Optical properties of canopies of the tropical seagrass Thalassia testudinum estimated by a three-dimensional radiative transfer model
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Limnol. Oceanogr., 55(4), 2010, 1537–1550
E 2010, by the American Society of Limnology and Oceanography, Inc.
doi:10.4319/lo.2010.55.4.1537
Optical properties of canopies of the tropical seagrass Thalassia testudinum estimated by
a three-dimensional radiative transfer model
J. Hedleya,* and S. Enrı́quezb
a School of Biosciences, University of Exeter, Exeter, United Kingdom
b Unidad Académica Puerto Morelos, Instituto de Ciencias del Mar y Limnologı́a, Universidad Nacional Autónoma de México, Cancún,
Mexico
Abstract
Three-dimensional models of seagrass canopies were constructed by treating leaves as flexible strips that fall
under their own weight into naturalistic canopy structures. Canopy structures incorporated shoot density, canopy
height, and physical and along-length optical characteristics of leaves from an empirical data set of six seagrass
canopies from a reef lagoon in Puerto Morelos, Mexico. Multiple runs of a radiosity method radiative transfer
model elucidated the dependence of various canopy optical properties on incident radiance zenith angle, such as
within-canopy diffuse attenuation, the absorption of photosynthetically active radiation (PAR) by different
canopy-complex components, along-leaf variation in PAR absorption, and canopy bidirectional reflectance
distribution functions (BRDFs). Intersite variation in mean PAR absorption by green leaf sections was primarily
associated with leaf area index (LAI). Variation in PAR absorption with incident radiance angle was generally
small for incident angles within Snell’s window (, 49u). Within canopies, absorption by water itself had a
negligible effect. Canopy BRDFs were not Lambertian and exhibited features related to canopy architecture.
Model outputs validated well in terms of energy conservation and empirical measurements of within-canopy PAR
attenuation. The model framework has clear applications to improve understanding of seagrass canopy light
harvesting and photosynthetic carbon fixation and to aid the development of quantitative biooptical remote
sensing methods for seagrass beds.
Seagrass beds rank among the most productive autotro- management of seagrass beds and associated marine
phic ecosystems, second only to swamps, marshes, and environments. Conversely, biooptical canopy properties,
tropical and temperate forests in terms of dry weight (dry such as use of photosynthetically available radiation (PAR)
wt) production per day (Duarte and Chiscano 1999). In and productivity, must be understood to evaluate the role
addition, representing important structural and biogeo- of seagrasses in local–regional carbon fluxes and global
chemical components of coastal environments, they are carbon cycling.
estimated to be among the most valuable ecosystems in the Optical remote sensing by airborne sensors or satellites
world in terms of value-added services they provide offers the opportunity to monitor both canopy biomass
(Costanza et al. 1997). The role that seagrass beds play in and canopy light use at scales greater than can be achieved
the global carbon budget may not yet be sufficiently by manual surveys alone and with fewer geographical
considered. Duarte and Chiscano (1999) estimated sea- restrictions (Green et al. 2000). The potential for quanti-
grasses to be responsible for 15% of the total net CO2 tative remote sensing of biooptical parameters of seagrass
uptake by oceanic biota, despite only covering around meadows has been demonstrated by various studies. Fyfe
0.15% of the ocean surface. At the same time substantial (2003) has shown for three Australian species that spectral
gaps in knowledge due to geographic bias in sampling and changes in seagrass reflectance with season and year can be
the problem of estimating belowground biomass have been statistically significant. Dierssen et al. (2003) have demon-
identified (Duarte and Chiscano 1999). strated a method for separation of bottom reflectance from
Seagrasses can display substantial morphological plas- water column effects and the successful estimation of leaf
ticity at seasonal and yearly timescales and also in response area index (LAI) at one test site. However, in comparison
to environmental deterioration (Enrı́quez and Pantoja- with terrestrial environments (Liang 2004), remote sensing
Reyes 2005). Their vulnerability to anthropogenic distur- techniques for estimating quantitative parameters of
bance has focused the interest of many researchers during submerged benthic vegetation are currently relatively
the last years, concerned by the magnitude of worldwide underdeveloped, a significant obstacle being the potential
seagrass biomass regression (Short and Wyllie-Echeverria complexity of the radiative transfer system involving three-
1996; Duarte 2002; Waycott et al. 2009). Seagrass beds are dimensional canopy structures in combination with an
also important associated ecosystems of coral reefs, and overlying water column. Estimation of biooptical param-
owing to their morphological plasticity may be useful early eters such as PAR use is complicated by self-shading and
indicators of local environmental stresses relevant to reef interreflections dependent on the interaction of incident
management. Hence effective monitoring of the expansion radiance distribution and canopy structure.
and reduction of canopy biomass is a key objective for In particular, LAI and irradiance incident on the canopy
may not alone give a reliable estimate of the distribution of
* Corresponding author: j.d.hedley@exeter.ac.uk PAR used per unit area of leaf, calculated as fAPAR,
15371538 Hedley and Enrı́quez
Methods
Physical model of canopy structure—The aim of this
study was to construct and validate an optical seagrass
canopy model based on a previously published empirical
data set of six Thalassia-dominated seagrass beds collected
in June 2000 at coastal lagoonal sites at Puerto Morelos,
Mexico (labeled SJ1–SJ6, Table 1, Enrı́quez and Pantoja-
Reyes 2005). Generating a full three-dimensional canopy
model is extremely data demanding, and the study
presented here was not envisaged when the data were
collected. Thus, some of methods described below represent
solutions to generate plausible data for features of the
canopy that were not fully characterized. In the results the
validation data are used to increase the confidence that
these features were adequately estimated.
Fig. 1. Reference PAR absorptance profiles, A(x), along the For each site, the length and width of individual leaves in
green section of generated leaves. Labels show example x1, x2, and every shoot in six 10 cm 3 20 cm quadrats were recorded
x3 positions for the SJ1 site reference leaf. together with the length of any senesced terminal segments.
