Tree Shading Factor as input for thermal model through hemispherical photography

Abstract

Solar irradiation contributes to heat gain through building envelopes and has a significant impact on building energy consumption. Trees help reduce incident irradiation and need to be considered as exterior obstructions in energy models. Deploying robust models in early design stages is integral to designing energy efficient buildings. The challenge lies with the limited research on individual tree shade characteristics, in the domain of building energy simulation. A simplified methodology considering tree shade factors incorporating the essence of the complex underlying geometry-without compromising on data accuracy for detailed energy estimation in various engines-is thus required. This work presents Shading Factor (SHF) as a dynamic temporal schedule, calculated using data measured from on-site hemispherical photographs and simulations performed in Honeybee tools in Rhino Grasshopper, for modelers to use as alternative to arbitrary shading values.

Key Innovations: Provides an easy methodology for various simulation engines to incorporate site trees and make informed decisions adhering to a site thereby reducing computational power and time in complex tree modeling for architects and energy analysts.

Full text

Tree Shading Factor as input for thermal model through hemispherical photography
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Suyashi Srivastava1, Swati Puchalapalli2, Marshal Maskarenj3
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1CEPT University, Ahmedabad, India
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2Terra Viridis, Hyderabad, India
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3Universite Catholique de Louvain, Louvain-la-Neuve, Belgium
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Abstract
Solar irradiation contributes to heat gain through building
envelopes and has a significant impact on building energy
consumption. Trees help reduce incident irradiation and
need to be considered as exterior obstructions in energy
models. Deploying robust models in early design stages is
integral to designing energy efficient buildings. The
challenge lies with the limited research on individual tree
shade characteristics, in the domain of building energy
simulation. A simplified methodology considering tree
shade factors incorporating the essence of the complex
underlying geometry – without compromising on data
accuracy for detailed energy estimation in various engines
– is thus required. This work presents Shading Factor
(SHF) as a dynamic temporal schedule, calculated using
data measured from on-site hemispherical photographs
and simulations performed in Honeybee tools in Rhino
Grasshopper, for modellers to use as alternative to
arbitrary shading values.
Key Innovations
• Provides an easy methodology for various
simulation engines to incorporate site trees and
make informed decisions adhering to a site.
• Reduces computational power and time in
complex tree modeling for architects and energy
analysts.
Practical Implications
The tree data presented is specific to the trees studied and
is not representative of their entire species. To form a
‘SHF library’, input of at least 20 trees in a climate is
representative of a specie’s characteristics. Individual
crown shade traits could further influence the selection of
tree for future landscape plantations.
Introduction
While the influence of static external obstructions towards
estimation of lighting energy use in built environment is
well understood (Yoon, Y., 2006), the understanding of
trees towards shade contribution is limited. Trees directly
affect solar heat gain component of building energy use
estimation (Villalba, A., 2014; Akbari, 1997), but the
available energy simulation tools do not consider trees as
exterior obstructions, due to complexity and time invested
in modelling these dynamic shading devices. Tree
shading over a building – especially windows –
significantly impacts building energy use (Berkeley L.,
2019), by influencing the cooling and heating loads –
through shading, obstructing wind flow and
evapotranspiration (Laband, D. N., 2009; Akbari, H.,
2001; Wang, Y., 2014). Parameters that impact shading
quantity and quality are determined by tree species,
canopy area, crown volume and shape, foliation period,
leaf area and density, leaf reflectance, tree location and
orientation with respect to building element (Abdel-Aziz,
2015; Hsieh, 2018). A single tree provides significant
shade even in winters and these results are applicable
wherever the studied tree species are common (Konarska,
J., 2013). While different species impact building loads
differently (Hes, D., 2011), the effect due to an individual
species is somewhat uniform: a medium-size deciduous
tree can reduce irradiance on south façade by 80% and
40%, with and without leaf cover, respectively (Heisler,
G. M. 1986). Integration of tree shading into dynamic
energy models has been proposed (Sattler, 1987),
considering geometry, transmissivity, and location with
respect to a building as the three influencing parameters
(Abdel-Aziz, 2015). While evergreen trees with dense
crowns are effective in reducing annual heat gain,
deciduous trees provide shade in summers yet allow solar
ingress in fall and winter seasons (Kamal, M. A., 2012).
A tree acts simultaneously as a mesh, awning and louvre,
and helps diffuse, reflect and obstruct irradiation and
daylight (Villalba, A., 2014) entering a space. The
geometrical tree representations are complex, since they
require inputs like leaf area, density, distribution, and
reflectivity which are difficult to accurately model, and it
is crucial to simplify tree modelling without
compromising on data accuracy for accurate energy
estimation.
Existing tools incorporate diverse methodologies for
modelling the tree-influences. The DOE-2 building
energy simulation tool calculates direct effect of trees by
Figure 1: The Linear Simulation loop.

