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1993 Proceedings of the Midwest Oak Savanna Conferences1993 Proceedings of the Midwest Oak Savanna Conferences



Jay R. Law, Paul S. Johnson, and Garry Houf 
USDA Forest Service
P.O. Box 460
South Main, Salem, MO 65560 
Tel: (314) 729-6656 


Stocking equations that quantify the growing space of trees based on their diameter have been widely used for controlling stand density in upland oak forests. Based on these relations bot the minimum amount of growing space needed by a tree of a given diameter and the maximum amount of growing space that a tree of given diameter can utilize may be determined. The latter relation is based on crown diameter/bole diamether relationships of open-grown trees or dominant trees in closed-canopy forests. We propose that the existing quadratic equations that define the maximum tree-area for oaks and associated species be used to quantify the degree of crown closure in oak savannas. These equations and the "crown-closure" charts derive from them can provide a basis for objectively defining and controlling crown cover in oak savannas.

Although oak savannas have been variously defined, they are usually characterized by scattered trees, largely comprised of oaks, and a sparse ground layer rich in grasses and forbs (Haney and Apfelbaum 1990). Nuzzo (1986, p. 11) more specifically defined oak savannas as plant communities "...dominated by oaks having between 10 and 80 percent canopy, with or without a shrub layer, and herbaceous cover, predominately a grassy layer, composed of both prairie and forest communities..." From these definitions, it is apparent that a certain range in crown coverage of trees is a characteristic of oak savannas that is central to their definition and thus their preservation, restoration, and management. This paper presents a method for estimating the crown coverage of open-grown oaks and hickories in oak savannas and similar plant communities.


To determine the maximum attainable crown diameter of a tree in relation to its bole diameter, Krajicek and others (1961) observed open-grown trees. A product of their study was the "maximum crown area" equation, which was derived from measurements of crown and bole diameters of 148 open-grown trees including white oak (Quercus alba L.), black oak (Q. velutina Lam.), northern red oak (Q. rubra L.), and shagbark hickory (Carya ovata (Mill.) K. Koch). Because differences among species in crown/bole relations were small, species were combined to produce a single maximum crown area (MCA) equation. The equation accounts for 97 percent of the variation in observed relative crown area and is given by:

MCA = 0.0175 + 0.0205D + 0.0060D2 (1)

where, MCA is percent of an acre and D is tree diameter in inches at breast height (d.b.h.), i.e. measured 4.5 feet above ground (Krajicek et al. 1961).

Equation 1 thus can be used to estimate the relative area of tree crowns (percent crown cover) in open-grown stands by summing the MCA's of all trees on an acre. Because of the high correlation between crown area and stem area at d.b.h., the resulting sums produce accurate estimates of relative crown cover when there is no overlap between crowns. Accordingly, the equation should be used only to estimate crown cover in stands where the sum of MCA's for all trees on an acre is 100 percent or less and trees are well dispersed. The equation is thus potentially applicable to estimating tree crown cover in oak savannas. In that context, crown cover is defined as the proportion of an acre (or other unit area) covered by the vertical projection of tree crowns onto an acre. The equation assumes that tree crowns are circular.

To facilitate field application, we developed a crown cover chart following Gingrich's (1967) format for relating stand stocking to other stand variables. The method assumes that a given measure of relative stand density (or, in our case, relative crown cover) can be graphically expressed as a function of mean stand diameter, basal area per acre, and number of trees per acre. Expressing those relations in a chart requires that equation 1be extended to the stand (population) level by the following relation: 

SCC = 0.0175N + 0.0205SD + 0.0060SD2 (2) 

where SCC is stand crown cover as a percent of an acre, N is the number of trees per acre above a given minimum threshold diameter, SD is the sum of tree diameters at d.b.h., and SD2 is the sum of the squared diameters. Solving equation 2 for N = 1 thus yields crown cover estimates identical to equation 1.

