Ci. e Nat., Santa Maria v.42, e18, 2020
DOI:10.5902/2179460X34031
ISSN 2179460X
Received 01/08/18 Accepted:
15/01/20 Published:24/06/20
Environment
Radiative behavior
and canopy light extinction coefficient in a savanna urban area
Levi Pires de Andrade^{I}
Jonathan Willian Zangeski Novais^{II}
Marta Cristina de Jesus
Albuquerque Nogueira^{III}
Luciana Sanches^{IV}
José de Souza Nogueira^{V}
Carlo Ralph de Musis^{VI}
^{I }Instituto Federal de Mato Grosso, MT, Brasil  levi.pires@hotmail.com
^{II }Programa de Mestrado em Ciências Ambientais, Universidade de Cuiabá, MT,
Brasil  jonathan.novais@kroton.com.br
^{III }Universidade Federal de Mato Grosso, MT, Brasil  mcjanp@gmail.com
^{IV }Universidade Federal de Mato Grosso, MT, Brasil – lsanches@ufmt.br
^{V }Universidade Federal de Mato Grosso, MT, Brasil – nogueira@ufmt.br
^{VI }Programa de Mestrado em Ciências Ambientais, Universidade de Cuiabá, MT,
Brasil  carlo.demusis@gmail.com
ABSTRACT
The knowledge of the radiative characteristics of an area is essential
to understanding the flows of matter and energy. The value of the Light
Extinction Coefficient (K) is a parameter that describes the efficiency of the
interception of light in a given canopy, being required, as input, for several
SWAP (SoilWaterAtmospherePlant) models, which allow the characterization of
the interactive properties among soil,
plant and atmosphere concerning these exchanges of matter and energy. This
study aimed to obtain the light extinction coefficient (K) for a savanna
fragment located in the urban area of Cuiabá. The used data correspond to one
measurement each month, totaling twelve measurements in 30 points during the
period from October 2014 to September 2015. The measured variables were the LAI (Leaf Area Index), the
photosynthetically active incident radiation (PAR_{inc})
and the transmitted radiation (PAR_{trans}), and the calculated ones were the
zenith angle (Zh) and the extinction coefficient (K).
Was observed an annual variability for the light extinction coefficient between
0.49 and 0.69. There are seasonal changes that interfere with the canopy
geometry and the position of the study area in relation to the solar radiation incidence,
concluding that the K variability is predominantly temporal.
Keywords: Leaf area index; Photosynthetically active radiation; Canopy Geometry
RESUMO
O conhecimento das características radiativas de
uma área é essencial para caracterização dos fluxos de matéria e energia. O
valor do Coeficiente de Extinção de Luz (K) é um parâmetro que descreve a
eficiência da interceptação da luz em um dossel servindo como dado de entrada
de vários modelos SWAP (SoilWaterAtmospherePlant), os quais permitem a
caracterização das propriedades interativas entre solo, planta e atmosfera no
que se refere a estas trocas de matéria e energia. Este estudo teve o objetivo
de obter o coeficiente de extinção de luz (K) para um fragmento de cerrado urbano
de Cuiabá. Os dados utilizados correspondem a uma medida a cada mês,
totalizando doze medições em 30 pontos durante o período de outubro de 2014 a
setembro de 2015. As variáveis medidas foram o IAF (Índice de Área Foliar), a
radiação fotossinteticamente ativa incidente (PAR_{inc}) e a
transmitida (PAR_{trans}), e as calculadas foram o ângulo zenital (Zh)
e o coeficiente de extinção luminosa (K). Foi encontrado que há uma
variabilidade anual no coeficiente de extinção de luz entre 0,49 e 0,69. Há
alterações sazonais que interferem na geometria do dossel e na posição da área
do estudo com relação à incidência dos raios solares, concluindo que a
variabilidade de K é predominantemente temporal.
PalavrasChave: Índice de área foliar; radiação
fotossinteticamente ativa; Geometria do Dossel
1 INTRODUCTION
The knowledge of the radiative characteristics of an
area, or set of vegetation, is a decisive step in its characterization, since
it pervades important aspects that allow the understanding of the flows of
matter and energy. The amount of light intercepted by a plant expresses the
amount of energy potentially available to the photosynthetic process and
constitutes the basis for crop growth and productivity (TEH, 2006). The solar
radiation intercepted by a canopy is a fundamental component in the analysis of
vegetation growth (BALANDIER et al., 2006). Thus, the form of radiative
interception and the interface with the growth of a certain area of vegetation
depend on a set of biophysical factors.
The growth rate of each vegetative portion and the
constitution of the various streams of energy and matter have an aspect of
multivariate origin permeating issues related to the canopy geometry, which in turn has aspects
related to the interactions and intrinsic characteristics of the researched
area, but also depend on characteristics external to the place where this
vegetative set is established. The analysis of vegetation growth depends on the
incident radiation, the optical properties of the leaves and the canopy
geometry (BALANDIER et al., 2006), and the analytical interpretation of these
factors is expressed in LAI (Leaf Area Index), in the radiations
photosynthetically active incident (PAR_{inc})
and transmitted (PAR_{trans}), zenith angle (Zh) and luminance extinction coefficient (K) (MONSI and
