.
  8. Climate does affect site although it is assumed not to do so. (Difficulty of getting and analyzing long-term records prevents it being included.)
  9. Proper tree selection is often difficult. Large trees in adequate number are rarely available. Great bias in yield curves can result.
  10. Good sites do not have the same shape curves as the poor sites.
  11. Average site index declines over time, not on a site, but due to harvests and shortage of old-growth stands on high sites.
  12. Lumping species is not appropriate when species have different growth curves.
  13. Latitude influences growth in height of species and curve slope.
  14. Curves differ in excessively and imperfectly drained soils.
  15. "Habitat type," a confounding map unit, suggested different site indices for ponderosa pine.
  16. The slop of curves, based on the procedures used (e.g., the guide curve method) has been called into question by Monserud. He found that height growth was overestimated by the traditional guide curve method before index age and underestimated after index age.
  17. Site index is not (at least rarely) connected to a yield table. Simulations are used, but most site index as an input.
  18. The index concept is difficult to apply in uneven aged stands. As Monserud (1984:174) said, "By definition, site index is almost exclusively an even-aged concept. Only with difficulty can site index be successfully used in a stand that has no single meaningful age."
  19. The largest or tallest trees are not necessarily the best indicators of site potential for they have survived early suppression from an older no-longer living portion of the stand.
  20. Stands may have grossly different volume yields while having the same site index. Basal are growth potential need not be assumed correlated to height growth potential.
  21. Trees can be genetically limited in height growth regardless of site quality.
  22. Past, not future, growth is measured (estimated).
  23. It has limited value in natural stands, especially where commercially important species are shade tolerant.

See Site Index

Note Use as index: The number of rings in 1.5-inch outside radius. (Stoze '63) (??)

Relevant Literature

Alexander, RR, G.R. Hoffman, and J.M. Wirsing.1986. Forest vegetation of the Medicine Bow National Forest in southern Wyoming: a habitat type classification. ASDA For. Serv., Research Paper RM-271, Rocky Mt. Forest and Range Exp. Sta., Ft. Collins, CO, 39pp.

Arno, S.F., E.D. Reinhardt, and J.H. Scott. 1993. Forest structure and landscape patterns in the Subalpine lodgepole pine type: A procedure for quantifying past and present conditions. USDA For. Serv., Intermountain Research Station, Gen. Tech. Rpt. INT-294, Ogden, UT, 17pp.

Brown, D.E. , C.H. Lowe, and C.P. Pase. 1980. A digitized systematic classification for ecosystems with an illustrated summary of the natural vegetation of North America. USDA For. Serv., Gen. Tech Rpt. RM-73, Ft. Collins, CO 93pp.

Burns, R.M. (tech. Compiler) 1983. Silvicultural systems for the major forest types of the United States. USDA For. Serv. Agric. Handbook No. 445, Washington, DC 191pp.

Carter, ?.?. 1990. Some effects of spatial resolution in the calculation of slope using the spatial derivative. Tech. Papers, ACSM-ASPRS Ann. Conv. 1:43-52 {check in library}

Chang, K. and B. Tsai. 1991. The effect of DEM resolution on slope and aspect mapping. Cartography Geogr. Inf. Systems 18:69-77.

Eberhardt, L.L. 1967. Some developments in distance sampling. Biometrics 23(2): 207-216.

Ecoregions Working Group. (Strong, W. and S.C. Zoltai, Compilers) 1989. Ecoclimatic regions of Canada, First Approximation. Ecological Land Classification Series No. 23, Sustainable Development Branch, Canadian Wildlife Service, Conservation and Protection, Environment Canada, Ottawa, Ontario. 119pp. (with map at 1:7500000)

Elassal, A.A. and V. M. Caruso. USGS digital cartographic data standards: digital elevation models. USGS Circ. 895-B, 40pp.

Evans, I.S., 1979. An integrated system of terrain analysis and slope mapping. Final Report DA-ERO-591-73-G0040. Dept. Geography, Univ. Durham {check before pub}

Hodgson, M.E. 1995. What cell size does the computed slope/aspect angle represent? Photogrammetric Engineering and Remote Sensing 61: 513 - 517.

