Measurement of Canopy Geometry Characteristics ... - IEEE Xplore

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 43, NO. 10, OCTOBER 2005

Measurement of Canopy Geometry Characteristics Using LiDAR Laser Altimetry: A Feasibility Study Caroline J. Houldcroft, Claire L. Campbell, Ian J. Davenport, Member, IEEE, Robert J. Gurney, and Nick Holden

Abstract—Airborne scanning laser altimetry offers the potential for extracting high-resolution vegetation structure characteristics for monitoring and modeling the land surface. A unique dataset is used to study the sensitivity of laser interception profiles and laser-derived leaf area index (LAI) to assumptions about the surface structure and the measurement process. To simulate laser interception, one- and three-dimensional (3-D) vegetation structure models have been developed for maize and sunflower crops. Over sunflowers, a simple regression technique has been developed to extract laser-derived LAI, which accounts for measurement and model biases. Over maize, a 3-D structure/interception model that accounts for the effects of the laser inclination angle and detection threshold has enabled the fraction of radiation reaching the ground surface to be modelled to within 0.5% of the observed fraction. Good agreement was found between modelled and measured profiles of laser interception with a vertical resolution of 10 cm. Index Terms—Canopy height, leaf area index (LAI), remote sensing, vegetation mapping.

I. INTRODUCTION A. Canopy Geometry Characteristics

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HE geometric shape of individual plants, and hence arrangement of leaves in space, results from the interaction between environmental factors and species-dependent morphology. Many plant species, however, appear symmetrical along the axial line [1], and their foliage assumes a regular predictable shape. This symmetry allows the foliage to be described by geometrical shapes such as cylinders, spheres, cones, or regular ellipses. In a canopy, composed of many plants, describing the distribution of foliage elements is very complex. In the same way that mathematical approximations have been used to describe plant structure, continuous statistical distributions based upon the properties of regular geometric shapes have been developed to represent canopy structure. Such simplifications have been found to be suitable for describing regular dense canopies such as those formed by agricultural

Manuscript received March 2, 2005; revised June 16, 2005. This work was supported in part by the Natural Environment Research Council under Grants F60/G6/12/03, NER/S/A/2000/03544, and GT04/1999/TS/0218, and and in part by the Environment Agency of England and Wales. C. Houldcroft is with the Climate Land Surface Systems Interaction Centre, University of Wales Swansea, Swansea SA2 8PP, U.K. (e-mail: [email protected]). C. L. Campbell is with the Centre for Ecology and Hydrology, Edinburgh EH26 0QB, U.K. I. J. Davenport and R. J. Gurney are with the Natural Environment Research Council, Environmental Systems Science Centre, University of Reading, Reading RG6 6AL, U.K. N. Holden is with the Technology Science Group, U.K. Environment Agency, Bath BA2 9ES, U.K. Digital Object Identifier 10.1109/TGRS.2005.856639

crops. Two parameters that are commonly used by such descriptions are leaf area index (LAI) and leaf angle distribution. These parameters are commonly incorporated into one-dimensional (1-D) models that assume horizontal homogeneity within the canopy. However, measurement methods to provide LAI over extensive areas, and with sufficient sampling to capture the inherent spatial variability, are currently lacking. LAI is a dimensionless quantity, defined as the single-sided, green leaf area per unit area of ground surface. By removing leaves from the canopy, LAI can be measured directly using a calibrated light-box or by inference based upon previously derived allometric relations (e.g., between dry weight and leaf area). Such direct techniques rely upon appropriate sampling such that local inhomogeneities in the canopy do not introduce bias into the average LAI. Sampling methods include leaf-litter collection, suited to deciduous forest canopies that lose their foliage during autumn leaf-fall [2], and the dispersed-individual-plant (DIP) method, suited to relatively homogeneous sites where the plants are large [1]. In the DIP method, the plants chosen to be representative of the canopy may also be used to obtain quantitative information on the vertical distribution of leaf area, leaf orientation, node height, stem diameters, etc. The standard equipment used for these determinations has previously included rulers and clinometers. New technologies in three-dimensional (3-D) digitizing devices can now acquire the same information with far greater accuracy. Digital images of plants are constructed by recording a few key structural positions of foliage elements within the electromagnetic field of the instrument. These can subsequently be manipulated to estimate canopy properties such as light partitioning among neighboring plants [3]. Warren-Wilson [4] has described an in situ method for indirect sensing of canopy structure, which involves passing long needles, called point quadrats, vertically through the canopy to determine a contact frequency. This measurement is a function of the area of foliage projected onto a horizontal plane and will be constant for a horizontally homogeneous canopy. The contact frequency obtained using horizontally inclined quadrats is a measure of the area of foliage projected onto a vertical plane. For flat, infinitely thin leaves, the projected area will vary between the following limits: 1) when the azimuth angle of the probe is perpendicular to that of the normal to the leaf surface; 2) when the azimuth angle of the probe is parallel to that of the normal to the leaf surface. It is possible to derive the total leaf area per unit volume (and hence LAI) and a mean foliage inclination angle within height bins of 1 cm, if quadrat measurements are made at these two extremes of inclination angle [4].

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HOULDCROFT et al.: MEASUREMENT OF CANOPY GEOMETRY CHARACTERISTICS

An extension of the inclined point quadrat method is to use simple measurements of sunlight transmission beneath the canopy to estimate the probability of zero interception (i.e., a gap in the canopy). For a dense population of leaves, with a random spatial distribution, the canopy may be approximated as an isotropic turbid medium, and Beer’s Law used to model the integral relationship between light transmission and LAI [5]. This type of single-scattering model is suitable for predicting the probability that a beam of direct radiation is intercepted independent and horizontally homogeas it passes through neous canopy layers. The probability function is analogous to a Poisson distribution, and for a beam of radiation traveling through canopy layer , the gap in direction probability is given by (1) is the thickness of layer is the cumulative LAI where is the extinction coefficient, and and in layer are the zenith and azimuth angles, respectively, of the radiation [1]. The extinction coefficient takes the form

(2) is the leaf normal distribution function, is where is the inclination angle the azimuth angle of the leaf normal, is the cosine of the angle of the leaf normal, and between two unit vectors corresponding to the directions of the is equivalent to the leaf normal and the radiation [1]. average projection of a unit area of foliage in direction , i.e., and an effective the cosine of the angle between direction may be used estimate the “effecleaf normal. Thus, tive” leaf area available to intercept incoming direct-beam radiation. Assuming foliage is oriented in all directions with equal and . Integrating probability, then between the top of the canopy and the soil surface, (1) becomes LAI

(3)

