Trunk Diameter and Permeability Parameters in Trees


This research paper is focused on analyzing the correlation between the two fundamental parameters: the permeability and diameter parameters for the trees investigated. However, two trees species are picked for the analysis of this hypothesis: the California Sycamore and Southern Magnolia. The null hypothesis assumed that there was no correlation between the two parameters to be investigated while the alternative hypothesis proposed a strong correlation. In order to reject or fail to reject the null hypothesis, a p-value statistical analysis was performed with α at 0.05. Thus, values below α let to the automatic rejection of the null hypothesis, otherwise, the alternative was accepted. For California Sycamore, the p-values were 0.5372, 0.7891 for two permeability pair categories while Southern Magnolia had p-values of 0.3945 and 0.9270 for the same two pairs. These values were higher than the selected alpha value of 0.05 and thus the null hypothesis was assumed to be true. This hypothesis assumed that there was not profound correlation between the tree trunk diameter and permeability parameters.



According to Eamus (2006), a number of influential factors directly affect the biomass development of trees, such as that related to their trunk diameters. These factors include permeability (measured in terms of the ground area around a plant that is permeable to water) and the general development of the tree, that is, growth in biomass (measured in terms of tree height or truck diameter). However, herein, measurements on biomass development are measured in terms of the trunk diameter of the tree. The permeability parameter has a direct influence on the hydrology of the tree, and consequently, its diameter (growth in biomass). These influential parameters are especially prominent in angiosperms and coniferous species. In this research, two trees were identified for the analysis: California Sycamore and Southern Magnolia. Albeit various theoretical parameters (such as a trunk diameter, foliage canopy, Global Positioning System, and permeability) are involved in trunk diameter increase, the analysis in this research focused on the determination of a correlation between two parameters: Trunk diameter and permeability.

In order to gain an insight into the diameter parameter in such trees as Southern Magnolia, an understanding of its girth growth is paramount. For instance, the proportion of expansion of the diameter of the heartwood zones (the core of tree trunks) directly correlates with the increase of the girth due to additional sapwood. This correlation and the resultant width of the tree trunk are determined by the inclusion of sapwood during the continuous growth of the three. The extent and effectiveness of permeability within the surrounding ground directly avails water to the plant roots and to the underground water reservoirs (Hoadley 2000; England and Attiwill 2007).

Intuitively, this can be said to happen in an uncorrelated manner to the amount of precipitation received in the area at any given time. That is, even if an area received a high amount of precipitation, seepage through the ground can be limited by impermeable ground cover such as concrete floors. Nevertheless, this research seeks to understand whether this effect has a direct influence on the availability of water to the plant. In an alternative hypothesis, it is assumed that an increase in the overall percentage in permeability leads to the inhibited hydrology functionality within a tree. Afterwards, this directly affects biomass growth leading to reduced trunk diameters. A null hypothesis, of course, shall deny this. Rejection of the null hypothesis is only ascertained through statistical manipulations relating the computed P-values to the randomly selected alpha (α) value.

Secondly, the increase in trunk diameter, and thus, the average growth of the tree (sapwood), may further directly correlate with the availability of water irrespective of level of ground seepage. This correlation corresponds to the null hypothesis and thus may be affected profoundly the levels of precipitation received in an area. However, in this foregoing accord, it is still fundamental to realize that the average width of the sapwood development in tree trunks (trunk diameter) actually varies with tree species. This even includes three species under the same climate, affected by the same levels of precipitation, aridity and water availability.

Thirdly, the understanding of the influence of impermeable pavements near trees can be considered from a layman’s perspective. To be more precise, impermeable pavements and concrete always pose a challenge to urban tree forestation, especially in concrete jungle cities. For instance, the construction of porous pavements has alleviated this problem for urban foresters. Furthermore, research has indeed indicated that the more the ground surrounding a tree is permeable to water (permeability), the higher the biomass development in most tree species (when comparison is done amongst species) (the tree trunk diameter). This discrete growth effects are inhibited by the presence of impervious growth around that tree. As a result, in theory, the more impervious the surrounding area of a particular tree is, the smaller its diameter is, compared to a tree of similar species encompassed by a porous ground cover. However, it is important to remember that Morgenroth and Visser (2011) did not find any inhibition regarding tree growth (trunk diameter and height), when impervious pavements formed most of their surrounding area.

Nevertheless, speculations about the influence of the principle or parameter of permeability of the ground to water is very convoluted and complex. For example, without registering ground permeability to water (especially in areas with clay soils or an arid climate), trees have been known to survive (with robust trunk diameters) in areas where ground water levels are elevated. In such a scenario, the null hypothesis described in the foregoing discussions can be assumed to be true. This is especially significant in areas where there are impermeable rocks that form aquifers for holding underground water. It has been known that the presence of variations in ground water levels directly influences trunk diameters (biomass development). Although in the research by Braun et al. (2004) introduces other parameters, the correlation between ground permeability to tree diameter can inducted from this research. That is, the effect of the ground water on the growth of trees is obvious and may overshadow permeability. Furthermore, theoretically from this research, the height, diameter, and biomass of trees can be expected to be inversely related to the increase in the ground water depth.

In addition, can it be speculated that areas with higher percentages of water permeability (better ground seepage) result in tree diameter increase due to the ability to allow water to collect into underground water over physical structures such as aquifers. Whether such a phenomenon casts a profound influence on the correlations between the trunk diameter and the permeability of the ground to water currently remains an area of inconclusive research (evidenced by the currently available literature). Most literature, disappointingly, focus on parameters other than permeability and tree diameter that form the focus of this research.