The number of shoots per square meter and grouping of
(Asner et al. 2003), or photosynthetically used radiation leaves into shoots was also recorded (Table 1). In the
(Zimmerman 2003), since attenuation within the canopy model, for each site the tabulated data were used to
will be dependent on both the bulk and structural generate a three-dimensional polygonal canopy structure
arrangement of biomass. In addition, seagrass leaves, on a 30 cm 3 30 cm segment of sand substrate by randomly
specifically Thalassia testudinum, have variable optical selecting shoots from the data table and constructing leaves
properties and photosynthetic performance along their according to the recorded dimensions until the substrate
length (Enrı́quez et al. 2002; Enrı́quez 2005; Cayabyab and segment was populated at the required shoot density
Enrı́quez 2007). Pigment absorptance typically reaches a (Fig. 2). Leaves were first created in a vertical position,
maximum in the leaf midsection (Fig. 1), and a nonpho- and a physical dynamic model was applied whereby the
tosynthetically active brown senesced terminal section is leaves are modeled as a strip of point masses joined by
often present, which will contribute to shading but not springs (House and Breen 2000). A constant gravity force
PAR use. While several simple two-flow irradiance models bends the strips under their own weight working against a
have been developed for estimating light attenuation and restorative elastic force acting to keep the strips locally flat.
reflection within seagrass canopies (Ackleson and Klemas Running this model allows the leaves to flop down
1986; Zimmerman and Mobley 1997; Zimmerman 2003), naturalistically to the required canopy height in high
these models use simplified statistical approximations of densities since an additional repulsive force prevents self-
canopy structure and do not incorporate the directional intersection (Fig. 2). The behavior of the physical model is
interaction of light with the canopy or the variation in dependent on several parameters that were set qualitatively
optical properties along seagrass leaves. from comparison to photographs of T. testudinum leaves
In this paper we demonstrate the capability for a bending in situ and in the lab. So, as with previous seagrass
structurally realistic three-dimensional seagrass canopy canopy models (Zimmerman 2003), direct data on leaf
model based on the application of a recently developed orientations were neither available nor used, and leaf
global illumination (or ‘‘radiosity’’) model for aquatic orientation was determined as an emergent feature of a
radiative transfer (Hedley 2008). A physical dynamic model physical model that seemed qualitatively plausible (Fig. 2).
was used to create canopy structures by treating seagrass In both the physical and optical modeling the 30 cm 3
leaves as flexible strips, which fold under their own weight 30 cm segment is treated as horizontally repeating in both
into an approximation of the desired canopy. A data set of directions. For each site five random realizations of a
physical and optical properties of six seagrass meadows, canopy were constructed and applied independently in the
which includes data on variation of optical properties along radiative transfer model (described below). The mean and
leaf lengths and within-canopy diffuse PAR attenuation, standard error of all estimated optical properties was
was used to parameterize and validate the model. Given the evaluated over the five canopy realizations. Thus the
reasonable agreement of measured parameters, additional influence of chance arrangements of leaves in a specific
results on the optical properties of the canopies, which are canopy realization was minimized and quantified.
difficult or impossible to measure in the field, were
evaluated. This included the bidirectional reflectance Leaf optical properties—In the radiative transfer model,
distribution functions (BRDF) of the canopies, absorption polygons of the underlying sand surface are treated as
of PAR by different components of the canopy complex Lambertian reflectors, while seagrass leaf polygons are
(i.e., green and brown parts of the seagrass leaves, the sand treated as bi-Lambertian reflectors and transmitters (Zim-
substrate, and water), and absorption of PAR as a function merman 2003). All modeling was performed in 15 spectral
of position along the leaf. bands of 20 nm from 400 to 700 nm, PAR being consideredThalassia testudinum optical properties 1539
Table 1. Basic canopy parameters of the six sites. LAI is calculated from the modeled canopies but is in close agreement to the empirical data of Enrı́quez and Pantoja-
the integral over this range converted to mmol quanta s21
(Mobley 1994). The underlying sand spectral reflectance
LAI
2.64
2.21
0.87
0.84
1.01
2.22
(Fig. 3c) was considered uniform and was obtained from a
previously collected spectral library (Hedley et al. 2004),
while each seagrass leaf polygon (approx. area 0.5 cm2) was
(cm)
assigned an individual spectral reflectance and transmit-
26
22
13
17
13
19
x3
tance in order to incorporate field data on the variation of
absorptance along leaf lengths from the six sites (Fig. 1).
The process of generating optical properties for the
(cm)
modeled leaves was as follows. Within the green section of
23
15
11
13
11
15
x2
a leaf, the along-leaf absorptance profile, A9(x), for a
generated leaf of length xG was determined by interpolation
of the along-length variation in absorptance measured from
a reference leaf absorptance profile, A(x), from each site.
(cm)
11
5
5
3
3
3
x1
Enrı́quez (2005) describes the leaf absorptance measure-
ment methodology, but note in particular that the epiphyte
load was very low at these sites and the leaves did not need
to be cleaned. While each site had a different mean leaf
Shoot density
11926198
16426118
length, a simple three-section model was used to make an
558647
575646
325634
840675
(m22)
approximate fit for the common observed pattern of initial
rapid increase in PAR absorptance from the leaf base to
position x1, followed by a slow then fast drop to the leaf
tip, positions x2 and x3, respectively (Fig. 1; Table 1).
Model generated leaves of differing lengths were accom-
Mean leaf length
modated by stretching or shrinking the x1 to x2 segment,
which represents the segment of the leaf that is photosyn-
(cm6SD)
17.667.1
16.267.3
8.063.9
12.966.8
7.563.7
9.964.9
thetically mature but has not yet reached the final section
of senescence and pigment recycling. The process can be
summarized by two equations. First, if the generated leaf
length, xG, is sufficient to accommodate a midsection, then
8
> AðxÞ for xƒx1
Canopy height
>
Reyes (2005). That paper also includes a map showing the locations of the sites.
<
½x{x1 |s2
A’ðxÞ~ A x1 z xG {s3 {x1 for x1 vxvxG {s3 ð1Þ
(cm)
>
24
22
10
16
10
10
>
:
Aðx3 {xG zxÞ for x§xG {s3
Otherwise, the third and first sections are truncated,
KPAR (water)
AðxÞ for xƒx1
A’ðxÞ~ ð2Þ
(m21)
Aðx{s2 Þ for xwx1
0.26
0.19
0.42
0.20
0.24
0.47
where s2 5 x2 2 x1 and s3 5 x3 2 x2.
Each polygon in a modeled leaf was assigned a PAR
absorptance, A9(x), based on the polygon center point
distance from the leaf base, x. However, since the radiative
Depth
transfer model operates spectrally in 15 bands from 400 nm
(m)
1.2
4.0
0.8
3.0
2.8
0.6
to 700 nm, a method was required to generate a polygon
spectral absorptance, AP(l, i), corresponding to the
required PAR absorptance. AP(l, i) was calculated by
scaling a typical Thalassia spectral absorbance profile, D(l)
North shore line
South shore line
North back reef
South back reef
(also measured from leaves from one of the study sites,
Close to shore
Enrı́quez 2005), and converting to absorptance with a
Location
Midlagoon
logarithmic model, AP(l, i) 5 1 2 102mD(l), thus finding
the m value that gave the desired PAR absorptance. Leaf
spectral reflectance RP(l, i) 5 R(l) was considered constant
and was again measured from leaves at the study sites
(Enrı́quez 2005) (Fig. 3a). Finally, spectral transmittance of
polygon i was calculated by TP(l, i) 5 1 2 AP(l, i) 2 RP(l,
i). Figure 3a shows a selection of transmittance spectra
Site
SJ1
SJ2
SJ3
SJ4
SJ5
SJ6
generated for different values of PAR absorptance.1540 Hedley and Enrı́quez
Fig. 2. Example generation of canopy structures for sites SJ1 (longest leaves) and SJ3
(shorter leaves but higher shoot density). A 30 cm 3 30 cm square segment of sand substrate is
randomly populated at the required density from the tabulated shoot data for each site (i.e., No.
of leaves and lengths). (a, d) Leaves are initialized vertically, (b, e) then fall under their own
weight in a physical model, (c, f) until the required canopy height (Table 1) is reached, assessed
qualitatively as when the bulk of the canopy is below the required height.
