# MORPHOLOGICAL PLANT MODELING: UNLEASHING GEOMETRIC AND TOPOLOGICAL POTENTIAL WITHIN THE PLANT SCIENCES

EDITED BY: Alexander Bucksch and Dan Chitwood PUBLISHED IN: Frontiers in Plant Science

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ISSN 1664-8714 ISBN 978-2-88945-297-2 DOI 10.3389/978-2-88945-297-2

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# **MORPHOLOGICAL PLANT MODELING: UNLEASHING GEOMETRIC AND TOPOLOGICAL POTENTIAL WITHIN THE PLANT SCIENCES**

Topic Editors:

**Alexander Bucksch**, University of Georgia, United States **Dan Chitwood**, Independent Researcher, United States

Cover image: Anna Jurkovska/Shutterstock.com

An increasing population faces the growing demand for agricultural products and accurate global climate models that account for individual plant morphologies to predict favorable human habitat. Both demands are rooted in an improved understanding of the mechanistic origins of plant development. Such understanding requires geometric and topological descriptors to characterize the phenotype of plants and its link to genotypes. However, the current plant phenotyping framework relies on simple length and diameter measurements, which fail to capture the exquisite architecture of plants.

The Research Topic "Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences" is the result of a workshop held at National Institute for Mathematical and Biological Synthesis (NIMBioS) in Knoxville, Tennessee. From 2.-4. September 2015 over 40 scientists from mathematics, computer science, engineering, physics and biology came together to set new frontiers in combining plant phenotyping with recent results from shape theory at the interface of geometry and topology. In doing so, the Research Topic synthesizes the views from multiple disciplines to reveal the potential of new mathematical concepts to analyze and quantify the relationship between morphological plant features. As such, the Research Topic bundles examples of new mathematical techniques including persistent homology, graph-theory, and shape statistics to tackle questions in crop breeding, developmental biology, and vegetation modeling. The challenge to model plant morphology under field conditions is a central theme of the included papers to address the problems of climate change and food security, that require the integration of plant biology and mathematics from geometry and topology research applied to imaging and simulation techniques. The introductory white paper written by the workshop participants identifies future directions in research, education and policy making to integrate biological and mathematical approaches and to strengthen research at the interface of both disciplines.

**Citation:** Bucksch, A., Chitwood, D., eds. (2017). Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-297-2

# Table of Contents

*07 Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences*

Alexander Bucksch, Acheampong Atta-Boateng, Akomian F. Azihou, Dorjsuren Battogtokh, Aly Baumgartner, Brad M. Binder, Siobhan A. Braybrook, Cynthia Chang, Viktoirya Coneva, Thomas J. DeWitt, Alexander G. Fletcher, Malia A. Gehan, Diego Hernan Diaz-Martinez, Lilan Hong, Anjali S. Iyer-Pascuzzi, Laura L. Klein, Samuel Leiboff, Mao Li, Jonathan P. Lynch, Alexis Maizel, Julin N. Maloof, R. J. Cody Markelz, Ciera C. Martinez, Laura A. Miller, Washington Mio, Wojtek Palubicki, Hendrik Poorter, Christophe Pradal, Charles A. Price, Eetu Puttonen, John B. Reese, Rubén Rellán-Álvarez, Edgar P. Spalding, Erin E. Sparks, Christopher N. Topp, Joseph H. Williams and Daniel H. Chitwood

*23 Quantification of Overnight Movement of Birch (***Betula pendula***) Branches and Foliage with Short Interval Terrestrial Laser Scanning*

Eetu Puttonen, Christian Briese, Gottfried Mandlburger, Martin Wieser, Martin Pfennigbauer, András Zlinszky and Norbert Pfeifer

Frank Götmark, Elin Götmark and Anna M. Jensen

*92 Sweet Pepper (***Capsicum annuum** *L.) Canopy Photosynthesis Modeling Using 3D Plant Architecture and Light Ray-Tracing*

Jee Hoon Kim, Joon Woo Lee, Tae In Ahn, Jong Hwa Shin, Kyung Sub Park and Jung Eek Son

*102 Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity* Talukder Z. Jubery, Johnathon Shook, Kyle Parmley, Jiaoping Zhang, Hsiang S. Naik, Race Higgins, Soumik Sarkar, Arti Singh, Asheesh K. Singh and Baskar Ganapathysubramanian

*112 Mistletoe Berry Outline Mapping with a Path Curve Function and Recording the Circadian Rhythm of Their Phenotypic Shape Change*

Renatus Derbidge, Stephan Baumgartner and Peter Heusser

Laura L. Klein, Madeleine Caito, Chad Chapnick, Cassandra Kitchen, Regan O'Hanlon, Dan H. Chitwood and Allison J. Miller

Johanna Roussel, Felix Geiger, Andreas Fischbach, Siegfried Jahnke and Hanno Scharr

*174 Using a Structural Root System Model to Evaluate and Improve the Accuracy of Root Image Analysis Pipelines*

Guillaume Lobet, Iko T. Koevoets, Manuel Noll, Patrick E. Meyer, Pierre Tocquin, Loïc Pagès and Claire Périlleu

*185 A Model Analysis of Mechanisms for Radial Microtubular Patterns at Root Hair Initiation Sites*

Pawel Krupinski, Behruz Bozorg, André Larsson, Stefano Pietra, Markus Grebe and Henrik Jönsson

Guillaume Cerutti, Olivier Ali and Christophe Godin

Dorjsuren Battogtokh and John J. Tyson

### *274 Morphogeometric Approaches to Non-vascular Plants*

Daniel E. Stanton and Catherine Reeb

*282 Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology*

Mathilde Balduzzi, Brad M. Binder, Alexander Bucksch, Cynthia Chang, Lilan Hong, Anjali S. Iyer-Pascuzzi, Christophe Pradal and Erin E. Sparks

# Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

Alexander Bucksch1,2,3 \*, Acheampong Atta-Boateng4 , Akomian F. Azihou5 , Dorjsuren Battogtokh6 , Aly Baumgartner7 , Brad M. Binder8 , Siobhan A. Braybrook9 , Cynthia Chang10, Viktoirya Coneva11, Thomas J. DeWitt12, Alexander G. Fletcher13 , Malia A. Gehan11, Diego Hernan Diaz-Martinez14, Lilan Hong15, Anjali S. Iyer-Pascuzzi16 , Laura L. Klein17, Samuel Leiboff18, Mao Li14, Jonathan P. Lynch19, Alexis Maizel20 , Julin N. Maloof21, R. J. Cody Markelz21, Ciera C. Martinez22, Laura A. Miller23 , Washington Mio14, Wojtek Palubicki9 , Hendrik Poorter24, Christophe Pradal25 , Charles A. Price26, Eetu Puttonen27,28, John B. Reese29, Rubén Rellán-Álvarez30 , Edgar P. Spalding31, Erin E. Sparks32, Christopher N. Topp11, Joseph H. Williams29 and Daniel H. Chitwood11 \*

1 Department of Plant Biology, University of Georgia, Athens, GA, United States, 2 Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA, United States, 3 Institute of Bioinformatics, University of Georgia, Athens, GA, United States, 4 School of Forestry and Environmental Studies, Yale University, New Haven, CT, United States, 5 Laboratory of Applied Ecology, Faculty of Agronomic Sciences, University of Abomey-Calavi, Cotonou, Benin, 6 Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, United States, 7 Department of Geosciences, Baylor University, Waco, TX, United States, 8 Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Knoxville, TN, United States, 9 The Sainsbury Laboratory, University of Cambridge, Cambridge, United Kingdom, 10 Division of Biology, University of Washington, Bothell, WA, United States, 11 Donald Danforth Plant Science Center, St. Louis, MO, United States, 12 Department of Wildlife and Fisheries Sciences–Department of Plant Pathology and Microbiology, Texas A&M University, College Station, TX, United States, 13 School of Mathematics and Statistics and Bateson Centre, University of Sheffield, Sheffield, United Kingdom, 14 Department of Mathematics, Florida State University, Tallahassee, FL, United States, 15 Weill Institute for Cell and Molecular Biology and Section of Plant Biology, School of Integrative Plant Sciences, Cornell University, Ithaca, NY, United States, 16 Department of Botany and Plant Pathology, Purdue University, West Lafayette, IN, United States, 17 Department of Biology, Saint Louis University, St. Louis, MO, United States, 18 School of Integrative Plant Science, Cornell University, Ithaca, NY, United States, 19 Department of Plant Science, The Pennsylvania State University, University Park, PA, United States, 20 Center for Organismal Studies, Heidelberg University, Heidelberg, Germany, 21 Department of Plant Biology, University of California, Davis, Davis, CA, United States, 22 Department of Molecular and Cell Biology, University of California, Berkeley, Berkeley, CA, United States, 23 Program in Bioinformatics and Computational Biology, The University of North Carolina, Chapel Hill, NC, United States, 24 Plant Sciences (IBG-2), Forschungszentrum Jülich GmbH, Jülich, Germany, 25 CIRAD, UMR AGAP, INRIA, VirtualPlants, Montpellier, France, 26 National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Knoxville, TN, United States, 27 Department of Remote Sensing and Photogrammetry, Finnish Geospatial Research Institute, National Land Survey of Finland, Masala, Finland, 28 Centre of Excellence in Laser Scanning Research, National Land Survey of Finland, Masala, Finland, 29 Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, Knoxville, TN, United States, 30 Unidad de Genómica Avanzada, Laboratorio Nacional de Genómica para la Biodiversidad, Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), Irapuato, Mexico, 31 Department of Botany, University of Wisconsin–Madison, Madison, WI, United States, 32 Department of Plant and Soil Sciences and Delaware Biotechnology Institute, University of Delaware, Newark, DE, United States

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems

#### Edited by:

Katrin Kahlen, Hochschule Geisenheim University, Germany

#### Reviewed by:

Evelyne Costes, Institut National de la Recherche Agronomique (INRA), France Leo Marcelis, Wageningen University and Research, Netherlands

#### \*Correspondence:

Alexander Bucksch<EMAIL_ADDRESS>Daniel H. Chitwood<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science

> Received: 05 October 2016 Accepted: 12 May 2017 Published: 09 June 2017

#### Citation:

Bucksch A, Atta-Boateng A, Azihou AF, Battogtokh D, Baumgartner A, Binder BM, Braybrook SA, Chang C, Coneva V, DeWitt TJ, Fletcher AG, Gehan MA, Diaz -Martinez DH, Hong L, Iyer -Pascuzzi AS, Klein LL, Leiboff S, Li M, Lynch JP, Maizel A, Maloof JN, Markelz RJC, Martinez CC, Miller LA, Mio W, Palubicki W, Poorter H, Pradal C, Price CA, Puttonen E, Reese JB, Rellán-Álvarez R, Spalding EP, Sparks EE, Topp CN, Williams JH and Chitwood DH (2017) Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences. Front. Plant Sci. 8:900. doi: 10.3389/fpls.2017.00900

is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Keywords: plant biology, plant science, morphology, mathematics, topology, modeling

### INTRODUCTION

#### Morphology from the Perspective of Plant Biology

The study of plant morphology interfaces with all biological disciplines (**Figure 1**). Plant morphology can be descriptive and categorical, as in systematics, which focuses on biological homologies to discern groups of organisms (Mayr, 1981; Wiens, 2000). In plant ecology, the morphology of communities defines vegetation types and biomes, including their relationship to the environment. In turn, plant morphologies are mutually informed by other fields of study, such as plant physiology, the study of the functions of plants, plant genetics, the description of inheritance, and molecular biology, the underlying gene regulation (Kaplan, 2001).

Plant morphology is more than an attribute affecting plant organization, it is also dynamic. Developmentally, morphology reveals itself over the lifetime of a plant through varying rates of cell division, cell expansion, and anisotropic growth (Esau, 1960; Steeves and Sussex, 1989; Niklas, 1994). Response to changes in environmental conditions further modulate the abovementioned parameters. Development is genetically programmed and driven by biochemical processes that are responsible for physical forces that change the observed patterning and growth of organs (Green, 1999; Peaucelle et al., 2011; Braybrook and Jönsson, 2016). In addition, external physical forces affect plant development, such as heterogeneous soil densities altering root growth or flows of air, water, or gravity modulating the bending of branches and leaves (Moulia and Fournier, 2009). Inherited modifications of development over generations results in the evolution of plant morphology (Niklas, 1997). Development and evolution set the constraints for how the morphology of a plant arises, regardless of whether in a systematic, ecological, physiological, or genetic context (**Figure 1**).

