Corresponding author: J. T. Van Stan II, Department of Geology and Geography, Georgia Southern University, Statesboro, GA 30640, USA. (firstname.lastname@example.org)
 To improve the water budgeting of forested catchments and inform relevant hydrologic theory regarding water cycling within forests, the scientific community has been seeking simple, inexpensive, direct methods for determining rain water storage on in situ tree canopies. This paper evaluates an installation arrangement and routine for one such method: mechanical displacement sensors placed on a tree's trunk to directly monitor compression under canopy water loading from rainfall. The evaluated installation routine aligns mechanical displacement sensors along orthogonal axes passing through the mechanical center of the trunk to reduce wind-induced noise. The experimental attainment of neutral bending axes for a subject hardwood and softwood tree suggests the routine is precise and approximates the trunk's mechanical center well regardless of differences in cellular axial stiffness between heart and sapwood. When installed in this precise sensor arrangement, bending tests of different loading directions produced a consistent signal ratio between sensor pairs of approximately −1 (1 unit compression/1 unit elongation), allowing the identification and removal of bending strains from the raw strain signals to isolate the compression component attributable to canopy water storage loads. The same experiments performed on sensors just 5 cm off the trunk's computed mechanical center were unable to produce neutral bending axes or consistent signal ratios during bending from variable loading directions. Results from the method evaluation were translated into a data processing technique that is then applied to strain data collected through two sample rain events (one each for the hardwood and softwood trees). The processed strain data showed a clear synchronicity between rainfall and canopy loading, as well as periods of maximized canopy water loading (canopy storage capacity). Our results indicate that the evaluated arrangement and installation procedure for mechanical displacement sensors may be able to provide scientists with simple, direct canopy water storage estimates at high temporal resolution and sensitivity.
 During storm events, tree canopies are capable of removing substantial amounts of water from wooded ecosystems through the interception, storage, and evaporation of precipitation from their bark and foliar surfaces [Herwitz, 1985; Friesen et al., 2008; Pereira et al., 2009; Carlyle-Moses and Gash, 2011]. The magnitude of this interception loss is highly dependent on species canopy morphology, precipitation type, meteorological conditions, and season [Schmidt, 1991; Crockford and Richardson, 2000; Keim et al., 2006; Klingaman et al., 2007; Muzylo et al., 2009]. Much of our knowledge regarding these effects on canopy interception processes and loss estimates relies on indirect monitoring methods and physically based models, which can produce negative estimates, overestimates and underestimates, as well as contrasting interpretations of interception processes [Price and Carlyle-Moses, 2003; Keim, 2004; Carlyle-Moses, 2004; Levia et al., 2011]. Although a variety of direct methods for monitoring canopy water storage and interception have been developed and adapted for implementation across select forest types [Hancock and Crowther, 1979; Calder and Wright, 1986; Bouten et al., 1991; Teklahaimanot and Jarvis, 1991; Huang et al., 2005], they have not been readily employed by most researchers, partly due to cost, safety considerations, or unfamiliarity with a given method. An exception has been the common use of eddy covariance to quantify evaporative flux from forests [Baldocchi and Ryu, 2011]. Eddy covariance, however, measures the integrated soil-plant-atmosphere signal, making it difficult to quantify different interception-related components (e.g., canopy water storage). Since canopy evaporation rates strongly depend on the amount of water stored within the canopy [Rutter et al., 1971; Levia et al., 2011], the absence of widely adapted, simple, inexpensive, nonenvironmentally disruptive, direct methods for monitoring canopy water storage within the natural forest setting during precipitation events has hampered quantitative investigation of canopy interception processes [Levia et al., 2011].