At the time the model was constructed there were no site we determined rerunning the model with the new data was
specific spectral data for the transmittance and reflectance unnecessary.
of terminal brown senesced leaf sections available. So these
properties were estimated using a previously collected Radiative transfer model—Radiative transfer modeling
spectral library reflectance of dead seagrass (C. Roelfsema of light propagation within the modeled canopy structures
pers. comm.) and, by assuming transmittance has the same was achieved using an implementation of a global
spectral shape as reflectance, scaling transmittance to give illumination method for aquatic environments (Hedley
the mean absorptance found at the end of the green section 2008). In the model all scattering surfaces and volumes are
of leaves (, 30%, Fig. 1). Subsequently, direct measure- represented by discrete polygons and voxels, the energy
ments of the brown senesced segment have now been made transfer between every pair of elements is established, then
at the study site, and the transmittance corresponds well to light energy is propagated around the system by repeatedly
the estimate used in the model. Although having a more iterating through all elements and updating their exitant
pronounced slope with wavelength, the overall magnitude radiance distributions based on their current incident
of PAR transmittance is extremely similar (Fig. 3b). radiance field and their scattering properties. Iteration is
Having already completed the model runs and analysis, continued until solution convergence is achieved, judged by
Fig. 3. Spectral reflectance (reflec.) and transmittance (trans.) employed for modeled Thalassia leaves (a) green living section (b)
brown senesced section, and (c) reflectance of sand substrate. (a) Shows three example spectral transmittances generated to correspond to
PAR absorptances, A, of 30%, 50%, and 70%. (b) Shows the senesced section spectral transmittance actually used (estim.) and the
recently measured data (meas.). (c) Shows the water absorption (abs.) within the canopies.Thalassia testudinum optical properties 1541 when the relative change in total element exitant energy for dense canopies can reduce currents by a factor of 2 to 10 one whole pass through the elements falls below some (Gambi et al. 1990). Hence suspended particle loads may be threshold fraction of the total energy in the system (here lower within canopies than in surrounding waters. 0.1%). The model can accommodate any arrangement of While the water at each of the six sites exhibited a range surface elements in three dimensions, and surfaces can be of PAR diffuse attenuations, KPAR(water), from 0.19 to assigned arbitrary directional spectral reflectance and 0.47 (Table 1), all modeled canopies employed a single transmission functions (Hedley 2008). The model imple- water spectral absorption profile corresponding approxi- mentation permits virtual sensors for irradiance or radiance mately to a water diffuse attenuation of KPAR(water) 5 0.2 to be placed anywhere within the scene and inherently (Fig. 3c). The potential effect of variation in water optical quantifies the light energy absorbed by every element at properties on within-canopy radiance is discussed later. every location in the model. Derivation of any biooptical canopy property of interest is therefore straightforward. In Model runs and outputs—When the radiative transfer a plane-parallel configuration the algorithm produces model is run the input light energy can either be a bottom estimations of directional radiance almost identical to of water column directional radiance distribution to give numerical integration solutions such as those implemented the canopy light field for specific natural lighting condi- in the commercial software Hydrolight (Mobley and tions, or alternatively a series of runs with light incident Sundman 2000; Hedley 2008). Global illumination models only from specific directions can be performed to populate have been previously applied to terrestrial vegetative a directional function such as the directional dependence of canopies for applications in remote sensing and computer PAR absorption or to generate a BRDF (Fig. 4). Here the graphics (Borel et al. 1991; Soler et al. 2003), but to our latter approach was used to build directional functions knowledge this is the first application in an aquatic canopy. according to the standard directional discretization of the Since the full mathematical description of the model is commercial plane-parallel software Hydrolight, which substantial, further details are not given here but are in segments the hemisphere into 10u by 15u quads with a Hedley (2008). circular end cap (Fig. 4a, Mobley and Sundman 2000). Dense seagrass canopies are a challenging environment This gives the maximum flexibility to the outputs of this with respect to the voxel-based treatment of scattering by study, since the canopy functions are ready to be water in the standard model implementation (Hedley 2008), incorporated into a standard methodology for modeling since voxelating the small interstices between canopy leaves water column light fields. Within the scope of this paper will produce a very large number of voxels and lead to these directional canopy functions are derived and the impractical solution times. Therefore an approximation consequences under natural light fields are inferred by was made whereby the redirection of light energy by water making simple assumptions about bottom of water column scattering within the canopy structure was neglected. In the radiance distributions. model, the spectral beam attenuation for water was set Horizontal rotational invariance of the canopies to the equal to the spectral absorption (data collected using a incident radiance distribution was assumed, so for each WETLabs AC-Spectra in a Caribbean coral reef lagoon, canopy a minimum of 10 model evaluations is required, one Fig. 3c). Excluding redirection by volumetric scattering will for each quad along a line of varying zenith angle in 10u make a negligible difference to within-canopy radiative steps, plus the end cap (Fig. 4b). In each run the incident transfer because path lengths between surfaces are likely to radiance value in the quad is set to give one downwelling be short. Given the complexity of the modeled canopy planar irradiance in each band, so that relative functions structures (Fig. 2), uninterrupted path lengths greater than can be derived. It should be noted that different directional around 30 cm will be uncommon. Given the highly peaked quads do not subtend the same solid angle, so the results forward scattering of natural water phase functions may not be strictly only h dependent. Each of the six sites (Mobley 1994) and based on the scattering coefficient from had five canopy realizations, so 6 3 5 3 10 5 300 model the AC-S data, over a path of 30 cm only around 5% of the runs were required. For each modeled site and incident h path radiant energy would scatter out of a solid angle of value the following outputs were calculated: (1) Down- 0.04 steradians (sr), which is approximately the standard welling PAR irradiance at 1-cm vertical steps from the top directional resolution of the model (and of HydroLight, of the canopy at nine locations (Fig. 4c)—by making a Mobley 1994). Note that this energy is not lost, it is just least-squares fit of an exponential function to each of these considered unscattered. Therefore, over these small dis- nine profiles and then calculating the mean coefficient, the tances, owing to the model directional discretization, the site mean within-canopy PAR diffuse attenuation as a model would not be able to distinguish between the function of incident zenith angle, KPAR(h), was calculated. majority of the water-scattered and transmitted radiance (2) The relative absorption of PAR by the four canopy anyway, so combining scattered components into the components of sand, green leaf sections, senesced leaf transmitted component introduces only a small error in sections, and the water itself—again dependent on incident the directional transmission of radiance within the canopy. zenith angle, h. (3) The mean absorption of PAR as a Path lengths of 5 cm or less are more likely to be the norm function of position along leaves and incident zenith angle, in the denser canopies (e.g., SJ1, Fig. 2) where the h—to determine where in the canopy the PAR is absorbed. directional error along the path is then less than 1% of (4) Directional upward spectral radiance distribution above the radiance. The validity of neglecting water scattering the canopy at nine locations—from the mean of these a within canopies is further strengthened by considering that canopy spectral BRDF can be calculated (Fig. 4c).
