Measurement of three-dimensional structure of plants with a simple device and estimation of light capture of individual leaves



1. A simple device called a ‘pocometer’ (POlar COordinate METER) was developed to measure three-dimensional structure of plants. It consists of a tape-measure to measure distance and two protractors to measure zenith angle and azimuth angle.

2. The pocometer can determine locations of points within a few metres distance with a resolution of less than 1cm. Location of any point on a plant can be measured in 10 to 30s depending on the ease of pulling the tape measure to the point of interest.

3. A system to use data obtained with the pocometer to calculate plant light capture was developed. The degree of shading at any point on a plant is estimated by checking obstruction by other plant parts of the view toward the sky at that point.

4. Photon flux density (PFD) on leaf surfaces was estimated for Aucuba japonica, a broad-leaved evergreen shrub, using the above system. The estimated PFDs for individual leaves of a plant corresponded to the sensor-measured PFDs with correlation coefficients of 0·67 to 0·92.


Above-ground structures of plants determine their light acquisition capabilities and the outcomes of competition for light (Lovell & Lovell 1985; Küppers 1989; Tremmel & Bazzaz 1993). Many researchers have analysed plant architectures to understand their functional consequences. Structural features studied include dimensional aspects of individual trees (Kohyama 1987; King 1990), density distribution patterns of light-capturing areas (Koike 1989; Tremmel & Bazzaz 1993) and various geometric traits, including leaf orientation (Nobel 1980; Clearwater & Gould 1995), the arrangement of leaves on a shoot (Niklas 1988; Takenaka 1994a) and branching patterns (Honda & Fisher 1978; Sakai 1990).

There have been few measurements of the three-dimensional (3-D) configuration of leaves and stems of an entire plant. Most of those studies dealt with plants with a simple monoaxial structure (e.g. Chazdon 1985; Rauscher et al. 1990). One of the exceptions is the work of Ackerly & Bazzaz (1995), who measured the location and orientation of all leaves and stem segments of tree seedlings with ramified structures growing under the canopy of tropical rain forest. The 3-D plant structure was reconstructed on a computer for the evaluation of light-capture efficiency. These authors succeeded in demonstrating that the seedlings have structures that are efficient in utilizing light from gaps in the forest canopy above.

As in Ackerly & Bazzaz (1995), a compass, level, protractor and ruler have been the main tools for field measurements of plant geometry (Norman & Campbell 1989). For plants with a complex structure, such measurements are often time consuming and laborious (Bacci et al. 1993). In addition, errors can accumulate when the relative locations of successive plant parts are repeatedly measured (Ackerly & Bazzaz 1995).

There are several other devices that can be used for plant structure measurement. A laser-scanning instrument (Walklate 1989) and an electronic instrument (Bacci et al. 1993), both specialized for the measurement of leaf orientation and inclination, have been developed and the latter is commercially available. Laser ranger theodolites are being used to map tree crown positions around towers in rain forests using geographical co-ordinates (A. Nobre, personal communication; N. Adachi, personal communication), although published reports of the results achieved with such devices do not appear to be available. Koike (1985) described a method which could be used to reconstruct two-dimensional profiles of foliage density from many photographs taken from various positions in a canopy. These techniques are each convenient for their own purposes, but they are of limited value for determination of the 3-D configuration of leaves and stems of a plant.

Lang (1973) devised an elaborate apparatus based on high-precision potentiometers to define the position of any point. This apparatus directly determines 3-D distributions of plant parts but it has never been commercially available. Spatial tracking systems developed as an interface of virtual reality environment and using electromagnetic fields are another option for measurements of plant structure. Such systems also determine 3-D co-ordinates directly, but require electricity and are not convenient to carry around in the field.

In this paper, a new device for measurement of 3-D structure of plants is introduced. This device gives direct definition of 3-D co-ordinates, is easy to carry around in the field and does not require electricity. A system to estimate plant light capture with geometric data obtained with the device is also described. The reliability of the light-capture estimation was tested against direct measurements with a photon sensor.

Materials and methods


The ‘pocometer’ (POlar COordinate METER) consists of two protractors and an arm with a tape-measure (Fig. 1). Distance to a point of interest is measured with the tape-measure and the protractors are used to measure the azimuth and zenith angles. The protractors are made of 2-mm-thick stainless steel with scales at 1° intervals. The device weighs c. 2·5kg.

