How does the Proximodistal Twisting of Spring Barley (Hordeum

Transcription

Dornbusch_and_wernecke.fm Seite 2 Freitag, 16. November 2007 1:56 13
Pflanzenbauwissenschaften, 11 (Sonderheft). S. 2–9, 2007, ISSN 1431-8857. © Eugen Ulmer KG, Stuttgart
How does the Proximodistal Twisting of Spring Barley (Hordeum
vulgare L.) Leaf Blades Influence the Leaf Angle Distribution?
Wie beeinflusst die proximodistale Verdrillung von Blattspreiten der Sommergerste
(Hordeum vulgare L.) die Blattwinkelverteilung?
T. Dornbusch & P. Wernecke
Institut für Agrar- und Ernährungswissenschaften, Universität Halle-Wittenberg
Summary
The angular orientation of leaves inside a canopy is one of
the major determinants of the radiation intercepted. In this
paper we discuss the impact of the twisting of spring barley
(Hordeum vulgare L. cv. Barke) leaf blades on the leaf angle
(azimuth and inclination angle) distribution. The three-dimensional morphology of field grown plants was digitized
using the silhouette method and reconstructed as a set of
elementary triangles with an architectural model. The leaf
angle distribution was calculated from the normal vectors
of the triangles. On the barley cultivar investigated here,
we observed that leaf blade surfaces twisted up to 1.5 times
around their proximodistal axis from the base to the tip.
In the model, leaf twisting is described by a mathematical
function (leaf-twist-function). To obtain the leaf angle distribution for hypothetical plants with straight (non-twisted)
blades, the parameters of the leaf-twist-function in the
model were set to zero. The resulting leaf angle distribution
was compared to the one computed previously for twisted
leaf blades. This revealed that twisting of leaf blade surfaces
leads to a homogenization of the azimuth angle distribution
and to a shift of the inclination angle towards steeper
angles.
Key words: leaf angle distribution, leaf orientation, barley,
architectural model, leaf twisting
Zusammenfassung
Die Winkelverteilung der Blattelemente in einem Pflanzenbestand ist eine der wichtigsten Kenngrößen, um die
Strahlungsinterzeption der Organe zu beschreiben. In dieser Arbeit soll der Einfluss der proximodistalen Verdrillung
von Blattspreiten auf die Blattwinkelverteilung (Azimutund Höhenwinkel) am Beispiel der Sommergerste (Hordeum vulgare L. cv. Barke) eingehender untersucht werden.
Zu diesem Zweck wurde die dreidimensionale Morphologie von Freilandpflanzen mit der Silhouettenmethode digitalisiert und als ein Satz von Dreiecken durch ein Architekturmodell rekonstruiert. Die Blattwinkelverteilung lässt
sich aus den Dreiecksnormalen berechnen. Die Blattspreiten der untersuchten Gerstensorte weisen eine starke Verdrillung von bis zu 1,5 Umdrehungen vom Blattgrund bis
zur Spitze auf.
Die Verdrillung der Blattspreiten wird im Modell durch
eine mathematische Funktion (Blattverdrillungsfunktion)
beschrieben. Um die Blattwinkelverteilung für hypothetische Pflanzen mit geraden (nicht verdrillten) Blättern zu
erhalten, wurden die Parameter in der Blattverdrillungsfunktion im Modell auf Null gesetzt. Die resultierende
Blattwinkelverteilung wurde dann mit der zuvor berechneten Verteilung für verdrillte Blattspreiten verglichen.
Dies zeigte, dass die Verdrillung von Blattspreiten zu einer
Homogenisierung der Azimutwinkelverteilung und zu einer Verschiebung des Höhenwinkels in Richtung steilerer
Blattwinkel führt.