1542 Hedley and Enrı́quez
Fig. 4. (a) Generation of BRDF functions in the Hydrolight standard directional
discretization. (b) Ten separate input directional radiance distributions are used, each has
uniform radiance in one quad representing a range of incident zenith angles, as shown in the
upward looking fish-eye projections. For each input distribution the model is solved and (c) nine
upward radiance distributions are collected by virtual high-resolution directional sensors. (d)
These outputs are then (e) directionally downsampled to the Hydrolight representation and a
mean over the nine outputs of the three canopy realizations is taken. Assuming rotational
invariance means varying the input azimuth is unnecessary, so these data are sufficient to
populate a mean BRDF function.
Model accuracy assessment and validation—The radiative downward diffuse attenuation in PAR irradiance collected
transfer model contains no inherent constraint to observe under natural light at a time and location that would
conservation of energy. Detection of convergence is based respond to an approximate subsurface solar zenith angle of
on the relative change in element radiances within an 10u (see Enrı́quez and Pantoja-Reyes 2005 for collection
iteration, so model failure could manifest either as failure details). Although the sky conditions, sea state, depth, and
to converge at all or discrepancy in the accounting of input, water optical properties will effect the direct vs. diffuse
output, and absorbed energy when convergence is achieved. nature of the canopy-incident light field, a comparison of
One model test employed was to check energy conservation the actual within-canopy KPAR at each site to the modeled
for every run by comparing the downwelling input canopy site mean KPAR(h) over a range of zenith angles
irradiance above the canopy to the sum of the upwelling from 0u to 20u would be expected to show good agreement
irradiance above the canopy and the energy absorbed by all if the model were accurate. So this comparison was made as
surface polygons in the modeled scene. Since volumetric an additional validation test.
voxelation was not used, there is no direct way to calculate
the energy absorbed by the water, as was done in the model Results
examples of Hedley (2008). Therefore two runs were done
for every setup. In the first run water absorption was set to Energy conservation—Of the 300 model runs performed
zero; this enabled energy conservation with respect to with no water absorption, 78% had energy conservation
radiative transfer between surfaces to be checked. As will errors in all 15 bands smaller than 1% of the input energy
be seen, in general energy conservation was adhered to well, to the system in that band, and 90% were within 2%. The
so a second identical run was then performed but with remaining errors were entirely due to model runs with input
water absorption set as previously described (Fig. 3c). The incident radiance distributions from the close to horizontal
apparent energy loss in the second run was therefore directional quad representing incident zenith angles of 85u–
attributable as the absorption by water. 90u (Fig. 4). Illumination from the close to horizontal
If energy conservation is adhered to, the only possible direction is particularly challenging since as the direction of
remaining inaccuracy can be in the distribution of radiant radiance approaches the horizontal its path length to the
energy within the modeled scene, the most likely cause of first interaction with the canopy may be very long and
which would be inaccuracies in modeled canopy structures exceed the finite number of scene repetitions (the radiative
or the optical properties of components. The empirical data transfer model cannot support an infinite number of
for the six sites contains measurements of within-canopy horizontal repetitions, Hedley 2008). The average percent-Thalassia testudinum optical properties 1543
age energy loss for incident zenith angles greater than 85u
was around 10%, which is tolerable since this incident
direction is likely to be a negligible contributor to any
biooptical process with the canopy. Nevertheless, for the
remainder of the paper only results for incident zenith
angles less than 85u are discussed.
Within-canopy downward diffuse attenuation of PAR—
For all canopies the directionally dependent diffuse
attenuation coefficient of downwelling planar PAR within
the canopies, site mean KPAR(h), increased rapidly as
incident radiance zenith angle, h, approached the horizon-
tal. However, the within-site range of KPAR(h) for zenith
angles less than 50u was relatively small, with the exception
of site SJ6 (Fig. 5a). The dependence of KPAR(h) on the
direction of incident radiance was a function of canopy
structure and not the along-path absorption by water, since
the estimated KPAR(h) values from the runs where water
absorption was set to zero were virtually identical to those
with water absorption (dotted lines, Fig. 5a).
In order to compare an overall model-estimated
KPAR with the empirically measured values KPAR(h) was
averaged weighted by solid angle multiplied by the cosine
of zenith angle, h, over the top two rows of directional
quads and the end cap, equivalent to calculating the
expected KPAR for isotropic illumination from a disk
described by zenith angle less than 25u. The radiance
distribution at the bottom of the water column when the
empirical KPAR data were collected is unknown, but the
incident solar angle would certainly have been within 25u,
and given the generally low variance in KPAR values for h
less than 25u (Fig. 5a) a more precise treatment of the
radiance distribution would make only a small difference to
the modeled KPAR estimates.
For all six sites the overall modeled site mean KPAR was
in good agreement with the empirical data, with all sites
having overlapping bounds of 6 1 standard error (SE;
Fig. 5b, modeled SE is over the five canopy realizations at
each site, measured SE is from Enrı́quez and Pantoja-Reyes
2005). Site SJ4 exhibited the greatest discrepancy and had
the lowest LAI. So this result may be indicative of the
difficulty of accurately determining KPAR within sparse
canopies, either in the field or within a model.