SAEKI, 1953). The value of K is a parameter that describes the efficiency of
light interception in a given canopy, a small K value indicates a larger
portion of radiation reaching the bottom of the canopy, on the other hand, a
higher K value results in a smaller amount of radiation below the canopy (ZHANG
et al., 2014).
In a canopy the amount of light decreases from the top
towards the ground, with different canopies having different gradients of light
extinction, and the light incident on each species of the canopy acts in
different ways (JURIK AND KLEINSTEIN, 2000). This heterogeneous composition
accentuates the dependence of light extinction on the canopy geometric
characteristics.
To make the analysis more precise in order to express
the real behavior of the canopy the ideal is the analysis of the growth phase,
or vegetative balance, of the area to be studied and the consideration of the
leaf areas in the horizontal and vertical plane in relation to the incidence of
the solar radiation, in order to consider the leaf angles, in more than in
level (height) in relation to the soil. (FORRESTER et al., 2014. The measurements in a heterogeneous canopy
structure, for instance, a portion of savanna or forest presents great
practical difficulty. Analytic interpretation with the tools of statistics,
although is a great challenge, is a more tangible way.
The delimitation of the variables involved in the
characterization of the light extinction passes through the understanding of
the functioning of the forest ecosystem. This work is strongly influenced by
the photosynthetically active radiation that effectively depends on the canopy
geometry and the biological characteristics of each species, limiting, in a
complex forest composition, the use of parametrized models especially regarding
the coefficient of extinction in many studies conceived in vegetation and sites
that have different biophysical characteristics of the savanna ecosystem. This
aspect strengthens the statistical analysis with an important tool to
characterize the studied area, in this case, the knowledge of the
characteristics of a portion of the savanna with a broad profile, containing
the main variations of this biome: the cerrado stricto sensu, cerradão, cerrado with a
higher and denser canopy, and the riparian forest. Thus, any generalization
must be taken very carefully through a good sampling design and if it resembles
the studied area.
In addition to the aspects related to the geometry and
biological characteristics of the canopy, the variation of the relative
position of the sun and the local relief or interference of the surroundings
can alter the radiation that enters the canopy. The coefficient of extinction
depends on the intrinsic characteristics of the vegetation, of the location of
the study area, latitude, and zenith angle (DUURSMA and MÄKELLÄ, 2007; FORRESTER
et al., 2014). The radiative characterization of a forest is not a simple task,
since it depends on the leaves layout, open areas in
the canopy, seasonal elements, meteorological conditions and the daily path of
the solar radiation (BALANDIER et al., 2006).
The light extinction coefficient is a fundamental
parameter in the modeling of the absorption efficiency of solar radiation by
crops (GUIMARÃES and BITENCOURT, 2010). Although the extension of this idea to
a portion of savanna is a great challenge, given the great variety of the savanna
canopy, both in terms of species composition, and in size differences, the
value of K is a parameter of great importance whose statistics can empirically
express numerically their variability.
The understanding of the flows of matter and energy
passes through the expression of several biophysical aspects represented by K.
SWAP (SoilWaterAtmospherePlant) models are software programs used in
simulations to understand these flows, and in their inputs, they need several
parameters, among them, the value of K. In the simulation related to the study
carried out in the region of Piracicaba, SP, in relation to the coffee crop, K
values between 0.2 and 2.2 were used for a sensitivity analysis, given to the
few studies of determination of the coefficient of light extinction (PINTO et
al., 2014). For one of the rare studies to determine K in the coffee crop, the
value of 0.53 was obtained (ANGELOCCI et al., 2008).
The value of K can be calculated by the LambertBeer
equation, with the adaptation proposed by (MONSI and SAEKI, 1953):
(1)
The calculation will not express the value with
spatial and temporal precision given the intrinsic variability of each canopy
and region, but it may allow conclusions about an average behavior of the
studied area with possibility of extension of the conclusions within certain
adaptations.
There is a range of K values for cultures. InmanBamber
(1994) determined a K value of 0.55 for sugarcane cultivated in South Africa.
The K value between 0.41 and 0.61 was obtained for four sugarcane varieties in
Zimbabwe (ZHOU et al., 2003). In the Southeastern Brazil, in a Napier grass
area, in the municipality of Coronel Pacheco, MG, the extinction coefficient
presented average values between 0.40 and 0.92 (CARVALHO et al., 2007). For
pastures of Cynodon spp., mean values were obtained