 To advance knowledge of canopy water storage within and among storm events, Friesen et al.  developed a method that directly monitors canopy water storage of individual trees during precipitation events using a set of mechanical displacement sensors (collectively termed “interceptometers”). Interceptometers monitor trunk compression and relaxation during storm events, largely attributing the mechanical displacement of the trunk to the loading or unloading of water stored on, or evaporated from, the tree canopy [Friesen et al., 2008]. However, without precise sensor positioning, these interception-related strain phenomena can be obscured by significant wind throw and off-center loading signals [Friesen et al., 2008; Van Stan et al., 2011a]. Using the LaserBark™ automated tree measurement system [Van Stan et al., 2010], Van Stan et al. [2011a] developed a theoretical installation procedure to enhance interceptometer sensor placement and, thereby, remove off-center loading and wind-related distortions. This technical note builds upon our previous theoretical advance by evaluating and validating how well the Van Stan et al. [2011a] method (1) characterizes a trunk's mechanical center and (2) therefore allows the isolation and removal of wind-induced bending phenomena for both non-monocot angiosperm (hardwood) and gymnosperm (softwood) tree species to remove or reduce wind-related bending signals during rainfall. We conclude by processing two example storm event compression signals to demonstrate the effectiveness of the method in reducing noise from wind-induced bending.
 It is important to note that the terms “hardwood” and “softwood” throughout the study do not reference wood hardness or density. Rather, the terms are used to distinguish between non-monocot angiosperms (which have been shown to have negligibly different elastic moduli between heartwood and sapwood) and gymnosperms (which have been found to contain differential axial stiffnesses between the heartwood and sapwood at the cellular level) [Gillette, 1914; Forest Products Laboratory (FPL), 1999; Berthier et al., 2001; Passialis and Adamopoulus, 2002; Grabner et al., 2005].
2. Study Areas
 The evaluation trees were instrumented at two study sites of differing climate and species composition. The hardwood tree, American beech (Fagus grandifolia Ehrh.), was located in the Fair Hill Natural Resource Management Area (NRMA) satellite site of the Christina River Basin Critical Zone Observatory (CRB-CZO). The Fair Hill NRMA CRB-CZO satellite site is a 12 ha catchment situated within a larger reserve in the tristate border area of Delaware, Maryland, and Pennsylvania, just above the Chesapeake Bay (39°42′N, 75°51′W). Mean annual 30 year precipitation amount is approximately 1200 mm, with the majority of precipitation falling as rainfall during frontal storm events from September through May [Maryland (MD) State Climatologist Office, 2012]. Summer precipitation (June–August) is dominated by convective rainfall events [MD State Climatologist Office, 2012]. Winter is the driest season and produces snowfall depths averaging 450 mm yr−1, which typically do not result in persistent snowpack [MD State Climatologist Office, 2012]. Beech codominates the temperate deciduous broadleaved canopy with yellow poplar (Liriodendron tulipifera L.) at Fair Hill NRMA, where beech represents nearly 50% of all identified trees. The typical beech canopy at Fair Hill NRMA casts deep shade due to a relatively high canopy closure (>75%), leaf area index (>4.5), and canopy depth (>60% of total tree height) in comparison to other represented tree species [Van Stan et al., 2011b]. Average diameter at breast height (DBH) is 30.8 cm (±17 cm standard deviation) for beech. Thus, the instrumented beech tree (at 21 cm DBH) is slightly smaller but representative of the average tree size within the study plot.
 The softwood tree, western hemlock (Tsuga heterophylla Sarg.), is a 28 cm DBH canopy tree representative of the experimental forest plot within the Cedar River Municipal Watershed. The Cedar River Municipal Watershed is approximately 50 km east of Seattle, Wash. (47°21′N, 121°38′W). The study site is located at an elevation of 630–640 m, on a gentle (<10°) slope with southwest aspect [Lutz et al., 2012]. The forest is located in the Tsuga heterophylla zone [Franklin and Dyrness, 1988] and receives a mix of winter rain and snow. Mean monthly maximum and minimum temperatures are, respectively, 20.3°C and 8.5°C in July and 1.9°C and −3.4°C in January. Average annual precipitation is 2420 mm (1971–2000 climate normals; derived from PRISM (Parameter-elevation Regressions on Independent Slopes Model), Daly et al. ). Annual snow accumulation varies between 0 and 2000 mm, depending on winter conditions. The forest was approximately 66 years old in 2011 and was established following clear-cut logging. Composition is primarily western hemlock and Douglas-fir (Pseudotsuga menziesii Franco).
