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\begin{document}

\title{On~ the Impact of Climatic Uncertainty in Building Energy Simulation for
Design and~ Decision Support}



\author[1]{Maryam Meshkinkiya}%
\author[2]{Enrico De Angelis}%
\affil[1]{Dipartimento ABC. Politecnico di Milano}%
\affil[2]{Politecnico di Milano}%


\vspace{-1em}



  
  \date{May 05, 2024}


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\par\null

\section*{Abstract}

{\label{284268}}

The~ accuracy of building energy needs estimation is one of the most
important challenges of building energy research. The boundary
conditions have a significant impact on building energy performance and
studies in the literature demonstrated that considering~ the uncertainty
in input parameters is essential to achieve a more realistic energy
model. One of the~ quantities defining the boundary condition that is
most subject to uncertainty- is the incident solar radiation on the
building envelope, composed ofdirect, diffuse and ground reflected
radiation. Trees, adjacent buildings and street optical-radiative~
properties affect the short-wave radiation incident on building facades.

This PhD research, will look for a framework to quantify the uncertainty
of incident radiation on the building envelope to provide a more
accurate representation of ~radiative exchange within an urban canyon
environment. Among the mentioned factors, the uncertainty quantification
of the ground reflectance parameter is discussed in the present paper .
The reliability of the performance estimation in two different shading
scenarios is~ assessed based on the outputs of the uncertainty
quantification. The first~ scenario is an on/off controlled shading
based on the incident solar radiation.~ After this~ analysis, designers
may find an optimal schedule for the presented shading~ system,
depending on the building use. The second scenario, proposes a fixed
~shade, highlighting the importance of uncertainty in ground reflected~
radiations while assessing the reliability of a shading design.

\section*{Key-words:}

{\label{179970}}

Uncertainty, solar incident, shading devices, Performance gap.

\par\null

\section*{Introduction}

{\label{780682}}

In the context of building performance, the discrepancy between building
energy simulation and measured observations is the focus of many
studies~\cite{Menezes_2012,de_Wilde_2014,Attia_2013,Fedoruk_2015}. Since building energy simulation models~
deal with an extensive number of input and parameters, imprecision and
lack of~ knowledge is inevitable. These short--comes, also known as
uncertainties, are~ major contributors to the gap between simulated and
measured building energy~ performance.

However, it is commonly believed that obtaining a correct understanding
of imprecisions as well as increasing the knowledge in unknown
contributors can result in better predictions. In order to achieve a
better understanding of the uncertainties and monitor their effects,
various techniques are invented. These methods span from the initial
part of collecting data for simulation input to post processing each and
every effect of the input parameters. Uncertainty Analysis (UA) deals
with quantitative modeling, which cannot be associated with
certainty~\cite{Kurowicka_2006}.The approach has various applications in
risk assessment\cite{Jiang_2013}, reliability
assessment\cite{Zhang_2013} and decision-making (decision~
support)\cite{Kim_2014}.

The uncertainty in Building Energy Simulation (BES) can be addressed
considering various sources. Hopfe and Hensen~\cite{Hopfe_2011} assumed
three sources: uncertainty in physical, design and scenario parameters.
They focused on the physical properties of wall, roof and floor area as
physical uncertainties. The uncertainty in design parameters was
referred to different design strategies, which are adopted in the
planning process. Finally, the scenario uncertainty that is derived the
future life of a building. The occupancy and future weather condition
are the main causes of these kinds of uncertainties. Fig. 1 displays the
different sources of uncertainty and their subcategories in BES.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}
\caption{{Sources of uncertainty in building energy performance%
}}
\end{center}
\end{figure}

Sensitivity analysis -- often executed simultaneously with Uncertainty
Analysis (UA) -- is a study which provides insights on the contribution
of uncertain input parameters over the outputs of a
model~\cite{kurowicka2006uncertainty} . Uncertainty and sensitivity analysis
generally follow two major objectives in the field of building energy
performance. One group of studies evaluate the embedded uncertainty in
early design evaluation to quantify the range of
outputs~\cite{Bucking_2013}, while others perform uncertainty and
sensitivity analysis in order to validate and calibrate previous
measurements\cite{Calleja_Rodr_guez_2013,westphal2005building}.

A vast variety of topics in building energy performance has been covered
in recent studies. De Wit et al.~\cite{de_Wit_2002} introduced a~
methodology for decision makers to quantify uncertainties in the design~
process. Such frameworks assist decision makers to deal with various
design~ possibilities that are derived from a series of sensitivity
analyses. Other~ studies have adopted comparable approaches to support
decision making in~ building energy assessment and the impacts of
possible design solutions on the~ energy performance~\cite{Kim_2014,de_Wit_2002,Attia_2013a}.
Eisenhower et al.~\cite{Eisenhower_2012} introduced an uncertainty and~
sensitivity decomposition model to study the effects of uncertain
quantities on~ a building's energy performance. The proposed framework
was aimed at evaluating~ the impact of sizing sub-components of a model
on the overall building energy~ performance. Hopfe et
al.~\cite{Hopfe_2011} argued that including~ uncertainty in physical
parameters during the design process will ensure a higher quality a
building's energy performance. Moreover, it was noted that~ assessing
uncertainty in design parameters can provide designers with better~
decision strategies. There has been a limited number of studies, which
has focused on UA in building performance simulation with respect to
uncertainty in weather parameters. Considering the complexity of
propagating weather parameters through an energy model, uncertainty
analysis has been either ignored or limited to a specific
season~\cite{Garcia_Sanchez_2014,Macdonald_2001,Corrado_2009}. Sun et al.~\cite{Sun_2013} presented a
quantification of uncertainty was addressed through the exploration of
the urban heat island effect. Temperature, wind speed, wind pressure and
solar radiation were considered as the most important climatic
parameters related to exterior building boundary conditions that affect
the overall energy performance of buildings.