An alternative extinction coefficient, the -function, has also been used in models of radiation transfer in vegetation canopies. It is the average projected area of canopy elements when projected onto a horizontal plane, and is related to the -function by [6] (4) The relationship between the gap probability and canopy structure represented by (3) may be mathematically inverted to obtain LAI from light transmission measurements, as applied in Section IV. If the extinction coefficient is not known a priori, . In then this method has two unknowns, LAI and , the gap probability must order to obtain both LAI and be measured over a range of solar elevation angles, and the resulting system of equations solved numerically [7]. Errors may arise when the real vegetation canopy does not conform to the model assumptions of horizontal homogeneity and uni-

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form leaf azimuth distribution. Canopy inhomogeneities may also influence the ability to obtain a representative sample of transmission measurements beneath the canopy. This method is inappropriate for retrieving canopy structure over large areas due to measurement requirements in space and time. Nevertheless, ceptometers using these techniques are widely used in field work where LAI is required. B. Laser Altimetry Airborne laser altimetry systems direct a laser pulse toward a target from an aerial platform and, by studying the returned light, may be used to retrieve information about the objects that have interacted with the laser pulse. Such systems have in common a differential global positioning system (DGPS) to establish the spatial location of the aircraft, and an inertial navigation system (INS) to establish the orientation of the aircraft, and hence the vector of the laser. There is some variation in the technique of measurement of the returned laser light between systems. Some altimetry systems record the complete intensity profile with time. By combining the aircraft location and orientation information, inferences can be made about atmospheric absorption along the path of the beam, and therefore about the atmospheric content. This approach is also used for vegetation canopies. Depending on the laser spot size and the leaf size of the incident vegetation, a single laser pulse incident on a vegetation structure from above will tend to yield a greater return from layers corresponding to higher vegetation density. Thus, the return waveform from a single pulse may be used to infer information about the vegetation target, such as the biomass vertical profile [8]. Systems which record the complete return profile in this way are uncommon, and because of the processing required and the vast amount of data generated, tend to acquire points infrequently, typically in a straight line directly below the aircraft, generating 1-D lines through the target site. Technical limitations also mean that they are more often used to examine tall vegetation such as trees. The more common technique for processing the returned laser pulse in laser altimetry systems is to record the time between the pulse emission, and the first significant return to the sensor. The return level trigger is typically an arbitrary threshold that prevents false returns due to light scattering into the instrument and internal electronic noise. Additionally, measurements are often made of the intensity of the first return, and the time and intensity of the last significant return. The positional and orientation information provided by the GPS and INS system are used to convert the first return time into a spatial location from which the laser pulse has been returned. Because of the relatively low amount of processing and storage required for this means of interpreting returns, a far greater number of pulses can be processed per unit time. This type of system usually incorporates an oscillating mirror to scan the laser perpendicular to the flight line, and build up a two-dimensional (2-D) swathe of points. Such a swathe will typically be between 200 and 500 m wide, and consist of around one point per square meter, depending on the particular instrument and user-adjustable settings. Each point indicates the height above sea level where a significant proportion of the energy contained in a laser pulse is

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reflected and depends upon surface type and geometry. By acquiring high-resolution topography of the underlying ground, in this case by laser altimetry of the site before vegetation growth, we can determine the return height above ground. If the return is from significantly above the ground level then this tells us that there is some vegetation at that point. By directing a number of pulses at an area, we obtain a range of return heights above ground. Without a ground height reference, by using the variation in return height, we are able to estimate the canopy height [9]. By incorporating the ground height we can estimate the vegetation density with height. This density is not a linear function of the number of returns intercepted at a given height, since the number of beams reaching the lower layers will usually be a fraction of the beams intercepted by the upper layer. Additionally, the different geometry of different plants may mean that a layer with few horizontal large leaves may return as many incident pulses as a layer with far more biomass structured as thin vertical leaves. In order to understand how we interpret the return distribution, we need to develop models of the target plant structure, and the interaction between the laser pulse and the plant structure. C. Objectives and Rationale The objective of this work is to test if scanning laser altimetry may provide nondestructive, repeatable, accurate, highly spatially resolved LAI and other canopy characteristics over large areas. Model relationships between canopy structure parameters and the interception of a beam of radiation have led to the development of methods analogous to ceptometry for indirect determination of canopy structure. In this study, such a dataset has been collected using the operational Light Detection And Ranging (LiDAR) system, used by the Environment Agency of England and Wales. Ideally these data could be used to derive structural parameters such as LAI to initialize land surface models. An area-average vertical profile of laser interception has been obtained from first return LiDAR data. This has been compared with forward model results over a well characterized, uniform maize canopy. Comparisons have been made for 1-D and 3-D structure representations and under varying assumptions regarding the laser interception process. Results obtained for the homogeneous surface provide a reference for the potential of the technique. Comparisons with analyses made using the same system over a sunflower crop with a more heterogeneous geometry and canopy density allowed an assessment to be made of the value of the technique for obtaining reliable canopy geometry information over heterogeneous land surfaces. A 1-D model was designed to incorporate field measurements of plant characteristics and enable these data to be scaled to represent the canopy. The purpose of this model was to describe the canopy structure in a simplified form. An equivalent 3-D model was also developed; this model was used to provide a more realistic, complex representation of the canopy, in order to assess the sensitivity of the technique to horizontal variability in canopy geometry. The interception of laser radiation incident from the measuring LiDAR system was modelled as a function of the model canopy extinction coefficient and LAI in each canopy layer. A

Beer’s Law attenuation model was used to predict the laser-return profile through the canopy, and the results compared with the observed profile. The fraction of the total returns reflected by the ground surface was used in an inverted form of Beer’s Law, given later in (10), to estimate LAI. The LiDAR-derived LAI was then compared with measurements of LAI derived from destructive measurements. Further assessment of the biases inherent in the LiDAR retrieval of LAI was implemented using the modelled LiDAR interception in the model canopy, within which the canopy characteristics were known explicitly. II. MEASUREMENTS The study site was located at Sonning Farm, a few kilometers northeast of Reading, Berkshire, U.K. (476 539 Northing, 176 416 Easting, 51.48 N, 0.9 W). Ground measurements have been made within an area approximately 150 200 m planted with sunflowers during 2001 and with maize during 2002. These crops differed in their planting specifications and structure. For both crops there was some variation in the heights of mature plants and the distribution of weeds across the study site. Properties of the vegetation structure were measured at locations that had previously been geolocated using a backpack DGPS system. Measurements of plant height, leaf-insertion height, and leaf inclination and azimuth at the insertion height, were made in situ using a ruler, clinometer and a compass. Leaf azimuth was taken along the line of the main rib of the leaf, relative to north. Plants were also removed from the field in order to make destructive measurements that provided information on the vertical distribution of leaf area and leaf widths. Leaf area was determined using a light-box technique. For the maize canopy, LAI has also been derived indirectly from light transmission measurements. The fractional interception of photosynthetically active radiation (PAR) was determined by making measurements above and below the canopy using a ceptometer (Decagon Devices, Inc., Pullman, WA). LAI was predicted using a modified form of (3) suggested by the manufacturer, which accounts for effects of direct and diffuse radiation and assuming the canopy has a uniform . Fig. 1 shows results obtained distribution of foliage over one day when cloud cover was low and the incident PAR radiation was dominated by direct radiation. The average LAI , which was predicted using this technique was within 10% of the value obtained from destructive characterization. This suggests that the uniform structure approximation is a reasonable representation of the true maize canopy structure. Four laser altimetry LiDAR acquisition flights were made of the experimental test field on Sonning Farm. These flights took place on June 25, 2001 (three swathes), August 23, 2001 (one swathe), July 14, 2002 (four swathes), September 23, 2002 (four swathes). The June 25, 2001 data were corrected for an error in the aircraft roll angle measurement, by a correcting plane shift based on unchanging areas identified in the two 2001 datasets. Examples of the LiDAR data are shown in the rendered images in Fig. 2. A fifth acquisition was made on April 3, 2002, when the surface was devoid of vegetation, to establish the ground topography. The returns from the four acquisitions made over vegetation were adjusted to represent heights above ground level,