Jakimchuk, R.D. 1982. The "what" and "why" of habitat inventory, p. 7-12 in Land/Wildlife Integration No.2, Tech. Workshop, March, Banff, Alberta, Lands Directorate, Env. Canada, 220 pp.

Jones, S.M. 1991. Landscape ecosystem classification for South Carolina, p. 59-68 in D.L. Mengel and D.T. Tew eds. Proc. of a Symposium: Ecological land classification: applications to identify the productive potentials of southern forests. Jan, 1991, Charlotte NC, USDA For. Serv., Southeastern Forest Exp. Sta., Gen Tech. Rpt. SE-68, Ashville, NC.

Laymon, S.A. (R.H. Barret,?}, and J.A. Reid. Effects of grid-cell size on tests of a spotted owl model. P 93-96 in J. Verner, M.L. Morrison, and C.J. Ralph (eds.), Wildlife 2000:modeling habitat relationships of terrestrial vertebrates. Univ. Wisconsin Press, Madison, WS

Meentemeyer, V. and E.O. Box. 1987. Scale effects in landscape studies, p. 15-33 in M.G. Turner (ed.) Landscape heterogeneity and disturbance. Springer-Verlag, New York, NY

Monserud, R.A. 1984. Problems with site index: an opinionated review. p. 167-180 in J. G. Bockheim, ed., Forest land classification: experiences, problems, perspectives: A symposium, Univ. Wisc., Madison. 276 pp.

Mueggler, W.F. 1988. Aspen community types of the Intermountain Region. USDA For. Serv., Gen. Tech Rpt INT-250, Ogden, UT 135pp.

National Vegetation Working Group.1990. The Canadian Vegetation Classification System. National Vegetation Working Group of the Canada Committee on Ecological Land Classification. W.L. Strong and E.T. Oswald and D.J. Downing. Ecological Land Classification Series No. 25.Sustainable Development Branch, Canadian Wildlife Service, Conservation and Protection, Environment Canada, Ottawa, Ontario. 22pp.

Ohmann,L.F. and R.R. Ream. 1971. Wilderness ecology:a method of sampling and summarizing data for plant community classification. USDA For. Service, North Central For. Exp. Sta., Research Paper NC-49, St. Paul, MN 14pp.

Paysen, T.E., J.A. Derby, H. Black Jr., V.C. Bleich, and J.W. Mincks. 1980. A vegetation classification system applied to Southern California. USDA For. Serv., Gen. Tech. Rpt. PSW-45, Pacific Southwest For. and Range Exp. Sta., Berkeley, CA 33pp.

Radloff, D.L. and D.R. Betters. 1978. Multivariate analysis of physical site data for wildland classification. For. Sci. 24:2-10

Ritter, P. 1987. A vector based slope and aspect generation algorithm. Photogrammetric Engineering and Remote Sensing 53:1109-1111

Smalley, G.W. 1991. No more plots; go with what you know; developing a forest land classification system for the Interior Uplands, p. 48-58 in D.L. Mengel and D.T. Tew eds. Proc. of a Symposium: Ecological land classification: applications to identify the productive potentials of southern forests. Jan, 1991, Charlotte NC, USDA For. Serv., Southeastern Forest Exp. Sta., Gen Tech. Rpt. SE-68, Ashville, NC.

Walsh, S.J., D.R. Lightfoot, and D.R. Bulter. 1987. Recognition and assessment of error in geographic information systems. Photogrammetric Engineering and Remote Sensing 53: 1423-1430.

Wirsing, J.M. and R.R. Alexander. 1975. Forest habitat types on the Medicine Bow National Forest, Southeastern Wyoming: Preliminary Report. USDA For. Serv., Gen. Tech. Rpt. RM-12, Rocky Mt. Forest and Range Exp. Sta., Ft. Collins, CO 11pp.

(Editorial assistance was provided by Kevin Killeen, Thresa Vinardi, and Susan Hamilton. )

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