### Plant Morphology from the Perspective of Mathematics

In 1790, Johann Wolfgang von Goethe pioneered a perspective that transformed the way mathematicians think about plant morphology: the idea that the essence of plant morphology is an underlying repetitive process of transformation (Goethe, 1790; Friedman and Diggle, 2011). The modern challenge that Goethe's paradigm presents is to quantitatively describe transformations resulting from differences in the underlying genetic, developmental, and environmental cues. From a mathematical perspective, the challenge is how to define shape descriptors to compare plant morphology with topological and geometrical techniques and how to integrate these shape descriptors into simulations of plant development.

#### Mathematics to Describe Plant Shape and Morphology

Several areas of mathematics can be used to extract quantitative measures of plant shape and morphology. One intuitive representation of the plant form relies on the use of skeletal descriptors that reduce the branching morphology of plants to a set of intersecting lines or curve segments, constituting a mathematical graph. These skeleton-based mathematical graphs can be derived from manual measurement (Godin et al., 1999; Watanabe et al., 2005) or imaging data (Bucksch et al., 2010; Aiteanu and Klein, 2014). Such skeletal descriptions can be used to derive quantitative measurements of lengths, diameters, and angles in tree crowns (Bucksch and Fleck, 2011; Raumonen et al., 2013; Seidel et al., 2015) and roots, at a single time point (Fitter, 1987; Danjon et al., 1999; Lobet et al., 2011; Galkovskyi et al., 2012) or over time to capture growth dynamics (Symonova et al., 2015). Having a skeletal description in place allows the definition of orders, in a biological and mathematical sense, to enable morphological analysis from a topological perspective (**Figure 2A**). Topological analyses can be used to compare shape characteristics independently of events that transform plant shape geometrically, providing a framework by which plant morphology can be modeled. The relationships between orders, such as degree of selfsimilarity (Prusinkiewicz, 2004) or self-nestedness (Godin and Ferraro, 2010) are used to quantitatively summarize patterns of plant morphology. Persistent homology (**Figure 2B**), an extension of Morse theory (Milnor, 1963), transforms a given plant shape gradually to define self-similarity (MacPherson and Schweinhart, 2012) and morphological properties (Edelsbrunner and Harer, 2010; Li et al., 2017) on the basis of topological event statistics. In the example in **Figure 2B**, topological

events are represented by the geodesic distance at which branches are "born" and "die" along the length of the structure.

In the 1980s, David Kendall defined an elegant statistical framework to compare shapes (Kendall, 1984). His idea was to compare the outline of shapes in a transformation-invariant fashion. This concept infused rapidly as morphometrics into biology (Bookstein, 1997) and is increasingly carried out using machine vision techniques (Wilf et al., 2016). Kendall's idea inspired the development of methods such as elliptical Fourier descriptors (Kuhl and Giardina, 1982) and new trends employing the Laplace Beltrami operator (Reuter et al., 2009), both relying on the spectral decompositions of shapes (Chitwood et al., 2012; Laga et al., 2014; Rellán-Álvarez et al., 2015). Beyond the organ level, such morphometric descriptors were used to analyze cellular expansion rates of rapidly deforming primordia into mature organ morphologies (Rolland-Lagan et al., 2003; Remmler and Rolland-Lagan, 2012; Das Gupta and Nath, 2015).

From a geometric perspective, developmental processes construct surfaces in a three-dimensional space. Yet, the embedding of developing plant morphologies into a threedimensional space imposes constraints on plant forms. Awareness of such constraints has led to new interpretations of plant morphology (Prusinkiewicz and de Reuille, 2010; Bucksch et al., 2014b) that might provide avenues to explain symmetry and asymmetry in plant organs (e.g., Martinez et al., 2016) or the occurrence of plasticity as a morphological response to environmental changes (e.g., Royer et al., 2009; Palacio-López et al., 2015; Chitwood et al., 2016).

#### Mathematics to Simulate Plant Morphology

Computer simulations use principles from graph theory, such as graph rewriting, to model plant morphology over developmental time by successively augmenting a graph with vertices and edges as plant development unfolds. These rules unravel the differences between observed plant morphologies across plant species (Kurth, 1994; Prusinkiewicz et al., 2001; Barthélémy and Caraglio, 2007) and are capable of modeling fractal descriptions that reflect the repetitive and modular appearance of branching structures (Horn, 1971; Hallé, 1971, 1986). Recent developments in functional-structural modeling abstract the genetic mechanisms driving the developmental program of tree crown morphology into a computational framework (Runions et al., 2007; Palubicki et al., 2009; Palubicki, 2013). Similarly, functional-structural modeling techniques are utilized in root biology to simulate the efficiency of nutrient and water uptake following developmental programs (Nielsen et al., 1994; Dunbabin et al., 2013).

Alan Turing, a pioneering figure in 20th-century science, had a longstanding interest in phyllotactic patterns. Turing's approach to the problem was twofold: first, a detailed geometrical analysis of the patterns (Turing, 1992), and second, an application of his theory of morphogenesis through local activation and longrange inhibition (Turing, 1952), which defined the first reactiondiffusion system for morphological modeling. Combining physical experiments with computer simulations, Douady and Coudert (1996)subsequently modeled a diffusible chemical signal

FIGURE 2 | Plant morphology from the perspective of mathematics. (A) The topological complexity of plants requires a mathematical framework to describe and simulate plant morphology. Shown is the top of a maize crown root 42 days after planting. Color represents root diameter, revealing topology and different orders of root architecture. Image by Jennifer T. Yang and provided by JPL (Pennsylvania State University). (B) Persistent homology deforms a given plant morphology using functions to define self-similarity in a structure. In this example, a geodesic distance function is traversed to the ground level of a tree (that is, the shortest curved distance of each voxel to the base of the tree), as visualized in blue in successive images. The branching structure, as defined across scales of the geodesic distance function is recorded as an H0 (zero-order homology) barcode, which in persistent homology refers to connected components. As the branching structure is traversed by the function, connected components are "born" and "die" as terminal branches emerge and fuse together. Each of these components is indicated as a bar in the H0 barcode, and the correspondence of the barcode to different points in the function is indicated by vertical lines, in pink. Images provided by ML (Danforth Plant Science Center).

produced by a developing primordium that would inhibit the initiation of nearby primordia, successfully recapitulating known phyllotactic patterns in the shoot apical meristem (Bernasconi, 1994; Meinhardt, 2004; Jönsson et al., 2005; Nikolaev et al., 2007; Hohm et al., 2010; Fujita et al., 2011), the number of floral organs (Kitazawa and Fujimoto, 2015), the regular spacing of root hairs (Meinhardt and Gierer, 1974), and the establishment of specific vascular patterns (Meinhardt, 1976).

### EMERGING QUESTIONS AND BARRIERS IN THE MATHEMATICAL ANALYSIS OF PLANT MORPHOLOGY

A true synthesis of plant morphology, which comprehensively models observed biological phenomena and incorporates a mathematical perspective, remains elusive. In this section, we highlight current focuses in the study of plant morphology, including the technical limits of acquiring morphological data, phenotype prediction, responses of plants to the environment, models across biological scales, and the integration of complex phenomena, such as fluid dynamics, into plant morphological models.

### Technological Limits to Acquiring Plant Morphological Data

There are several technological limits to acquiring plant morphological data that must be overcome to move this field forward. One such limitation is the acquisition of quantitative plant images. Many acquisition systems do not provide morphological data with measurable units. Approaches that rely on the reflection of waves from the plant surface can provide quantitative measurements for morphological analyses. Time of flight scanners, such as terrestrial laser scanning, overcome unitless measurement systems by recording the round-trip time of hundreds of thousands of laser beams sent at different angles from the scanner to the first plant surface within the line of sight (Vosselman and Maas, 2010) (**Figure 3**). Leveraging the speed of light allows calculation of the distance between a point on the plant surface and the laser scanner.

Laser scanning and the complementary, yet unitless, approach of stereovision both produce surface samples or point clouds as output. However, both approaches face algorithmic challenges encountered when plant parts occlude each other, since both rely on the reflection of waves from the plant surface (Bucksch, 2014). Radar provides another non-invasive technique to study individual tree and forest structures over wide areas. Radar pulses can either penetrate or reflect from foliage, depending on the selected wavelength (Kaasalainen et al., 2015). Most radar applications occur in forestry and are being operated from satellites or airplanes. Although more compact and agile systems are being developed for precision forestry above- and belowground (Feng et al., 2016), their resolution is too low to acquire the detail in morphology needed to apply hierarchy or similarity oriented mathematical analysis strategies.

Image acquisition that resolves occlusions by penetrating plant tissue is possible with X-ray (Kumi et al., 2015) and magnetic resonance imaging (MRI; van Dusschoten et al., 2016). While both technologies resolve occlusions and can even penetrate soil, their limitation is the requirement of a closed imaging

FIGURE 3 | Terrestrial laser scanning creates a point cloud reconstruction of a Finnish forest. (A) Structure of a boreal forest site in Finland as seen with airborne (ALS) and terrestrial (TLS) laser scanning point clouds. The red (ground) and green (above-ground) points are obtained from National Land Survey of Finland national ALS point clouds that cover hundreds of thousands of square kilometers with about 1 point per square meter resolution. The blue and magenta point clouds are results of two individual TLS measurements and have over 20 million points each within an area of about 500 m2 . TLS point density varies with range but can be thousands of points per square meter up to tens of meters away from the scanner position. (B) An excerpt from a single TLS point cloud (blue). The TLS point cloud is so dense that individual tree point clouds (orange) and parts from them (yellow) can be selected for detailed analysis. (C) A detail from a single TLS point cloud. Individual branches (yellow) 20 m above ground can be inspected from the point cloud with centimeter level resolution to estimate their length and thickness. Images provided by EP (Finnish Geospatial Research Institute in the National Land Survey of Finland). ALS data was obtained from the National Land Survey of Finland Topographic Database, 08/2012 (National Land Survey of Finland open data license, version 1.0).

volume. Thus, although useful for a wide array of purposes, MRI and X-ray are potentially destructive if applied to mature plant organs such as roots in the field or tree crowns that are larger than the imaging volume (Fiorani et al., 2012). Interior plant anatomy can be imaged destructively using confocal microscopy and laser ablation (**Figure 4**) or nano- or micro-CT tomography techniques, that are limited to small pot volumes, to investigate the first days of plant growth.

FIGURE 4 | Imaging techniques to capture plant morphology. (A) Confocal sections of an Arabidopsis root. The upper panel shows a new lateral root primordium at an early stage of development (highlighted in yellow). At regular intervals new roots branch from the primary root. The lower panel shows the primary root meristem and the stem cell niche (highlighted in yellow) from which all cells derive. Scale bars: 100 µm. Images provided by AM (Heidelberg University). (B) Computational tomographic (CT) x-ray sections through a reconstructed maize ear (left and middle) and kernel (right). Images provided by CT (Donald Danforth Plant Science Center). (C) Laser ablation tomography (LAT) image of a nodal root from a mature, field-grown maize plant, with color segmentation showing definition of cortical cells, aerenchyma lacunae, and metaxylem vessels. Image by Jennifer T. Yang and provided by JPL (Pennsylvania State University).

### The Genetic Basis of Plant Morphology

One of the outstanding challenges in plant biology is to link the inheritance and activity of genes with observed phenotypes. This is particularly challenging for the study of plant morphology, as both the genetic landscape and morphospaces are complex: modeling each of these phenomena alone is difficult, let alone trying to model morphology as a result of genetic phenomena (Benfey and Mitchell-Olds, 2008; Lynch and Brown, 2012; Chitwood and Topp, 2015). Although classic examples exist in which plant morphology is radically altered by the effects of a few genes (Doebley, 2004; Clark et al., 2006; Kimura et al., 2008), many morphological traits have a polygenic basis (Langlade et al., 2005; Tian et al., 2011; Chitwood et al., 2013).

Quantitative trait locus (QTL) analyses can identify the polygenic basis for morphological traits that span scales from the cellular to the whole organ level. At the cellular level, root cortex cell number (Ron et al., 2013), the cellular basis of carpel size (Frary et al., 2000), and epidermal cell area and number (Tisné et al., 2008) have been analyzed.

Natural variation in cell, tissue, or organ morphology ultimately impacts plant physiology, and vice versa. For example, formation of root cortical aerenchyma was linked to better plant growth under conditions of suboptimal availability of water and nutrients (Zhu et al., 2010; Postma and Lynch, 2011; Lynch, 2013), possibly because aerenchyma reduces the metabolic costs of soil exploration. Maize genotypes with greater root cortical cell size or reduced root cortical cell file number reach greater depths to increase water capture under drought conditions, possibly because those cellular traits reduce metabolic costs of root growth and maintenance (Chimungu et al., 2015). The control of root angle that results in greater water capture in rice as water tables recede was linked to the control of auxin distribution (Uga et al., 2013). Similarly, in shoots, natural variation can be exploited to find genetic loci that control shoot morphology, e.g., leaf erectness (Ku et al., 2010; Feng et al., 2011).