Schlüsselworte: Blattwinkelverteilung, Blattausrichtung,
Gerste, Architekturmodell, Verdrillung
Introduction
The position and orientation of assimilating organs within
a canopy affect their ability to exchange mass and energy
with the environment, including photosynthesis and transpiration. A quantitative description of these complex interactions requires the application of mathematical models. In ecophysiological research, emphasis has been put
on modeling canopy - environment interactions, beginning with the pioneering work of MONSI & SAEKI (1953),
who pointed out that information on canopy architecture
is of great importance. Building on that work further
approaches to model canopy - environment interactions
were developed (e.g. DE WIT 1965, NORMAN 1974, ROSS
1981, 1998). Canopy architecture is approximated in such
models as a so-called turbid medium (KUBELKA & MUNK
1931). A turbid medium consists of an amalgam of small
surfaces (i.e. foliage elements) with a certain size, position
and angular orientation as well as certain optical properties. The surfaces are homogeneously distributed within a
horizontal plane in a defined volume. In the vertical direction (z) the distribution of foliage area and their angular
orientation is described by mathematical functions of z.
Several methods were developed in the past and applied to
quantify the vertical distribution and orientation of leaves
in a specific canopy (NORMAN & CAMPBELL 1989, ROSS 1981).
While in those approaches the canopy is described as a turbid medium, JAHNKE & LAWRENCE (1965) brought up the
idea to describe the crown structure of trees with simple
geometric shapes. With the upcoming availability of computer resources and three-dimensional (3D) measurement
techniques (MOULIA & SINOQUET 1993) it was possible to refine the 3D description of canopies with geometric shapes
up to the level of individual organs. Nowadays several
architectural models have been developed and parameterized for several crops and for specific environmental conditions (PRÉVOT et al. 1991, PEARCY & YANG 1996, FOURNIER
Pflanzenbauwissenschaften Sonderheft 2007
Dornbusch & Wernecke: Proximodistal Twisting of Spring Barley (Hordeum vulgare L.) Leaf Blades
& ANDRIEU 1998, GENARD et al. 2000, EVERS et al 2005,
WATANABE et al. 2005, GUO et al. 2006). Such detailed 3D
models of plant architecture are the prerequisite to describe plant - environment interactions on an organ scale
and allow to compute the microclimate inside the canopy
in detail (CHELLE 2005). Coupling of architectural and process based models gave rise to so-called functional-structural plant models (FSPMs; GODIN & SINOQUET 2005),
which potentially allow a better understanding and prediction of the spatiotemporal patterns of plant structures and
related processes during ontogenesis.
Size, position, optical properties and the angular orientation of foliage elements in the 3D space calculated with
an architectural model are the determinants to describe
the radiation field inside a canopy with radiation transfer
models (DE WIT 1965, ROSS 1981, GOUDRIAAN 1988) and
thus to determine the absorption of photosynthetically
active radiation used for primary production. The vertical
distribution of the foliage (leaf) area, e.g. expressed as the
downward cumulative leaf area index, was extensively discussed for numerous graminaceous species (BISCOE et al.
1975, BARNES et al. 1988, DWYER et al. 1992, BOEDHRAM et al.
2001, CATON et al. 2002). Much fewer studies deal with the
leaf angle distribution. For example, under fully irrigated
conditions, i.e. no water stress, INNES & BLACKWELL (1983)
associated wheat cultivars with more erect leaves with
more biomass and yield compared to cultivars with more
horizontal leaves. In contrast, ANGUS et al. (1972) found no
significant differences in yield between two barley cultivars contrasting in leaf angle distribution, but measured a
more evenly distributed net photosynthesis in the canopy
with more erect leaves.
In this paper we want to assess the magnitude of the
proximodistal twisting of spring barleys leaf blades and
discuss its impact on leaf angle distribution as one determinant of the radiation absorption of a plant stand. The study
presented here was embedded in a research project on the
development of an FSPM for spring barley (German Research Foundation (DFG), projects 'Virtual Crops' and 'Virtual Crops – Barley').
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some quantification of it. On his plants leaves twisted less
than one complete rotation. However, he did not evaluate
the impact on leaf angle distribution.
For our study the 3D architecture of sample plants
grown in a field trial was digitized and yielded a unique set
of parameter values for the architectural model to rebuild
the measured (real) 3D architecture for each plant as a set
of polygons, where each polygon represents a foliage (leaf
and stem) element. The angular components (azimuth and
inclination, definition given later) of the direction vectors
of polygon normals determine the leaf angle distribution.
We then used the same values for model parameters, but
set the ones describing leaf twisting to zero to obtain
straight (non-twisted) blades. The resulting leaf angle distribution was computed and compared to the leaf angle
distribution of the corresponding canopy with twisted leaf
blades.