for K between 0.88 and 1.94 (FAGUNDES et al., 2001). In a corn survey in
Piracicaba, SP, values of K were found between 0.23 and 0.42 (CAMACHO et al.,
1995), and in the same municipality, 0.72 and 0.84 (PEDREIRA and PEDREIRA,
2007).
The determination of the K value in a culture leads to
a lower variability due to a more homogeneous composition of the canopy. The
determination of the extinguishing coefficient for a heterogeneous fragment of
vegetation, which is the case of an savanna area, should start from the random
composition of the sample, with independent elements, and the application of
statistical tests seeking the inference for the area of research, in relation to the constituted
sample, and the possible extension of this analysis to other areas with similar
floristic composition. A sample with a good number of points, and measurements
that ensure the randomness and independence of the data, strengthen the
inference to be performed (GOTELLI and ELLISON, 2011). Measurements made for
one year, covering the rainy and dry seasons, and the characteristics of the
area that maintains a composition denoting few human interventions are
characteristics that may strengthen the possible inferences. The mean monthly
values and the annual average of K can be a good parameter for the
understanding of the photosynthetic canopy behavior and as input data for other
studies that need the value of the extinction coefficient of a portion of savanna with the
similar composition to the studied area.
Thus, the objective of this work is to obtain the
light extinction coefficient (K) for a urban savanna fragment,
located in CuiabáMT, Brazil.
2 MATERIALS AND METHODS
2.1 Experiment location
Measurements
were made in a savanna fragment, transformed into a conservation unit, called Mãe Bonifácia urban park, located
in Cuiabá municipality in the North, limited to SoutheastSouthwest by a set of
buildings, residences and buildings, and bordered on the other contour , along
a main avenue of the municipality, Miguel Sutil
avenue.
The
park has an area of 77 hectares and a variation of altitude between 164 and 195
m, and has great floristic diversity, which is divided into three strata: the
ciliary forest bordering the streams, cerradão away from the watercourse and in the higher regions
the cerrado sensu stricto (BARROS, 2009).
Figure 1 –Mãe Bonifácia
urban park, CuiabáMT (JOAQUIM et al., 2018)
In
the park, thirty randomly distributed measurement points were chosen to allow
the radiative characterization of the area of coverage of its three strata as
well as the canopy geometry by the leaf area index (LAI).
The
municipality of Cuiabá is the capital of the state of Mato Grosso and geodetic
center of Latin America (Figure 1), belonging to the CentralWestern region of
Brazil. In the present study, it was observed that the total area of the urban
area was 7,89% of the urban area and 2,970,11 km² (92.1%) of the rural area
(SANTOS, 2008). The regional climate is Aw, according to the climatic
classification of Köppen, characterized by being hot
and humid with rainfall in the summer and dry season in the winter, with wet
and dry seasons (ALVARARES et al., 2013).
2.2 Period of data collection
Data were collected from
photosynthetically active incident radiation (PAR_{inc}),
photosynthetically active radiation transmitted by the canopy (PAR_{trans}) and leaf area index (LAI), point by
point, one measurement per point per month, totaling twelve measurements at
each point during the period from October 2014 to September 2015, from 10 am to
12 noon, time of the greatest incidence of solar radiation. Days were chosen
that had little or no cloudiness and did not rain on the day to minimize
external influences on the variables.
2.3 Instrumentation and
estimation method
The PAR_{inc},
PAR_{trans} and LAI were measured with the linear model ceptometer (AccuPar  LP 80),
which consists of a microprocessor datalogger that interprets the signals that
arrive at the metal rod, called probe, where the sensors that detect the
radiation are installed . The apparatus measures the photosynthetically active
radiation, in the wavelength range from 400 to 700 nm. The radiation values
are expressed in micromols per square meter per
second (μmol.m^{2.s1})
and LAI in m^{2}.m^{2}. The measurements were taken at the
points marked under the canopy at 1.1 m above ground level.
2.4 Statistical analysis
The initial sample consisted of three hundred and
sixty measurements for each variable. The PAR_{inc},
PAR_{trans}, LAI and K variables were
subjected to descriptive statistics in SPSS 23.0 software. Box points
identified the points that constituted discrepant points, outliers, in relation
to the statistical tendency of the sample. Within certain care the outliers can
be removed, especially in samples composed of a considerable number of
measurements (ELLISON and GOTELLI, 2011). Of the three hundred and sixty
measurements, a total of 25 measurements were not considered in the statistical
tests. The canopy variability and possible measurement errors can make this
suitability tolerable.
The database with the adaptations were subjectd to descriptive statistics to analyze the trend and
variability of the values of the variables and tested for adherence to
