3.2. Allometric curves vary between species of the Quercus genus and sites
We identified 17 studies in the literature in which the allometric As-DBH relationship was determined for oak trees (Table 1). Within these 17 studies, 14 relationships have the shape of a power law function (Fig. 4), while two others were linear and one exponential (Table 1). The As-DBH relationship was established for 13 different species from the Quercus genus (Fig. 4a - Table 1). Beside our study, four others determined the As-DBH relationship on Quercus petraea (Aranda et al., 2005; Schmidt, 2007; Jonard et al., 2011; Grossiord et al., 2014). Our study has, on average, seven times more samples than the average of previous studies (138 vs an average of 20). Our As-DBH relationship presents a R² 36% lower (0.65 vs an average of 0.88). The area covered by the sampling is almost a thousand time larger (904) than the mean area of all the other studies.
>>>>>>>>>>>Table 1. Inserted here<<<<<<<<<<<<<<
As topography does not significantly influence the As-DBH relationship in our data set, a wider range of topographical characteristics compared to other studies cannot be held responsible for the lower level of R² displayed by our data. Other potential reasons for the lower level of R² include a much larger sampling area, the higher number of sampled trees, a wider range of tree’s DBH, or errors coming from the methodology.
Within studies on Quercus petraea displaying power-law functions, Aranda et al., (2005), Schmidt (2007), and Grossiord et al., (2014) had DBH ranges of 14, 20 and 36 cm, respectively while our range of DBH covered 61 cm and our number of sampled trees was substantially higher. Also, our panel encompasses many trees with large DBH while both Schmidt (2007) and Grossiord et al., (2014) have no trees larger than 50 cm and 19 cm for Aranda et al., (2005). However, excluding the 85 trees larger than 50 cm in DBH from our data set lead to a substantially lower R² (0.28) of the As-DBH relationship.
Our data set presents sapwood depth values varying between 10 and 86 mm with a mean of 42 mm. If we consider a deviation of 1 mm due to the measurement of the sapwood depth using a tape scale, this one mm deviation would result in a deviation of 2.17% (14cm²) of the As of a tree with average DBH (53 cm). For our smallest tree (DBH = 29.3 cm), the deviation increases to 9% (8.5 cm²). However, the potential effect of a systematic measurement mistake remains far too weak for explaining the observed spread of the points around the allometric curve (Fig. 3). Also, dyeing experiments suggest that As is likely susceptible to be overestimated by the determination solely on heartwood coloration (Aparecido et al., 2019), despite other studies contradict this suggestion (e.g. Githiomi and Dougal, 2012). Another point that may introduce some deviation of the measurement from the As-DBH curve is that we assume the sapwood depth to be constant on all tree’s sides (Čermák et al., 2004; Tsuruta et al., 2010; Benson et al., 2019). The variability in radial sap-flux densities was found to be considerable in temperate broadleaved species (Gebauer et al., 2008). For boreal trees, sapwood depth was shown to be dependent on the species; some species displaying constant sapwood depth, while others are growing thicker in the North-East side (Quiñonez-Piñón and Valeo, 2017). For trembling aspen and white spruce, the influence of azimuthal direction on sapwood depth had a low impact (Merlin et al., 2020). In oak trees, the xylem vessel size was found to be larger on the northern side of Quercus suber, compared with the southern side (Barij et al., 2011), but the influence of azimuthal direction on sapwood depth remains unexplored to our knowledge.
The influence of the sampling area cannot be ignored. Most studies presented in Table 1 aim at quantifying stand transpiration, and their main objectives are not to determine the As-DBH allometric relationship which is commonly done only on few trees outside the field setup. In our experiment, we sampled within a catchment of 0.455 km², which is by far wider than all previous studies on oak trees. Therefore, our As-DBH curve is likely to be influenced by non-accounted micro-topographical and micro-climatic conditions, influencing the resources availability (i.e. water and radiation) and the evaporative demand. Further research on sapwood allometry of Quercus petraea could help untangling these effects.
>>>>>>>>>>>Fig. 4 Inserted here<<<<<<<<<<<<<<
Interestingly, parameters from Schmidt (2007) almost perfectly fit our data set so that one curve can fit both data sets (H0: two models, p-val = 0.16, Fig. 4b). In Jonard et al., (2001), authors found a linear relationship, probably because of the too low DBH range of the sample trees (mean DBH = 31 ± 7 cm SD). Nevertheless, their relationship seems to match our data in this low DBH range. Schmidt’s study was carried out in northern Bavaria, less than 300 km from Weierbach, and Jonard’s study was carried out in the Belgian Ardennes, at less than 100 km from Weierbach. Aranda’s study was held in Spain and Grossiord’s study took place in Tuscany. One explanation for the different curve parameters within the same species could therefore be the growing conditions effect on the trees. The total annual precipitation amount and mean annual temperature are comparable between these five studies on Quercus petraea, and therefore cannot be implicated (Table 2). Tree densities appeared to be substantially different (Table 2). Sites with lower tree densities display lower sapwood area for a given DBH. One possible explanation lies in the structural role of heartwood. In denser forests, tree community is supposed to resist more efficiently to storms and strong winds as the crown of each tree slow down the sway of the neighboring trees more efficiently. Therefore, trees growing in denser forest require a lower proportion of heartwood compare to sapwood as they need less individual mechanical stability. To our knowledge, no study investigated the effect of heartwood proportion on storm resistance in the Quercus genus.
>>>>>>>>>>>Table 2. Inserted here<<<<<<<<<<<<<<
Other potential explanation for the difference in As-DBH allometric relation of Quercus petraea is the total radiation received by each site and the associated potential evapotranspiration. While these data are not available in the original papers, we can expect Spanish and Tuscan sites to receive higher level of annual radiation and to be exposed to higher evaporative demands due to their southern locations compared with Luxembourgish, Belgian and German sites. Sapwood proportion is suspected to depend on the availability of light (Sellin, 1994; Thurner et al., 2018) and the water demand (Gebauer et al., 2008, Horna et al., 2011). Trees exposed to higher level of light and potential evapotranspiration require to maximize sapwood area for sustaining the higher evaporative demand and thus, preventing leaf overheating and dehydration (Aparecio et al., 2019). Larger scale investigations on the influence of radiation and evaporative demand on sapwood proportion would help confirming this result.