Field trial
A field trial was conducted at Bad Lauchstädt (51°24’ N,
11°53’ E). A characterization of the site can be found in
ALTERMANN et al. (2005). Spring barley (Hordeum vulgare L.
cv. Barke) was sown on March 29, 2005 (280 seeds m–2).
Nitrogen was applied as calcium ammonium nitrate at a
dose of 60 kg N ha–1 shortly after sowing. The application
of the required nutrients, cultivation procedures and plant
protection followed official German recommendations.
Subplots of 1 m2 were marked after the appearance of the
first leaf. The total number of plants and the number of
tillers in each subplot were counted to determine the average number of tillers per plant. Plants having an average
number of tillers were defined as median plants and used
for sampling at three ontogenetic stages. Tillers of about
50 plants were marked with small colored metal rings in
order to ensure a clear identification of tillers while
sampling according to the nomenclature after SKINNER &
NELSON (1992). At each sampling date 5 to 10 marked
median plants were carefully removed from the plot, transferred into a pot and watered. Measurements were then
performed in the laboratory.
Materials and methods
3D digitization
Architectural model
In the architectural model, two different types of organs
are specified: i) blades and ii) stems. The proximodistal
axis of each organ is described by a set of discrete points
denoted as Pa. In contrast to DORNBUSCH et al. (2007), who
used measured 3D point clouds as a data base for the model, here we applied the silhouette method after BONHOMME
& VARLET-GRANCHER (1978). The required procedure comprises: i) measurement of organ azimuth angle, ii) careful
separation of the plant from its roots, iii) taking a photo of
the separated plant shoot in front of an evenly-spaced reference grid using a digital CCD camera with the camera
normal to the reference grid (Fig. 1a), iv) selection of organ axis points in the acquired image (image processing)
and v) transformation of pixel coordinates into Cartesian
coordinates taking the organ azimuth into account
(Fig. 1b). From the photo, only the two-dimensional (2D)
organ orientation can be quantified, but not the organ
azimuth angle, which must be measured manually on the
plant before it is removed from the pot. We used a protractor for this.
The processing of the acquired 2D images of a whole
plant involves the selection of points along respective
organ axes via mouse click. Beforehand, a rectangular reference coordinate system must be defined on the reference
grid. Pixel coordinates of the axis points selected are trans-
To give an answer to the question posed the use of a 3D
architectural model, which describes the twisting of leaf
blades, is required. Such a model was introduced in a previous paper by DORNBUSCH et al. (2007). It distinguishes
between the 3D description of blades and stems. Here we
only look at blades, which are described as a set of polygons, whose conjoint surface represents the measured
organ shape. In the model, blades are attached to the stem
in a vertical sequence according to the phyllotaxis and have
a specific proximodistal curvature. The lateral blade axis
(left to right side) is represented as a line and the dorsiventral axis (thickness) is assumed to be zero. In reality blades
have a more complex 3D structure. They can be twisted
along their proximodistal axis (e.g. barley, wheat), be
undulated (maize), have a U- or V-shaped lateral axis and,
of course, have a certain thickness. Only a few of these
morphological traits have been subject to research to assess their potential impact on the radiation balance. ESPAÑA
et al. (1999) concluded that the undulation of maize leaf
blades could induce significant changes of the leaf inclination distribution function when looking at the specular direction for specular leaves. LEWIS (1999) incorporated leaf
twisting into his architectural model for wheat and gave
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Fig. 1: a) Image of a spring barley plant (shoot) in front of an evenly-spaced reference grid; black crosses indicate the coordinate system for the transformation of pixel into Cartesian coordinates; dots indicate points selected via mouse click to represent
the axis of the main stem (black) and of a leaf blade (white); b) set of organ axis points Pa extracted from Fig. 1a.
a) Foto einer Sommergerstenpflanze (Spross) vor einem Referenzgitter; schwarze Kreuze kennzeichnen das Koordinatensystem für die
Umwandlung der Pixelkoordinaten in kartesische; Kreise markieren die mit der Maus selektierten Achsenpunkte des Haupttriebes
(schwarz) und einer Blattspreite (weiß); b) Satz von Achsenpunkten Pa, die aus Abb. 1a entnommen wurden.
formed into Cartesian coordinates in the reference coordinate system (determined by the grid) using the given
image resolution in dots per inch (dpi). For further details
see BONHOMME & VARLET-GRANCHER (1978) or SINOQUET et al.