Figure 1.

. Schematic diagram of the pocometer, a device for measuring components of polar co-ordinates. Top: view from above; bottom: side view. A, arm; B, base; Ha, hand for the azimuth; Hz, hand for the zenith angle; M, tape measure; O, axis connecting the arm and the protractor for the zenith angle; Pa, protractor for the azimuth; Pz, protractor for the zenith angle; S, screws for level adjustment; T, tripod; X, the point to be measured. Arcs with arrowheads on both ends indicate rotation.

The pocometer is set on a sturdy flat base fixed on a tripod. The tape-measure is connected to an arm (A in Fig. 1) which is attached to the zenith-angle protractor (Pz). The arm rotates freely around this protractor's centre and the protractor itself rotates around a vertical axis that goes through the centre of the azimuth-angle protractor (Pa) at a right angle. The latter protractor should be horizontally adjusted with the screws (S).

When the tape-measure is pulled to the point of interest (X), the hand (Hz) on the arm indicates on protractor Pz the zenith angle of that point. At the same time, another hand (Ha), fixed to protractor Pz, indicates the azimuth on protractor Pa. The distance to the point is read on the tape-measure.

The azimuth reading can be calibrated later with the reading on Pa for true south (or any other known direction). For later analysis, it is convenient to convert the polar co-ordinates to Cartesian co-ordinates with the origin at the base of the plant and the x-axis due south. Once converted in this way, data sets for the same plant measured from different locations can be merged.

The closer the pocometer is to the sample plant, the wider the angles vary, reducing the relative importance of reading errors. Moreover, the same degree of angular reading error matters less for nearer points: for example, an error of 0·1° in azimuth and zenith angle corresponds to 5·2mm for a point 3m away from the pocomter, while it corresponds to only 0·9mm for a point 0·5m away.

To test the accuracy of the pocometer, the locations of the two ends of a 15-cm-long ruler, set in various orientations at 1, 2 or 3m away from the pocometer, were measured. The calculated distances between the two ends of the ruler were close to the true value of 15cm at each of the three distances from the pocometer (Table 1). Standard deviations of the measured distance increased with the further away the ruler was from the pocometer, but remained <1·0cm even at 3m.

Table 1.  . Length of a 15-cm ruler calculated as the distance between the two ends as measured with a pocometer Thumbnail image of


The structures of saplings of five tree and shrub species were measured with the pocometer (Table 2). Aucuba japonica Thunb., a broad-leaved evergreen shrub common on the forest floor of Japanese warm temperate forests, was measured on the campus of Tsukuba University at 36°N 140°E in central Japan. Other deciduous broad-leaved trees, Magnolia obovata Thunb., Quercus crispula Blume, Juglans mandshurica Maxim. var cordiformis (Makino) Kitamura and Pterocarya rhoifolia Sieb. et Zucc., were measured at Hitsujigaoka Experimental Forest at 43°N 141°E on Hokkaido, in northern Japan.

Table 2.  . Sample plants for the measurement of three-dimensional structures. For each sample, the variables indicated with + were measured Thumbnail image of

A standard leaf shape (see below for definition) was determined for sampled leaves for each species. For A. japonica and M. obovata, the lengths of all leaves were measured with a ruler so that comparisons could be made with the calculated distances between the apical and basal ends of leaves measured with the pocometer.


A computation system was developed for the estimation of plant light capture considering mutual shading among plant parts. In this system, a plant is reconstructed on a computer as a group of flat leaves and cylindrical stem segments connected at branching and bending points (Fig. 2).

Figure 2.

. Schematic diagram of a plant reconstructed on a computer using geometric data. Placement of a leaf is determined by: B, the location of the basal end of the leaf; Llf, length of the leaf; Wlf, width of the leaf; v, vector from the basal to the distal end of the leaf; α, rotation angle of the leaf around v. A stem segment is treated as a cylinder, placement of which is determined by: C1 and C2, centres of the two ends; Wst, the diameter. Lower left figure shows an example of a standard leaf shape as a polygon defined with a series of vertices (P0, P1, ...). Sample points (S1, S2 ...) to calculate light capture are set on the standard leaf shape and placed in a 3-D space with the leaf.