simulating buildings with and without trees using typical
weather data, where indirect effects are calculated by
modifying weather data to account for urban microclimate
(Akbari H, 2001). Energy Plus calculates shading factor
through homogeneous coordinate procedure, which
couples sunlit area with irradiation data from ASHRAE
clear sky model (2005). While the effect of reflected
radiation on obstructions is kept simple, still it requires
detailed inputs for considering multiple bounces through
each obstruction (Cascone, Y., 2011). Recent
developments include hemispherical imagery for
modelling trees, as inputs for daylighting and thermal
simulations (Balakrishnan, 2019): where high dynamic
image-based data is used to assess the void ratio or SVF
(Al-Sallal, 2012).
The existing methods to model trees in thermal models
comprise of complex geometry and boundary conditions
and can be broadly divided into TYPE-1 and TYPE-2
categories, based on how they model trees as shading
element, and the type of site data needed for simulation.
TYPE 1 requires geometrical input of shading device in
the form of coordinates apart from defining a
transmissivity value or a schedule for simulation engines
to consider a variable external source. Simulation engines
that require Transmissivity schedule are: Energy plus
(Design Builder and Open Studio), IESVE and e-QUEST.
TYPE 2 does not require geometrical input to consider
external shading device for simulation engines, therefore
Shading Factor (SHF) for the building element can be
defined as a schedule. Simulation engine that allows
direct input of SHF schedule is EDSL Tas.
A methodology to avoid the need of creating complex tree
geometries in thermal models is highly needed, where
shading factors of native trees are used to generalize
shading factor for different tree species. This will aid
energy analysts and modelers alike in faster simulations
while incorporating the advantages offered by
surrounding vegetation. Therefore, this paper proposes a
way to avoid complex geometry yet consider trees, i.e. as
a numeric input without compromising on the readily
available site data. The comparison between the proposed
methodology and the existing techniques is demonstrated
in Fig.3.
Although several studies state that shading factor of a tree
would change with seasons, only the Leaf Area Index
(LAI) is considered (Eiko K., 2011) in assessing
transmissivity of trees, and not the Plant Area Index
(PAI). However, since tree trunk and branches also
contribute to tree shadow, PAI should be considered
instead, and this is addressed in this paper. Further,
shading is temporally divided: summer shading includes
leaves along with tree branches and trunk, while winter
periods will consider shading from branches and trunk.
Shading factor is identified as:
Shading Factor= Void area/Projected Non-void area
Owing to various underlying factors, tree transmittance
depends on specie, climate and direction of view. SHF
depends on solar altitude for most tree species in summer
while it is constant for winters. Therefore, the calculation
of SHF would require both solar altitude and tree
geometry (Tregenza p., N.D.). This paper addresses this
through providing SHF, which has spatial geometric
dependence, and the data provided as temporally
dynamic.
Methodology
The methodology for this work includes data measured
through processing hemispherical High Dynamic Range
(HDR) photography of representative tree samples, along
with parameters simulated using honeybee modules in
Rhino Grasshopper. For measurements, two evergreen
trees – Neem (Azadirachta indica) and Banyan (Ficus
bengalensis), and a deciduous tree - Peepal (Ficus
religios) native to hot-and-dry climate of India are
selected. In continuation, irradiation data with- and
without- a tree scenario is simulated for annual, monthly
and seasonal basis using location-specific weather files.
For a holistic study, at least one year of site-measured data
comprising of information like transmissivity, Leaf area
index, and seasonal canopy density is desirable to assess
shading input of a specie. The scope of disconnecting the
streamlined approach of geometry modeling in
established tools was identified, to allow for piping-in
real-world data and derived metrics in Figure 1.
Simultaneously, it was assessed if transmissivity (τ) data
of a tree could be added as a model input for different tree
species. Since various simulation engines cause data loss
by considering trees as external shading devices and
Figure 2: Research Methodology comprising of both simulated and site data.