3.1. Mechanical Displacement Sensor Installation
 High-resolution trunk cross sections for each of the study trees were collected in the center of the installation area using the LaserBark automated tree measurement system [Van Stan et al., 2010]. Then, two orthogonal axes, which pass through the centroid of the trunk cross section, were derived using the operations described in equations (1)-(4) of Van Stan et al. [2011a]. These equations rely on the assumption that the elastic modulus (E) of live heartwood and sapwood are statistically indistinct from each other (as reported by Gillette , FPL , Berthier et al. , and Passialis and Adamopoulus ). This may be an oversimplification—for the softwood tree, especially—as research has shown differences in chemical compounds related to cellular-level axial stiffness between the heartwood and sapwood of softwood tree species [Grabner et al., 2005]. However, the assumption of constant E was applied to both the softwood and hardwood study trees to allow for the evaluation of whether the assumption is an oversimplification for either.
 Interceptometer sensors were precisely installed as in-line pairs, positioned directly over the axes [Van Stan et al., 2011a]. Two pairs of sensors positioned on either side of two orthogonal axes which intersect at the computed centroid are necessary to evaluate how the “true” mechanical center compares to the centroid computed via the Van Stan et al. [2011a] method. However, since only one pair of oppositely positioned interceptometer sensors along a single axis through the centroid is theoretically enough to resolve bending and compression processes [Gere and Timoshenko, 2004], one of the sensor pairs was moved 5 cm off their axis to evaluate the effects of misalignment with the cross-section centroid after the requisite data were collected for the centroid-to-mechanical center comparison (Figure 1). The experimental misalignment was only done for the beech tree, as the more uniform E between hardwoods' heartwood and sapwood reported by previous studies should reduce error from off-axis sensor placement compared to the more mechanically complex softwoods [Gillette, 1914; FPL, 1999; Berthier et al., 2001; Passialis and Adamopoulus, 2002; Grabner et al., 2005]. Thus, it is assumed that if sensor misalignment can affect measurement signals for the beech tree, it would most certainly (and more markedly) affect measurement signals collected from softwoods.
 Individual mechanical displacement sensors at both sites consisted of linear motion potentiometers (per Friesen et al. ). At the Fair Hill CRB-CZO satellite site, the potentiometers were interfaced with a custom data logger from Technical University Delft (24-bit (20 effective bits) 15-channel data logger per Friesen et al. ) capable of near-simultaneous measurement via track and hold circuits. Each sensor at the Cedar River Municipal Watershed was connected to a Campbell Scientific CR10X 12-channel data logger, which sampled in succession with a delay of 2.6 ms per successive reading. Linear resolution for each potentiometer sensor was 4.4 µm mV−1 and 1.5 µm mV−1 at Fair Hill CRB-CZO and Cedar River Municipal Watershed, respectively.
3.2. Bending Tests
 Bending tests were performed to assess how identifiable bending behavior was within the raw signal, evaluate the installation accuracy about the Van Stan et al. [2011a] computed centroid, and assess the proximity of this computed centroid to the trees' true mechanical center. Rope was secured to the trunk above the interceptometers (at about 6 m high), where a sideways load was applied to induce bending (Figure 2). To ensure that the bending signal contained no compression component, the sideways loading was not applied at an angle, but along a constant elevation by running the rope through a friction hitch connected to a neighboring tree (Figure 2). Loads were applied by tensioning the rope at the base of the neighboring tree using a 4:1 pulley system connected to a hanging strain gauge that recorded the load (kg; Figure 2). Bending tests were done for four different directions (at least 60° from each other), with one bending direction aligned with one of the sensor sets (and, therefore perpendicular to the other sensor set). It is important to note that because this arrangement will also bend the neighboring tree, the loads exerted on the subject trees were likely less than the values reported by the hanging strain gauge. Since one objective of this study was to identify and remove bending signals, accurate accounting of load magnitude was not as important as capturing a significant range of sideways loading. Significant loading ranges in each direction were accomplished simply by bending the tree from its resting point to the maximum loading attainable via rope strain (approximately 100 kg). This loading procedure produced a range of bending strain signals equal to and exceeding (up to approximately 50 mV for the beech and 300 mV for the hemlock) those measured by natural winds (which rarely exceeded 25 mV at the Fair Hill CRB-CZO site and 50 mV at the Cedar River Municipal Watershed site).
