2-2-6- Step 6: Modeling the spatial distribution of carbon
sequestration and CO2 absorption across the city
To model the spatial distribution of carbon sequestration within the
city, we created a regression relationship between the spectral values
of the Worldview2 satellite image with calculated carbon sequestration
(described in the previous steps) in a single tree unit.
In this step, first, we needed to do image pre-processing and
processing, and then created a regression model that is as follows:
Image Preprocessing
Image preprocessing included georeferencing and atmospheric corrections.
We used the removal haze tool for atmospheric correction. In this study,
to ensure the accuracy of the geometric correction of the image, a
topographic map (1/1000) was used. The exact matching of the road layer
from the topographic map with the image showed the geometric accuracy of
the image.
Image processing
To investigate the regression relationships between the spectral
variables o with the calculated carbon in a tree, the processes were
applied on the spectral bands. Then, the most important spectral
variables were extracted from the image to estimate the amount of
carbon. The processes that applied to the satellite imagery in this
study can be classified into three groups. The first group included
spectral ratios obtained from the three red, green, and blue bands. The
second group consisted of three plant indices, including the Excess
Green Plant Index (ExG), the Excess Red Plant Index (ExR), and the
difference between these indices (ΔExGR). Their equations are expressed
in relations 1 to 3, respectively (Meyer and Neto, 2008).
Also, in the third group, texture analysis was separately performed on
each band (blue (B), green (G), and red (R) bands).
\begin{equation}
ExG=\left(2*G\right)-R-B\ \ \ \ Eq.1\ \nonumber \\
\end{equation}\begin{equation}
ExR=\left(1.4*R\right)-G\ \ \ \ \ \ \ Eq.2\nonumber \\
\end{equation}\begin{equation}
\text{ΔExGR}=ExG-ExR\ \ \ \ \ \ Eq.3\ \nonumber \\
\end{equation}Creating a GWR to model the relationship between
calculated carbon sequestration and spectral variables
In this section, we modeled the relationship between the spectral
variables of the satellite image with the amount of carbon that was
measured for a tree unit. To do so, first, a buffer around the tree with
a radius of the drip line (approximate radius of the canopy) was
defined. Dripline is the area, which is located completely below the
outer perimeter of the tree branches˗ saying that its area is
approximately equal to the area of the canopy. To determine the actual
radius of the critical root protection zone (drip line), first, the
perimeter of the tree trunk was measured at the height of 1.3 meters
above the ground. Then the perimeter of the trunk was divided by the pi
constant (3.14) to calculate the DBH. Finally, the DBH was multiplied by
12. The general rule of this method is that for every 1 cm of tree trunk
diameter, the radius of the critical root protection zone increases by
12 cm (Council, 2013, Design et al., 2019, Limited, 2009, Matheny and
Clark, 1998, Moore, 2018, Roloff, 2016, Rust, 2015, Standard, Suchocka,
et al., 2019).
In this study, the drip line was used as a buffer for each sampled tree.
Then 70% of these drip lines (vectors layers) that their DBH were 5 cm
or larger than 5 cm randomly selected. After that, we used the zonal
statistics tool to derive the pixel value of the spectral variables
(bands, vegetation indices, and texture analysis) for each sampled
tree.
Finally, the amount of calculated carbon sequestration for a sampled
tree was considered as a dependent variable, whereas the spectral values
(image bands, plant indices, and image texture analysis results) were
regarded as an independent variable. The independent and dependent
values entered into the GWR model.
GWR is a statistical technique that is used to model the spatial
heterogeneous processes. It has high accuracy in analyzing
location-affected relationships (Fotheringham et al., 2001). This model
is a generalized version of the ordinary least square regression method
in which the spatial pattern of relationships between variables is
examined in the sample space (Gao and Li, 2011). Instead of calibrating
a single regression equation, this method produces a separate regression
equation for each observation (for more information, see the
references: Brunsdon et al., 1996, Fotheringham et al., 2001, Gao and
Li, 2011; Tu and Xia, 2008, Zhao et al., 2018).
After evaluating different models with different arrangements of
independent variables, the best significant model was selected, and its
weight matrix was determined. Then, the model was implemented using a
significant independent variable on the entire study area. After that,
the amount of carbon sequestration in the tree biomass was estimated for
the whole green space of the study area.