Figure 5 shows that water absorption within canopies
has a negligible effect on PAR attenuation, the difference
between the with and without water absorption estimates
on the overall KPAR estimate for h less than 25u varies from
0.2 to 0.4 m21 and so is barely visible in the figure. Sites SJ3
and SJ6, which had a particularly high water attenuation,
might therefore more correctly be shifted up by around 0.2 Fig. 5. (a) Modeled site mean diffuse PAR attenuation,
to 0.4 m21 in Fig. 5b, which is insufficient to change the KPAR, as a function of radiance incident zenith angle, h, for the six
interpretation of the results. Therefore, the validity of both sites (averaged over the five realizations of each site) and (b) site
the K PAR results and those presented later is not mean KPAR for isotropic illumination with h less than 25u
compromised by neglecting the actual variation in water compared to the empirically measured diffuse attenuations (b).
optical properties between sites. Error bars are 6 1 SE over the five canopy realizations for each
site, or as published in Enrı́quez and Pantoja-Reyes (2005) for the
Relative PAR absorption by different canopy compo- empirical data. The dotted lines in (a), which are hard to see since
nents—For all modeled canopies the percentage of quanta they are very close to the solid lines, show the KPAR estimation
with the water absorption set to zero.
absorbed by the green sections of leaves increased up to a
maximum around incident zenith angle of 70u followed by a1544 Hedley and Enrı́quez
reduction for h greater than 70u (Fig. 6a). The trade-off in
all cases was with absorption by the sand substrate for h
less than 70u and with water absorption for the shallowest
incident angles (Fig. 6a). Radiance incident from a shallow
angle has a greater path length through the canopy before
being incident upon the substrate and, hence, more
opportunity for interaction with a leaf. The absorption by
water for very shallow angles is to some extent an artifact
of the model setups. The path length through the overlying
water is dependent on the maximum height of any leaf in
the canopy, since this determines the minimum possible
height of the virtual sensors.
For canopies SJ3 to SJ5, reflectance of PAR is also
significant and almost uniform at 20% regardless of
incident direction. Canopies SJ1, SJ2, and SJ6, which have
the higher LAIs, have lower reflectance with more
directional dependence and also are the only canopies for
which green leaves are the dominant absorbing component
(Fig. 6a). In all modeled canopies, for all incident angles,
absorption by water and brown senesced leaf sections is
only a small component of quanta absorption.
Owing to refraction at the water surface, the majority of
direct solar radiance will occur within zenith angles of less
than 50u, perturbation of the water surface spreads the
incident angle of direct solar radiance out of this range only
slightly (Kirk 1994). An overall estimate for relative quanta
absorption by canopy components was therefore calculated
by assuming isotropic irradiance at zenith angles less than
45u (Fig. 6b).
PAR absorption within the canopy—The model outputs
enabled the fraction of incident PAR absorbed by the green
segments of leaves to be further decomposed to give the
relative percentage absorbed along the lengths of individual
leaves. Figure 7a shows which parts of the individual leaves
absorb the most PAR (summed over all leaves in the
canopy). For all canopies the majority of PAR is absorbed
much closer to the leaf bases than the full distribution of
leaf lengths might imply, and the difference between sites is
greater than the differences in the along-leaf absorption
profiles (Fig. 1). This is a canopy-level ‘‘optical property’’
that occurs because the canopies as a whole include many
juvenile short leaves; hence there is relatively more leaf area
closer to plant bases. The profile of absorption along leaf
length is only weakly dependent on the direction of the
incident radiance for zenith angles less than 45u (Fig. 7a),
so again generating summary results based on isotropic
illumination from a 45u zenith angle disk is justifiable, such
as the PAR absorption profile along an average leaf
(Fig. 7b).
r
angles, h. Lines show the absorption by the green and brown
portions of leaves, the sand substrate, the water itself, and the
Fig. 6. (a) Relative reflection and absorption of PAR by upwardly reflected light energy. Note the sum of all five lines for
different components of the canopy complex as a function of any h is 100%. (b) The overall breakdown of absorption for
directional partition quad centered at different incident zenith isotropic illumination of zenith angle less than 45u.Thalassia testudinum optical properties 1545
Canopy BRDFs—Key features of the model derived
BRDFs are illustrated in Figs. 8 and 9. For all canopies,
the directional reflectance above the canopy was rarely
close to Lambertian, but the shape of the BRDF varied
widely depending on canopy structure. Canopies exhibited
clear hot-spot features, where reflectance had a maximum
peak at the same direction as incident radiance (Figs. 8a,
9). This phenomenon is well known in remote sensing of
terrestrial surfaces (Liang 2004). When the view direction
is the same as the illumination direction, shadows within
the canopy are least apparent, and in particular for these
canopies any visible sand substrate will also be minimally
shaded. Hot-spot effects were less apparent in the
canopies with LAI less than one (Fig 8a, SJ4). For the
higher LAIs, forward projection of light at shallow exitant
angles was apparent, i.e., zenith angles greater than 60u in
magnitude. This is seen predominantly as the high exitant
radiance at angles close to horizontal opposite the incident
radiance direction (Fig. 8a, SJ1, h less than 270u, and
Fig. 9), but also in the backward and side directions
(Fig. 8b, SJ1).
Discussion
The physical dynamic model coupled with a global
illumination radiative transfer model has proved a feasible
approach to optical modeling of seagrass canopies.
Considering the canopy model has been derived from the
optical properties of the leaves at centimeter scales and is
based on an emergent canopy structure model without a
direct parameterization of leaf position, the level of
agreement between modeled and measured site mean KPAR
is quite acceptable. Combined with the excellent adherence
to conservation of energy, these validation results lend
sufficient confidence to consider further biooptical proper-
ties of the model.
Relationship between LAI and PAR absorption—An
important question with respect to seagrass canopy light
use and productivity is the relationship between LAI and
proportion of quanta absorbed by the green leaf sections,
since only this portion of the absorbed irradiance is
photosynthetically relevant. For the modeled canopies the
relationship is clearly nonlinear, and self-shading is
apparent in canopies SJ1, SJ2, and SJ6, which absorb
relatively fewer quanta per unit leaf area than the sparser
canopies (Fig. 10).
From a cross-species global review of seagrass literature
Duarte and Chiscano (1999) suggest aboveground produc-
Fig. 7. Relative absorption of PAR along the lengths of tivity, PA, scales approximately to 0.64 power of above-
leaves. (a) Percentage of canopy-incident light energy for incident ground biomass, mA (g dry wt m22), giving the following
zenith angles of 0u, 40u, and 80u absorbed with respect to distance relation,
from leaf bases, summed over all leaves. (b) The relative light
environment experienced by an ‘‘average’’ leaf in each canopy, PA ~0:1|m0:64+0:06
A g dry wt m{2 d{1 ð3Þ
i.e., the percentage of canopy-incident PAR absorbed per unit
area of leaf for a unit area of substrate, taken as the average over and a similar relation for belowground productivity with an
all leaves in the model. In (b) the incident irradiance is spectrally exponent 0.67 6 0.12. An intraspecific comparison of the
flat and isotropic over a disk defined by zenith angle less than 45u. covariation of leaf productivity and aboveground biomass
of T. testudinum showed a similar association (Pantoja-
Reyes 2003),1546 Hedley and Enrı́quez
Fig. 8. Example features of the mean BRDF for three canopies of differing LAI, for incident radiance in the directional quad at
zenith angle 20u, in wavelengths of 410 nm, 510 nm, and 610 nm. (a) The ratio of exitant radiance, L, to incident irradiance, Ed, in the
plane of the incident radiance; the arrow shows the incident direction. (b) The corresponding exitance in the crosswise plane at right
angles to the incident plane. Error bars are shown on the 510-nm line only and are 6 1 SE over the five canopy realizations.