4. Evaluation Results for the Van Stan et al. [2011a] Interceptometer Installation Method
4.1. Evaluation of Accurate Positioning About the Mechanical Center
 To assess both the accurate positioning of mechanical displacement sensors about the Van Stan et al. [2011a] computed centroid and whether this computed centroid appropriately represents the tree's mechanical center, bending loads were applied perpendicular to the installation axes. If the interceptometer sensors are positioned correctly about the tree's mechanical center, the axis between them should act as a neutral bending axis during this specific loading scenario. Under the conditions of a neutral bending axis, one should observe no strain (or deviation from the sensor noise) along the sensor pair perpendicular to the bending direction despite a strong response from the sensor pair in-line with the bending [Gere and Timoshenko, 2004]. In Figure 3a, the beech sensor pairs perpendicular to the bending direction (sensors 0° and 180°) measured negligible-to-no strain despite a strong response from the sensor pair in-line with the bending direction (sensors 90° and 270°). Thus, the axis between the 0° and 180° sensors acted as a neutral bending axis likely passing within very close proximity to (if not directly crossing through) the mechanical center of the beech tree (Figure 3a). The hemlock 0° and 180° sensor pair also showed little response to bending applied perpendicularly across their axis despite a strong signal from the 90° and 270° sensors (Figure 3b). Just as observed for the hardwood species, the axis between the 0° and 180° sensors acted as a neutral bending axis through the tree's mechanical center. Although similar bending loads were supplied to these similarly sized trees, the softwood species' 90° and 270° sensor set produced much larger strain responses than the hardwood species (Figures 3a and 3b). Despite the greater strain signal along the bent axis, the hemlock neutral axis displayed little more deviation from the instrument noise than observed for the beech (Figures 3a and 3b).
 When the beech interceptometer sensors were misaligned by 5 cm along the 90°–270° axis, a neutral bending signal was unattainable under bending directions perpendicular to that installation axis (Figure 3c). Voltages measured from the sensors along the misaligned axis also fluctuated unevenly with the loading trends (shown by the properly aligned 0° and 180° sensors), increasing over time to a maximum voltage between the 4 and 8 min period, where, alternatively, the 0° and 180° sensors show bending loads lowering to a steady consistent signal (Figure 3c). While the 0° and 180° sensors generally mirrored each other in both trend and magnitude, the 90° and 270° sensors were less well behaved, producing similar trends but different magnitude deviations from the instrument noise (Figure 3c).
4.2. Identification and Isolation of Bending Strains
 With sensors aligned precisely per installation protocol [Van Stan et al., 2011a], bending due to wind may be identified regardless of wind direction. Three simulated wind directions were chosen to evaluate the effect of direction on a correctly installed sensor pair for the hardwood (Figures 4a and 4b) and softwood (Figures 4c and 4d) and on a sensor pair installed slightly off-axis for the hardwood (Figure 5). Regardless of bending direction, the precisely aligned sensor pair installed on the beech and hemlock produced consistent signal ratios of approximately 1 unit compression: 1 unit of elongation (1/−1; Figures 4a and 4c). All data collected from the sensor pair during the bending tests confirmed this approximate −1 signal ratio under pure bending strain (Figures 4b and 4d). Also important to note for both species, the signal ratio under bending remains relatively constant despite fluctuations in the bending force (Figures 4a–4d). In point of fact, the beech's standard deviation from mean voltage ratio under differing bending directions was only ±0.03, yet the standard deviation in the bending voltages themselves was 2 orders of magnitude greater (approximately ±3.1 mV). For the hemlock, under the applied bending directions, the standard deviation from mean voltage ratio was again more than an order of magnitude smaller than the deviation of the bending voltages themselves (±0.20 mV versus ±79.2 mV, respectively). Data for the softwood species showed greater variability across bending directions than was observed for the hardwood species (Figures 4a–4d).
 The interceptometer sensor pair installed 5 cm off the LaserBark-derived axis on the beech trunk, however, did not produce consistent voltage ratios of −1 (Figure 5a). Rather, the ratio of the opposing sensors ranged from about −1.5 to −0.75 across the three bending directions, varying linearly with simulated wind direction (Figure 5a). The sensor pair installed 5 cm off-alignment also exhibited much greater variability within the signal ratio than was observed for the properly aligned pair (Figures 4a and 5a), resulting in greater scatter in the sensor comparison plot (Figure 5b). Although the misaligned sensor comparison scatterplot clearly shows a statistically significant linear trend, each bending direction can be seen clustered together above or below the line of best fit (Figure 5b). Average ratio of the three simulated wind directions provided for evaluating these misaligned sensors is, surprisingly, near −1, as shown by both the central tendency of the ratios in the bending plot (Figure 5a) and the slope of the regression line in the comparison scatterplot (Figure 5b).