High-throughput phenotyping techniques are increasingly used to reveal the genetic basis of natural variation (Tester and Langridge, 2010). In doing so, phenotyping techniques complement classic approaches of reverse genetics and often lead to novel insights, even in a well-studied species like Arabidopsis thaliana. Phenotyping techniques have revealed a genetic basis for dynamic processes such as root growth (Slovak et al., 2014) and traits that determine plant height (Yang et al., 2014). Similarly, high-resolution sampling of root gravitropism has led to an unprecedented understanding of the dynamics of the genetic basis of plasticity (Miller et al., 2007; Brooks et al., 2010; Spalding and Miller, 2013).

### The Environmental Basis of Plant Morphology

Phenotypic plasticity is defined as the ability of one genotype to produce different phenotypes based on environmental differences (Bradshaw, 1965; DeWitt and Scheiner, 2004) and adds to the phenotypic complexity created by genetics and development. Trait variation in response to the environment has been analyzed classically using 'reaction norms,' where the phenotypic value of a certain trait is plotted for two different environments (Woltereck, 1909). If the trait is not plastic, the slope of the line connecting the points will be zero; if the reaction norm varies across the environment the trait is plastic and the slope of the reaction norm line will be a measure of the plasticity. As most of the responses of plants to their environment are nonlinear, more insight into phenotypic plasticity can be obtained by analyzing dose-response curves or dose-response surfaces (Mitscherlich, 1909; Poorter et al., 2010).

Seminal work by Clausen et al. (1941) demonstrated using several clonal species in a series of reciprocal transplants that, although heredity exerts the most measureable effects on plant morphology, environment is also a major source of phenotypic variability. Research continues to explore the range of phenotypic variation expressed by a given genotype in the context of different environments, which has important implications for many fields, including conservation, evolution, and agriculture (Nicotra et al., 2010; DeWitt, 2016). Many studies examine phenotypes across latitudinal or altitudinal gradients, or other environmental clines, to characterize the range of possible variation and its relationship to the process of local adaptation (Cordell et al., 1998; Díaz et al., 2016).

Below-ground, plants encounter diverse sources of environmental variability, including water availability, soil chemistry, and physical properties like soil hardness and movement. These factors vary between individual plants (Razak et al., 2013) and within an individual root system, where plants respond at spatio-temporal levels to very different granularity (Drew, 1975; Robbins and Dinneny, 2015). Plasticity at a microenvironmental scale has been linked to developmental and molecular mechanisms (Bao et al., 2014). The scientific challenge here is to integrate these effects at a whole root system level and use different scales of information to understand the optimal acquisition in resource limited conditions (Rellán-Álvarez et al., 2016) (**Figure 5**).

### Integrating Models from Different Levels of Organization

Since it is extremely difficult to examine complex interdependent processes occurring at multiple spatio-temporal scales, mathematical modeling can be used as a complementary tool with which to disentangle component processes and investigate how their coupling may lead to emergent patterns at a systems level (Hamant et al., 2008; Band and King, 2012; Band et al., 2012; Jensen and Fozard, 2015). To be practical, a

multiscale model should generate well-constrained predictions despite significant parameter uncertainty (Gutenkunst et al., 2007; Hofhuis et al., 2016). It is desirable that a multiscale model has certain modularity in its design such that individual modules are responsible for modeling specific spatial aspects of the system (Baldazzi et al., 2012). Imaging techniques can validate multiscale models (e.g., Willis et al., 2016) such that simulations can reliably guide experimental studies.

To illustrate the challenges of multi-scale modeling, we highlight an example that encompasses molecular and cellular scales. At the molecular scale, models can treat some biomolecules as diffusive, but others, such as membrane-bound receptors, can be spatially restricted (Battogtokh and Tyson, 2016). Separately, at the cellular scale, mathematical models describe dynamics of cell networks where the mechanical pressures exerted on the cell walls are important factors for cell growth and division (Jensen and Fozard, 2015) (**Figure 6A**). In models describing plant development in a two-dimensional cross-section geometry, cells are often modeled as polygons defined by walls between neighboring cells. The spatial position of a vertex, where the cell walls of three neighboring cells coalesce, is a convenient variable for mathematical modeling of the dynamics of cellular networks (Prusinkiewicz and Runions, 2012). A multiscale model can then be assembled by combining the molecular and cellular models. Mutations and deletions of the genes encoding the biomolecules can be modeled by changing parameters. By inspecting the effects of such modifications on the dynamics of the cellular networks, the relationship between genotypes and phenotypes can be predicted. For example, Fujita et al. (2011) model integrates the dynamics of cell growth and division with the spatio-temporal dynamics of the proteins involved in stem cell regulation and simulates shoot apical meristem development in wild type and mutant plants (**Figure 6B**).

### Modeling the Impact of Morphology on Plant Function

Quantitative measures of plant morphology are critical to understand function. Vogel (1989) was the first to provide quantitative data that showed how shape changes in leaves reduce drag or friction in air or water flows. He found that single broad leaves reconfigure at high flow velocities into cone shapes to reduce flutter and drag (**Figures 7A,B**). More recent work discovered that the cone shape is significantly more stable than other reconfigurations such as U-shapes (Miller et al., 2012). Subsequent experimental studies on broad leaves, compound leaves, and flowers also support rapid repositioning in response to strong currents as a general mechanism to reduce drag (Niklas, 1992; Ennos, 1997; Etnier and Vogel, 2000; Vogel, 2006) (**Figure 7C**). It is a combination of morphology and anatomy, and the resultant material properties, which lead to these optimal geometric re-configurations of shape.

From a functional perspective, it is highly plausible that leaf shape and surface-material properties alter the boundary layer of a fluid/gas over the leaf surface or enhance passive movement that can potentially augment gas and heat exchange. For example, it has been proposed that the broad leaves of some trees flutter for the purpose of convective and evaporative heat transfer (Thom, 1968; Grant, 1983). Any movement of the leaf relative to the

movement of the air or water may decrease the boundary layer and increase gas exchange, evaporation, and heat dissipation (Roden and Pearcy, 1993). Each of these parameters may be altered by the plant to improve the overall function of the leaf (Vogel, 2012).

The growth of the plant continuously modifies plant topology and geometry, which in turn changes the balance between organ demand and production. At the organismal scale, the 3D spatial distribution of plant organs is the main interface between the plant and its environment. For example, the 3D arrangement of branches impacts light interception and provides the support for different forms of fluxes (water, sugars) and signals (mechanical constraints, hormones) that control plant functioning and growth (Godin and Sinoquet, 2005).

#### MILESTONES IN EDUCATION AND OUTREACH TO ACCELERATE THE INFUSION OF MATH INTO THE PLANT SCIENCES

Mathematics and plant biology need to interact more closely to accelerate scientific progress. Opportunities to interact possibly involve cross-disciplinary training, workshops, meetings, and funding opportunities. In this section, we outline perspectives for enhancing the crossover between mathematics and plant biology.

#### Education

Mathematics has been likened to "biology's next microscope," because of the insights into an otherwise invisible world it has to offer. Conversely, biology has been described as "mathematics' next physics," stimulating novel mathematical approaches because of the hitherto unrealized phenomena that biology studies (Cohen, 2004). The scale of the needed interplay between mathematics and plant biology is enormous and may lead to new science disciplines at the interface of both: ranging from the cellular, tissue, organismal, and community levels to the global; touching upon genetic, transcriptional, proteomic, metabolite, and morphological data; studying the dynamic interactions of plants with the environment or the evolution of new forms over geologic time; and spanning quantification, statistics, and mechanistic mathematical models.

Research is becoming increasingly interdisciplinary, and undergraduate, graduate, and post-graduate groups are actively trying to bridge the gap between mathematics and biology skillsets. While many graduate programs have specialization tracks under the umbrella of mathematics or biology-specific programs, increasingly departments are forming specially designed graduate groups for mathematical/quantitative biology1,2 to strengthen the interface between both disciplines.

1BioQuant at University of Heidelberg, http://www.bioquant.uni-heidelberg.de (retrieved February 28, 2017)

2Quantitative Biosciences at Georgia Tech in Atlanta, http://qbios.gatech.edu (retrieved February 28, 2017)

leaves in wind moving from right to left. The wind speed is increased from 3 m/s (left) to 6 m/s (middle) and 12 m/s (right). Note that the entire cluster reconfigures into a cone shape. This is different from the case of tulip poplars and maples where each leaf individually reconfigures into a conic shape. Images provided by LM (University of North Carolina, Chapel Hill, NC, United States).

This will necessitate team-teaching across disciplines to train the next generation of mathematical/computational plant scientists.

### Public Outreach: Citizen Science and the Maker Movement

Citizen science, which is a method to make the general public aware of scientific problems and employ their help in solving them3 , is an ideal platform to initiate a synthesis between plant biology and mathematics because of the relatively low cost and accessibility of each field. Arguably, using citizen science to collect plant morphological diversity has already been achieved, but has yet to be fully realized. In total, it is estimated that the herbaria of the world possess greater than 207 million voucher specimens4 , representing the diverse lineages of land plants collected over their respective biogeographies over a timespan of centuries. Digital documentation of the millions of vouchers held by the world's botanic gardens is actively underway, allowing for researchers and citizens alike to access and study for themselves the wealth of plant diversity across the globe and centuries (Smith et al., 2003; Corney et al., 2012; Ryan, 2013).

The developmental changes in plants responding to environmental variability and microclimatic changes over the course of a growing season can be analyzed by studying phenology. Citizen science projects such as the USA National Phenology Network5 or Earthwatch6 and associated programs such as My Tree Tracker7 document populations and individual plants over seasons and years, providing a distributed, decentralized network of scientific measurements to study the effects of climate change on plants.

3For example, see the White Paper on Citizen Science for Europe, http://www. socientize.eu/sites/default/files/white-paper\_0.pdf (retrieved May 29, 2016)

4List of herbaria, https://en.wikipedia.org/wiki/List\_of\_herbaria (retrieved May 29, 2016)

5https://www.usanpn.org/# (retrieved May 29, 2016)

6http://earthwatch.org/scientific-research/special-initiatives/urban-resiliency (retrieved May 29, 2016)

7http://www.mytreetracker.org/cwis438/websites/MyTreeTracker/About.php? WebSiteID=23 (retrieved May 29, 2016)

Workshops such as these, bringing mathematicians and plant biologists together, will be necessary to create a new synthesis of plant morphology.

Citizen science is also enabled by low-cost, specialized equipment. Whether programming a camera to automatically take pictures at specific times or automating a watering schedule for a garden, the maker movement—a do-ityourself cultural phenomenon that intersects with hacker culture—focuses on building custom, programmable hardware, whether via electronics, robotics, 3D-printing, or time-honored skills such as metal- and woodworking. The focus on programming is especially relevant for integrating mathematical approaches with plant science experiments. The low-cost of single-board computers like Raspberry Pi, HummingBoard, or CubieBoard is a promising example of how to engage citizen scientists into the scientific process and enable technology solutions to specific questions.

#### Workshops and Funding Opportunities

Simply bringing mathematicians and plant biologists together to interact, to learn about new tools, approaches, and opportunities in each discipline is a major opportunity for further integration of these two disciplines and strengthen new disciplines at the interface of both. This white paper itself is a testament to the power of bringing mathematicians and biologists together, resulting from a National Institute for Mathematical and Biological Synthesis (NIMBioS) workshop titled "Morphological Plant Modeling: Unleashing Geometric and Topologic Potential within the Plant Sciences," held at the University of Tennessee, Knoxville, September 2– 4, 20158 (**Figure 8**). Other mathematical institutes such as the Mathematical Biology Institute (MBI) at Ohio State University9 , the Statistical and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle Park10 , the Institute for Mathematics and Its Applications at University of Minnesota11, and the Centre for Plant Integrative Biology at the University of Nottingham12 have also hosted workshops for mathematical and quantitative biologists from the undergraduate student to the faculty level.