PA ~0:15|m0:65+0:1 g dry wt m{2 d{1 ð4Þ saturate (Pmax) at a specific irradiance level (Ek) and that
A
that Ek is generally above the irradiance experienced by the
bulk of the canopy (Falkowski and Raven 2007), and leaf
Equation 4 was determined over a range of leaf production area is proportional to aboveground biomass (mean
from 0.096 g dry wt m22d21 from a 3.2 g dry wt m22 specific leaf area [SLA] only varied from 0.027 to
meadow in the Virgin Islands (Williams 1987) to a 0.032 m2 g21 dry wt across sites, Enrı́quez and Pantoja-
maximum of 16.5 g dry wt m22 d21 from a dense meadow Reyes 2005)—allows a least-squares fit to the same
in Bermuda (4.4 kg dry wt m22, Patriquin 1973). equation form as Eq. 3 from the modeled canopy results
Making two assumptions—a linear relationship between of LAI and PAR absorption. This gives a similar exponent
light and productivity, i.e., that photosynthetic rates of 0.71 6 0.1. However, the form of Eqs. 3 and 4 imply that
Fig. 9. Surface plots of the 510-nm BRDF features of modeled sites SJ1 and SJ4 for incident
radiance at a zenith angle, h, 20u and an azimuth angle, Q, of zero, as in Fig. 8. The plots show
BRDF values at for reflection angles (hr, Qr). The central peak in both plots is the hotspot
or ‘‘retroreflection.’’Thalassia testudinum optical properties 1547
Enriquez 2007). This species has limited capability for
photoacclimation at the leaf level; therefore, canopy
architecture is crucial to maintain a suitable light environ-
ment. Light harvesting and net assimilation rate per unit
area of substrate increases as LAI increases (Asner et al.
1998; Scurlock et al. 1999), but LAI may increase by
vertical growth, i.e., longer leaves, or from horizontal
growth, i.e., greater shoot density (Enrı́quez and Pantoja-
Reyes 2005). A morphological seagrass response that
favors vertical growth promotes a more efficient use of
the entire leaf for light harvesting; Fig. 7b shows that long-
leaved canopies SJ1 and SJ2 maintained a fairly consistent
PAR absorption over the majority of their leaf lengths, and
hence have higher energy input per shoot than SJ6, which
has shorter leaves. In contrast, if the morphological
Fig. 10. Leaf area index vs. percentage of canopy-incident response favors increased shoot density the resulting
quanta absorbed by the green sections of the leaves. Lower and canopy growth form will generate larger light gradients
upper bars represent the range over zenith angles from 0u and 45u, (Enrı́quez and Pantoja-Reyes 2005), i.e., a larger within-
while filled dots are the solid angle weighted mean, i.e., equivalent canopy KPAR as seen in site SJ6 (Fig. 5b). This shading
to absorption if the illumination were isotropic for a disk of zenith within the canopy may provide photoprotection (Bjørkman
angle less than 45u. Zero-point constrained straight line best fit 1981; Jones 1992; Enrı́quez et al. 2002) and the optimal leaf
with c 5 23.7, and an exponential model with b 5 87.3 6 23.84, g light environment to minimize photodamage and the cost
5 0.408 6 0.172, are also shown (6 1 SE). of maintenance of the photosynthetic apparatus. Site SJ6 is
the shallowest site at 0.6 m, and while Table 1 indicates a
relatively high water attenuation it may be that episodically
productivity can increase without bound with aboveground water clarity increases and hence the canopy requires a
biomass, whereas clearly at some high LAI an asymptotic photoprotective morphology to persist. Figure 7b shows
level of quanta will be absorbed, such that greater biomass that leaves in the high-density canopy SJ6 absorb a much
(or leaf area) cannot absorb more light. This asymptotic lower relative percentage of canopy-incident PAR than
level of light absorption implies a suboptimal increment in those of the sparser canopies SJ3–SJ5. In addition, previous
self-shading within the canopy at higher LAI values, work in this region has shown underground biomass
explaining the origin of an optimum LAI for the increases exponentially with shoot density (Pantoja-Reyes
production rate of some species (Black 1963) or just a 2003). Therefore in SJ6 photosynthesis may be balanced by
saturation of the canopy net photosynthetic rates beyond a maintenance of belowground biomass with little produc-
specific LAI value (McCree and Troughton 1966; Miyaji tivity available for shoot growth or leaf extension. This
1984). So, based on this concept of an asymptotic canopy morphological response may therefore increase plant
absorptance, an exponential equation was fit to the model respiratory demands for the maintenance of the under-
outputs for the relationship between LAI (denoted by L) ground biomass and hence strongly reduce quantum
and percentage of green leaf quanta absorbed, qp, efficiency of plant growth (Cayabyab and Enrı́quez 2007).
qp ~b|½1{ expð{g|LÞð%Þ ð5Þ Observation indicates that the short-leaved high-density
canopy architecture of SJ6 is usually developed by T.
which gave b 5 87.3 6 23.84, g 5 0.41 6 0.17 (6 1 SE), and testudinum near the shoreline of reef environments (En-
a residual error similar to the fit of the Eq. 3 form (Fig. 10). rı́quez and Pantoja-Reyes 2005), where light availability is
both adequate to maintain this canopy morphology and is
Canopy morphology, PAR absorption, and photoprotec- also such that photoprotection may be required.
tion—While canopies SJ2 and SJ6 have almost identical The ecological success of T. testudinum in this region
LAIs (Table 1), their structures differ substantially, with might therefore be explained not at the physiological leaf
respective shoot densities of 575 m22 vs. 1642 m22 and level but at the morphological canopy level, since the
mean leaf lengths of 16.2 and 9.9 cm (Table 1). Differences growth-form plasticity of this species may provide the
in the directional absorption of quanta by canopy-complex ability to regulate leaf self-shading and, hence, the optimal
components (Fig. 6) and the twofold variation in within- light environment of the seagrass leaves. The consequence
canopy site mean KPAR (Fig. 5) reflect this structural of the short-leaved dense canopy strategy and, in general,
difference and indicate that LAI alone is insufficient to of the large LAI values generated in some seagrass beds is
parameterize the biooptical properties of the canopy. that canopy production and leaf photoacclimation respons-
The differing canopy structures of SJ2 and SJ6 could be es cannot be easily predicted from the water column light
considered to reflect two possible morphological strategies fields (Herzka and Dunton 1997; Enrı́quez et al. 2002;
in canopy-level photoacclimation, developed to maximize Olesen et al. 2002). The model outputs highlight optical
leaf production under contrasting environmental condi- properties of seagrass canopies that emerge from their
tions. T. testudinum is essentially a shade-adapted species morphology. Therefore, canopy production will be not
living a highly illuminated environment (Cayabyab and only be dependent on nutrient use, light availability, leaf1548 Hedley and Enrı́quez
photoacclimation, leaf age, epibiont colonization, and LAI, radiance distribution approaches rotational invariance
but also on the seagrass growth form. (Fig. 8).