The placements of leaves and stem segments are determined by parameters indicated in Fig. 2. Each leaf is treated as a transformation of a ‘standard leaf shape’ (Fig. 2, lower left). If there is significant variation in the leaf shape of the target species, two or more standard shapes should be defined as required. The shape is described as a polygon, or a group of polygons for a compound leaf. The standard leaf shape is scaled to the length and width of each leaf of a plant and placed in a 3-D space. Leaf bending and curvature are not considered but if neglecting these factors causes a serious error, then the leaf should be divided into several parts each of which can be treated as a flat area.

Photon flux density (PFD) is calculated for one or more points distributed over each leaf (see below for the calculation procedure). The points, hereafter called ‘sample points’, are originally set on the standard leaf shape (S1, S2, ... in Fig. 2) and placed in a 3-D space with the leaf.

Leaf light capture can be calculated by summing the PFD of sample points on the leaf multiplied by the area each sample point represents. When only one sample point is set on a leaf, the point represents the whole leaf area. When there is more than one point, portions of the leaf area are divided equally among the points. Summation of the light capture of all leaves gives the plant light capture.

PFD at a sample point is calculated as follows:

1. The sky hemisphere is divided into ‘cells’ in a way similar to that used by Anderson (1964), but all the cells are of the identical solid angle. In the present system the hemisphere consists of 200 cells but it can be changed as required. The density of the photon flux coming from each cell is determined by referring to the modelled or observed light distribution over the sky. Both diffuse light and the solar beam can be assigned to these cells.

2. For plants overtopped by canopies of other plants, canopy openness is determined for individual cells using a hemispherical photograph taken from the top of the plant. PFD for light from each cell of the sky is reduced by (1·0–canopy openness).

3. Obstruction by other plant parts of the ‘looking-up-at-the-sky’ view from the sample point is assessed for each cell by 3-D analytical geometry calculations. If obstructed, PFD of light from the cell is reduced by the light transmittance of the obstructing plant part. Reflection of light at the surface of plant parts is not considered in the present system.

4. Cosine-corrected PFDs of light from all cells are summed to give the PFD at the sample point.


The geometry of young A. japonica plants was measured to calculate light capture. Four sample plants growing under a canopy of evergreen pine, Pinus densiflora Sieb. et Zucc., on the campus of Tsukuba University, were selected for measurement. For each sample plant, the locations of apical and basal ends of leaves were measured with the pocometer. The length and width of each leaf was measured with a ruler. Rotation angles of leaves around the midrib were measured with a level and a protractor.

PFD measurement with a photon sensor was carried out on a cloudy day. Sample points were set a quarter, a half and three-quarters of the way along the midrib of each leaf. PFDs at the sample points were measured with a photon sensor (LI-190S, LiCor, Lincoln, NE, USA), with the sensor surface kept parallel to the plane of the leaf.

As a reference, PFD just above the plant was measured a few seconds before and after the measurement at each sample point and averaged. These reference PFDs were measured with the sensor facing the zenith.

At the top of each sample plant, hemispherical photographs of the forest canopy were taken with a fish-eye lens to determine the canopy openness. Uniform skylight distribution was assumed to estimate the light capture following the procedure described above.



On average it took about 1·5h for two or three workers to measure the locations of apical and basal ends of 100 leaves on a sapling (Table 2). The projected images of the saplings reconstructed on a computer adequately reproduced the structures of the sample plants (Fig. 3).

Figure 3.

. Projected images of above-ground structure of saplings of trees and shrubs reconstructed on a computer using geometric data obtained with the pocometer. (a), Magnolia obovata; (b) Aucuba japonica; (c) Quercus crispula; (d) Juglans mandshurica var. cordiformis; (e) Pterocarya rhoifolia. A scale is shown for each drawing (vertical line). Horizontal bars at the bottom of each drawing represent the ground surface. Rotation angles of leaves around the midrib are assumed to be zero except for A. japonica. For Q. crispula, for which only the locations of the apices of shoots were measured, the zenith angle of the leaf midribs is assumed to be 120°. For other samples, inclination and azimuthal angles of leaves were calculated from the location of the bases and apical tips of the leaves.

The leaf lengths calculated from the pocometer measurements corresponded well with those measured with a ruler, with correlation coefficients between them as large as 0·96 (62 leaves, P<0·001) and 0·97 (112 leaves, P<0·001) for A. japonica and M. obovata, respectively.