There are efforts to unite biologists and mathematics through initiatives brought forth from The National Science Foundation, including Mathematical Biology Programs13 and the Joint DMS/NIGMS Initiative to Support Research at the Interface of the Biological and Mathematical Sciences14 (DMS/NIGMS). Outside of the Mathematics and Life Sciences Divisions, the Division of Physics houses a program on the Physics of Living Systems. Societies such as The Society for Mathematical Biology and the Society for Industrial and Applied Mathematics (SIAM) Life Science Activity Group15 are focused on the dissemination of research at the intersection of math and biology, creating many opportunities to present research and provide funding. We emphasize the importance that funding opportunities have had and will continue to have in the advancement of plant morphological modeling.

### Open Science

Ultimately, mathematicians, computational scientists, and plant biology must unite at the level of jointly collecting data, analyzing it, and doing science together. Open and timely data sharing to benchmark code is a first step to unite these disciplines along with building professional interfaces to bridge

8http://www.nimbios.org/workshops/WS\_plantmorph (retrieved May 29, 2016) 9https://mbi.osu.edu/ (retrieved May 29, 2016)

10http://www.samsi.info/ (retrieved May 29, 2016)

11https://www.ima.umn.edu/ (retrieved May 29, 2016)

12https://www.cpib.ac.uk/outreach/cpib-summer-school/ (retrieved May 29, 2016)

13https://www.nsf.gov/funding/pgm\_summ.jsp?pims\_id=5690 (retrieved May 29, 2016)

14http://www.nsf.gov/funding/pgm\_summ.jsp?pims\_id=5300&org=DMS (retrieved May 29, 2016)

15https://www.siam.org/activity/life-sciences/ (retrieved May 29, 2016)

between the disciplines (Bucksch et al., 2017; Pradal et al., 2017).

A number of platforms provide open, public access to datasets, figures, and code that can be shared, including Dryad16, Dataverse17, and Figshare18. Beyond the ability to share data is the question of open data formats and accessibility. For example, in remote sensing research it is unfortunately common that proprietary data formats are used, which prevents their use without specific software. This severely limits the utility and community building aspects of plant morphological research. Beyond datasets, making code openly available, citable, and user-friendly is a means to share methods to analyze data. Places to easily share code include web-based version controlled platforms like Bitbucket19 or Github20 and software repositories like Sourceforge21. Furthermore, numerous academic Journals (e.g., Nature Methods, Applications in Plant Sciences, and Plant Methods) already accept publications that focus on methods and software to accelerate new scientific discovery (Pradal et al., 2013).

Meta-analysis datasets provide curated resources where numerous published and unpublished datasets related to a specific problem (or many problems) can be accessed by researchers22. The crucial element is that data is somehow reflective of universal plant morphological features, bridging the gap between programming languages and biology, as seen in the Root System Markup Language (Lobet et al., 2015) and OpenAlea (Pradal et al., 2008, 2015). Bisque is a versatile platform to store, organize, and analyze image data, providing simultaneously open access to data and analyses as well as the requisite computation (Kvilekval et al., 2010). CyVerse23 (formerly iPlant) is a similar platform, on which academic users get 100 GB storage for free and can create analysis pipelines that can be shared and reused (Goff et al., 2011). For example, DIRT24 is an automatic, high throughput computing platform (Bucksch et al., 2014a; Das et al., 2015) that the public can use hosted on CyVerse using the Texas Advanced Computing Center25 (TACC) resources at UT Austin that robustly extracts root traits from digital images. The reproducibility of these complex computational experiments can be improved using scientific workflows that capture and automate the exact methodology followed by scientists (Cohen-Boulakia et al., 2017). We emphasize here the importance of adopting open science policies at the individual investigator and journal level to continue strengthening the interface between plant and mathematically driven sciences.

#### CONCLUSION: UNLEASHING GEOMETRIC AND TOPOLOGICAL POTENTIAL WITHIN THE PLANT SCIENCES

Plant morphology is a mystery from a molecular and quantification point of view. Hence, it fascinates both mathematical and plant biology researchers alike. As such, plant morphology holds the secret by which predetermined variations of organizational patterns emerge as a result of evolutionary, developmental, and environmental responses.

The persistent challenge at the intersection of plant biology and mathematical sciences might be the integration of measurements across different scales of the plant. We have to meet this challenge to derive and validate mathematical models that describe plants beyond the visual observable. Only then we will be able to modify plant morphology through molecular biology and breeding as means to develop needed agricultural outputs and sustainable environments for everybody.

Cross-disciplinary training of scientists, citizen science, and open science are inevitable first steps to develop the interface between mathematical-driven and plant biology-driven sciences. The result of these steps will be new disciplines, that will add to the spectrum of researchers in plant biology. Hence, to unleash the potential of geometric and topological approaches in the plant sciences, we need an interface familiar with both plants and mathematical approaches to meet the challenges posed by a future with uncertain natural resources as a consequence of climate change.

#### AUTHOR CONTRIBUTIONS

AB and DC conceived, wrote, and organized the manuscript. All authors contributed to writing the manuscript.

### FUNDING

This work was assisted through participation in the Morphological Plant Modeling: Unleashing geometric and topological potential within the plant sciences Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville, Knoxville, TN, United States.

#### ACKNOWLEDGMENTS

The authors are grateful to the National Institute for Mathematical and Biological Synthesis (NIMBioS, University of Tennessee, Knoxville) for hosting and funding the workshop "Morphological Plant Modeling: Unleashing geometric and topological potential within the plant sciences" that inspired this manuscript. We thank the reviewers Evelyne Costes and Leo Marcelis for creative and open discussions.

16http://datadryad.org/ (retrieved May 29, 2016)

17http://dataverse.org/ (retrieved May 29, 2016)

18https://figshare.com/ (retrieved May 29, 2016)

19https://bitbucket.org/ (retrieved May 29, 2016)

20https://github.com/ (retrieved May 29, 2016)

21https://sourceforge.net/ (retrieved May 29, 2016)

22BAAD: a Biomass And Allometry Database for woody plants, https://github. com/dfalster/baad (retrieved May 29, 2016)

23http://www.cyverse.org/ (retrieved August 20, 2016)

24http://dirt.iplantcollaborative.org/ (retrieved August 20, 2016)

25https://www.tacc.utexas.edu/ (retrieved August 20, 2016)

### REFERENCES

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Milnor, J. W. (1963). Morse Theory. Princeton: Princeton University Press.

platform for plant modelling. Funct. Plant Biol. 35, 751–760. doi: 10.1071/ FP08084

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Bucksch, Atta-Boateng, Azihou, Battogtokh, Baumgartner, Binder, Braybrook, Chang, Coneva, DeWitt, Fletcher, Gehan, Diaz-Martinez, Hong, Iyer-Pascuzzi, Klein, Leiboff, Li, Lynch, Maizel, Maloof, Markelz, Martinez, Miller, Mio, Palubicki, Poorter, Pradal, Price, Puttonen, Reese, Rellán-Álvarez, Spalding, Sparks, Topp, Williams and Chitwood. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Quantification of Overnight Movement of Birch (Betula pendula) Branches and Foliage with Short Interval Terrestrial Laser Scanning

Eetu Puttonen1, 2 \*, Christian Briese3, 4, Gottfried Mandlburger 3 , Martin Wieser 3 , Martin Pfennigbauer 5 , András Zlinszky 6 and Norbert Pfeifer 3

1 Department of Remote Sensing and Photogrammetry, Finnish Geospatial Research Institute, National Land Survey of Finland, Masala, Finland, 2 Department of Remote Sensing and Photogrammetry, Centre of Excellence in Laser Scanning Research, National Land Survey of Finland, Masala, Finland, 3 Department of Geodesy and Geoinformation, Technische Universität Wien, Vienna, Austria, 4 EODC Earth Observation Data Centre for Water Resources Monitoring, Vienna, Austria, 5 RIEGL Laser Measurement Systems, Horn, Austria, 6 Balaton Limnological Institute, Centre for Ecological Research, Hungarian Academy of Sciences, Tihany, Hungary

#### Edited by:

Alexander Bucksch, Georgia Institute of Technology, USA

#### Reviewed by:

Monica Herrero-Huerta, Delft University of Technology, Netherlands Jean-Francois Cote, Natural Resources Canada, Canada

> \*Correspondence: Eetu Puttonen<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science

Received: 21 November 2015 Accepted: 09 February 2016 Published: 29 February 2016

#### Citation:

Puttonen E, Briese C, Mandlburger G, Wieser M, Pfennigbauer M, Zlinszky A and Pfeifer N (2016) Quantification of Overnight Movement of Birch (Betula pendula) Branches and Foliage with Short Interval Terrestrial Laser Scanning. Front. Plant Sci. 7:222. doi: 10.3389/fpls.2016.00222 The goal of the study was to determine circadian movements of silver birch (Petula Bendula) branches and foliage detected with terrestrial laser scanning (TLS). The study consisted of two geographically separate experiments conducted in Finland and in Austria. Both experiments were carried out at the same time of the year and under similar outdoor conditions. Experiments consisted of 14 (Finland) and 77 (Austria) individual laser scans taken between sunset and sunrise. The resulting point clouds were used in creating a time series of branch movements. In the Finnish data, the vertical movement of the whole tree crown was monitored due to low volumetric point density. In the Austrian data, movements of manually selected representative points on branches were monitored. The movements were monitored from dusk until morning hours in order to avoid daytime wind effects. The results indicated that height deciles of the Finnish birch crown had vertical movements between -10.0 and 5.0 cm compared to the situation at sunset. In the Austrian data, the maximum detected representative point movement was 10.0 cm. The temporal development of the movements followed a highly similar pattern in both experiments, with the maximum movements occurring about an hour and a half before (Austria) or around (Finland) sunrise. The results demonstrate the potential of terrestrial laser scanning measurements in support of chronobiology.

Keywords: terrestrial laser scanning, plant movement, chronobiology, circadian rhythm, time series

## INTRODUCTION

Terrestrial laser scanners have gone through rapid development during the past 10 years (Dassot et al., 2011). They produce accurate 3D point clouds of target objects often down to millimeter resolution. Thus, the point clouds provide detailed information about the structure and spatial properties of the targets.

In addition to structural modeling and scene mapping, terrestrial laser scanning (TLS) data are widely used in engineering applications to monitor possible changes in the targeted objects or in a target area. TLS-based change detection studies cover a wide range of different applications. These include geodynamic processes such as landslide detection and monitoring (Travelletti et al., 2008; Ghuffar et al., 2013) and morphodynamic changes in coastal beaches (Lindenbergh et al., 2011), thermal karst formations (Barnhart and Crosby, 2013), or in riversides (Milan et al., 2007; Vaaja et al., 2011; Saarinen et al., 2013). Short interval scans are also used in determining dynamic structural stress (Grosse-Schwiep et al., 2013). TLS techniques are utilized to improve safety in quarries and mines by monitoring wall stability over time (Abellan et al., 2011; Hu, 2013; Kovanic and Blištan, 2014). In vegetation studies, TLS is being actively used in static forest and forest parameter mapping (Hopkinson et al., 2004; Moskal and Zheng, 2012; Liang, 2013), tree modeling (Fleck et al., 2004; Hosoi and Omasa, 2006; Bucksch and Fleck, 2011; Eysn et al., 2013; Raumonen et al., 2013), and in estimating forest biomass (e.g., Kaasalainen et al., 2014).

Although TLS is utilized in a wide range of both temporal and vegetation studies for scientific and engineering applications, one field of study which has not yet gained wider interest in the TLS community is circadian or diurnal and nocturnal changes in vegetation. In ecology and plant physiology, these changes in plants and their driving factors have been studied intensively for a long time. It has been known for centuries that plants show diurnal cycles of leaf motion, described as "sleep" already by Darwin and Darwin (1880). It has been observed that these motions also happen if the plant is placed in darkness, therefore suggesting an internal mechanism for measuring time. The molecular mechanism of this circadian oscillator has been most extensively studied in Arabidopsis (Barak et al., 2000), but orthologues of the Arabidopsis genes controlling the diurnal rhythm of flowering time have been identified in various tree species such as Poplar (Populus tremula) and Chestnut (Castanea sativa) (Solomon et al., 2010). However, for obvious reasons, carrying out controlled experiments or even quantitative observations on fully grown trees is much more difficult, therefore both the background and the effects of sleep motions in trees are less well-understood. Circadian rhythms of leaf motion are evident for some tree species such as Robinia pseudoacaia. The movement of leaves is connected to changes in turgor pressure (Holmes and Shim, 1968) which is controlled by the osmotic state of the cells. Changes in water transport and in the concentration of various metabolites result in changes in osmotic flow and thus, through changes in the shape of individual plant cells, eventual movement at the scale of individual plants or plant parts. The literature identifies two common reasons that drive these changes, namely plant water balance (Chapin et al., 2002) and photoperiodism (McClung, 2006; Nozue and Maloof, 2006; Sysoeva et al., 2010). It would be plausible that the changes in turgor pressure resulting in a circadian rhythm of leaf movement also apply to the branches and thus cause a circadian rhythm of branch movements in trees. However, in an earlier case study where quantification of diurnal movement was attempted using height measurement of weighted lines attached to branches in a Walnut orchard (Juglans regia), diurnal change was found insignificant (Way et al., 1991). To our best knowledge, circadian movement of tree branches has never been successfully quantified before in the presented level.