simplifying complex tree geometry – where the
granularity in measured data is reduced to save
computation and simulation time, this study aimed to pre-
process the detailed measured inputs to a numeric input.
This temporally dynamic numeric input could be piped-in
to the simulation engines, without compromising quality
of the originally measured data. A methodology
framework to achieve the purpose of this research is
derived.
Figure 2 explains various ways by which site data is
collected, with two most widely used site instruments.
Preference is given to photographic method over
Pyranometer, due to reported accuracy of its realistic data
acquisition. This is further used to derive tree canopy
Transmissivity, which when collected over the span of a
year, would yield a schedule. This schedule could be
combined with geometric input of simulated tree models
to yield a Shading factor schedule. This would follow a
similar timeline as obtained through Transmissivity. The
resultant schedules would involve both site and simulated
data and would be used as input into energy modeling
softwares.
The finalized research methodology is segregated into
two phases as discussed in the objectives earlier. Briefly,
the former deals with tree data collection and modeling
while the latter deals with ways to input the results
obtained in suitable simulation models. The First phase
involves hemispherical photography of selected tree to
calculate Void ratio or canopy transmissivity, followed by
modeling a geometric tree within Honeybee modules to
obtain Irradiation data for with- and without-tree
scenarios for a building element. Set of parameters or
algorithms required for tree shadowing could help in
evaluation of geometrical tree representation, shading
projection, and solar radiation data. The Second phase
consists of finding easiest pathway to incorporate the
collected first phase tree data into various simulation
engines like – Energy plus (Design Builder and Open
studio), Tas, eQUEST and IESVE by deriving parameters
that affect the input results for thermal models. The result
of second phase is analysed to form an appropriate
schedule as input for both TYPE 1 and TYPE 2 simulation
engines.
Figure 4: Hemispherical image acquisition steps on site for selected tree to calculate void ratio.
Figure 3: Simulation engines and their respective inputs required to simulate external shading devices