normality with the application of the KolmogorovSmirnov test (HAIR, 2009). The
violation of the normality assumption made the parametric statistics
impracticable. In these situations the statistical
analysis is performed by the application of nonparametric tests that allow the
comparison of data set for one or more factors. In the research the factors
were the temporal aspect and the characteristic of the vegetation in two
groups, one the cerrado stricto sense,
and another, cerradão
and the ciliary forest. To verify the possible temporal and spatial
differences, the nonparametric MannWhitney U test was used to verify these
possible differences. Spearman's bivariate correlation analysis, which does not
necessarily indicate a linear correlation or a common variance ratio among the
variables, was used to verify the correlations, but can be considered as a
monotonicity index, showing a common tendency of the variables in terms of
growth or decay (BUNCHAFT and KELLNER, 1999).
Spearman's bivariate correlation allows the
calculation of the correlation coefficients (ρ), which is based on the
comparison of the positions of the various measurements and indicates the
correlation regarding the tonicity of the variables (SPEARMAN, 1904).
In figure 2 the following are exhibitd:
the results for
photosynthetically active incident radiation (PAR_{inc})
and transmitted by the canopy (PAR_{trans}),
leaf area index (LAI) and light extinction coefficient (K) for the Mãe Bonifácia urban park, from
October 2014 to September 2015.
The highest values of PAR_{inc}
are observed in the period from December 2014 to February 2015, which coincides
with the period during which the summer solstice occurs. This period coincides
with the highest values of global radiation for the Southern hemisphere. The
unexpected variation in the month of January 2015 may have occurred due to the
sharp precipitation that occurred in January and the presence of cloudiness,
imperceptible to the naked eye, but detected by the ceptometer.
The lowest values of PAR_{inc} occurred in
July and September, 1788.57 μmol.m^{2}.s^{1} , 1786.7 μmol.m^{2}.s^{1},
respectively, at the end of the winter period and at high season (NOVAIS et
al., 2017), in which for the month of September of 2015 were registered 1584
outbreaks of fire, according to data from the National Institute for Space
Research  INPE (<http: // www. . This large quantity of particulate
material suspended in the atmosphere promotes a decrease in PAR_{inc},
since part of the radiation flux that arrives in the atmosphere is reflected
and / or undergoes scattering.
Between December 2014 and June 2015, the PAR_{trans} values, which included the highest
rainfall indexes in the rainy season, ranged from 161.8 to 179.3 μmol.m^{2.s1}
(Figure 2 ). The period of July corresponds to the period of rain reduction
with the respective change in the canopy geometry, due to the phenomenon of
foliar senescence, which is a metabolic process caused by the redirection of
nutrients to other zones of the plant, that in the savannah occurs only in the
aerial part of the plant that culminates in foliar abscission (MAILLARD et al.,
2015), which allows considerable savings in water loss in the transpiration
process and in the availability of nutrients to maintain a leaf surface with
low photosynthetic productivity due to severe water deficit in the dry season (DALMAGRO
et al., 2013). In this period the average value of PAR_{trans}
varies from 315 μmol.m^{2.s1} in July 2015 to 504.2 μmol.m^{2}.s^{1}
in September 2015, while in the same period LAI reduced from 4.06 m^{2}.m^{2}
to 3.18 m^{2}.m^{2}. In October 2014 the measured value of PAR_{trans} was 477.4 μmol.m^{2.s1 }and
LAI had a reduced value to approximately 3.01 m^{2}.m^{2}.
Figure 2  Monthly averages
of the incident photosynthetically active radiation (PAR_{inc})
and transmitted by the canopy (PAR_{trans}),
leaf area index (LAI) and light extinction coefficient (K) for the Mãe Bonifácia urban park, from
October 2014 to September 2015
The
variation of the canopy geometry is accentuated, since in the rainy season
there is an increase in the leaf area index, where in February of 2015 the
measured value reached an average value of 6.8 m^{2}.m^{2},
while in September 2015 this figure reaches 3.18 m^{2}.m^{2}.
The
values of K were calculated for each element of the sample, being analyzed for
the spatiotemporal variation. As for the temporal
variation, the average values ranged from 0.49 in February 2015 to 0.69 in July
2015.
K
values were classified into two groups, smaller and larger, with the lowest K
values occurring from October 2014 through February 2015, including September
2015, and from March 2015 to August 2015, the highest values. The data set were
tested for adherence to normality by the KolmogorovSmirnov test, and the found
results are presented in Table 1. Since the values of K did not adhere to
normal in the set of all months, the application was chosen of the
nonparametric MannWhitney U test to verify temporal variability.
Table
1  Coefficient of light extinction (K) distributed in two sets of different
values and their types of distribution
Classification 
Months 
K values 
Distribution 
Minor 
Jan15 
0,50 
Normal 
Feb15 
0,49 
Normal 