Methods to monitor plant water balance at a diurnal time scale include: (a) leaf or fruit sample collection and water content measurements (Klepper, 1968; Acevedo et al., 1979); (b) sap flow monitoring (Köstner et al., 1998); (c) leaf and stem conductance measurements (García-Orellana et al., 2013); (d) leaf and stem water potential, photosynthetic capability and hydraulic conductivity measurements (Andrews et al., 2012); (e) branch growth and xylem morphometry measurements (Correia and Martins-Loucao, 1995; Correia et al., 2001). Most of these are invasive processes that involve sampling and are difficult (but possible) to carry out regularly in intervals of a few hours (Chapotin et al., 2006). Therefore, in case of trees, the most common way of observing circadian rhythms is with a dendrograph, an instrument that measures changes in tree diameter or circumference with sub-millimeter precision (e.g., Pesonen et al., 2004).

In order to monitor photoperiodism, the amount of light received by plants can be controlled by constructing external shading structures (Wayne and Bazzaz, 1993) or by using external lighting setups with selected filters (e.g., Mockler et al., 2003). Alternatively, in order to monitor the internal clock, a plant can be placed in continuously lit or dark conditions to observe periodic changes in its physiology.

Plant physiology measurements are localized and typically consider selected parts of a plant. The measurements often take place in laboratory conditions. This presents a clear challenge when results are extrapolated to model wider areas of multiple plants. Acquiring results also involves a significant amount of manual labor, as experiment setups and sample collection are hard to automatize.

TLS measurements offer a potential solution to generalize plant physiology results on larger spatial scales, like whole individual trees, or on orchard plot, and stand levels. Laser scanners can measure individual targets accurately tens of meters away with sub-centimeter point resolution. Moreover, scanning can be performed outdoors with short intervals between individual scans. Furthermore, as the scanners are active measurement devices that both produce and receive the signal, they are insensitive to varying external lighting conditions, i.e., available sunlight and cloudiness.

Laser scanning point clouds cannot provide direct biochemical parameters from plants, but they can be used in plant shape and dimension monitoring over time (e.g., branch inclination, branch, and stem swelling, leaf inclination distribution at crown level). If a clear correlation between the geometric changes in point clouds and laboratory or in situ results can be established and verified, the parameterized spatial changes can then act as proxies that estimate physiological changes in a plant.

Puttonen et al. (2015) detected and reported birch branch movements during a day-long classification study. The study was carried out with the Finnish Geospatial Research Institute (FGI) Hyperspectral Laser Scanner (HSL) (Hakala et al., 2012). The movements were detected from the variation of the birch Normalized Difference Vegetation Index (NDVI) response during on an observation period of ca. 26 h. A more detailed inspection revealed a visible change in birch branch stances over time. The study is to our knowledge the first to report spatial changes in tree branch geometry over a day-long cycle. However, the authors did not attempt to quantify the movement amplitude.

Hitherto, vegetation time series in TLS have been collected mainly for longer scale time series analyses, typically to determine seasonal changes in tree canopy (e.g., Hosoi and Omasa, 2009; Nevalainen et al., 2014; Hakala et al., 2014; Portillo-Quintero et al., 2014; Calders et al., 2015; Griebel et al., 2015).

In imaging, longer term time-series studies have been carried out both in the field and in a laboratory with a close range setup (e.g., more recently by Li et al., 2013; Nijland et al., 2014). However, the use of cameras inherently limits the experimental setup to daylight hours or requires the use of external light sources. Additionally, radiometry measurements and their calibration are typically rather complex. Furthermore, even a short use of external light sources may interrupt the plant photoperiod (e.g., Salisbury, 1981). Meanwhile, since laser scanners are active measurement systemstheir working efficiency is stable in nighttime conditions with no external light (Arslan and Kalkan, 2013). With modern laser scanners, the laser beam footprint up to a few centimeters in diameter illuminates only a localized patch of the plant surface at a time. Moreover, the footprint swipes over each spot in sub-second scale and the typically used infrared (IR) wavelengths have strong reflectance from green vegetation. Therefore, most of the transmitted energy is not absorbed by the plant. Thus, we assume that plant disturbance with a modern laser scanning system is not significant during an individual scanning measurement.

This study now aims (i) to analyze to which degree overnight birch branch movements can be measured with two different TLS scanners and (ii) whether quantifications of crown/branch movements are possible. With these goals in mind, we aim to show that TLS data provides an effective tool to detect and to monitor circadian changes in tree geometry with a centimeter scale spatial and within-hour temporal resolution. As the main focus of the study is in confirmation and quantification of geometric changes in birch branches over time, without further investigation of the cause or mechanism of these movements, the measurement setups did not include comprehensive weather or soil data.

#### MEASUREMENTS AND DATA

This section is structured as follows: In section Measurement Sites and the Collected Data, descriptions of both the Finnish and the Austrian measurement sites and data collected from them are given. Section Object Point Cloud Delineation describes object delineation from the scanned point clouds. Section FGI Hyperspectral Lidar provides a detailed description of FGI HSL and its properties. Section RIEGL VZ-4000 Long Range Laser Scanner gives a detailed description of the RIEGL VZ-4000 laser scanner.

#### Measurement Sites and the Collected Data

Measurements were carried out in two geographically different locations, in southern Finland (Kirkkonummi, 60◦ 09′ 40′′N, 24◦ 32′ 48′′W) and in northern Austria (Horn, 48◦ 39′ 31′′N,

15◦ 39′ 48′′E). Both measurements were performed in the middle of September close to the solar equinox to guarantee approximately similar lengths of night at both sites (http:// www.timeanddate.com, accessed on 25th February 2015). Measurement dates were 13–14 September 2013 (Finland) and 19–20 September 2014 (Austria). In both measurements, the test trees were measured from sunset to sunrise. In Finland, the nighttime measurements lasted about 11 h in total, during which 14 separate scans were collected with FGI HSL. Scan intervals were approximately 1 h. Near sunrise and sunset the scan interval was shortened to 40 min. In Austria, data acquisitions were repeated every 10 min for about 12 and half hours, resulting in 77 separate scans.

The Finnish measurement site was located on a shallow slope facing southward. The size of the test site was about 7 × 20 m2 . The site included the main target, a small silver birch (Betula pendula). Low understory, a large silver birch and goat willows (Salix caprea) were located behind the target. The site was partially surrounded from its eastern side with a sparse, halfopen canopy of full-grown birches. The nearby FGI building was located on the western side of the site. The shadow of the building shaded the target site for about half an hour before the sunset. **Figure 1** illustrates the Finnish test tree and the reference markers placed around it. The markers were used to validate the distance measurement stability over the experiment. The measurement setting also included an external reference plate (Spectralon R ) to calibrate laser radiometry during the experiment. The FGI HSL was mounted on a solid platform and a plastic tent was set up around the scanner to protect it from possible rain and moisture. A heating fan was kept on whole night time inside the tent. This guaranteed a constant airflow and prevented possible surface condensation.

The Austrian measurement site was located on the northern part of an outdoor test and calibration range, an open, cut grass field of size about 130 m by 100 m. The target birch had four stems and it was standing about 10 m away of a manufacturing hall. Thus, the tree was not shaded during sunrise or sunset. The scans were taken to the westward direction and the laser scanner was under a protective roof. Four white polystyrene foam spheres were attached to the birch as reference markers to detect branch movement. **Figure 2** illustrates the Austrian test tree and the branches of which movements were followed during the experiment. The branch point clouds were manually selected in CloudCompare software [Available in: http://www. cloudcompare.org/ (Girardeau-Montaut, 2014)].

The weather conditions in both measurement sites were similar during data acquisition. The air was calm, with no wind (qualitative observation), during the night. For this reason, the time of sunset was selected as the initial point for monitoring the branch movement. There was no rainfall during either measurement. In the Finnish test site, the leaves of lower branches were verified not to have visible moisture condensation on their surfaces during nighttime.

### Object Point Cloud Delineation

A manual workflow was used to delineate birch and reference target point clouds spatially from the whole point cloud. The same procedure was used for both datasets.

The differentiation was started by viewing an object (birch or reference target) point cloud as a 2D projection from a user selected angle and then cutting the object outline by hand with a clear buffer zone. Points inside the outline were included and the rest were rejected. After the cut, a new 2D projection of the included points was taken from another angle and the manual cutting was repeated. In total, 4–5 projections were required to form a sufficiently accurate 3D delineation for the objects in both cases. As the objects had no spatial overlap in either measurement setup, there was no mixing between the object point clouds. The buffer zones in each cut were selected so wide that possible temporal movements within the object point cloud and noise point fluctuations around the object edges (e.g., due to partial hits) were captured for all measurements. All points within the selection area were kept. Intensity-based filtering was not performed.

#### FGI Hyperspectral Lidar

The FGI Hyperspectral Lidar (HSL) is a laser scanning system that transmits hyperspectral (white) laser pulses with a continuous spectrum of 400–2500 nm to the target. It can measure up to eight separate wavelength bands from returning pulses. The number of bands is limited by the spectral sensitivity of the silicon detector, but the wavelengths are selectable within the transmittance range. In this study, spectral information was used only to emphasize differences between leaf and stem returns with the Normalized Difference Vegetation Index (NDVI).

The main components of the HSL system are the SM5-he supercontinuum laser source (Leukos, Limoges, France), a 2D scanning mechanism (Newport Corp., Irvine, CA, USA), the wavelength separating spectrograph (Specim, Oulu, Finland), a 16-channel high speed detector element (First Sensor AG, Berlin, Germany), and the measurement computer with digitizer cards (National Instruments Corp., Austin, Texas, USA). The HSL works by sending laser pulses to the target in a sweeping pattern and then recording returning waveforms for each wavelength band detected. The waveforms are digitized with 1 GHz frequency, thus giving the system a nominal 15 cm range resolution. However, individual laser pulses can be localized to the waveforms with a de facto range resolution of a few centimetres. The HSL can measure up to 5000 waveforms per second and a maximum of three discrete returns are fitted in each waveform.

A more detailed description of the HSL system, its properties, and its measurement configuration are given in articles by Hakala et al. (2012) and Nevalainen et al. (2014).

The properties of both the FGI HSL and RIEGL VZ-4000 scanners are compared in **Table 1**.

#### RIEGL VZ-4000 Long Range Laser Scanner

The RIEGL VZ-4000 has been developed for surveying applications in which very long ranges are required (RIEGL, 2014). The scanner has a net measurement rate of up to 222 kHz. The maximum measurement range of the VZ-4000 is 4 km for targets with 90% reflectance at 23 kHz measurement rate. At 222 kHz the instrument is still capable of measuring targets with only 20% reflectance up to 1000 m.

The RIEGL VZ-4000 works, like the HSL, by sending laser pulses to the target, but analyses the recorded waveform internally. The nominal ranging precision is 10 mm.

The VZ-4000 can be controlled via its built–in touch screen, via WIFI or LAN. It has a built-in camera, GPS receiver, compass, and tilt sensor, and there are interfaces to attach an additional camera (e.g., IR camera) and/or a high-precision RTK GNSS.

#### RESULTS

### Finnish Point Cloud Time Series

A total of 14 scans were selected from the Finnish point cloud time series in order to determine the temporal variation in the birch crown. Since the FGI HSL is a prototype device, its relative ranging precision during the experiment was first validated. Movements of the reference targets set around the birch were monitored for the duration of the experiment. **Table 2** lists the reference target distances to the scanner and their relative movements compared to the initial scan. The target ranges and movements were calculated with respect to the target center that was determined with a least squares sphere fitting (MATLAB code by Alan Jennings, available in www.mathworks.com/matlabcentral/fileexchange/34129). The table shows that the reference targets were detected reliably and with higher precision (less than 5 mm standard deviation) than the nominal sampling frequency of the system would imply. This assumption is valid as long as the laser returns can be TABLE 1 | Property comparison between the laser scanners used in the Finnish and Austrian test sites.

expected to come from a single reflection, but cannot be directly generalized to more irregular targets, like differently positioned leaves, or to partial hits coming from edges. Nevertheless, the ranging stability test verified the HSL system accuracy for fixed target distances and that the HSL point cloud did not present a systematic drift during the measurement period.