In the measurement segment of Phase 1, Hemispherical
HDR imagery coupled with image processing technique
is used to identify Void ratio of a given tree species, as
presented in Figure 4. A Raspberry-pi coupled with a
fisheye module is used for the measurements. The fisheye
lens has a viewing angle of 180- and 135-degrees for the
long- and short-edge respectively and can effectively
capture the canopy of a tree. HDR images are generated
by stitching 8 images captured at increasing exposures
[1/8000, 1/4000, 1/2000, 1/1000, 1/500, 1/250, 1/125 and
1/100] through a custom Python script. The colored
channels are flattened to capture grayscale images, by
using factors of 0.2989, 0.5870 and 0.1140 respectively
for the red, green and blue channels.
The HDR pixel-data is then converted to luminance map
using single point calibration, cropped, and resized to
800x800 pixels, and exported to CSV for post-processing.
This technique is capable of capturing data of high
resolution as compared to spot-measurement through a
luminance gun.
For the simulation part of Phase 1, a geometrical model of
the tree canopy is created along with the building element
to be studied, using RHINO grasshopper, and radiation
analysis is done using Honeybee through visual scripting.
The Visual script developed in honeybee-grasshopper
obtains SHF in 3 steps. In step-1, the inputs of the site-
measured tree data obtained through hemispherical HDRi
is incorporated, and tree parameters consisting of Bole
radius & height, crown radius are added: Tree
transmissivity obtained from the site is matched with the
mesh model made in the script. The shape of tree canopy
is determined by capturing a vertical image of the entire
tree shape. From options, of circular, conical, and
cuboidal, the appropriate one is selected in a custom
Grasshopper recipe, and the model is generated in Rhino
workspace. Modifications in the options for different tree
shapes can be incorporated by connecting a different
shape, for example, the trees in hilly regions have a
tapered canopy shape, and replacing the spherical shape
with a conical shape can make the desired changes in the
model. Other parameters inputs – bole (trunk) height, bole
radius, crown radius and Transmissivity of the tree
obtained from the site are incorporated.
In step-2, relation between the tree and the area under
investigation: the location of the tree with respect to the
resultant wall, the direction, orientation, and location of
building element to be studied is determined and
incorporated into the visual script. Also, for the surface
under investigation, the size of the building element, the
angle at which the tree is positioned with respect to it, and
the vertical and horizontal distances are incorporated in
further defining the model. With appropriate
modifications, the floor-wise SHF may be obtained by
altering shape and size of a building element. In step 3,
the temporal assessment is done, where the weather file
of a location is added, and dynamic SHF is derived by
changing the time period from months to annual basis.
The final irradiation output is achieved by averaging the
grid size of the entire building wall element. The data-
series thus generated is exported as CSV output, as a
ready to use SHF schedule.
The Void ratio obtained from the HDRi-based site study
is then incorporated to the simulations, and the resulting
decrease in solar irradiation is mapped and calculated to
obtain SHF of a given tree.
Radiation analysis is done for the with- and without-tree
scenario for various parametric options, and this process
is repeated for various distance from the building element.
The irradiation data is exported to a workbook to
determine monthly and annual SHF of a tree element
through post-processing, and data collected for various
independent trees of same species is averaged to obtain
SHF for a given tree species.
Each outcome of this dataset is specific at a given distance
from the building element, based on the physical
parameters of the tree as on-site. Since most of the trees
are found in clusters at any given site, averaging out SHF
Figure 5: Workflow to derive SHF of different tree species from site-based parameters.

of all the tree species in each direction could give the
resulting SHF required for the building element. The
process in Fig.5 can be deployed to map SHF of various
trees with parameters as listed here. This representational
seasonal variation can be added as schedule-input in
simulation-based-optimization of building elements.
In this study, two evergreen trees – Neem (Azadirachta
indica) and Banyan (Ficus benghalensis), and a deciduous
tree - Peepal (Ficus religios) are selected for the hot-dry
climate of Ahmedabad. Following the process presented,
the SHFs are derived. Transmissivity is obtained from site
study for TYPE 1 simulation engine input. The TYPE 2
analysis consists of mapping resulting decrease in solar
irradiation and calculating SHF of a given tree for a given
distance from the building element. This process would
be used to find SHF for annual, monthly, and seasonal
basis under uniformly overcast or clear sky conditions.
The resultant trendline is added as a schedule to the given
simulation engine as an optimization for building
element. The individual tree canopy in Figure 6(1), is
captured by placing the Raspberry Pi fisheye camera right
below the tree’s canopy on flat ground, and data is
captured for both North and South directions as shown in
Figure 6(2). The resulting HDR image is converted into
workbook data (.csv format) through the custom script. A
threshold value is used to separate the background, after
single-point calibration of electronic data received on the
camera sensor, which helps identify the minor voids in the
tree canopy. The full tree canopy is further formed by
combining two HDR hemispherical images of North and
South directions, as shown in Figure 6(3). Since the tree
Figure 6: Steps followed to obtain transmissivity value of selected trees in Ahmedabad.