Oct14 
0,52 
Normal 

Nov14 
0,50 
Normal 

Dec14 
0,53 
Normal 

Sep15 
0,54 
Normal 

Major 
Mar15 
0,60 
Nonnormal 
Apr15 
0,57 
Nonnormal 

May15 
0,68 
Normal 

Jun15 
0,65 
Normal 

Jul15 
0,69 
Normal 

Aug15 
0,60 
Normal 
A
pvalue equals to zero was found as a result of the test and confirmed that
there is a statistically significant difference, at a significance level of 5%,
in the K values among the measurement months. This statistically validated
difference favors the use of these values in other studies with greater safety
in the statistical sense, demonstrating seasonality in the coefficient of light
extinction.
The
spatial variability was tested with the separation in two strata of savanna: a
stratum of cerrado stricto sensu and another stratum composed of cerradão and
ciliary forest. A K value of 0.53 was found for the first stratum and for the
second stratum a value of 0.55. The results of the extinction coefficient for
this composition are lower than those found by Resende
et al. (2010), who found for the Amazon / Savanna transition forest average K
values of 0.74.
The
distribution of the set of K values for the two vegetation strata did not show
adherence to normality indicating the application of a nonparametric
statistical test. The nonparametric comparison of the two strata was performed
with the MannWhitney U test, whose test output resulted in a pvalue equals to
10%, a result that allows the inference that there is no statistically
significant difference between the K values in two layers of vegetation. This
accentuates the safety in the values of K obtained, since the geometric
variations of the two strata are similar and the values of K tend to have a
value close to that calculated for a certain area of savanna, close to 0.5,
with a variation around of this value due to the time factor (months).
The
two highest values of PAR_{trans}
occurred in the months of October 2014 and September 2015, coinciding with the
group of six months that had the lowest values for K. However, analyzing other
months, there is no uniform behavior that makes possible generalization of an
inverse correlation between K and PAR_{trans},
as Zhang (2014) states. In this area of savanna this generalization is not
shown safe when considering the monthly evaluation. However, the annual data
set confirms that there is this inverse correlation with a Spearman correlation
coefficient ρ =
0.375.
The
variables that define K, established in equation (1), violated the assumption
of adherence to normality and thus it was not possible to apply parametric
statistics. The option was the bivariate analysis with the calculation of Spearman's
ρ
and the evaluation of the correlations.
Table
2  Spearman correlation for photosynthetically active incident radiation (PAR_{inc}) and transmitted by the canopy (PAR_{trans}), leaf area index (LAI), light
extinction coefficient (K) and zenith angle (Zh) for
the Mãe Bonifácia urban
park, from October 2014 to September 2015.