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The observed vertical profile of laser interception has been 20 m and derived using point data taken from an area 20 from which the underlying topography had been removed. By summing the returns in 0.1 m vertical height bins, interception in each layer has been expressed as a percentage of the total returns. When LiDAR observations were acquired as multiple separate swaths of measurements, a small flat-roofed building at the experimental site was used as a stable reference to check for consistency between swaths, because errors due to instrumental drift may sometimes affect LiDAR measurements collected over an extended period of time [11]. III. LIDAR INTERCEPTION MODEL Fig. 1. Results of using the beam transmission method for estimating LAI of the maize canopy.

(a) 2001 Topography

(b) 2002 Topography

Fig. 2. (a) LiDAR first return heights in August 2001 over the sunflower crop, shown in shaded relief. (b) LiDAR first return heights in September 2001 over the maize crop, shown in shaded relief. In each case, bare soil elevations have been subtracted from the return heights above the crop.

by subtracting the height of the (planimetrically) closest point found in the April 3 data. The detection of a return signal by the LiDAR system is known to be a function of an intensity threshold set by the manufacturer. Each laser pulse will have a finite width and differ from the return signal according to the scattering processes occurring at the surface. Electronic processing of a return signal gives rise to a digital waveform representing the sum of returns from all the reflecting surfaces within the footprint of the laser [10]. The LiDAR data used in this study were first return data. m has been A vertical height error for laser returns of estimated from the observed spread of height data around an interpolated trend surface that was assumed to be the mean ground level. This analysis used LiDAR data acquired in a single swath over bare soil on April 3, 2002 . The height error derived in this way represents a combination of the laser timing error and errors due to the DGPS [10]. Height data retrieved over the vegetation have been adjusted using the same interpolated ground surface. The uncertainty in the LiDAR measurements returned from the vegetation may be somewhat greater, because the laser will be reflected from foliage at different heights. For simplicity, it has been assumed that errors in both the ground and vegetation m and that these errors are measurements are of the order independent. Then by combination, the height error in adjusted m. laser returns is expected to be within

The simulation of the LiDAR laser interception was carried out to assess the accuracy of the method of deriving LAI from the LiDAR return profile. The model canopy provides a known leaf area index, and the path of the LiDAR beam may be traced through the model canopy architecture, thus simulating the reflection of the incident laser beam. Some prior knowledge of the laser radiation field has been used to support a number of simplifying model assumptions. These included the use of a single laser azimuth angle and narrow range of laser inclination angles. For each foliage element the model calculates area projected onto planes that are orthogonal to beams of radiation inclined at 0 , 10 , and 20 from vertical. These angles were chosen to represent the expected range in the LiDAR data from an acquisition in which the OPTECH system was configured in a scanning mode with a sweep angle of 20 . The true incidence angles for laser returns from the 20 20 m area were also estimated knowing the exact location of the area within the swath, and the simultaneous location of the plane on the north–south transect. However, this does not account for variation in the incidence angle due to the attitude of the aircraft. For nadir laser radiation, the projection of foliage area in the direction of the laser beam depends solely upon the inclination angle of the normal to the foliage element. The projection at incidence angles other than nadir, however, depends upon the inclination and azimuth angles of the radiation and the foliage element. To calculate the “effective” area available for intercepting laser radiation in the model, each foliage element has been defined as the cross-product of two vectors representing the two perpendicular lengths of the rectangular element. These vectors, shown in Fig. 3 and assigned labels OA and OB, correspond to the length perpendicular to the leaf midrib within the same grid cell and the length along the leaf midrib, respectively. The result of multiplying the two vectors is a third vector, with magnitude equal to the “true” element area. The model accounts for differences between projected area for foliage elements with positive and negative inclination angles relative to the plant stem, by assigning an inclination angle greater than 90 to elements with negative inclination angles. With respect to laser interception, the same result would be obtained by assuming equivalence between an element with a negative inclination angle and an element with a positive inclination at the opposite azimuth [12]. All LiDAR data were acquired along a north–south flight-line. Thus, the across-track sampling, which is a function of the scanning laser, will be oriented approximately along an east–west transect. Therefore, the azimuth angles of the inclined

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Return heights have been linearly interpolated over a height range of 0.1 m to account for height errors in laser returns. By summing the returns in each 0.1 m vertical height bin, interception in each layer has been expressed as a percentage of the total returns. This led to the ground return being spread out over two to 0 m, and 0 to 0.1 m); their sum was used height levels ( as input to (3) to estimate LAI. A. One-Dimensional Canopy and LiDAR Interception Models Fig. 3. Perpendicular vectors OA and OB used to model the areas of foliage elements in 3-D canopy models. is the zenith angle from vertical, and ' is the azimuth angle from north of the foliage element.

laser beams will be either approximately 90 or approximately 270 . In order to simplify the model, the vector corresponding to laser radiation has been assigned a single laser azimuth angle of 90 . This assumes that the plants are symmetric, and the same results would be obtained for an azimuth of 270 . Thus, the unit vector for the laser beam is given by

(5) is the inclination angle from vertical of the laser and . In reality, the effects of row structure, solar orbit and other environmental factors such as prevailing wind direction may contribute to small systematic differences between the distributions of foliage when the canopy is viewed from the two different directions. Finally, the effective area of foliage elements available for interception is equal to the true area weighted by the cosine of the angle between the laser unit vector and the normal to the foliage element. This has been calculated using the dot-product, given by where

(6) where is the vector normal to the foliage element, with magnitude equal to the element area. A threshold return intensity must be achieved in order to record a return; the purpose of this threshold is to avoid false returns due to light scattering or electronic noise. The intensity threshold cannot be stated as a simple fraction of the total radiation incident on the target because of the variation in detector altitude, target reflectance and atmospheric conditions. In view of this uncertainty, the model does not explicitly account for the proportions of transmitted and reflected radiation and multiple scattering by canopy elements. Specular returns therefore, are modelled purely as a function of the relative amount of projected foliage area within the laser footprint in any one 0.1 m height bin. As described above, the detection of a first return signal is a function of an intensity threshold. Therefore, the model assumes that layers are independent, i.e., “effective” foliage area in one layer that is below the window threshold and allows a beam to be transmitted has no influence upon the intercepting capacity of the layer below. When the “effective” foliage area sampled in any one layer exceeds the window threshold, a return height has been recorded.