canopy obtained includes the irrelevant surrounding data
captured by the hemispherical lens, a circular ‘sky mask’
is applied to the CSV file with the sky image threshold as
shown in Figure 6(4). By flattering the foregroung and
background to binary values of 1 and 0, a count of the
number of cells representing the cells of the foreground
with those of the background generates the solid-to-void
ratio for a given tree at a given location and direction.
Similarly, a count of the cells representing the
background, along with count of all the cells in the mask
yields the void ratio, This helps generate the
transmissivity data to be added to the script used for
creating the mesh geometry.
Results
Figure 7 presents the outcome – a temporally varying SHF
for the studies trees. A brief comparison between the two
studied evergreen trees, shows that Neem behaves as a
semi-evergreen tree in harsh weather and drought-like
conditions, demonstrating reduced foliage density which
varies across topographical and geographical locations.
The foliage density of Banyan tree varies by less than than
3% throughout the year. Repercussions of this in building
domain is this, that dense foliage of Banyan would not
allow sunlight penetration across seasons, while the semi-
evergreen Neem could allow winter sun through reduced
foliage in the season.
It is observed that shading factor decreases linearly as the
building element is placed away from the evergreen tree
for the Banyan tree, yet it varies slightly for the Neem
tree. Transmissivity value obtained from hemispherical
photography of Peepal tree is added to the simulation
model with similar geometry to determine the percentage
decrease in irradiation received at building element
through a tree. Shading coefficient for deciduous tree is
reported to range from 0.07 to 0.38 in summers, and from
0.27 to 0.89 in winters (Rights A. P, 2017), according to
a study done in Tucson, Arizona, which has a similar
climate as Ahmedabad, India (hot semi-arid climate)
where the present study was conducted. The minimum
difference observed between the two major seasons is
roughly about 0.2, while the maximum is about 0.6. The
minimum difference is selected to represent the worst-
case scenario with less foliage growth to complete the
data series for a deciduous tree in this research. As seen
in Figure 7, the results obtained from this research can
directly be directly integrated into the TYPE 1 simulation
engines.
It is identified that tree transmissivity is a property of its
canopy is not dependent on the direction, hence a schedule
may be formed specific to the trees studied. The monthly
average graph could also be plotted hourly as per
requirement. This study can be taken forward and annual
data may be recorded using the proposed methodology for
more accurate results specific to tree type.
Conclusion
Traditionally, simulation tools do not categorise tree
types, and a generic value is considered for all trees, even
when it is understood that species hugely impact the built
environment. This reinforces the importance of studying
vegetation around a site for determining accurate tree
impact. The mentioned methodology can be used to study
various species of tree at a given site and its shading effect
on the building element, provided that transmissivity data
for all seasons is available. The timeline of this research
was limited, which restricted year-long collection of
selected tree-data. To fill-in the gaps, literature that
reported approximate change in transmissivity values for
deciduous and evergreen trees for summer season were
referred. A general convergence was seen between
measured outcomes of this study with those in literature,
however, the site data collection was done for winter
month – which denotes worst-case scenario of tree
transmissivity with least shading factor. An average
variation in void ratio of 2-3% on an average is considered
for the evergreen trees as well, to account for new leaves
and branches for a given mature tree. The stated
percentage would vary within and between various
species due to climate, environmental conditions, size,
Figure 7: Transmissivity schedule for TYPE 1 simulation engines - Energy plus (DB and OS), eQUEST, IESVE.

and genetics, among others. Therefore, it is understood
that summer SHF is high for deciduous as well as
evergreen trees. This study derives a methodology to
incorporate a tree’s shading effect into a simulation
engine, by jointly using measured data (through
hemispherical photography) and parameters identified
from simulations (from honeybee/grasshopper) as inputs.
The simulations are conducted in DIVA, a user-friendly
tool that supports simulation-based decisions in early
design stages.
As contribution to the domain, this study reports
methodology and limited results for tree transmissivity
schedule, as resultant inputs to simulation engines that
require geometrical input: like Energy Plus, eQUEST and
IESVE. Also, shading factor schedule is obtained as input
for simulation engine that do not require geometrical
input: like EDSL Tas.
Exceptions and assumptions include Neem’s ability to
adopt deciduous tree traits and change its transmissivity
under extremely harsh conditions as confirmed by various
studies. Yet for this study, the selected standalone Neem
tree is considered as an evergreen tree, since the above
hypothesis could not be confirmed in the timeframe of this
research. Since data was collected solely for the winter
period, the results represent a worst-case scenario for both
evergreen and deciduous trees.
Acknowledgement
Mayuri Agrawal and Vardan Soi assisted in on-site
measurements and simulation phases, respectively.
Shoumik Desai and Maaz Dixit offered valuable insights,
and Professors Rajan Rawal and Rashmin Damle gave
detailed comments through various phases of this project.
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