(1991).
After extraction of the organ axis points, the remaining
parameters describing the shape of blades need to be evaluated, i.e. the parameters of the so-called leaf-twist-function ψ(s) and of the leaf-width-function b(s). First we look
at the former:
ψ ( s ) = ψ 0 + ∆ψ ⋅ s ⋅
(1 + c 3 ⋅ s )
, (0 ≤ s ≤ 1; c 3 > −1)
(1 + c 3 )
(1)
where ψ0 = basal rotation angle, ∆ψ = ψ1 – ψ0, i.e. the
difference between distal (ψ1) and basal rotation angle,
c3 = curvature parameter and s = normalized axis position,
which is obtained by dividing the distance from the organ
base by the total length of the organ. Eq. 1 is a second order
polynomial in s, written in a way such that function parameters are directly interpretable in terms of surface characteristics (DORNBUSCH et al. 2007). Looking at a 2D image of
a blade (schematically illustrated in Fig. 2a) the projected
blade width along the proximodistal axis shows a characteristic pattern, where a local maximum is followed by a
local minimum (and vice versa). This pattern arises due to
the twisting of the surface, i.e. an increase in the rotation
angle (in radians) ψ(max ↔ min) = π/2 from the base to
the tip. The axis points related to these extrema can be
visually identified by the user and marked during the selection of Pa (cf. Fig. 1a). In Fig. 2a local maxima are at
x ≈ 3.2 cm and 7.3 cm, local minima at x = 0 cm, x ≈ 5.7 cm
and 9.0 cm, where x is axis position, i.e. the distance from
the organ base. The corresponding rotation angles ψ(x)
are ψ(0) = 0, ψ(3.2) = π/2, ψ(5.7) = π , ψ(7.3) = 3π/2 and
ψ(9) = 2π. Dividing x by the total axis length yields the
normalized axis position s. The crosses in Fig. 2b show the
rotation angle as a function of s. These points are used to
parameterize the leaf-twist-function using least squares
minimization.
While the organ axis points and the twisting of blades
can be estimated by processing the 2D digital images of
whole plants obtained with the silhouette method as just
described, this approach is not appropriate for the quantification of organ shape, i.e. the evaluation of the parameters in the leaf-width-function:
b( s ) = bmax ⋅
(c
1
+ s )⋅ c 2 ⋅ (1 − s )
c2

 c 2 

(1 + c1 )⋅ 
 c 2 + 1 

c 2 +1
, (0 ≤ s ≤ 1; c1,c2 > 0; c1 ⋅ c2 ≤ 1)
(2)
where bmax = maximum blade width, c1, c2 = curvature parameters and s = normalized axis position. The derivation
of Eq. 2 was given by DORNBUSCH et al. (2007). Blades were
cut from the corresponding tiller after a picture of the
whole plant had been taken (cf. Fig. 1a) and then placed
on a flat-bed scanner (Epson GT 15000, Seiko Epson Corp,
Nagano, Japan). Blade surfaces were scanned at a resolution of 300 dpi using a black background surface with low
reflectivity. Sets of pixels in the acquired image are related
to each organ and transformed into Cartesian coordinates
using the given image resolution (300 dpi). As a result one
gets clusters of points (with z-coordinate = 0) related to
Fig. 2: a) Leaf blade surface (side view) computed with the
architectural model using a given set of values for the parameters in the leaf-twist-function (Eq. 1; ψ0 = 0, ∆ψ = 2π, c3 = 1);
x is the distance from the organ base; black dots represent the
points of local minima and maxima of the projected area
along the organ axis (selected via mouse click), where the surface is twisted by a further π/2 (90°); b) rotation angle ψ(s) vs.
normalized axis position s; crosses represent the rotation
angle (at π/2 steps) obtained from Fig. 2a; the solid line represents Eq. 1 fitted by least squares minimization.