After the range precision measurements, points were manually delineated into a new individual point cloud of the studied tree for each measurement as described in Section Finnish Point Cloud Time Series. Then, the point cloud was differentiated into crown and stem point clouds. The differentiation was based on the NDVI distribution of all birch points. The differentiation was performed using a hard NDVI threshold of 0.2, where the points with NDVI values below the threshold were classified as stem and thick branches. The bounding box of the crown point clouds had dimensions of 3.7 × 3.0 × 6.6 m3 (depth, width, height) when averaged over all measurements. The median point number for the crown point clouds was 154,310 ± 10,030 points corresponding to 6.5% variability in the total point number.

The goal of the division was to select the returns reflecting from leaves and most of the branches of the birch and to leave the trunk and the thickest branches out of the analysis. After this, five different height percentiles were calculated for the crown point cloud for each scan (**Figure 3**). The height percentiles in the analysis were: 10th, 30th, 50th, 70th, and the 90th percentile. For example, the 90th percentile is located at the height at which 90% of the points of the whole cloud are below it. Height percentiles were calculated because a manual selection of corresponding points in consecutive scans was not possible due to the low volumetric point density. Height percentiles, on the other hand, are robust descriptions of the measurement height distribution and should therefore allow a reliable tracking of vertical movements of the crown point cloud.

The results show clear and systematic temporal variation in height statistics of the birch crown point cloud (**Figures 3**, **4**, o'clock).

**Video 1**). In **Figure 3**, all height percentiles show a declining temporal trend about 1 h after sunset (blue vertical line). The four highest percentiles also share another common trend: the height percentiles after sunrise (red line) were still lower than their sunset value. At this point, their values have decreased about 0.05 m from their sunset value. After reaching the minimum, all four percentiles show a rapid return toward the sunset value. The return takes about 3 h. The lowest percentile shows a differing temporal response compared to the others. Its value declines more slowly than the others during night, to about 0.03 m from the sunset value. Furthermore, the lowest point is reached about an hour later than for the other percentiles. The overall trend of the lowest percentile is also not as clear as with the other percentiles: the declining trend is less clear and shows more variance.

#### Austrian Point Cloud Time Series

The RIEGL VZ-4000 was factory calibrated and mounted on a solid pillar throughout the experiment, and so its ranging properties were not inspected as with the Finnish datasets. The bounding box around the birch had average dimensions of 6.0 × 7.0 × 9.3 m3 (depth, width, height). The median point number inside the bounding box was 9,388,000 ± 724,000 corresponding to 7.7% variability in the total point number.

Manual branch point selection was carried out for three branches. Reference target movement was measured from the fitted sphere center. Three of the four attached reference targets

The table shows the reference target distances from the scanner and the radii fitted in their point clouds. Both the ranges and radii were compared to the initial measurement close to sunset. All standard deviation values were calculated from 14 scans.

were detected reliably. The fourth one was not detected due to it being occluded from the scan position by birch branches and leaves. **Figure 5** illustrates the total movements of the selected points on the branches and the reference target centers.

The graphs in **Figure 5** show clearly how all points measured on branches had a similar movement pattern over time. The absolute branch point movement was limited mainly to within 2 cm, with the exception of a few points, until 5 h after the sunset. Thereafter the movement trend began to increase, reaching its maximum around 9–11 h after sunset. The maximum movements varied from 5.0 to 8.5 cm for Branch 1, from 3.5 to 7.0 cm for Branch 2, and from 6.5 to 10.0 cm for Branch 3. After the movement maximum was reached, all branches returned

mark zoomed in boxes in the upper (B) and in the lower (C) crown. Video 1 visualizes the geometrical change in the Finnish birch point cloud over night. It is provided in the Supplementary Material.

rapidly toward their sunset values around sunrise (about 07:00 h in the graph). The movement was dominated by the downwards component, but included also a comparatively small radial contribution.

In addition to the similar time response, the amplitude of point movements was dependent on the point distance from the trunk in general. For every branch, the point indexing was selected so that the index increased when moving away from the trunk (**Figure 2**). As a general trend, points with higher index values moved more compared to points with smaller indices. The subplots show exceptions from this rule at different times, but the general trend is visible.

For reference targets attached to the branches, movement of their centers showed a similar, but attenuated, temporal trend compared to the branch points. Reference targets 1 and 3 showed relatively little movement until about 6 h after sunset, excluding occasional noise points. Then, both reference target centers showed a sharp movement with amplitude of 1 cm. The movement then increased until 05:30 o'clock, after which it diminished rapidly by about an hour after sunrise. Reference target 2 differed from the two others in that its movement amplitude was lower and the maximum movement occurred already around 05:00 o'clock. However, the movement diminished in the same way as in the case of the other reference targets.

### Considerations on Result Comparability

The results show similar temporal behavior between the two birches. This is despite the difference in location of over 12 degrees of latitude, and the difference in form of growth: the Austrian tree was a cultivar with mainly hanging branches while the Finnish study tree had more erect branches with only the branchlets hanging. Growing conditions in the measurement sites also differed from each other, the Finnish site was more covered and in a slope, whereas the Austrian site was on an open and flat grass field.

Although both experiments showed clear temporal correlation in birch branch movement overnight, the absolute branch movements cannot be compared directly. The spatial resolution obtainable with the FGI HSL was not detailed enough to determine individual branch points reliably between consecutive scans. Thus, the temporal development of the Finnish birch was treated on a crown level. The use of crown point height percentiles shows how the different parts of the crown move with respect to each other, but this level of detail was not sufficient to analyze the movement amplitude of individual branches.

The RIEGL VZ-4000 point clouds were dense enough for individual representative point monitoring. In addition, the reference markers attached to birch branches gave another point of reference to determine the movement amplitude. Since the representative points on branches were picked by hand, this

FIGURE 5 | (A) Total movements of the representative points on Branch 1 over time. (B) Total movements of the representative points on Branch 2 over time. Branch 2 is missing the last epoch due to internal occlusion. (C) Total movements of the representative points on Branch 3 over time. (D) Total movement of reference target centers over time. Vertical lines in all subplots mark sunset and sunrise. All values in (A–D) represent the absolute 3D movement compared to the initial point selection at the scan closest to sunset. Manual point selection in (A–C) was performed by picking scans once per hour which was sufficient to represent the general movement trend over time. In (D), reference centers were extracted automatically for all 77 scans. The reference spheres were attached on thicker branches and closer to the stem than Branches 1–3. This resulted in smaller movement amplitudes in the sphere center movement than with the branches.

resulted in an uncertainty of about 1 cm. However, all manually selected branch points showed systematic movement amplitudes of several centimeters that was several times larger than the point ranging uncertainty and were thus interpreted as a result of changes in branch position. In the Finnish dataset, the thickest lower branches adjacent to the stem were measured to be about 15 mm in diameter. In the Austrian dataset, the selected branches were about 10–20 mm in diameter as measured from the point clouds.

In order to better compare the results for estimating required point densities for future measurement planning, a comparative table of the two measurement setup is presented in **Table 3**. The table sums up both the differences and the similarities between the measurements.

The question arises, which density of the point cloud is required for doing the first or the second type of movement analysis, i.e., height percentiles vs. points on individual branches. To achieve this, the point density must be quantified. This was done by calculating the number of populated 5×5 × 5 cm3 voxels for the point clouds, and this was further monitored through time. The normalized cumulative number of voxels populated with at least a given number of points is illustrated in **Figure 6** for both cases. In other words, the metric shows how many voxels contain at least n points within the voxel point cloud. This value is normalized by dividing through the number of voxels which have at least 1 point. The point density graphs were drawn at three different times in order to evaluate whether scanning time would have had a significant effect on point cloud density due to any external factors.

In the Finnish full canopy point clouds, the **Figure 5A** illustrates clearly how the cumulative point density in voxels decreases rapidly. This means that most of the populated voxels had only a few hits in them. Only about 35–40% of the populated voxels have five or more laser returns localized in them. There is also about a 5% percentage point difference between the scans taken at sunset and at night. In the Austrian point cloud, the corresponding number shows that over 65% of the populated voxels have at least five hits in them and there is no significant difference between the scans taken at different times.

The amount of voxels with one or two laser returns is important as they represent spatially isolated returns of which a significant portion may consist of noise, and partial or otherwise low quality hits on target. The graphs in **Figure 6A**) show that while there is some variation in the point density on the crown and tree level, the point densities between different scans drop

in a consistent manner for both scanners regardless of scanning time.

The graphs in **Figure 6A**) showed the point density for the full crown and tree point clouds. Thus, the inherently noisy backsides of the point clouds with lower point densities are also included. Therefore, similar graphs were also produced separately for the differentiated Austrian birch branches (**Figure 6B**) that were used for movement measurements to see if they would show different point density variations compared to the full tree point cloud. The branches were selected on the outer edge of the birch and with clear visibility to the scanner (**Figure 2**). The graphs show that about 85% of all populated voxels inside the bounding boxes of branches 1 and 2 have five or more hits, and over 75% of the voxels have 10 or more hits. The only exception here is the sunrise measurement of the branch 1, where the results are several percentage points lower. Branch 3 results show systematically lower point densities. About 80% of these voxels have at least five hits, and about 65% of the voxels have at least 10 hits. In general, the number of multi-hit branch voxels is over 10% points higher than the number of corresponding voxels in the whole birch point cloud.

Results on the point density variation in the Finnish and Austrian datasets and their effect on manual branch point selection give a rough metric to estimate required point densities for future studies. The representative point monitoring was possible with manual selection for all branches delineated from the Austrian datasets, whereas for the Finnish data similar monitoring was not possible due to lower point density. The lowest tested branch point density here had about 80% of hits coming from voxels with at least five points or more, which would correspond to a point density of at least 40,000 pts/m3 . Voxels with 10 or more hits (at least 80,000 pts/m3 ) constituted about 65% of all voxels. In the Finnish dataset, the voxel population ratio of over 65% was obtained only when voxels with at least two points (16,000 pts/m3 ) were included. Thus, to perform a similar point selection from a natural birch branch surface (i.e., without additional reflective material), the point densities should be at least close to 40,000 pts/m3 . This estimated value is not a universal lower limit, but it gives an initial approximation for planning new similar experiments.

Measurement settings and weather conditions were also similar between the experiments:

an enclosed setting, for example in a greenhouse. However, in our experiments no disturbance by wind occurred.

#### DISCUSSION

### The Study in Context with Previous Research

In this study we quantified a diurnal cycle of branch motion in mature birch (Betula pendula) trees growing under natural conditions, and therefore demonstrated the potential of TLS point clouds to monitor diurnal branch movements in birch trees. To our knowledge, the study is the first to report overnight branch and crown movement with centimeter level spatial resolution and with (less than) hourly intervals. The study approach presented here is novel in utilizing TLS point clouds with short interval outdoor scanning.

The study comprises two separate measurement settings with different equipment and geographic location, namely Finland and Austria. Target objects were individual birch trees located in the study areas and night time movements were detected by scanning their canopies for a period lasting from sunset to sunrise. The results obtained from the measurements showed that the crown movement in the Finnish and the branch movement in the Austrian study case presented similar temporal

response. Close to sunrise, the branches were hanging lower than at the time of sunset. Detected crown and branch movement amplitudes varied from a few centimeters up to 10 cm from their initial locations at sunset, depending on the position of the branch and the measurement point on it. The movements were observed to happen systematically over a time span of several hours, which ruled out occasional wind effects.

Both the molecular background of the circadian rhythm and the resulting movement of various plant parts (the leaf, stem, and flower) have been extensively described for small herbs growing under laboratory conditions. The circadian activity pattern of trees is also of interest, both for generalizing the findings of experimental chronobiology and for commercial use of tree products such as the tree sap [e.g., for the gum tree (Hevea brasiliensis)] and the wood (which is best harvested when it has a low water content). Understanding ecophysiological processes of individual trees, including their diurnal water use pattern and how this changes under water stress is becoming increasingly important for climate research, as near-global coverage of high-resolution remote sensing has revolutionized the up-scaling of findings from individual tree-based models to continental scale (Shugart et al., 2015). Until now, in situ measurements at the scale of full trees were not possible due to the lack of a non-invasive, non-contact method with high spatial accuracy. Our study demonstrates that TLS satisfies these criteria.