Within each height bin leaf area was assumed to be distributed uniformly, and receive equal illumination from a single infinite diameter laser beam. The Beer’s Law approach may thus be used to model the attenuation of direct beam radiation passing through each homogeneous layer according to (7) is the radiation incident upon the upper boundary where is an extinction coefficient, and is the depth of layer , or path length for layer . Equation (7) assumes that leaves in the model do not rest on or shade other leaves immediately below them. When laser radiation is incident upon the canopy equal to 0 (nadir), at an inclination angle from vertical then the “effective” area of foliage available for interception is the area projected onto a horizontal plane. Hence, the extinction coefficient (in units of per meter) may be expressed as (8) and the path length (in units of meters) given by (9) where is the cumulative projected leaf area per unit area of with depth 0.1 m. For the ground surface, in vertical layer is simply equal to the path length. Scatnadir laser beam, tering elements are assumed to reflect 100% of the radiation incident upon them. B. Three-Dimensional Canopy and LiDAR Interception Models The modelled 3-D canopy array was comprised of grid cells, which were each 0.03 0.03 0.1 m, 100 100 where is the number of vertical levels, each with a thickness of 0.1 m, beginning at a height of 0.1 m below the ground surface (see the Appendix for details of the maize and sunflower canopy models). To estimate the typical nadir footprint of the laser beam, the altitude of the aircraft and the field of view of the laser are required. The instantaneous field of view of the laser is 0.3 mrad, and assuming a typical altitude of 700 m during data acquisition, a nadir footprint will have a diameter approximately 0.21 m (346 cm ). Incident laser beams have been simulated as extending over a square window measuring 324 cm , as 6 6 grid boxes with both width and length dimensions equal to 0.03 m. Thus, the error associated with this approximation to the beam diameter is approximately 6% with a nadir beam inclination


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reaches the ground surface. The 1-D model for laser radiation incident at nadir, predicts a gap fraction of 15%. This fraction may be used to estimate the canopy LAI from the inverted form of (3) LAI

Fig. 4. Comparison between vertical profiles of laser interception predicted by the 1-D model for maize and derived directly from laser returns.

angle. The square window has been used to sample the effective projected area from grid boxes in each horizontal layer in the model canopy along the path of the incident laser beam. C. Implementation of the 3-D LiDAR Interception Models 1) Maize: The canopy array contained 30 vertical levels, reaching a maximum height of 2.9 m above the ground surface. The extinction coefficient estimated from the ratio of total projected leaf area to true leaf area for the simulated canopy, varied between 0.58 and 0.55 for beam inclination angles from nadir to 20 off nadir. 2) Sunflower: The canopy array contained 18 vertical levels, up to a maximum of 1.7 m. The extinction coefficient varied between 0.88 and 0.84, decreasing as the beam inclination angle increased from nadir to 20 off vertical. In simulating the interception of the laser beam by the canopy, the model beam began at the top layer of the bottom left corner of the canopy grid. After a return was recorded, the beam was moved to an adjacent, but nonoverlapping area of the canopy grid. This continued until interception in all areas of the grid was simulated. This method provided approximately 250 returns in the 3 3 m area, which was similar to the number of returns received from 400 m areas in the test field. IV. VALIDATING THE LiDAR INTERCEPTION MODEL It is necessary to demonstrate that the model accurately simulates the observed profile of LiDAR returns in the canopy. The modelled LiDAR interception is determined by the projected leaf area density structure, as is the true interception. Correlation between the shapes of modelled and observed profiles suggests that the interception model simulates the LiDAR interception and detection process reasonably well. A. Results for Maize 1) One-Dimensional Model: The vertical profile of laser interception predicted using the 1-D approach has been compared with LiDAR returns and is shown in Fig. 4. The return signal retrieved from the top of the canopy is shifted to a lower level compared with that predicted by the model. A possible explanation for this may be that the finite width of the laser beam, and hence averaging area, results in differences between profiles when the real canopy is not horizontally homogeneous. The most significant difference between the profiles is the fractional percentage of radiation that

(10)

may be estimated from the ratio Assuming that of projected to total leaf area for the whole canopy, then an LAI of 3.27 is predicted using (10). This is within 10% of the true LAI derived from measured leaf areas used to initialize the model. This result shows that using the extinction model to deindependent canopy layers and a rive attenuation through single extinction function for the entire canopy depth, that the Beer’s Law model can be inverted to predict LAI for the complete maize canopy. By comparison the probability of zero interception determined from LiDAR measurements, also shown in Fig. 4, is 0.5%. This estimate has been derived assuming ground returns m of the interpolated are represented by all returns within ground surface. Inversion of the Beer’s Law model of interception using this estimate for the gap fraction would result in overestimation of LAI. Because the laser return profile is a measure of the radiation that is returned along the same trajectory as the incident beam, and the complete maize canopy is approximately a homogeneous structure, then the single-scattering Beer’s Law model was assumed to be a reasonable first approximation for the attenuation of laser returns. It was found, however, that the 1-D model cannot adequately represent the physical interception and measurement processes in order to describe the relationship between the canopy structure and laser return profile. Various factors may contribute toward this, including the following: 1) nonuniform distribution of foliage area in each horizontal layer, in conjunction with the following: 2) sampling differences between the average 1-D model attenuation, derived from average structure parameters using a small sample of plant measurements, and laser returns that sample the canopy discontinuously; 3) the influence of a detection threshold in the LiDAR system; 4) variation in elevation angle of the incident laser radiation. A more complex 3-D canopy structure model is required that incorporates these factors by describing the interception of individual laser beams, and may be used to investigate their effects upon the laser return profile. 2) Three-Dimensional Model: Assuming a return threshold of 15% and that laser radiation is incident from nadir, the 3-D structure/laser interception model for maize was found to predict a gap fraction of 15%. This is equivalent to that predicted by the 1-D model and does not agree with the observed gap fraction. It may therefore be concluded that either: 1) the 3-D representation has not improved the spatial description of the canopy due to inappropriate selection of grid cell size, or 2) the model assumptions regarding the physical interaction between the laser and the foliage are incorrect. Reasons for the differences between observed and modelled profiles have been investigated in Section V.