Materials and Methods

Using the Focal Tree ID key, various trees types were identified to comply with the expected tree conditions (good and excellent). After this identification, the geographical location of each identified tree was determined with the help of the GPS location app in a smartphone. In order to collect the most accurate GPS location data, the smartphone was attached to the tree using a cello-tape, and left there for approximately four minutes. The collected data (longitudes and latitudes) was rounded off to 4 decimal places and recorded. Afterwards, the diameter of the same tree was measured by tightly wrapping a measuring tape around the tree trunk at a height of 54 inches above the ground. The obtained measurements were then used to compute the diameter of the tree. Since most of the trunks were not forked or profoundly bulging, no additional measurements were required.

After the above measurements, the canopy size of the tree was measured. This was done by estimating and recording the lengths of the shade cover in all four cardinal compass directions (North, East, South, and West). The length was calculated by taking the distance between the trunk and the edges of the tree shade in all these four directions. The results were then recorded in inches.

Finally, the ground permeability percentage was measured by comparing the impermeable portion (such as concrete pathways and building verandahs) to the permeable portion (such as grass and uncovered or bare ground). In order to estimate this proportionality, an area of 33 feet was measured around the tree with the truck as the center of the resultant circle. The determined circular area was then divided in terms of the water percentage it could seep through and the results led to its categorization under five classifications. These were: 0-5%, 6-35%, 36-65%, 66-95%, and 96-100% respectively.

In the end (using the results and statistical computations), graphs were drawn to compare the diameter of the tree and these categories are as shown in figures 1 in the results section below. Furthermore, a statistical analysis to determine the mean, p-value and standard deviations of the tree diameters from their permeability categories was also performed. The results were then tabulated as shown in table 1. However, the results shown in figures 1 and 2 and in tables 1 and 2 account for only two tree species: The California Sycamore and Southern Magnolia.


























Table 1. The statistical analysis of the trunk diameter of California Sycamore in different permeability categories. The mean, p-values and the standard deviations for each ground-water percentage permeability category were determined as recorded above.






















Table 2. The statistical analysis of the trunk diameter of Southern Magnolia in different permeability categories. The mean, p values and the standard deviations of each ground-water percentage permeability category were determined as recorded above.


From the results above, it is possible to conclude that the optimal ground-water permeability percentage category for both tree species was 6-35%. This category is characterized as optimal for both tree species because it produced the largest mean tree diameters compared to other 4 categories of permeability in both species. The reasons why a higher permeability (say 96%-100%) or a lower permeability percentage lead to lower trunk diameter averages is not immediately predictable or cannot be immediately interpreted from the graphs. As it has been indicated, one can speculate that the ground water permeability parameter has a direct correlation with the trunk diameter parameter and thus fail to reject the null hypothesis (Morgenroth and Visser 2011).

In order to effectively determine whether a correlation between the two parameters (trunk diameter and mass exists), the computation of the p-values for the 0-5% and 6-35% categories for was determined as 0.3945 for the Southern Magnolia species. Also, the p-values for higher permeability percentages 36-65% and 96-100% was 0.9270 for the same species. These p-values are actually higher than the alpha value (α=0.05), and thus, the null hypothesis that the trunk diameter parameter is not directly influenced by permeability fails to be rejected.

Moreover, this is supported by the p-values obtained from the first species in this analysis: The California Sycamore. In this species, the p-values for two paired categories (0-5% with 6-35% and 36-65% with 96-100%) was found to be 0.5372 and 0.7891 respectively. Once again, it this scenario the alpha value that depicted the level of significant data variations is exceeded and thus the null hypothesis is assumed to be true. Such as statistical analysis method gives credibility to a speculated conclusion based on the analysis of the availed raw data. From this analysis, we can comfortably conclude that truck diameter (or biomass growth) in trees does not directly depend on the levels of permeability of the surrounding ground. However, some theoretical research analyzed within the theory section points to a different clue.

As a result of these results, it can be speculated that a second significant parameter may have a profound influence on the trunk diameter other than the permeability parameter investigated. A suggested parameter is the level of water availability in ground water aquifers that overshadows the influence of the ground permeability parameter. Nevertheless, the anomaly can still be attributed to statistical manipulations or computational errors (Manning et al. 2015). From table 1, it can be seen that the same permeability category (66-95%) registered a standard deviation of 21.49046 (the highest in all the permeability categories). This simply means that the data may not be evenly distributed and it may be a statistical mistake to assume a normal predictable pattern for that category alone (since the data obtained maybe highly skewed and may reveal a non-collinear correlation).

Moreover, the statistics above offer a predictable stance on the adaptability of both tree species under varied environmental conditions (Artiola et al. 2004). That is, irrespective of ground permeability, the diameter of tree trunks maybe increasing due to adaptability (for instance, towards arid environments). The fact that California Sycamore registered mostly lower trunk diameters compared to the Southern Magnolia (especially in the first four permeability percentage categories) may have been caused by ingrained differences between the species. This is further supported by the fact that the null hypothesis was not rejected. For example, different tree species have differing growth rates, abilities to integrate and develop biomass for growth in diameter and susceptibility to diseases. In fact, the latter is the main reason why the trees in this research were categorized as having either a good or excellent condition. It was a prerequisite condition before the other measurements (such as GPS and trunk diameter were conducted).


To sum it up, this research paper and experiment are focused on the results of two fundamental parameters in selected trees: the tree trunk diameter and ground-water permeability. The core intent was to determine the correlations between the two parameters. In order to do this in the best scientific way possible, statistical p-values were used to express extreme data changes, and thus, facilitates decision making. As a result of this analysis the null hypothesis was assumed to be true while the alternative hypothesis simultaneously rejected. All the p-values obtained (0.5372, 0.7891, 0.3945 and 0.9270) were higher than the alpha value of 0.05. This was a perfect phenomenon to assume that the null hypothesis was indeed true.

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