a) Oberfläche einer Blattspreite (Seitenansicht), die mit einem
gegebenem Satz von Parameterwerten für die Blattverdrillungsfunktion (Gleichung 1; ψ0 = 0, ∆ψ = 2π, c3 = 1) mit dem
Architekturmodell berechnet wurde; x ist der Abstand vom Blattgrund; schwarze Punkte markieren die lokalen Minima und Maxima der projizierten Fläche (mit der Maus selektiert), an deren
Position die Blattoberfläche um einen Winkel von π/2 (90°) weitergedreht ist; b) Drehwinkel ψ(s) als Funktion der normalisierten
Achsenposition s; Kreuze markieren die Drehwinkel (Schrittweite
π/2), die in Abb. 2a ermittelt wurden; die Linie repräsentiert
Gleichung 1, deren Parameter mit der Methode der kleinsten
Abweichungsquadrate geschätzt wurden.
specific blades or stems, which can be used to quantify
organ dimensions as proposed by DORNBUSCH et al. (2007).
The basic idea of their approach is to generate a triangulated surface and to find the optimal values for the respective
parameters in the architectural model by least squares
minimization.
To demonstrate the effect of blade twisting on leaf angle
distribution, plants sampled from the field at three ontogenetic stages (BBCH; cf. MEIER 1997) were used: i) BBCH 30
– beginning of stem elongation, ii) BBCH 37 – beginning of
flag leaf emergence and iii) BBCH 45 – late boot stage. A
3D representation of sampled plants is given in Fig. 3. In
order to evaluate the impact of blade twisting on the leaf
angle distribution, all plants shown in Fig. 3a-c were
recomputed with straight (non-twisted) blades. To do this
the same measured values for the model parameters were
employed, except the ones in the leaf-twist-function (Eq. 1),
which were set to zero (ψ0 = ∆ψ = c3 = 0). This yields 3D
representations of blades, which are not twisted (Fig. 3e).
In the following, plants computed with the measured set of
parameter values for twisted blades are referred to as BLtw,
the corresponding ones with straight blades as BLst.
Computation of leaf angle distribution
In the architectural model the organ surfaces of a virtual
plant are represented by a set of elementary triangles (a
triangle being the simplest polygon) TriL (1 ≤ L ≤ntri),
where ntri is the total number of triangles. The vector rL
normal to TriL is defined as:
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Fig. 3: Spring barley plant stand at three different ontogenetic stages (BBCH), computed with the architectural model
and using Matlab® visualization routines: a) BBCH 30, b) BBCH
37, c) BBCH 45, d) magnified view of Fig. 3a, e) plant stand displayed in Fig. 3a computed with the same set of values for the
model parameters, but with twisting of leaf blades removed.
Sommergerstenbestand, der mit dem Architekturmodell berechnet und mit Matlab® visualisiert wurde, zu drei Ontogenesestadien (BBCH): a) BBCH 30, b) BBCH 37, c) BBCH 45, d) vergrößerte
Ansicht von Abb. 3a, e) Pflanzenbestand von Abb. 3a, der mit
dem gleichen Satz von Parameterwerten, aber ohne die Verdrillung der Blattspreiten, berechnet wurde.
 cos (θ L )⋅ cos (ϕ L )


rL =  sin (θ L )⋅ cos (ϕ L ) , (1 ≤ L ≤ ntri )


sin (ϕ L )


(3)
where θL = angular displacement in radians of the vector rL
in the horizontal direction measured clockwise from the
positive x-axis (azimuth angle) and φL = angular displacement of rL in radians in the vertical direction measured
counterclockwise from the x-y plane (inclination angle).