To our knowledge, previous and present TLS time series literature on vegetation mainly concentrates on detecting seasonal changes. The seasonal change studies have mainly focused on collecting physiological parameters, like leaf or needle chlorophyll content (Hakala et al., 2014; Nevalainen et al., 2014), or to follow the growth and phenological changes by studying changes in Leaf area index (LAI), plant area index (PAI), and Plant Area Volume Density (PAVD), e.g., in Griebel et al. (2015) and Calders et al. (2015). A study by Hosoi and Omasa (2009) determined the seasonal changes in vertical leaf area density (LAD) profiles. Measurement intervals in these studies vary from daily and weekly measurements to individual seasonal scans. These scan intervals are sufficient for detecting overall changes on crown level, but cannot capture systematic inter—and intraday dynamics as reported here.

Most of the TLS time series studies are performed during light hours, mainly due to technical restrictions that require presence of measurement staff to set up and monitor the data collection. A change to this is a new operational system, VEGNET, that has been developed and successfully applied for long-term forest monitoring (Portillo-Quintero et al., 2014; Griebel et al., 2015). The main limitation of VEGNET is its limited spatial resolution and a fixed angle rotation plane that have been designed to monitor overall crown structural dynamics around the system instead of focusing on individual trees. The VEGNET operates night time to optimize its ranging capabilities and to minimize possible wind effects. In general, any wind or local airflows present a significant source of noise in TLS point clouds and have to be accounted for either during the measurement. Another reported error source is precipitation on the scanning equipment and on target.

Another feasible approach to collect longer-term time series data with high temporal resolution is short-interval photography. Li et al. (2013) performed a plant growth analysis study where they studied the structural changes in a pot plant in laboratory conditions for 35 days where the same viewing geometry was repeated every 5 min. A 4D (3D structure and time) point cloud representation was then post processed from the imagery to study geometrical changes in the plant. Nijland et al. (2014) used infrared converted consumer grade cameras to collect plant health and phenology information in an outdoor setting for several months with 1-h interval. The main weakness of the imaging approach is the requirement of external lighting and comprehensive radiometric calibration to guarantee correct radiometry between imagery taken in dynamic lighting conditions. Li et al. (2013) applied constant lighting on their targets, whereas Nijland et al. (2014) had to limit their outdoor imaging sequences to light hours. Neither solution allows studying of possible dark time dynamics in plants as reported in this study.

### SUMMARY AND FUTURE WORK

The study scope was limited to analysis and quantification of the geometric movements in birch crown and branches. The validation of possible mechanisms behind the movement was not possible within the study scope and further investigations are required. Possible mechanisms contributing to the branch and crown movement may be related to plant water balance or to plant photoperiodism, but their validation was out of the scope of this article.

Circadian changes in plants have been studied extensively in plant physiology and they can be quantified with high detail in laboratory conditions or in-situ for individual plants and their parts (e.g., Perämäki et al., 2001). However, extending the results to larger areas is prohibitively laborious. We conclude that whereas laser scanning point clouds are not able to give as detailed information about the physiological changes in plants as laboratory or on-the-spot measurements, they still have a significant potential to provide additional geometrical information that can be correlated with the physiological measurements, and then possibly extended to cover whole plants in their natural environment and over wider areas. Perhaps the most important open question is whether the observed branch movements take place under the influence of light from sunset and sunrise, or if they are independent from light and governed by the internal circadian clock of the plant. The fact that some branches started returning to their daytime position already before sunrise would suggest this latter hypothesis, but the temporal frequency of our investigations is not sufficient for confirming or rejecting it: ideally, measuring several full 24-h cycles of a tree isolated from natural light would be required for this.

To explore the potential of TLS-based sleep movement of trees as an indicator of water use and water stress, further studies are required with simultaneous physiological measurements of trunk diameter, water potential, and photosynthetic activity and reference comparisons. This will allow (i) quantification of the limits of reliability of different terrestrial laser scanners to detect the temporal movements in different plant and tree species and (ii) modeling and further simulation of the relationship between the detected geometric behavior and direct physiological observations of plant water use and circadian rhythms.

## AUTHOR CONTRIBUTIONS

EP is the main author and took part in the planning of both experiments, collection of Finnish data, and performed the data analysis. CB, GM, and NP planned the Austrian dataset collection and contributed to the writing. MP planned and arranged the collection of Austrian dataset and contributed to writing the manuscript. MW processed the Austrian dataset for analysis. AZ strengthened introduction and discussion from biological and ecological perspective, and commented the whole manuscript.

## FUNDING

This article received support from Academy of Finland grants no. 265949 and no. 272195, and from the Finnish foundations mobility grant "Tutkijat maailmalle, osaamista Suomeen." AZ was supported by the OTKA grant PD 115833 of the Hungarian Research Fund.

### ACKNOWLEDGMENTS

The authors thank Sanna Kaasalainen, Teemu Hakala, Olli Nevalainen, Mika Karjalainen, Anssi Krooks, and Kati Anttila for their help with collecting the Finnish data, and Reinhard Plessl for collecting the Austrian data. We also acknowledge the support of Hermann Heilmeier, Biology and Ecology group at TU BAF in Freiberg (Germany).

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fpls.2016. 00222

Video 1 | Animation of the overnight movement in the Finnish birch point cloud from sunset to sunrise. Video is created by drawing birch point cloud of each scan collected during night. The point cloud scanned around sunset (19:40 o'clock) is drawn with black as a reference. The laser scanner was located in origin (0,0).

## REFERENCES

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Puttonen, Briese, Mandlburger, Wieser, Pfennigbauer, Zlinszky and Pfeifer. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Application of Leaf Ultrasonic Resonance to Vitis vinifera L. Suggests the Existence of a Diurnal Osmotic Adjustment Subjected to Photosynthesis

Domingo Sancho-Knapik1,2, Hipólito Medrano3 \*, José J. Peguero-Pina1,2 , Maurizio Mencuccini4 , Maria D. Fariñas5 , Tomás G. Álvarez-Arenas5 and Eustaquio Gil-Pelegrín1,2

#### Edited by:

Daniel H. Chitwood, Donald Danforth Plant Science Center, USA

#### Reviewed by:

Tobias Gebauer, University of Freiburg, Germany Tsu-Wei Chen, Leibniz University of Hanover, Germany

#### \*Correspondence:

Hipólito Medrano<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science

Received: 23 March 2016 Accepted: 11 October 2016 Published: 26 October 2016

#### Citation:

Sancho-Knapik D, Medrano H, Peguero-Pina JJ, Mencuccini M, Fariñas MD, Álvarez-Arenas TG and Gil-Pelegrín E (2016) The Application of Leaf Ultrasonic Resonance to Vitis vinifera L. Suggests the Existence of a Diurnal Osmotic Adjustment Subjected to Photosynthesis. Front. Plant Sci. 7:1601. doi: 10.3389/fpls.2016.01601 1 Unidad de Recursos Forestales, Centro de Investigación y Tecnología Agroalimentaria de Aragón, Gobierno de Aragón, Zaragoza, Spain, 2 Centro de Investigación y Tecnología Agroalimentaria de Aragón, Instituto Agroalimentario de Aragón, Universidad de Zaragoza, Zaragoza, Spain, 3 Research Group on Plant Biology under Mediterranean Conditions, Departament de Biologia, Universitat de les Illes Balears, Palma de Mallorca, Spain, 4 ICREA at CREAF, Barcelona, Spain, 5 Sensors and Ultrasonic Technologies Department, Information and Physics Technologies Institute, Spanish National Research Council, Madrid, Spain

The main objective of this study was to apply the air-coupled broad-band ultrasonic spectroscopy in attached transpiring leaves of Vitis vinifera L. to monitor changes in leaf water potential (9) through the measurements of the standardized value of the resonant frequency associated with the maximum transmitance (f/fo). With this purpose, the response of grapevine to a drought stress period was investigated in terms of leaf water status, ultrasounds, gas exchange and sugar accumulation. Two strong correlations were obtained between f/fo and 9 measured at predawn (pd) and at midday (md) with different slopes. This fact implied the existence of two values of 9 for a given value of f/fo, which was taken as a sign that the ultrasonic technique was not directly related to the overall 9, but only to one of its components: the turgor pressure (P). The difference in 9 at constant f/fo (δ) was found to be dependent on net CO2 assimilation (A) and might be used as a rough estimator of photosynthetic activity. It was then, the other main component of 9, osmotic potential (π), the one that may have lowered the values of md 9 with respect to pd 9 by the accumulation of sugars associated to net CO2 assimilation. This phenomenon suggests the existence of a diurnal osmotic adjustment in this species associated to sugars production in well-watered plants.

Keywords: diurnal osmotic adjustment, drought, gas exchange, leaf ultrasonic frequency, Vitis vinifera, water potential

**Abbreviations:** A, net CO2 uptake; Ca, ambient CO2 concentration; em, early morning; f/f o, standardized frequency; gs stomatal conductance; md, midday; pd, predawn; P, turgor pressure; RWC, relative water content; π, osmotic potential; 9, water potential.

## INTRODUCTION

fpls-07-01601 October 24, 2016 Time: 11:37 # 2

Grapevines are one of the world's most important commercial crops, not only from an economic point of view, but also because of the extension of its worldwide cultivation. A significant proportion of these vineyards grows under Mediterranean-type climates (Tonietto and Carbonneau, 2004), where Vitis vinifera L. has to cope with a summer water deficit that may affect berry quality (Chaves et al., 2007; Chaves et al., 2010). In such environments, climate change models (García-Mozo et al., 2010) predict an increment in extreme high temperature and drought events, which may represent a risk for the wine industry forcing it to a more frequent use of irrigation for affordable crop production (Chaves et al., 2007). The high water requirements of grapevines during the growing season (Netzer et al., 2005; Zhang et al., 2007) and the large dependence of berry quality parameters on soil water availability (Medrano et al., 2003; Keller et al., 2008; Flexas et al., 2010; Romero et al., 2010; Pou et al., 2011) justifies special attention in the optimization of water use during vineyard irrigation to achieve a more environmentally sustainable viticulture with a reasonable fruit quality (Jones, 2004).

Direct measurements of the plant stress response, 'plant stress sensing' according to Jones (2004), have been suggested as a better way to implement adequate irrigation scheduling compared to only estimating atmospheric water demand or soil moisture status (Jones, 1990, 2004, 2007). Among the methods that use the plant as an indicator, the air-coupled broad-band ultrasonic spectroscopy technique (Álvarez-Arenas et al., 2009; Sancho-Knapik et al., 2010, 2011, 2012), has been proven recently as a non-destructive, non-invasive and non-contact method for the dynamic determination of leaf water status in V. vinifera (Sancho-Knapik et al., 2013a; Fariñas et al., 2014). This method is based on the excitation of thickness resonances of the leaves and on the analysis of the spectral response in the vicinity of the first order thickness resonance (Álvarez-Arenas et al., 2009), and has been revealed as a good indicator of the water potential (9) and the RWC of leaves through changes in the f/f o at the maximum transmittance (Sancho-Knapik et al., 2010, 2013a). These changes in f/f o that occur before turgor loss can be attributed to changes in the macroscopic effective elastic constant of the leaf in the thickness direction (c33) (Sancho-Knapik et al., 2011) that are mainly associated with changes in the tautness of the microfibrils in the cell wall (Gibson and Ashby, 1997) and therefore with changes in the bulk modulus of elasticity of the cell wall (ε the change in turgor pressure for a given fractional change in the weight of symplasmic water) (Tyree, 1981; Sancho-Knapik et al., 2011). As ε is dependant on the variations in turgor pressure (Tyree and Jarvis, 1982), changes in f/f o before the turgor loss point can be attributed mainly to the variations in turgor pressure.

Leaf 9 is the sum of turgor pressure, or the outward hydrostatic pressure which is opposed by the cell wall (P, positive), osmotic potential, the component of the water potential due to the presence of solutes (π, negative) and matric potential, the component relative to the binding of water molecules to non-dissolves structures of the cells, which is negligible as compared with the other two (Koide et al., 1989). Loss of water from turgid attached leaf tissues in response to transpiration can decrease 9 not only through a significant decline in P, but also through a decline in π. Although variations in π can occur following passive concentration of solutes, this is generally less important when compared with the variation in P (Richter, 1978; Koide et al., 1989), associating the decrease in 9 when a turgid leaf losses water, mainly with a decrease in P. In this case, the relation between f/f o and 9 in attached leaves may be in line with previous works where processes occurring during leaf dehydration were studied (Sancho-Knapik et al., 2010, 2013a). On the other hand, photosynthetic products, besides being upload immediately to the phloem or converted into starch, can be accumulated, reducing also leaf π by a net increase in solutes (Acevedo et al., 1979). This process, called diurnal osmotic adjustment, has been revealed as a mechanism playing a key role in leaf expansion by minimizing the opportunities for significant water loss from leaf tissues (Acevedo et al., 1979; Girma and Krieg, 1992). Diurnal osmotic adjustment induces a significant reduction in 9 without any decrease in P, so that, a variation in 9 caused only by a net increase of solutes in the leaf may not induce a variation neither in RWC nor in f/f o. In this second case, the air-coupled broad-band ultrasonic spectroscopy technique may be used to appreciate mechanisms at leaf level that have been interpreted as the consequence of diurnal osmotic adjustment associated to photosynthesis when no changes in f/f o occur during a decrease in 9. In this sense, the aim of this study is to apply the air-coupled broad-band ultrasonic spectroscopy on V. vinifera to (i) monitor changes in f/f o with changes in leaf water potential on attached transpiring leaves and (ii) analyse the mechanisms that can suggest the existence of a diurnal osmotic adjustment associated with photosynthesis.