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(a) Fig. 5. Comparison between vertical profiles of laser interception predicted by the 1-D model for sunflowers and derived directly from laser returns.

(b)

(a)

(b) Fig. 6. Comparison between profiles of laser interception predicted by the 3-D model for sunflowers and derived directly from laser returns. The canopy model used in this figure assumes a fixed between-row spacing, with variation in interrow plant spacings from 0.1 m (model v1), 0.2 m (model v2), to 0.4 m (model v3). In (a), the laser radiation is assumed to be incident at nadir and in (b) for laser inclination angles of 10 . A constant return threshold of 1% has been assumed in both cases.

B. Results for Sunflower 1) One-Dimensional Model: The vertical profile of laser interception predicted using the 1-D approach has been compared with LiDAR returns and is shown in Fig. 5. The 1-D model does not account for interception in the lower canopy, as observed in the LiDAR returns. Further, the modelled interception underestimates the gap fraction in comparison with the LiDAR

Fig. 7. Comparison between profiles of laser interception predicted by the 3-D model for sunflowers and derived directly from laser returns. The canopy model used in this figure assumes a fixed between-row spacing, with variation in interrow plant spacings from 0.1 m (model v1), 0.2 m (model v2), to 0.4 m (model v3). The laser radiation is assumed to be incident at nadir. In (a), a 1% threshold is applied, and in (b), a 10% detection threshold has been applied.

returns. This poor relationship follows because the sunflower canopy structure does not conform to the assumptions of horizontal homogeneity nor uniform leaf azimuth distribution for a 1-D model. There was also a significant weed understorey, and nonuniform planting of the canopy. 2) Three-Dimensional Model: Sunflower canopy arrays were generated for typical ranges of vegetation density both horizontally and vertically through the canopy (see the Appendix for details). LiDAR interception was simulated for two values of return threshold (1% and 10%) and for two beam inclination angles (nadir and 10 ) in model canopies based on four 400 m grid squares in the field. These profiles have been compared with the measured interception profile (Figs. 6 and 7). As in the case of the 1-D model, the presence of weeds in the sunflowers contributes to uncertainty in the ground returns. Figs. 6 and 7 also illustrate that the modelled interception profile is most sensitive to inclination angle and return threshold for the sparse canopy where an interrow plant spacing of 0.4 m has been used. Manual measurements recorded an average planting density of seven plants per square meter; equivalent to an interrow plant spacing of 0.2 m. However, no single planting density for the simulated canopy gave the best agreement compared to the real return profile over the range of return thresholds and inclination angles. In Section V, the vegetation model is used to estimate the bias in percentage ground returns as measured by the LiDAR due to beam angle and return threshold.


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(a)

(a)

(b)

(b)

Fig. 8. Comparison between profiles of laser interception predicted by the 3-D model for maize and derived directly from laser returns. The canopy model used in this figure retains measured leaf azimuth information from four maize plants with some randomization to compute the average foliage area projected onto a horizontal plane for grid boxes with dimensions 0.03 0.03 0.1 m. In (a), the laser radiation is assumed to be incident at nadir for return thresholds of 5% (model v1), 10% (model v2), and 15% (model v3), and in (b), a constant return threshold of 10% has been used for laser inclination angles of 0 (model v1), 10 (model v2), and 15 (model v3).

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2

V. LIDAR SENSITIVITY A. Sensitivity of LiDAR Return Profiles The observed laser return profile has been compared with laser interception predicted using the 3-D maize canopy model (Figs. 8 and 9). The model has been used to show the effects of changing the laser inclination angle and/or threshold intensity. Two azimuth dispersion scenarios have been tested. In the first, leaf azimuth angles have been randomized over a range from the measured azimuth. For the second, the leaf azimuth angle of the first leaf in any plant has been chosen at random but within the plant, leaf azimuth relationship between leaves follows the measured pattern or genetic spiral [12]. Using the 3-D canopy model initialized with measured leaf azimuth angles, interception profiles have been simulated with very different shapes compared with the smooth observed profile [Fig. 8(a) and (b)]. This is particularly evident when using the smallest value of return threshold and the largest inclination angle investigated here, 5% and 20 , respectively. The small threshold value increases sensitivity to foliage area in each vertical layer, as does the increase in inclination angle due to a longer path length. This is reflected by a stronger return signal from the uppermost canopy layers; foliage distribution of individual plants is highly correlated with the canopy return profile. However, increasing the inclination angle and decreasing the return threshold have reduced the modelled gap fraction to less than 5%. This compares more closely with the

Fig. 9. Comparison between profiles of laser interception predicted by the 3-D model for maize and derived directly from laser returns. The canopy model used in this figure assumes random leaf azimuth dispersion to compute the average foliage area projected onto a horizontal plane. In (a), the laser radiation is assumed to be incident at nadir for return thresholds of 5% (model v1), 10% (model v2), and 15% (model v3), and in (b), a constant return threshold of 10% has been used for laser inclination angles of 0 (model v1), 10 (model v2), and 15 (model v3).

observed gap fraction. Because only four maize plants have been used to simulate the canopy, overestimation of the gap fraction may partly be attributed to sampling biases. Modelled interception profiles have been further improved using the 3-D canopy model and assuming random leaf azimuth dispersion. Fig. 9(a) and (d) corresponds to the same adjustments in laser inclination angle and/or threshold intensity as illustrated in Fig. 9(a) and (b) but for a canopy created using a different procedure to randomize measured plant. Decreasing the threshold intensity and increasing the inclination angle have resulted in similar effects upon the modelled profiles as predicted using the 3-D canopy with random leaf azimuth. The gap fraction has been reduced to values comparable with the observed profile; however, the shape of the modelled profile is simultaneously skewed due to an increased sensitivity to foliage area in the uppermost canopy layers. 1) Sensitivity of LIDAR LAI Retrievals: The relationship between modelled ground return percentages [from which LAI was estimated using (10)] and the actual LAI of the model canopy has been investigated over a range of beam angles and return threshold values. This used model data generated from 3-D sunflower canopy arrays described in Section IV. The LAI estimated by (10) was compared with the model canopy LAI, as shown in Fig. 10. A clear logarithmic relationship exists between the simulated LiDAR estimate for LAI and the “true” LAI used in the vegetation model, which may allow correction of the measured LiDAR-derived estimates. Uncertainty in the bias correction relationship, which does not lie on

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Fig. 12. Comparison of LAI derived from simulated LiDAR ground returns and the simulated canopy LAI over sunflowers. The incident laser inclination angle was set at nadir (model v1), 5 (model v2), 10 (model v3), 15 (model v4), and 20 (model v5). Fig. 10. Comparison of LAI from simulated LiDAR returns and the simulated canopy LAI, for four grid boxes and eleven values of within-row spacing over sunflowers. The fit to the data is a logarithmic regression (r = 0:91).