The resulting chart (Fig. 1) and equation 2 produce comparable estimates of crown cover. Equation 2 produces more accurate estimates of crown cover because a given variance in tree diameters must be assumed to construct the chart, whereas in equation 2, this variance is inherent in the relation between åD and åD2 for a given sample of diameters (Gingrich 1967). However, comparisons of estimates across the range of diameter distributions likely to be encountered in oak savannas revealed that the two methods of estimation will be within +5 percent more than 95 percent of the time.


To use the crown cover chart, only two stand parameters need to be estimated from sample plots within a savanna: (1) basal area per acre, and (2) number of trees per acre. Variation in tree size and spatial distribution determine how many sample points are required for a given degree of accuracy in estimation. In most applications, at least ten well-distributed sample points will be required to obtain acceptable estimates.

The average basal area in square feet per acre can be determined by the point sampling method using an angle gauge or prism (Hays et al. 1981). This variable-radius plot sampling method can be used to estimate average basal area per acre of trees above some minimum threshold diameter (e.g., 4 inches d.b.h.) (Dilworth and Bell 1979, Hays 

et al. 1981, Husch et al. 1982, Kulow 1967, Roach and Gingrich 1968). In the eastern United States, the 10-factor (English unit) prism has been widely used (Kulow 1965, Rogers 1980). For a 10-factor prism or angle gauge, each tree counted at a sample point represents 10 square feet of basal area per acre. 

In addition to obtaining a tree count at each point-sample plot with a prism or angle-gauge, tree counts on fixed-radius plots also should be obtained. To do this, we recommend using 1/20-acre plots (26.4 feet in radius) centered on each point-sample plot. These tree counts then are used to estimate number of trees per acre.

Application of the chart is illustrated below. In this example, the number of trees sampled on ten basal area factor-10 plots total 38 (24 post oaks, 4 white oaks, 4 black oaks, 4 hickories, and 2 other species. Because "other" species were a minor component of this savanna, they were included in crown cover estimates even though the crown cover chart may not accurately estimate their crown areas. Because each tree represents 10 square feet of basal area and there are 10 sample points, the estimated basal area is 38 x 10/10 or 38 square feet per acre. The total tree count on the ten 1/20-acre fixed-radius plots (1/2-acre) is 24. Thus, the estimated number of trees per acre is 24/0.5 or 48.

Inventory of trees on ten point-sample plots and ten fixed-radius plots in a post oak (Quercus stellata Wangenh.) savanna restoration project, Mark Twain National Forest, Missouri.


Point-Sample Tree Count by Species

(10-factor prism)

Hickory Other Total 1/20-acre
Tree Count
24 4 4 4 2 38 24

With this information, the average crown cover for the savanna can be estimated from the crown cover chart (Fig. 1). This is done by locating 48 trees per acre on the horizontal axis of the upper chart, which pertains to stands averaging 3 to 14 inches d.b.h. From that point, the corresponding basal area value is located by moving vertically along the basal area scale until a value of 38 is reached. Note that this intersection of basal area and trees per acre occurs between the 50- and 60-percent crown cover curves, which are shown as diagonal lines. Crown cover thus must be interpolated, which in this case is approximately 55 percent. 

Potential applications of the chart include monitoring changes in savanna crown cover, determining needed reductions in crown cover, and defining the savanna "state." In restoring savannas that have grown into closed canopy stands, the chart can be used to estimate initial crown cover before restoration work is begun and again after crown cover has been reduced. In stands where crown cover initially exceeds 100 percent, individual tree crowns are likely to be smaller for a given d.b.h. than that represented by their potential crown areas. Consequently, when stand density is reduced by burning or other means, actual crown area may be temporarily smaller than that shown by the crown cover chart. 