The height of the A. japonica plants ranged from 45 to 80cm, each with 14 to 38 leaves (Fig. 4). Each plant had 2 to 3 years’ cohorts of leaves.

Figure 4.

. Projected images of four sample plants of Acuba japonica used for the light-capture estimation. Numbers of leaves were 34, 14, 18 and 23 for (a), (b), (c) and (d), respectively.

Estimated relative PFDs (PFD at sample points divided by the reference PFD above the plant) for individual leaves were significantly correlated with the measured PFDs with a mean correlation coefficient of 0·83 (Fig. 5). The variation of the relative PFD within a plant was larger for a plant with more leaves, suggesting more severe mutual shading among leaves occurred in such plants. The most shaded leaves of the plant with 34 leaves received only c. 20% of light incident to the least shaded leaves (Fig. 5a).

Figure 5.

. PFD (photon flux density) on leaf surfaces relative to that on a horizonital surface above a sample plant. Values estimated from the geometric data of the plants and openness of the forest canopy above are plotted against those obtained from photon sensor measurements. Note that the relative PFD can be larger than 1·0 when the directionality of openings of forest canopies is biased from the zenith. Each solid circle represents the mean of relative PFDs at three sample points on a leaf. Each scattergram represents one sample plant. Scattergrams (a), (b), (c) and (d) correspond to the sample plants (a), (b), (c) and (d) in Fig. 4. Correlation coefficients are shown for each plant with the significance levels: **<1%; ***<0·1%. Solid line represents 1:1 relationship.


The pocometer is efficient and sufficiently accurate to be used for the measurement of the 3-D structure of plants in the field. In addition to being portable, the pocometer is particularly useful for measuring plant parts in the middle of a leaf cluster which are not clearly visible from outside. The location of any point can be measured as long as the tape-measure can reach. The pocometer has a great advantage when it is applied to plants with multi-layered structures for which analysis of visual images is of limited use.

There are, however, some constraints on using the pocometer: for example, it cannot be used with tall trees and measurements on plants with small, densely packed leaves that the tape-measure cannot easily penetrate are difficult. The pocometer is best suited to measure plants of a few metres in dimension and with less than several hundreds of points to be measured.

Pocometer measurements can be applied not only for measurements of within-plant structure but also for measurements of community structure. The spatial distribution pattern of light affects the structural development of plants in a community and vice versa (Ford & Sorrensen 1992; Sorrensen-Cothern, Ford & Sprugel 1993; Takenaka 1994b). Spatial relationships among plant individuals critically affects their interaction via competition for light (Pacala & Deutschman 1995). Continuous non-destructive measurement of the structures of individual plants in a community will contribute much to the analysis of dynamic processes of plant interaction.

Light-capture capacity is often assessed by the plant's projected area (e.g. Niklas 1988; Ackerly & Bazzaz 1995; Sprugel, Brooks & Hinckley 1996). Projected area is a useful index but it does not reveal the distribution pattern of light within a plant. The ‘looking-up-at-the-sky’ algorithm used in the method described here enables the estimation of among-shoot, among-leaf or even within-leaf variation of light capture. Information on light capture by individual leaves can be used for various purposes. For example, cost–benefit analysis of the production rate and longevity of leaves requires knowledge of the photosynthetic environment of leaves of different ages. In addition to the estimation of the present light environment, estimation of hypothetical light environments by addition or elimination of leaves on a computer would contribute much to the optimization analysis of the birth and death of leaves.

The 3-D structures of plants are easy to see but not so easy to measure. Because geometric structure has profound importance in plants’ lives in nature, much greater effort should be made to investigate it quantitatively: We consider the pocometer to be a substantial contribution toward this end.


We thank H. Nagashima, K. Noguchi, K. Kimura, N. Kurachi,Y. Matsuura, T. Kohyama and K. Sato for their assistance with the fieldwork. N. Kachi is acknowledged for suggestive discussion. A. Raschi, A. Nobre and N. Adachi are acknowledged for providing the information about instruments for the measurement of plant structure. We thank the Hokkaido Research Center of Forestry and Forest Products Research Institute for allowing our field measurements in its facilities.


  1. Present address: Faculty of Intercultural Communication, Ryukoku University, Seta, Ohtsu 520-21, Japan.