Fig. 11. Comparison of LAI derived from simulated LiDAR ground returns and the simulated canopy LAI over sunflowers. The detection threshold was set at 1% (model v1), 5% (model v2) and 10% (model v3).

the 1 : 1 line, will depend upon the model assumptions and the accuracy of the returns. Figs. 11 and 12 illustrate the influence of return threshold and beam angle on the relationship between the simulated LiDAR estimate for LAI and the canopy model LAI. These suggest that over the expected range of beam inclination angles and return threshold values, beam inclination angle has a greater effect upon the bias correction relationship.

VI. CONCLUSION Over an agricultural maize canopy, which was relatively homogeneous and thus straightforward to describe, comparisons between modelled and measured profiles of laser interception have shown that the laser altimeter may retrieve structure information with a vertical resolution of 10 cm. Such high-resolution information could be used to extract useful parameters that may improve the parameterization of energy transfer in land-surface models at regional scales. Vegetation structure/laser interception models have been used in this study to investigate the effects of various assumptions made to simplify the description of laser interception by a vegetation canopy. These include assumptions about the variation in plant and canopy structure parameters, the spatial distribution of foliage area, and the physical measurement process. LiDAR data acquired over a 20 20 m area of a maize canopy have been found to be most realistically represented by a range of inclination angles between 10 and 20 . Results also show that inadequate representation of the laser return threshold may have a significant effect upon the prediction of laser interception. Additional information about the physical detection process could therefore be used to improve the model. Additional uncertainties in the canopy information extracted from the LiDAR data will be associated with the definition of ground returns. In this study, the position of the ground surface was derived from LiDAR data acquired over the bare soil prior to crop growth. Laser returns from the ground have been reprem of the interpolated ground sented by all returns within surface. In the absence of such data, a ground surface could have been interpolated from local minima in the LiDAR data. Senescent leaves in the lowest levels of the canopy, which have not been included in manual characterization, may contribute a measurable laser return. In the case of the sunflower canopy, weeds may also have contributed to errors in the return signal. If these returns could be included into the ground return fraction, the measured gap fraction would have been increased thus


improving the comparison with predictions, which have tended to overestimate the amount of radiation reaching the ground. Simple inversion of a Beer’s Law relation to extract LAI from the gap fraction derived from LiDAR data will be affected by measurement errors. The 3-D vegetation model derived for sunflower has been used to demonstrate a method for correcting biases, which accounts for the effects of leaf overlap, beam angle and return threshold. Currently, this method requires a degree of scaling and fitting to adjust the model representation of the true canopy. A forward modeling approach such as this may benefit from additional information about the type and heterogeneity of the vegetation, which could be obtained from other remote sensing techniques such as Compact Airborne Spectrographic Imaging. This work demonstrates that the first return data obtained by laser altimetry have information about vegetation structure, and presents an approach for how it may be exploited. APPENDIX A grid, with cell dimensions 0.03 0.03 0.1 m in and , respectively, has been used to distribute foliage element-, leafand plant-scale parameters in 3-D space. The vertical resolution chosen for height bins was required to be sufficiently small to capture enough information about the vertical structure of individual plants, but also suitable for the subsequent binning of laser returns. It was concluded that 0.1 m height bins were adequate to model both the maize and sunflower plants given their large leaf dimensions and would also be compatible with the resolution of the altimeter, accounting for the majority of returns dimensions of from a flat surface found within a layer. The the grid were selected such that the LiDAR beam should remain location as it passed through a 10 cm layer in with a single , with a beam inclination of up to 20 off nadir. Leaf area alone contributes to light interception in the maize and sunflower models; the influence of stem and/or flower head area has been ignored. A. Maize Canopy Models Numerous models have been developed to quantify leaf inclination and orientation within maize canopies from mathematical descriptions of the foliage distribution [12]–[14]. The following are some common features of these models. 1) A polynomial function is used to describe the curvature of leaves mathematically. 2) Leaf shape is described by a regular ellipse. 3) Leaf shape and size parameters are correlated with insertion height (and therefore order of emergence). 4) For densely planted canopies, random leaf azimuth distribution is assumed for the true dispersion. 1) One-Dimensional Maize Canopy Model: The main stem of model plants, which was assumed to be vertical, has been used as a point of reference for the origin (or insertion height) of maize leaves relative to the ground surface. Leaf laminae were assumed to be flattened in the direction perpendicular to their length and symmetrical along their midrib, with area distributed as a regular rectangle. Their curvature has been characterized

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Fig. 13. One-dimensional profile of a model maize plant.

by the quadratic polynomial function given by [14], which describes the 2-D leaf curvature in terms of Cartesian coordinate variables and such that (A1) where and are horizontal and vertical distance from the leaf insertion point, respectively, and is the leaf inclination angle and , may be evaluat the insertion point. Coefficients ated in terms of measured leaf parameters and . For straight leaves, (A1) may be simplified [15] and becomes (A2) Equations (A1) and (A2) were used to calculate as was increased by 1 mm increments from the leaf insertion to the leaf tip . Fig. 13 shows an example of a 2-D plant profile generated by the model. This information has been used to accumulate leaf length into 10 cm vertical height bins. For each leaf, the fractional leaf length in different bins was subsequently used to distribute measured leaf area between height bins. A similar procedure was used to distribute projected leaf area using the projected leaf length in each height bin and a pro/(total leaf length), to reduce the jection factor given by total amount of leaf area available for interception. This process was repeated for all leaves enabling plant leaf area and projected area to be quantified in discrete vertical layers. Ground-based measurements of plant structure characteristics have been used to model the vertical leaf area density for the canopy. These measurements were carried out on four maize plants in September 2002, when the maize canopy was dense and fairly homogeneous. The maize crop was regarded as having a very uniform morphology that justified using a small number of plants to represent the canopy. Ground-based observations were made within 24 h of laser altimetry acquisitions. Plants were chosen from a central area of the field that had previously been geolocated using a backpack DGPS system. Measured leaf areas and dimensions were retained in the 1-D canopy model, m however, leaf insertion heights were randomized over