Theoretically, the crowns of residual overstories should expand over time to the potential areas assumed by the chart. However, the crowns of some trees may die back from sudden exposure. Dieback is most likely to occur in trees of suppressed and intermediate crown classes, especially in stands drastically reduced in density in one cultural operation. On the other hand, there is evidence that crown areas of dominant oaks in closed stands do not differ from those in open-grown stands (McGill et al., in press). Therefore, the crown areas of large relic trees persisting from an earlier savanna may be accurately represented by the crown cover chart even when canopies are closed.

Although equation 2 will consistently yield more accurate estimates of crown cover than the chart, for many applications the chart may be more convenient. However, when estimates within +5 percent accuracy are not acceptable, the equation may be the preferred basis of estimation. Either method provides a potentially useful tool for describing, restoring, and managing oak savannas because it: (1) establishes a standard for describing crown cover, (2) establishes a standard for defining the range in crown cover that characterizes the savanna state, (3) provides reproducible and objective estimates of crown cover, and (4) when the chart is used, requires estimates of only two easily determined stand parameters: basal area per acre and number of trees per acre. The primary limitations in application will be in savannas where there is considerable overlap in tree crowns and where oaks and hickories do not predominate.

1 Respectively, USDA Forest Service, Rolla, MO (retired); USDA Forest Service, North Central Forest Experiment Station, Columbia, MO; and USDA Forest Service, Mark Twain National Forest, Rolla, MO.


Dilworth, J. R. and J. F. Bell. 1979. Variable probability sampling--variable plot and three-P. Oregon State University Book Store, Inc. Corvallis, Oregon. 130 p.

Gingrich, S. F. 1967. Measuring and evaluating stocking and stand density in upland hardwood forests in the Central States. Forest Science 13:38-30.

Haney, A. and S. I. Apfelbaum. 1990. Structure and dynamics of midwest oak savannas. In: J. S. Sweeney, ed., Management of dynamic ecosystems, pp. 19-30. North Central Section, The Wildlife Society. West Lafayette, Indiana.

Hays, R. L., C. Summers, and W. Seitz. 1981. Estimating wildlife habitat variables. USDI Fish and Wildlife Service Publication FWS/OBS-81/47. USDI Fish and Wildlife Service, Washington, DC. 111 p.

Husch, B., C. I. Miller, and T. W. Beers. 1982. Forest mensuration. Wiley and Sons. New York. 402 p.

Krajicek, J. E., K. A. Brinkman, and S. F. Gingrich. 1961. Crown competition--a measure of density. Forest Science 7:35-42.

Kulow, D. L. 1965. Elementary point-sampling. West Virginia University Agricultural Experiment Station Circular 116. Morgantown, West Virginia. 24 p.

McGill, D. W., R. Rogers, A. J. Martin, and P. S. Johnson. [in press.] Measuring stocking in northern red oak stands in Wisconsin. Northern Journal of Applied Forestry

Nuzzo, V. A. 1986. Extent and status of midwest oak savanna: pressettlement and 1985. Natural Areas Journal 6:6-36.

Roach, B. A. and S. F. Gingrich. 1968. Even-aged silviculture for upland central hardwoods. USDA Forest Service Agriculture Handbook 355. USDA Forest Service, Washington, DC. 39 p.

Rogers, R. 1980. Evaluating stocking in upland hardwood forests using metric measurements. USDA Forest Service Research Paper NC-187. USDA Forest Service, North Central Forest Experiment Station. St. Paul, Minnesota. 5 p.

Figure 1. Relation between tree crown cover and tree basal area, numbers, and average diameter in open-grown oak-hickory stands for stands ranging in mean diameter from 3 to 14 inches (upper chart) and stands ranging from 14 to 30 inches (lower chart). (The relation assumes that trees are oaks or hickories at maximum crown expansion for a given diameter. Stands at or above 100 percent crown cover represent closed-canopy forests. Percent crown cover is based on the maximum crown area equation of Krajicek and others (1961). Average tree diameter is the diameter of the tree of average basal area.)

Figure 1. Relation between tree crown cover and tree basal area, numbers, and average diameter in open-grown oak-hickory


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