PAR_{inc} 
PAR_{trans} 
LAI 
K 
Zenital angle 

PAR_{inc} 

1 
0,050 
0.250 
0.373 
0.399 
pvalor 
 
94% 
0% 
0% 
0% 

PAR_{trans} 

0.050 
1 
0.874 
0.375 
0.052 
pvalor 
0.249 

0% 
0% 
34% 

LAI 

0% 
0.874 
1 
0.053 
0.250 
pvalor 
0% 
0% 

16% 
0% 

K 

0.373 
0.375 
0.053 
1 
0.380 
pvalor 
0% 
0% 
16% 

0% 

Zenital angle 

0.399 
0.052 
0.250 
0.380 
1 
pvalor 
0% 
34% 
0% 
0% 

An
inverse relationship between PAR_{trans} and
the light extinction coefficient (K), ρ
negative, was found, showing an inverse relationship between these two
quantities, demonstrating the geometric dependence of the extinction
coefficient, which is observed by the strong correlation between PAR_{trans} and LAI. The variation of the zenith
angle, in the area and time of this research, was from 1.6 degrees to 41.6
degrees, considering the Julian days in which the measurements were made,
affecting the way in which the solar rays enter the canopy, subsequently
affecting other indices, such as surface albedo (NOVAIS et al., 2016). There is
an inverse correlation between K and the zenith angle (Table 2), more inclined
solar rays in relation to the vegetated area decrease the geometric
interception capacity of the solar rays. The values of K calculated and
subjected to the statistical tests can bring the numerical representation of
this geometric variation, not only those that originate in the zenith angle
variation but also the geometric variability of the canopy itself, the place
where the area is inserted and also the geometry urban, buildings placed in the
surroundings that may be affecting the extinction of light. The very variation
of the relief in the place, whose altitude varies from 165 to 195 m, can
influence in the K value.
There
was a strong correlation between PAR_{trans}
and LAI, with a ρ
equal to  0.874, that is also an inverse correlation between these two
variables, confirming several studies, the increase of the leaf area of the
canopy reduces the PAR radiation below the canopy and vice versa. The
correlation between K and PAR_{inc}, PAR_{trans} and Zh with
the very close correlation force accentuates the dependence K has on the canopy
geometry and the zenith angle. Although the test does not demonstrate a direct
correlation between K and LAI, there is an indirect influence if we consider
the strong correlation between PAR_{trans}
and LAI. For the same site, Novais et al. (2018)
found similar significant correlations between leaf area index and
photosynthetically active radiation transmitted and canopy transmittance.
There
is no basis for explaining a causal relationship between the intensity of PAR_{inc} and K, but the correlation obtained with
statistical significance allows the inference of the possibility of the
correlation being supported by the geometric variations of the canopy and the
zenith angle and of the solar declination itself, being thus correlating more
closely with the seasonal aspects.
4 CONCLUSIONS
It is concluded that the luminance extinction
coefficient (K) does not only depend on the nominal values of PAR_{inc}, PAR_{trans},
LAI and Zh, confirming affirmations of other works,
the geometric dependence of the canopy of the researched area and the variables
related to the land translation movements (temporal variability), such as the
zenith angle. The values of the light extinction coefficient (K) of savanna
varied in the studied area between 0.49 and 0.69. The small floristic changes
in the research area that contain three strata of vegetation do not seem to
interfere significantly in the K values, which reinforces the temporal
variability.
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