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to improve the representation of a homogeneous canopy and account for return height errors. Mean plant spacing was used to up-scale plant-level statistics and thus generate a 1-D leaf area density profile for the canopy. 2) Three-Dimensional Maize Canopy Model: Models that describe 3-D canopy structure may enable a better representation of the natural variance found in vegetation canopies. The mean and variance of leaf and plant parameters have been incorporated into models that describe foliage distribution using continuous statistical functions such as the G-function [12]. A simple analytical solution exists for the G-function, if a uniform leaf angle distribution may be assumed. This makes computation simpler but may obscure the true 3-D canopy structure. This may be the case even where the canopy is divided into a regular 3-D grid and a function assigned to each grid cell. An alternative approach is to treat each leaf as a composite of small planar elemental areas that may be uniquely described in space. Myneni et al. [12] have pointed out that such methods may improve accuracy at the cost of generality. The 3-D model used to describe canopy structure in the current study uses this approach because detailed measurements characterizing plant structure were available and, owing to the uniformity of the maize plants, a small sample was likely to be adequate for describing the canopy. By incorporating leaf azimuth information into the 1-D model described above, leaf insertion height and midrib profile have been described in terms of Cartesian coordinate variables and , where refers to grid north. As in the 1-D model, polynomial functions for each leaf, given by (A1) or (A2), have been used to calculate leaf length as the horizontal distance along the midrib from the stem was increased in 1 mm increments. Planar foliage elements have been defined at each increment as the rectangular area enclosed between the length along the leaf midrib and that perpendicular to the leaf midrib that is contained within the same grid cell or the edge of the leaf whichever occurs first. Because 1 mm is used for the incremental increase in horizontal length, uncertainty in the area calculation of these rectangular elements caused by leaf curvature is assumed to be negligible. The Cartesian coordinates of each element have been used to locate elements in the 3-D grid and to accumulate leaf areas into discrete grid cells. Hence, the model enables a detailed partitioning of “true” and “effective” leaf area over the 3-D grid, and an accurate description of the distribution of leaf area between discrete angle classes. To increase accuracy in the 3-D model, variation in leaf width has been accounted for by representing leaf shape by a rectangle and a triangle. From a sample of leaf width measurements, leaf width was found to be approximately constant along 2/3 of the leaf length, which was then used to form the base of the triangle representing the leaf tip. Measured leaf areas and dimensions have been retained in both cases and m. leaf insertion heights have been randomized over An illustration of a 3-D model plant is shown in Fig. 14. This has been derived from the same measurements used to obtain the 1-D representation shown in Fig. 13, but with additional azimuth information. Canopies have been simulated by filling a 9 m area with model plants, selected at random from those simulated from measurements, using values for mean plant spacing and row separation corresponding to 0.12 and 0.75 m, respec-

Fig. 14. Three-dimensional profile of a model maize plant, where x refers to grid north.

tively. The canopy area has been defined using the same 3-D grid coordinate system as that used for individual plants, where refers to grid north. This has enabled local grid frames around individual plants to be incorporated into the 9 m area and also the orientation of crop rows to be accurately specified. The result is a discrete 3-D representation of projected foliage area for a small region of canopy that is assumed to be representative of the “true” canopy. B. Sunflower Canopy Models The sunflower model differs from the maize canopy model in a number of ways: 1) description of the individual leaves and plants; 2) method of creating a randomized canopy by scaling plant parameters according to measured variation in plant height. The sunflower model differs from the maize in its representation of the leaves. The leaf laminae were assumed to be entirely planar, and the cordate morphology was approximated by an ellipse. The measured length and width of the leaf were assumed to be the major and minor axes of each leaf ellipse. With grid cell dimensions of 0.03 0.03 0.1 m, and approximating the leaves as ellipses, led to an average underestimate of the leaf area by 9%. Decreasing the grid cell size would lead to increased accuracy, but with enlarged requirements for array storage and processing time. A simplified form of (A2) was used to calculate as was increased by 1 mm increments from the leaf insertion to the leaf tip . As described above, the fractional leaf length in different vertical bins was subsequently used to distribute measured leaf area between height bins. This process was repeated for all leaves, quantifying plant true and projected leaf areas in discrete vertical layers. The model begins at the leaf insertion to the stem and increments in 1 mm steps along the ellipse major axis. After each 1 mm increment the and coordinates were calculated, and the leaf area distributed to cells between the ellipse major axis and the leaf perimeter, along the leaf half-width at that point (see Fig. 15). It is assumed that the coordinate does not change along the leaf width. Thus, as the leaf width is traversed, again in millimeter steps, the coordinate is assumed, but the and coordinates are calculated after every millimeter step. The length of the path perpendicular to the major axis ,


xy

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xz

Fig. 15. Approximating an individual sunflower leaf in the - , and planes. is the distance along major axis from the current location to the center of the ellipse; is the leaf half-width at that point. and are in the horizontal plane, and is the vertical. The plan view shows the and coordinates, the path along the midrib and from the midrib to the leaf perimeter. The profile view ( - ) shows the change in the coordinate due to the leaf inclination angle.

m

p

xz

z

x

z

for the current location on the major axis based on the standard equation of an ellipse

y x

y

, was calculated (A5)

rearranging to (A6) (A7) where is the semimajor axis of the ellipse, is the semiminor axis, is a point on the major axis, and is on the minor axis, but both are relative to the center of the ellipse. Fig. 15 illustrates an example of the position of and on the modelled leaf. The leaf area for a cell is calculated and accumulated if the or boundary of that grid cell is crossed. The trapezium method was used to calculate the area under the curve at the edge of the leaf. This process is repeated for the leaf width on the opposite side of the midrib. After this is complete, the 1 mm increment along the major axis is added, and the process repeated until the end of the leaf, and for all leaves. The process is similar for true and projected leaf area; the location of the center of the ellipse is the midway point of the measured leaf length and width parameters for true leaf area, whereas the projected leaf area calculation uses the halfway point of the projected leaf length and projected leaf width. True and projected leaf areas are accumulated in each grid cell providing the total area in each cell for the whole plant. Fig. 16 shows the leaf perimeters as modelled for one sunflower plant in plan view. This plot illustrates the degree of leaf overlap observed in a sunflower plant. The ground-based measurements of sunflower plant structure characteristics, used to model the vertical leaf area density, were carried out on three sunflower plants in August 2001. Seven parameters were required: leaf inclination, leaf azimuth angle, leaf length, leaf width, the height of the leaf stem (petiole) at insertion to the main stem, length of the petiole, and inclination angle of the petiole. Where leaf length and width data were unavailable, (A3) and (A4) were used to estimate leaf length and width from leaf area measurements (A3) (A4) These data were acquired from plants of Helianthus var. Teddy Bear and were provided courtesy of Dr. A. Diaz-Espejo.

Fig. 16. Model representation of the perimeter of the 16 leaves of one measured sunflower plant. This illustrates the degree of overlap that is seen in sunflower plants, and thus the need for 3-D canopy structure and radiation models.