4.3. Processing of Storm Strain Signals to Remove Bending Voltages
 During most precipitation conditions, measured strains are likely the composite result of superimposed bending and compression strains. With a consistent voltage ratio between a pair of precisely aligned sensors, regardless of the direction of the bending force (i.e., wind or off-center loading), it may be possible to separate a storm's composite strain signal into its bending (εb) and compression strains (εc). If we assume that the trunk is an orthotropic, linearly elastic material [FPL, 1999; Lyons et al., 2002] and, therefore, εc is equally expressed throughout the bole cross section, we can compute εc by algebraically solving the following set of equations:
where ε1 and ε2 and εb1 and εb2 are the composite and bending strain signals from sensor 1 and sensor 2, respectively; ϕ is the ratio of the composite strain signals for a sensor pair aligned about the trunk's center of mass experimentally attained during pure bending tests; and εc has been previously defined as the component of the composite strain signal attributable to compression. When solved for εc, the solution provides the following formula:
 Equation (4) has been applied to an example rain event for the beech and hemlock (Figures 6 and 7, respectively), to isolate the compression phenomena. Because bending forces from winds can produce strain measurements many orders of magnitude greater than that of compression forces from intercepted rainwater, the composite strain signal from the example rainfall event over the beech canopy (Figure 6, top) primarily shows the interceptometer sensors mirroring each other in response to bending phenomena. Thus, Figure 6 (top) illustrates no discernible relationship between the composite strain signal and rainfall barring increased bending or off-center loading behavior that further obscures the compression component. Yet, once the signal is processed using equation (4) and composited to the rainfall monitoring interval (5 min), a clear synchronicity emerged between rainfall and the computed εc voltages (Figure 6, bottom). During all periods of significant rainfall, εc increases as the canopy intercepts rain droplets, and then diminishes as the canopy sheds the intercepted rainfall (presumably as throughfall, stemflow, or evaporative loss; Figure 6, bottom). The compression strain response seemed to react quicker to rainfall earlier in the event (during the wet-up phase) than throughout the later portion of the storm event (Figure 6, bottom). High variability in the strain signal was still apparent throughout the monitored rain event (Figure 6, bottom).
 The raw storm event strain signal from the hemlock tree in Figure 7 (top) also contains discernible bending strains throughout the rain event, yet the significant rain amounts (96.5 mm total rainfall) create a clear compression signal even before processing. In the raw storm signal panel, individual sensor readings still diverge under wind-related bending despite these strong compression voltages from heavy rainfall (Figure 7, top). After processing via equation (4), the compression component becomes clearer, rising with the cumulative rainfall until reaching a steady canopy weight (Figure 7, bottom). After maintaining what appears to be the hemlock tree's canopy water storage capacity, the compression component then subsides back to zero (Figure 7, bottom). Note that the steady day-and-a-half maximum canopy water storage trend seems to fluctuate slightly as the storm event progresses and intrastorm meteorological conditions vary (Figure 7, bottom).
 The experimental attainment of a neutral bending axis and the consistent ratio of compression to elongation (−1) under bending stresses of differing direction along the LaserBark-derived installation axes indicate that the Van Stan et al. [2011a] computed centroid approximates the true mechanical center relatively well for the subject hardwood and softwood trees (Figures 3 and 4). When sensors were installed only 5 cm off the indicated installation axis on the beech tree, it resulted in voltage ratios that varied with bending direction (Figure 5) and prevented the attainment of a neutral bending axis under orthogonal bending loads (Figure 3c) [Gere and Timoshenko, 2004]. When the sensors are misaligned, they may be capturing just a portion of the bending signature from various directions, resulting in variable voltage ratios [Gere and Timoshenko, 2004]. For elastic deformation of orthotropic tree trunks, it is no surprise that the signal ratio between the misaligned sensors produces a linear trend with bending direction (Figure 5a). What was surprising was that the signal ratios between the misaligned sensor sets appeared to vary in response to load, resulting in greater scatter across and within bending directions (Figures 3c, 5a, and 5b). This load response may be a result of an “impure” bend (accidentally applying some compression strains during the bending tests), the canopy's sensitivity to low winds, an expression of differing directional stiffnesses (although past studies on other species have shown this to be quite small [Launay et al., 2005; Koponen et al., 2005]), or an alteration to overhead canopy compressive loads during bending or may simply be illustrative of another pitfall of misaligned interceptometer sensors. As the axial stiffness is more variable across the sapwood and heartwood for softwoods, the effects of misalignment may result in even greater error [Grabner et al., 2005].