The definition of these angles is illustrated in Fig. 4. The
leaf angle distribution functions g(θL) and g(φL) are calculated as:
g (θ L ) = g (θ i′) =
∑ A′
∑ A
L,i
L
, (i = 1, ..., 36 )
(4.1)
∑ A′
∑ A
(4.2)
L
g (90 ° − ϕ L ) = g (ϕ i′) =
L,i
L
, (i = 1 ,...,18 )
L
′ i = sum of the area of triangles, whose normal
where ∑ AL,
falls into the i-th angle class θ i′ or ϕ i′ , respectively, and
∑L AL = sum of the area of all triangles. Since it is more
common to present the inclination angle of the surface rather than the one of the normal, we used g(ϕL) = g(90° − ϕL)
for the presentation of the results. Here the azimuth angle
θ (0° ≤ θ ≤ 360°) is divided into 36 angle classes θ i′ , each
10° wide. For example, all triangles, whose normal vector
rL has an azimuth angle 0° ≤ θL < 10°, are put into the first
angle class θ1′ . The inclination angle ϕ (0° ≤ ϕ ≤ 90°) is
divided into 18 classes ϕ i′ , each 5° wide. Note that rL can
point into the upper (ϕL > 0) or into the lower hemisphere
(ϕL < 0). For light interception, it does not matter whether
the upper or the lower side of a leaf is illuminated so that we
always consider the side pointing towards the upper hemisphere. In the following we differentiate between the distribution functions g~ (θ L ) and g~ (ϕ L ) for BLtw (twisted leaf
blades) and g (θ L ) and g (ϕ L ) for BLst (straight leaf blades).
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Fig. 4: Normal vector rL of an elementary triangle TriL with its
centroid at the origin (triangle not shown) with the components azimuth angle θL and inclination angle ϕL (cf. Eq. 3).
Normalenvektor rL eine Dreiecks TriL mit dem Schwerpunkt am
Ursprung (Dreieck nicht dargestellt) mit den Komponenten
Azimutwinkel θL und Höhenwinkel ϕL (vgl. Gleichung 3).
Results
Measured parameters of the leaf-twist-function
Using the silhouette method explained above, the values
for the parameters in ψ(s) (Eq. 1) for the various leaf
blades in Fig. 3 were estimated. Values for ψ0 were very
close to zero in all measurements (data not shown), which
means that the basal part of the blade surface is horizontally oriented. The parameter with the most important impact on blade twisting is the cumulative rotation angle ∆ψ.
Values obtained for ∆ψ are shown in Fig. 5a. The magnitude of ∆ψ = π means that a blade surface is twisted such
that the morphological upper side of the blade is pointing
towards the soil at the tip. The magnitude of ∆ψ increases
with leaf blade rank up to ∆ψ > 2π for blade B4 on the main
stem, which is more than a complete rotation of the blade
surface, and then decreases towards the flag leaf blade B9.
Blades of axillary tillers show a similar pattern (data not
shown). As the error bars indicate, values for ∆ψ show a
large variability owing to biological variability on the one
hand and to inaccuracies of the measurement method
applied on the other.
Estimated values for the curvature parameter c3 also
show a great variability (Fig. 5a) and are always positive,
which means that the course of ψ(s) describes a concave
parabola, i.e. dψ(s)/ds increases linearly towards the blade
tip. In a few cases we received very large values for c3.
However, for values > 10 it has only a negligible impact on
the course of ψ(s). In Fig. 5b we therefore did not consider
values > 100, in which case no error bars are shown.
Azimuth angle distribution functions
The azimuth angle distribution functions g~ (θ L ) for BLtw
and g (θ L ) for BLst were calculated from the set of triangles as explained in the materials and methods section.
The results are given in Fig. 6. Estimated values for g~ (θ L )
(Fig. 6 ~
a -~
c ; solid lines) do not deviate very much from an
ideal spherical distribution g ref (ϕL ) (dotted line), except
for some outliers. There is no trend in the data towards a
preferred azimuthal orientation of blade area, e.g. south or
Fig. 5: Estimated values for a) the cumulative rotation angle
∆ψ and b) the curvature parameter c3 (both from Eq. 1) of
main stem leaf blades for all (5 to 10) digitized plants for three
ontogenetic stage (BBCH). Missing error bars indicate that no
data was available, because blades were not fully emerged or
already dead (small bars), or that some values were not considered (large bars).
Berechnete Parameterwerte a) für die kumulativen Drehwinkel
∆ψ und b) für den Krümmungsparameter c3 (beide aus
Gleichung 1) von Blattspreiten des Haupttriebes aller (5 bis 10)
digitalisierten Pflanzen für drei Entwicklungsstadien (BBCH).