Measured leaf area, dimensions, and insertion heights were scaled in the canopy model, to account for observed diversity in plant size. In order to approximate the observed variability 108 model plants were generated from the detailed measurements of three individual plants. This was carried out by rotating each of the three plants through 360 , in steps of 60 . Each plant was also scaled to obtain plant heights of 0.5, 0.7, 0.9, 1.1, 1.3, or 1.5 m. The length and width of each leaf were adjusted such that the leaf area and height scaled together. Sunflower canopies were generated by filling a 9 m area with model plants, selected at random from the 108 plants simulated from measurements. Technical difficulties during sowing of the sunflower crop led to a random spacing within rows, although between-row spacing was approximately constant. Therefore, in the representation of the canopy, the between-row spacing was fixed at 75 cm, and the model within-row spacing varied between 25 and 60 cm, in increments of 5 cm. The rows were aligned northwest–southeast. The number of plants in each size class was determined by the measured height distribution. The azimuthal orientation of the selected plants was random. A random number generator was run for the total number of plants in the 9 m area (as determined by the within- and between-row plant spacings). The random number generator used the measured mean and standard deviation of mature height in the area of interest. This was only possible for areas where height had been manually measured. The random number generator provided a statistical estimate of the frequency of the six modelled plant heights in that area. This is an approximation, particularly at lower planting densities, as the random number generator will approach the true distribution only with a large sample size. Thus, the canopy model was constrained to have the same frequency distribution of heights as the measurements of the area. This method was used to give a more realistic representation of the sunflower canopy, which was more heterogeneous than the maize canopy. REFERENCES [1] J. Ross, Tasks for Vegetation Sciences, 1st ed. The Hague, The Netherlands: W. Junk, 1981, vol. 3, The Radiation Regime and Architecture of Plant Stands.

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[2] H. H. Neumann, G. Den Hartog, and R. H. Shaw, “Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall,” Agricult. Forest Meteorol., vol. 45, pp. 325–345, 1989. [3] L. Farque, H. Sinoquet, and F. Colin, “Canopy structure and light interception in Quercus petraea seedlings in relation to light regime and plant density,” Tree Physiol., vol. 21, pp. 1287–1267, 2001. [4] J. Warren-Wilson, “Analysis of the spatial distribution of foliage by twodimensional point quadrats,” New Phytol., vol. 58, pp. 92–101, 1959. [5] J. M. Norman and J. M. Welles, “Radiative transfer in an array of canopies,” Agron. J., vol. 75, pp. 481–488, 1983. [6] G. S. Campbell, “Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution,” Agricult. Forest Meteorol., vol. 36, pp. 317–321, 1986. [7] S. G. Perry, A. B. Fraser, D. W. Thomson, and J. M. Norman, “Indirect sensing of plant canopy structure with simple radiation measurements,” Agricult. Forest Meteorol., vol. 42, pp. 255–278, 1988. [8] M. A. Lefsky, D. Harding, W. B. Cohen, G. Parker, and H. H. Shugart, “Surface Lidar remote sensing of basal area and biomass in deciduous forests of eastern Maryland, USA,” Remote Sens. Environ., vol. 67, pp. 83–98, 1999. [9] I. J. Davenport, R. B. Bradbury, G. Q. A. Anderson, G. R. F. Hayman, J. R. Krebs, D. C. Mason, J. D. Wilson, and N. J. Veck, “Improving bird population models using airborne remote sensing,” Int. J. Remote Sens., vol. 21, no. 13&14, pp. 2705–2717, 2000. [10] D. J. Harding, J. L. Bufton, and J. J. Frawley, “Satellite laser altimetry of terrestrial topography-vertical accuracy as a function of surface slope, roughness and cloud cover,” IEEE Trans. Geosci. Remote Sens., vol. 32, no. 2, pp. 329–339, Mar. 1994. [11] I. J. Davenport, N. Holden, and R. J. Gurney, “Characterizing errors in airborne laser altimetry data to extract soil roughness,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, pp. 2130–2141, Oct. 2004. [12] R. B. Myneni, G. Asrar, E. T. Kanemasu, D. J. Lawlor, and I. Impens, “Canopy architecture, irradiance distribution on leaf surfaces and consequent photosynthetic efficiencies in heterogeneous plant canopies,” Agricult. Forest Meteorol., vol. 37, pp. 189–204, 1986. [13] L. Prevot, F. Aries, and P. Monestiez, “A model of maize plant morphology,” Agronomie, vol. 11, pp. 491–503, 1991. [14] D. W. Stewart and L. M. Dwyer, “Mathematical characterization of maize canopies,” Agricult. Forest Meteorol., vol. 66, pp. 247–265, 1993. [15] M. A. H. Antunes, E. A. Walter-Shea, and M. A. Mesarch, “Test of an extended mathematical approach to calculate maize leaf area index and leaf angle distribution,” Agricult. Forest Meteorol., vol. 108, pp. 45–53, 2001.

Robert J. Gurney received the Ph.D. degree from the University of Bristol, Bristol, U.K., in 1975. He has worked at the Institute of Hydrology in the U.K. for five years, at the Hydrological Sciences Branch of NASA Goddard Space Flight Center for eight years, five as Head, two years at the Department of Civil Engineering, University of Maryland, five years as Director of the Unit for Thematic Information Systems, Natural Environment Research Council (NERC), Reading, U.K., and from 1995 to the present as Director of the NERC Environmental Systems Science Centre. His main research interest is global environmental change.

Caroline J. Houldcroft received the Ph.D. degree from the University of Reading, Reading, U.K., in 2004. This was a Natural Environment Research Council (NERC) studentship with a CASE award from the UK Environment Agency. She is currently with the NERC Climate Land Surface Systems Interaction Centre, University of Wales Swansea, Swansea, U.K., using models and remote observations to understand feedbacks between surface properties and the diurnal surface temperature signature.

Nick Holden received the degree in applied chemistry from the University of Portsmouth, Portsmouth, U.K., and the Masters degree from the University of Chelsea, Chelsea, U.K. He is currently a Science Manager in the Environment Agency’s Technology Group, Bath, U.K. He has 29 years experience in the environmental monitoring field, ten of which have been devoted to remote sensing, and the need to address the problems of spatial and temporal robustness inherent in single point sampling has been the main driver.

Claire L. Campbell received the Ph.D. degree from the University of Reading, Reading, U.K., in 2004. This was a Natural Environment Research Council studentship with a CASE award from the Centre for Ecology and Hydrology, Wallingford, U.K. She is currently with the Atmospheric Sciences section, Centre for Ecology and Hydrology, Edinburgh, U.K., using mechanistic models and micrometeorological measurements. The current focus of her work is process understanding of terrestrial and atmospheric carbon–nitrogen interactions and their consequences for net greenhouse gas exchange, at plot- and European-scales.

Ian J. Davenport (M’04) received the Ph.D. degree in physics with astronomy from the University of London, London, U.K., in 1993. His research at the National Engineering Research Council’s Unit for Thematic Information Studies and currently at the Environmental Systems Science Centre at the University of Reading, Reading, U.K., has concentrated on the applications of novel sensors in environmental science.