For all modeled BRDFs the magnitude of reflection was
Significance of canopy BRDF features—Mobley et al. lowest in the red wavelengths (Fig. 8). This occurs because
(2003) estimated that non-Lambertian benthic BRDFs in order to accommodate the canopy height, the BRDFs
would in general cause fewer than 10% errors on remote are evaluated a short distance above the substrate (Fig. 4c).
sensing reflectance relative to assuming a comparable Water absorption over this distance reduces the red
Lambertian reflectance. While our modeled BRDFs reflection (Fig. 3c). In practice, if these BRDFs were used
(Fig. 9) exhibit some features quite different from those in a plane-parallel model then the overall water column
of the terrestrial vegetative models used in Mobley et al. depth to the substrate should be reduced by the height of
(2003), in general our results do not show strong features in the canopy, since this segment is incorporated into the
the close-to-nadir directions. The hotspot peaks are small, BRDF.
for example. Therefore, for the sites studied here at least, In summary, the effect of LAI on shape of the BRDFs is
assuming Lambertian benthic reflectance when modeling as follows: High LAI—hotspot effect, forward propagation
remote sensing reflectance in a plane-parallel model such as features at shallow angles dependent on azimuth angle,
Hydrolight would probably introduce errors smaller than exitant radiance distribution varies rotationally. Low
Mobley et al.’s (2003) 10% figure. LAI—no hotspot effect, reduced reflectance at shallow
One of the unique features of our BRDFs not seen in the angles, rotational invariance of exitant radiance distribu-
figures of Mobley et al. (2003) is the strong forward tion. These features suggest that a simple parameterized
projection of light at close to horizontal directions. Similar form of a seagrass canopy BRDF based on LAI could be
features are seen in models of terrestrial grassland BRDFs derived or an existing model could be applied (Liang 2004).
(Rahman et al. 1993), but in those the effect is generally This work, as well as the consequences of canopy BRDF
stronger in the backward direction. Examination of the for remote sensing, will be pursued in a future study.
model outputs indicated that the forward projection is a Several opportunities for further work can be identified.
consequence of leaves having a higher transmission than The current empirical data set lacked data on above
reflectance and being treated as bi-Lambertian. A compar- canopy reflectances; accuracy assessment of these would be
atively large fraction of the radiance incident on one side of useful for remote sensing applications. The physical
a leaf is propagated diffusely from the opposite side. So, if a dynamic model generation of canopy structures used in
leaf is orientated vertically, radiance incident on one side is this study was analogous to the situation of completely still
scattered forward and upward from the canopy. The water, which is probably a reasonable first approximation
resulting forward scattering looks like a specular reflection to the lagoonal situation of the empirical data set.
feature, but here leaf surfaces are locally Lambertian and However, temporal variations in leaf positions due to
have low reflectance. The validity of this feature with water movement, either cyclically from wave motion or
respect to real canopies is open to speculation. That persistent from currents, could easily be incorporated into
seagrass leaf transmissions can be substantially greater than the physical model, allowing canopy movement to be
reflectance is reported elsewhere (Fyfe 2003; Runcie and modeled as an emergent feature. The temporal effect of
Durako 2004; Enrı́quez 2005). The bi-Lambertian assump- canopy movement on PAR absorptance and bidirectional
tion is often used for vegetative canopies and generally reflectance could then be quantified and may be significant,
considered robust (Shultis and Myneni 1988; Zimmerman since the distribution of leaf orientations has previously
2003) but may need to be reassessed for Thalassia given the been demonstrated as a potentially important factor
high transmission. While transmission clearly facilitates (Zimmerman 2003). The effect of leaf epiphytes has also
light propagation through dense canopies and the distri- been neglected here (Cebrián et al. 1999; Drake et al. 2003),
bution of PAR absorption through biomass (Fig. 7), the since epiphyte load at the six sites was low, but this could
consequences of the directional nature of leaf transmission be incorporated in future work. Temporal light fluctua-
are less clear with respect to canopy PAR absorption. tions due to wave focusing are an important feature of
The BRDFs for low LAI canopies did not exhibit the shallow water environments. The radiosity model is
forward propagation effect; conversely there was a capabile of capturing wave focusing if an air–water
substantial decrease in exitant radiance at shallow angles interface surface is included and multiple time-step runs
(Figs. 8b, 9). Sand substrate contributes strongly to the are performed (Hedley 2008). However, there are several
overall reflectance of the low-LAI canopies, giving them a issues in practice, computational complexity, and deter-
higher overall reflectance. The sand itself is treated as mining the required temporal, spatial, and directional
Lambertian, which would be represented by a horizontal resolution to accurately capture the duration and intensity
line in Fig. 8. However, as the exitant angle becomes of the light peaks.
increasingly shallow the sand contributes less to reflectance While the model has the theoretical capability of
since the radiant path becomes longer and has more incorporating all the features listed above, an important
potential for interception by leaves. Reflectance decreases limiting factor is the ability to collect the concurrent data
as the magnitude of the exitant zenith angle increases. Note sets required for characterization and validation. Never-
that the exitant radiance distribution in both the incident theless, the model clearly has a potential role in gaining a
plane and crosswise plane for modeled site SJ4 were very greater understanding of light harvesting and productivity
similar, indicating that for low LAI canopies the exitant by seagrass canopies and to assist development ofThalassia testudinum optical properties 1549
quantitative methods for biophysical remote sensing of DUARTE, C. M. 2002. The future of seagrass meadows. Environ.
seagrass beds. Conserv. 29: 192–206.
———, AND C. L. CHISCANO. 1999. Seagrass biomass and
Acknowledgments production: A reassessment. Aquat. Bot. 65: 159–174,
This work has been supported by the Natural Environment doi:10.1016/S0304-3770(99)00038-8
Research Council (NERC) under grants NER/Z/S/2001/010129, ENRÍQUEZ, S. 2005. Light absorption efficiency and the package
NE/C513626/1, and NE/E015654/1 and by the World Bank and effect in the leaves of the seagrass Thalassia testudinum. Mar.