Wenn keine Fehlerbalken dargestellt sind, fehlen entweder Daten,
da die Blattspreiten noch nicht vollständig entfaltet oder schon
tot waren (kleine Säulen), oder einige Werte wurden nicht berücksichtigt (große Säulen).
perpendicular to the row direction. This result obtained for
spring barley supports the assumption of a ideal spherical
distribution of the azimuth angle of the leaf area, which is
made in most radiation transfer models (DE WIT 1965, ROSS
1981, VERHOEF 1984). In contrast to g~ (θ L ) , the azimuth
angle distribution function g (θ L ) (Fig. 6 a - c ) obtained
for BLst shows a clear deviation from g ref (ϕL ) . There are
peaks for specific azimuthal orientations of blade area for
all three plant stands, but there is no obvious trend concerning the direction of these peaks. Comparing the results
of both simulations one can say that the twisting of blade
surfaces leads to a homogenization of the azimuth angle
distribution so that blades in the canopy are able to capture
the radiation, which comes from different directions, more
efficiently.
Inclination angle distribution functions
The inclination angle distribution functions g~ (ϕ L ) and
g (ϕ L ) are presented in Fig. 7a-c. The course of g~ (ϕ L ) reveals that the total blade area pointing into a specific direction ϕL increases as this angle ϕL gets bigger. The calculatPflanzenbauwissenschaften Sonderheft 2007
Fig. 6: Azimuth angle distribution functions g~ (ϕ L ) (Eq. 4.1)
for the three measured plant stands with twisted leaf blades
(hyperscript ˜, left side), and g (ϕ L ) for the simulated plant
stands with straight ones (hyperscript ˜, right side); a)
BBCH 30, b) BBCH 37, c) BBCH 45; the dotted circle represents
an ideal spherical distribution function g ref (ϕL ) , the arrow indicates the direction of the rows.
Verteilungsfunktion der Azimutwinkel g~ (ϕ L ) (aus Gleichung 4.1)
für die drei gemessenen Pflanzenbestände mit verdrillten Blattspreiten (Hyperskript ˜, linke Seite), und g (ϕ L ) für die simulierten Pflanzenbestände mit geraden Blattspreiten (Hyperskript ˜,
linke Seite); a) BBCH 30, b) BBCH 37, c) BBCH 45; die gepunktete
Linie zeigt die ideale sphärische Verteilungsfunktion g ref (ϕL ) ,
der Pfeil kennzeichnet die Reihenausrichtung.
ed mean inclination angles for the plants at the three different ontogenetic stages are: 65.1° (BBCH 30), 67.8°
(BBCH 37) and 61.4° (BBCH 45). This compares to a mean
inclination angle for an ideal spherical distribution of
57.4°. Here the observed pattern of g~ (ϕ L ) deviates from
an ideal spherical distribution by having more blade area
at steeper inclination angles, but less at lower ones.
Looking at g (ϕ L ) computed from BLst the pattern is
similar to g~ (ϕ L ) . However, the course of g (ϕ L ) reveals
that in the canopy with straight blades there are fewer
blade surfaces with steep (leaf) angles and more with flat
(leaf) angles. This is also reflected in lower values for the
mean inclination angles: 54.3° (BBCH 30), 59.0° (BBCH
37) and 53.6° (BBCH 45). In conclusion, the twisting of
blades observed in the cultivar under investigation leads to
a shift of the inclination angle towards steeper values compared to non-twisted blades.
7
Fig. 7: Inclination angle distribution functions g~ (ϕ L )
(Eq. 4.2) for the three measured plant stands with twisted leaf
blades (circles), and g (ϕ L ) for the simulated plant stands
with straight ones (triangles); a) BBCH 30, b) BBCH 37, c) BBCH
45; 0° = horizontal, 90° = vertical; the dotted line represents
an ideal spherical distribution function g ref (ϕL ) .
Verteilungsfunktion des Höhenwinkels g~ (ϕ L ) (aus Gleichung
4.2) für die drei gemessenen Pflanzenbestände mit verdrillten
Blattspreiten (Kreise), und g (ϕ L ) für die simulierten Pflanzenbestände mit geraden Blattspreiten (Dreiecke); a) BBCH 30,
b) BBCH 37, c) BBCH 45; 0° = horizontal, 90° = vertikal; die
gepunktete Linie zeigt die ideale sphärische Verteilungsfunktion
g ref (ϕL ) .