### MATERIALS AND METHODS

### Plant Material and Experimental Conditions

Two-year-old rooted cuttings of Vitis vinifera cv. Grenache were planted in 75-L containers with a mixture of 80% compost (Neuhaus Humin Substrat N6; Klasman-Deilmann GmbH, Geeste, Germany) and 20% perlite. Plants grew during 2 years in a common garden located at CITA de Aragón (41◦ 390N, 0◦ 520W, Zaragoza, Spain; mean annual temperature 15.4◦C, total annual precipitation 298 mm) with irrigation employed when necessary. Two weeks before the beginning of the experiment (starting date on 16 July 2014), three pots of each variety were placed under a transparent greenhouse tunnel of alveolar polycarbonate that allowed passing 90% of PPFD. The use of covers in water-stress experiments had the advantage of performing measurements in more controlled environmental conditions, avoiding re-watering by storms or unwanted rainfall events.

Watering was stopped on 15 July 2014 and measurements in well watered plants started on 16 July 2014. During the following days, measurements of water potential, gas exchange and ultrasounds were performed every 2 or 3 days with increasing levels of drought stress. pd measurements of ultrasounds and

water potential (9pd) were conducted strictly between 3 and 4 h (solar time), while md measurements of ultrasounds and water potential (9md) were made at 12 h (solar time). Measurements of gas exchange were made at 8 h solar time (em) and at md. Drought stress was imposed during 20 days. Finally, after the last measurement under drought stressed conditions, plants were rewatered and measurements were performed again after 2 days. In addition, leaves were collected at pd, em, and md for the measurement of sugars concentration, osmolality and RWC during the first and the last days of the drought period (when plants were well watered and just before rewatering, respectively). Leaves for RWC were previously measured with ultrasounds and water potential was also measured at em.

A second complementary experiment was carried out during summer 2015 on a well watered specimen located inside a plant chamber at low CO2 concentration (40–80 µmol mol−1 ). Water potential, ultrasounds and sugars concentration were measured on 10 leaves at pd and at md in order to obtain the response of a well watered plant when photosynthetic activity was impaired due to the almost complete absence of CO2. Under these conditions, the decrease of water potential at midday (9md) with respect to that measured at predawn (9pd) would be only affected by concentration of solutes due to the loss of water through transpiration and not by the accumulation of photosynthates. For more details of the plant chamber, see section below. The effect of low CO2 concentration on plant photosynthesis was previously checked on the same specimen during the previous day by measuring gas exchange at controlled cuvette CO2 concentration (Ca) between 30 and 90 mol mol−1 ).

#### Air-Coupled Ultrasonic Measurements

Two attached mature leaves per plant from three plants were selected and marked at the beginning of the experiment in order to perform all the pd and md ultrasonic measurements systematically on the same leaves. Magnitude and phase of the transmission coefficient were measured in the frequency domain (Sancho-Knapik et al., 2012). Then, in real time, the computer program adjusted theoretical curves to the measured curves of magnitude and phase and gave the value of the resonant frequency associated with the maximum transmitance at the peak curve (f, Hz) (Sancho-Knapik et al., 2010, 2012). One ultrasonic measurement was taken between 30 and 60 s. Afterward each value of f was divided by the value obtained before dawn at the beginning of the experiment when the plants were well watered (f o, Hz). The f/f o (non-dimensional) associated with the maximum transmittance at the peak curve was then obtained (Sancho-Knapik et al., 2011).

The air-coupled ultrasonic system used to obtain the resonant frequency of the leaves in this study was a more portable and easy-to-handle device (Álvarez-Arenas et al., 2016) compared to the one used in previous physiological studies (Sancho-Knapik et al., 2013a,b). The new device (**Figure 1**) consists in one pair of air-coupled transducers embedded in a U-shaped holder which was connected to a small pulser/receiver and to a laptop. The transducers were developed, designed and built at the Spanish National Research Council with a center frequency of 650 kHz, frequency band of 350–950 kHz and area diameter of 20 mm (see Álvarez-Arenas, 2004 for further details). The U-shaped holder maintains the transducers facing each other at a distance of 20 mm providing the necessary robustness that can be easily manipulated without affecting the integrity of the signal. The holder also had a slot in which leaves could be easily positioned between the transducers for the measurements (see Álvarez-Arenas, 2013 and Fariñas et al., 2014 for further details). The pulser/receiver is a commercial device (ULTRASCOPE USB, Dasel Sistemas, Madrid, Spain) which was used to drive the transmitter transducer with a semicycle of square wave (200 V amplitude), tuned to the transducers centre frequency, to amplify (40 dB) the electrical signal provided by the receiver transducer and to digitize this received signal for further processing. It includes pass-band digital (filtering) and extraction of the Fourier transform (using a built-in FFT algorithm). The measurement process was controlled via a graphical user interface (GUI) managed in LABVIEW and also designed by the Spanish National Research Council for this purpose.

### Water Potential, Gas Exchange and Relative Water Content

Predawn and midday leaf water potentials (9pd and 9md, MPa) were measured in one mature leaf per plant of V. vinifera with a Scholander pressure chamber following the methodological procedure described by Turner (1988). Briefly, in this technique a leaf was cut and placed in the pressure chamber with the cut end of the petiole just protruding from the chamber. The pressure inside the chamber was gradually increased by compressed nitrogen gas until the sap just returned to the severed ends of the xylem vessels. In this moment the pressure inside the chamber was recorded and taken as the value of water potential with the opposite sign. Net CO2 uptake (A, mol CO2 m−2 s −1 ) and gs (mmol H2O m−2 s −1 ) were measured in two mature leaves per plant located along the middle of the stem with a portable gas exchange system (CIRAS-2, PP-Systems, Herts, UK). Measurements were performed at controlled cuvette CO2 concentration (Ca = 400 mol mol−1 ), PPFD incident on the leaf surface [∼1300 and 1800 mol photons m−2 s −1 at em and md, respectively] and ambient relative humidity. RWC was calculated at the beginning and the end of the drought period as a ratio of the difference between leaf fresh weight (FW) minus leaf dry weight (DW) and the difference between leaf turgid weight (TW) minus leaf DW. To obtain RWC, 5 discs per leaf (1.8 cm in diameter) from one half of each blade from two leaves per plant were obtained with a cork borer and subsequently weighed (FW). Afterward discs were introduced in a stove (70◦C, 72 h) to obtain DW. The other half of the blade was rehydrated to full turgor by cutting carefully their petioles and submerging them in distilled water. Leaves were wrapped in plastic seal and stored in the fridge overnight. TW was then obtained from 5 disks per leaf.

#### Pressure-Volume Curves

Pressure-Volume (P-V) curves were determined using a Scholander pressure chamber following the free-transpiration

method described in previous studies (Turner, 1988; Dreyer et al., 1990). The weight and water potential were measured at different levels of RWC, starting at full turgor (TW) and until close to −2.5 MPa were reached. Two leaves per plant were collected at pd from well watered plants. Their petioles were carefully cut and submerged in distilled water until full rehydration. Afterward, leaves were wrapped in plastic seal and left overnight in the refrigerator. After the measurements, leaf DW was obtained by keeping the plant material in a stove (70◦C, 72 h). RWC was then calculated as explained above being FW the sample fresh weight at any moment. Additionally, ultrasounds measurements were simultaneously performed in order to relate the values of turgor pressure (P) derived from P-V curves with f/f o.

### Leaf Sugars Analysis and Osmolality

Two leaves per plant of three different plants were collected at pd, at em and at md from well watered plants (at the beginning of the experiment) and from drought stressed plants (just before rewatering). Leaves were cut from the plants and were introduced in glass tubes closed hermetically and kept in ice for leaf preservation. Immediately after, tubes were carried to the laboratory and were stored in a freezer at −80◦C until analysis. To obtain the expressed leaf sap, frozen leaves were easily broken with a glass rod and they were centrifuged at 5000 rpm for 20 min (Yu et al., 1999). For sugars analysis, 20 µL of the expressed sap extract was filtered by 0.45 µm nylon filters and injected in a HPLC 360 (Kontron, Milan, Italy), equipped with a double piston pump, self-sampler, and regulated furnace at 40◦C. The column

used was a 250 mm × 4.6 mm i.d., 5 mm, Kromasil Amine. The mobile phase was an isocratic elution of acetonitrile:water (75/25). Detection of sugars (fructose, glucose, and sucrose) was based on a liquid chromatographic method (AOAC, 1990) using a differential refractive index (RI) detector model ERC-7512 (Erma Inc., Tokyo, Japan) at 40◦C temperature. The linear range for the concentration determination of each compound was 0.05–2 g/100 ml. Identification of chromatographic peaks was based on retention times by comparison with known standards (Merck, Darmstadt, Germany). An external calibration curve was prepared for each carbohydrate standard to calculate the amount of these compounds present in the leaf extract. The percentage weight:volume (% w:v) of sugars (fructose, glucose and sucrose) was finally obtained. On the other hand, another aliquot (10 µl) was used for measuring the osmolality (mmol Kg−1 ) of expressed sap of em and md samples with a calibrated vapor pressure osmometer (Wescor Vapro model 5500, Wescor, Logan, UT). Osmotic potential of the expressed sap was then calculated from the osmolality using the Van't Hoff equation (Callister et al., 2006).

#### Plant Chamber

The chamber consisted of a Teflon FEP (Fluorinated Ethylene Propylene copolymer) film rolled and stapled into a wood rectangular frame (80 cm × 80 cm × 150 cm). A tape was used to seal the chamber and a 10-cm2 hole was left in one of the upper corners to have an open flow. Teflon FEP was used because of its low permeability to liquids and gasses and its excellent transmission in the infrared and visible range of the solar spectrum (Liu et al., 2000). The plant chamber was screwed on a wood base (100 cm × 100 cm) where a few holes were cut to accommodate the plant stem (3.8 cm in diameter) and the air inlet tubes (10 mm in diameter). The base was then cut in half through the stem opening so that it could be moved on and off the plant. Two chest-latches held the base together during operation. A sleeve of sealed-cell foam was placed around the plant stem. The foam was slightly larger in diameter than the opening for the vine stem, enabling the chamber base to compress the sleeve and form a tight seal around the stem. This design separated the plant from the potting soil to eliminate the effects of soil and root respiration on CO2 determinations (Miller et al., 1996). Finally, the joining between the chamber and the base was sealed with a plastic adhesive tape.

The air-supply system consisted of an air compressor (model LX 108, Atlas Copco AB, Stockholm, Sweden) with an output of c.a. 2000 l/min and a maximum pressure of 10 bar. This compressor was attached to a "T" connector through an 8-mmi.d., polyamide tube. From the connector, two polyamide tubes ended in two clear acrylic pipes (38-mm-i.d., and 1.30 m in length) that were filled up with soda lime and molecular sieve (90:10) in order to lower the air CO2 concentration inside the chamber. Two more polyamide tubes connected the end of the pipes to the base of the plant chamber. CO2 concentration was measured during the experiment with a Carbon Dioxide Probe (GMP343, Vaisala CARBOCAP, Helsinki, Finland) obtaining concentrations levels inside the chamber between 40 and 80 ppm. Two small electric fans (12 cm × 12 cm × 3.8 cm) were located on the wood base to stir the air throughout the chamber. Finally, a small rocking piston (model ROA-P201-BN; Gast Manufacturing Inc., Benton Harbor, MI, USA) with an output of 35 l/min and a maximum pressure of 6.9 bar was used to recirculate the chamber air through another acrylic pipe filled with silica gel in order to dry the chamber air and avoid a water-saturated atmosphere.

#### Statistical Analysis