Global Environment Facility Coral Reef Targeted Research Ecol. Prog. Ser. 289: 141–150, doi:10.3354/meps289141
Project. Field data were obtained from a study partially funded ———, M. MERINO, AND R. IGLESIAS-PRIETO. 2002. Variations in
by a grant from Programa de Apoyo a Proyectos de Investigación the photosynthetic performance along the leaves of the
e Innovación Tecnológica (Dirección General de Asuntos del tropical seagrass Thalassia testudinum. Mar. Biol. 140:
Personal Académico grant IN218599) to S.E. Data on water 891–900, doi:10.1007/s00227-001-0760-y
inherent optical properties were collected using instrumentation ———, AND N. I. PANTOJA-REYES. 2005. Form-function analysis
held by the NERC Field Spectroscopy Facility. We thank Chris of the effect of canopy morphology on leaf self-shading in the
Roelfsema for supplying the spectral reflectance of senesced seagrass Thalassia testudinum. Oecologia 145: 235–243,
seagrass leaves and Norma Pantoja-Reyes and Irene Olivé for doi:10.1007/s00442-005-0111-7
their support in the description of T. testudinum morphological FALKOWSKI, P. G., AND J. A. RAVEN. 2007. Aquatic photosynthe-
variation. We also thank two anonymous reviewers and the sis, 2nd edition. Princeton Univ. Press.
associate editor Dariusz Stramski, whose comments greatly FYFE, S. K. 2003. Spatial and temporal variation in spectral
improved the manuscript. reflectance: Are seagrass species spectrally distinct? Limnol.
Oceanogr. 48: 464–479.
References GAMBI, M. C., A. R. M. NOWELL, AND P. A. JUMARS. 1990. Flume
observations on flow dynamics in Zostera marina (eelgrass) beds.
ACKLESON, S., AND V. KLEMAS. 1986. Two-flow simulation of the Mar. Ecol. Prog. Ser. 61: 159–169, doi:10.3354/meps061159
natural light field within a canopy of submerged aquatic GREEN, E. P., P. J. MUMBY, A. J. EDWARDS, AND C. D. CLARK.
plants. Appl. Opt. 25: 1129–1136, doi:10.1364/AO.25.001129 2000. Remote sensing handbook for tropical coastal manage-
ASNER, G. P., J. M. O. SCURLOCK, AND J. A. HICKE. 2003. Global ment. UNESCO.
synthesis of leaf area index observations: Implications for HEDLEY, J. 2008. A three-dimensional radiative transfer model for
ecological and remote sensing studies. Glob. Ecol. Biogeogr. shallow water environments. Opt. Express 16: 21887–21902,
12: 191–205, doi:10.1046/j.1466-822X.2003.00026.x doi:10.1364/OE.16.021887
———, C. A. WESSMAN, AND S. ARCHER. 1998. Scale dependence ———, P. J. MUMBY, K. E. JOYCE, AND S. R. PHINN. 2004.
on absorption of photosynthetically active radiation in Spectral unmixing of coral reef benthos under ideal condi-
terrestrial ecosystems. Ecological Applications 8: 1003–1021. tions. Coral Reefs 23: 60–73, doi:10.1007/s00338-003-0354-x
BJØRKMAN, O. 1981. Responses to different quantum flux HERZKA, S. Z., AND K. H. DUNTON. 1997. Seasonal photosynthetic
densities, p. 57–107. In O. L. Lange, P. S. Nobel, C. B. patterns of the seagrass Thalassia testudinum in the western
Osmond and H. Ziegler [eds.], Physiological plant ecology I. Gulf of Mexico. Mar. Ecol. Prog. Ser. 152: 103–117,
Responses to the physical environment. Encyclopedia of plant doi:10.3354/meps152103
physiology, vol. 12A. Springer-Verlag. HOUSE, D. H., AND D. E. BREEN. 2000. Cloth modeling and
BLACK, J. N. 1963. The interrelationship of solar radiation and animation. A. K. Peters.
leaf area index in determining the rate of dry matter
JONES, H. G. 1992. Plants and microclimate, a quantitative
production of swards of subterranean clover (Trifolium
approach to environmental plant physiology, 2nd ed. Cam-
subterraneoum L.). Aust. J. Agr. Res. 14: 20–38,
bridge Univ. Press.
doi:10.1071/AR9630020
BOREL, C. C., S. A. W. GERSTL, AND B. J. POWERS. 1991. The KIRK, J. T. O. 1994. Light and photosynthesis in aquatic
radiosity method in optical remote sensing of structured 3-D ecosystems, 2nd ed. Cambridge Univ. Press.
surfaces. Remote Sens. Environ. 36: 13–44, doi:10.1016/ LIANG, S. 2004. Quantitative remote sensing of land surfaces.
0034-4257(91)90028-5 Wiley.
CAYABYAB, N. M., AND S. ENRÍQUEZ. 2007. Leaf photoacclimatory MCCREE, K. J., AND J. H. TROUGHTON. 1966. Prediction of growth
responses of the tropical seagrass Thalassia testudinum under rate at different light levels from measured photosynthesis and
mesocosm conditions: A mechanistic scaling-up study. New respiration rates. Plant Physiol. 41: 559–566, doi:10.1104/
Phytol. 176: 108–123, doi:10.1111/j.1469-8137.2007.02147.x pp.41.4.559
CEBRIÁN, J., S. ENRÍQUEZ, M. FORTES, N. AGAWIN, J. E. VERMAAT, MIYAJI, K. 1984. Longevity and productivity of leaves of a
AND C. M. DUARTE. 1999. Epiphyte accrual on Posidonia cultivated annual, Glycine max Merrill. II. Productivity of
oceanica (L.) Delile leaves: Implications for light absorption. leaves in relation to their longevity, plant density and sowing
Bot. Mar. 42: 123–128, doi:10.1515/BOT.1999.015 time. New Phytol. 97: 479–488, doi:10.1111/j.1469-8137.
COSTANZA, R., AND oTHERS. 1997. The value of the world’s 1984.tb03613.x
ecosystem services and natural capital. Nature 387: 253–260, MOBLEY, C. D. 1994. Light and water: Radiative transfer in
doi:10.1038/387253a0 natural waters. Academic.
DIERSSEN, H. M., R. C. ZIMMERMAN, R. C. LEATHERS, T. V. DOWNES, ———, AND L. SUNDMAN. 2000. HydroLight 4.1 user’s guide
AND C. O. DAVIS. 2003. Ocean color remote sensing of seagrass [Internet]. Sequoia Scientific Available from http://www.
and bathymetry in the Bahamas Banks by high resolution sequoiasci.com/products/Hydrolight.aspx (accessed 27 April
airborne imagery. Limnol. Oceanogr. 48: 444–455. 2010).
DRAKE, L., F. DOBBS, AND R. ZIMMERMAN. 2003. Effects of epiphyte ———, H. ZHANG, AND K. J. VOSS. 2003. Effects of optically
load on optical properties and photosynthetic potential of the shallow bottoms on upwelling radiances: Bidirectional reflec-
seagrasses Thalassia testudinum Banks ex König and Zostera tance distribution function effects. Limnol. Oceanogr. 48:
marina. L. Limnol. Oceanogr. 48: 456–463. 337–345.You can also read