Discussion
The leaf angle distribution within a stand is among the
factors which have to be considered to understand the
radiation regime within canopies (SCOTT & WELLS 2006).
As a contribution to evaluating the impact of morphological characteristics of plant organs on the leaf angle distribution, we looked at the impact of twisting of spring barley
leaf blades with the help of an architectural model for leaf
blades. On the barley cultivar investigated here we ob-
8
served cumulative rotation angles of up to ∆ψ = 3π, which
means that leaf blades rotate up to 1.5 times from their
base to the tip. Only leaf blades were considered here as
the source of leaf angle variation in cereals, since leaf
sheaths are usually oriented approximately vertical. As
outlined in the previous section, twisting of leaf blades
leads to a homogenization of the azimuth angle and to a
shift towards steeper inclination angles.
The amount of data available in our study is too small to
allow a statistical analysis of the impact of leaf blade twisting on leaf angle distribution. This is due to the fact that
quantification of canopy architecture with the procedures
described above is quite time-consuming. To digitize the
architecture of a field-grown barley plant at heading, two
workers need about two hours for sampling and subsequent analysis. Hence, it is difficult to obtain sufficient replications on one sampling day for statistical analysis. To get
more data, faster digitization or more workers would be
needed. However, the aim of this paper is a first look at the
influence of leaf blade twisting on the angle distribution to
identify further research aspects concerning this topic. For
this purpose the amount of data is sufficient.
The procedures applied to obtain values for the architectural model parameters, in particular i) the cutting of plants
and their positioning in front of a reference grid, ii) the measurement of organ azimuth angle and iii) the selection of organ axis points and of points, where the blade is twisted by
a further 90°, are prone to inaccuracies. However, in the
field, plant architecture shows a large variability, too, and
sometimes changes rapidly due to external forces such as
wind or precipitation. Hence, the procedural inaccuracies
do not seriously impair the ability of the architectural model
to depict the 3D morphology of a plant stand realistically.
The proposed method for obtaining values for the model
parameters, i.e. a combination of digitization and destructive sampling of organs in the laboratory, has some advantages. It offers the possibility of further organ-related analyses such as e.g. optical properties, dry mass or carbon/
nitrogen content. Such data are necessary for the calibration of FSPMs (MÜLLER et al. 2007, WERNECKE et al. 2007).
The use of other 3D digitizing devices, which can be
applied in the field, such as techniques using ultra sound
(HANAN 1997) or magnetic fields (RAAB et al. 1979), is also
worth considering. However, these methods also require
an interactive selection of organ points, which again limits
the number of measurements. Nowadays, new digitizing
techniques are available to measure the 3D surface structure of objects holisticly (KRIJGER et al. 1999, STUPPY et al.
2003, HANAN et al. 2004, KAMINUMA et al. 2004). The application of such techniques to quantify the 3D architecture of
plants seems to be promising as discussed in detail in a
previous paper (DORNBUSCH et al. 2007).
Further work should focus on the coupling of our architectural model with process models as mentioned in the introduction, in particular i) a radiation transfer model (e.g.
VERHOEF 1984, ROSS & MARSHAK 1988, CHELLE & ANDRIEU
1998) to assess the amount of radiation absorbed, ii) a
model to calculate photosynthetic carbon assimilation
(e.g. COLLATZ et al. 1991, NIKOLOV et al. 1995, MÜLLER et al.
2005) and iii) a model for the carbon distribution within
the plant, which drives growth processes (MINCHIN et al.
1993, LACOINTE 2000, WERNECKE et al. 2007).
Acknowledgements
The authors would like to thank Prof. Dr. H. Borg for critical
reading of the manuscript. We thank the German Research
Foundation (DFG) for supporting this study (DI 294/23).
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Received on December 15, 2006;
accepted on April 20, 2007
Address of the authors: Tino Dornbusch, Peter Wernecke, Martin-Luther-Universität Halle-Wittenberg, Institut für Agrar- und Ernährungswissenschaften,
Crop Science Group, Ludwig-Wucherer-Strasse 2, D-06108 Halle/Saale

How does the Proximodistal Twisting of Spring Barley (Hordeum

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