 Despite reported differences in cellular axial stiffness between softwoods and hardwoods, the assumption of constant modulus of elasticity across the entire cross section for the determination of mass center and sensor alignment worked well for the trees examined in this study (Figures 3, 4, and 6). The softwood tree, hemlock, produced higher bending strains and signal noise in response to bending tests than did the hardwood tree, beech (Figures 3 and 4). Perhaps this was, in part, an expression of these stiffness differences [Gillette, 1914; FPL, 1999; Berthier et al., 2001; Passialis and Adamopoulus, 2002; Grabner et al., 2005]: tree-related wood and canopy characteristics, different linear resolutions between potentiometers, and/or site conditions.
 The computed compression component of the strain signal collected during rainfall produced a clear trend and synchronicity with the storm hyetograph (Figure 6), indicating that εc over the short time period of a single rain event is directly resultant from intercepted rainwater stored on canopy surfaces [Friesen et al., 2008]. The hemlock's example storm event signal, once processed, shows the potential for Friesen et al.  interceptometers installed via the Van Stan et al. [2011a] procedure to capture direct estimates and temporal variations in canopy water storage and its maximum capacity (Figure 7), which may advance interception loss modeling efforts [Keim and Skaugset, 2004; Pypker et al., 2005; Levia et al., 2011]. Slight delays in response to rainfall peaks may be a product of slightly differing rainfall patterns between the precipitation monitoring area and interception monitoring study site, or a result of the canopy's compression loading response being quicker than the rainfall gauges. Sudden changes in the εc signal could be due to wind-related deformations apart from the pure bending phenomenon: like torsion along the trunk, sudden canopy uplift and push-down, or the ephemeral reorganization of canopy biomass into greater/lessened axial loads. However, sudden changes in εc may also indicate water storage-related phenomena, such as moments of wind-induced throughfall shedding, or enhanced droplet entrainment and stemflow production under directional wind-driven rainfall [Levia and Frost, 2006; Nanko et al., 2006; Van Stan et al., 2011b]. Perhaps, future studies could pair εc observations with simultaneous throughfall and stemflow measurements to identify conditions conducive to these water storage-related phenomena. Alterations in canopy weight due to changes in root water uptake may also influence εc, yet its influence is expected to be low, as transpiration (and, therefore, sapflow) during rainfall is typically low as a result of the surrounding air being saturated [Whitehead, 1998].
 The results of our study show that the Van Stan et al. [2011a] method for determining sensor placement of Friesen et al.  interceptometers can indicate precise installation locations orthogonally about the mechanical center of the selected softwood and hardwood trees. Our results also demonstrate the importance of the installation arrangement and precision for the isolation and removal of the wind-related bending phenomenon from raw strain data through providing data processing methodology and example rain events. This evaluation validates an installation procedure and arrangement that can be practically and quickly applied in any forested watershed. In doing so, this study builds upon previous literature calling for clear standardized methodology for the direct monitoring of canopy water storage within the natural environment via inexpensive and environmentally nondisruptive means so that watershed managers may improve interception loss estimates and the hydrology community can improve our understanding of water cycling in forests.
 The authors thank the National Science Foundation for their support of this work (EAR-0724971 and CBET-0931780), the Pennsylvania State University CZO International Student Travel program, and the Terrestrial Environmental Observatories initiative for supporting the development of interceptometers. The authors are also grateful to the staff at Fair Hill NRMA and the Cedar River Municipal Watershed for granting access to the sites.