Clearly, the outdoor climate is one of the main factors that~ affect the
overall performance of buildings. The outdoor climate is also affected
by the Urban Heat Island effect (UHI) in large cities. Investigation on
the~ long-term hygrothermal performance of a residential building has
demonstrated~ the difference in design requirements for urban and rural
contexts~~\cite{paolini2016hygrothermal}. ~According the recent studies, the
Meanwhile, it has also shown that the impact of boundary conditions in
smaller~ scales of the built environment, may also affect the
performance of the~ building\cite{Karlsson_2006}. This has been
investigated in a variety of studies related to the building envelope
such as shading devices~\cite{Tzempelikos_2007},
daylight~\cite{Loutzenhiser_2007} and solar heat gains\cite{Lee_2013}.
~The role of boundary conditions also discussed in the risk assessment
of mold growth. The knowledge of the boundary conditions can be improved
optimizing the modeling of some variables like weather parameters, such
as the estimation of the solar irradiance incident on a
facade\cite{Freitas_2015}. ~Since the uncertainty in weather parameters
is clarified in previous studies~\cite{de_Wit_2002,sun2013uncertainty}~ and according to
literature the application of UA analysis in building outdoor boundary
conditions merits to be considered.

Solar irradiance is among the weather parameters that affect different
building energy performance parameters such as indoor air quality,
visual comfort, building integrated photovoltaic system, etc. Building
simulation tools compute the incident solar irradiance on building
surfaces. Mostly these models use a set of observed global solar
irradiance to compute diffuse solar irradiance. Solar models are
developed based on data collected at different locations and different
climatic conditions. However it is argued that solar models cannot be
considered as generally valid models and the uncertainty in calculations
based on these models is inevitable~\cite{Prada_2014,pernigotto2015impact}.

The mentioned solar radiation models are applied to calculated diffuse
and direct irradiation, however, the incident solar irradiance on the
building surfaces (I\textsubscript{H}) is divided to three components.
The direct normal solar irradiance (I\textsubscript{DI}), diffuse solar
irradiation (I\textsubscript{DIF}) and ground reflected irradiation
(I\textsubscript{GR}).

\begin{equation}
I_{H}=I_{\text{DI}}+I_{\text{DIF}}+I_{\text{GR}}\nonumber \\
 \end{equation}

According to literature, another source of uncertainty in
I\textsubscript{H} arises from the reflected irradiations. However, the
model of calculations for these parameters (in the area of building
energy analysis), is a simplified version of reality (Fig. 2). Recent
studies tried to expand the mentioned equations in order to consider
more dominant parameters, which affect the amount of incident solar
irradiance on the building surface. Lou et al~\cite{Lou_2016}
evaluated the solar irradiation on obstructed building fa\selectlanguage{ngerman}çade. To
evaluate the reflectance of adjacent buildings, they proposed an
additional value to equation (1):

\begin{equation}
I_{H}=I_{\text{DI}}+I_{\text{DIF}}+I_{\text{BR}}+I_{\text{GR}}\nonumber \\
 \end{equation}

Where the I\textsubscript{BR} is related to reflected solar irradiation
from adjacent buildings.

Proposing a more accurate model of solar radiation on the building
fa\selectlanguage{ngerman}çade calls for considering more detailed variables. This issue caused
other studies to focus on the role of vegetation on the uncertainty of
incident solar irradiation within the street canyon~\cite{Fogl_2016,Krayenhoff_2013,Bourbia_2004}.
Cascone et al~\cite{Cascone_2011}investigated the impact of different
shapes of vegetation in different orientations and seasons on the
shading factor. In their investigations, they found about 24.1\%
difference of shading factor in the case of various foliage shapes on
the south façade and the same conditions for the east façade showed the
23.9 \% difference of shading factor.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig2/Fig2}
\caption{{left: Horizon angle considered in ISO 13790-Right: the reality of a
street canyon
{\label{204276}}%
}}
\end{center}
\end{figure}

The research in this Ph.D. study is divided into main segments. First,
uncertainty quantification of incident solar radiation on building
facades, and second, reliability assessments of proposed shading
strategies. The strength and novelty of this research are derived from
both segments, however, the first part merits a more in-depth focus
since a detailed approach~ to~uncertainty quantification of incident
solar radiation has been less~ noticed in the topic of building energy
simulation. Most of the current~ literature on solar availability over
building surfaces have been performed on an urban scale. This study
tends to merge urban and building scales and provide a more detailed
model of solar radiation diffraction from the urban canyon. The~
sensitive role of incident radiation in different aspects of building
energy~performance calls~for more accurate approximations of this
measure. Quantifying the incident solar radiation on the building
surfaces can help to reduce the~ performance gap between simulation and
reality, as this analysis provide a~ better vision on the long-term
performance of different building component (e.g. memberings, external
venetions, paint/coatings and etc). Consequently, it will facilitate
decision-making for designers as they face various options. Incident
solar radiation on the building envelope has an important role on the
temperature of the exterior layer of the wall, and~ consequently,
affects the hygro-thermal performance of the building. Considering~ that
the hygro-thermal performance of the wall is among the parameters which~
affect microbiological growth risk, uncertainty quantification of the
incident radiation on the facade, and the resulting envelope temperature
merit careful considerations\cite{paolini2016application}.~The outcome of the first
part of this study could be combined with the occupant~ behavioral
models, concerning the importance of interaction between building users~
and visual/thermal comfort. A better estimation of the amount of
incident~ radiation over the building facade will result in more
accurate estimations of~ solar heat gains as well as internal
daylight.~~

In this paper, uncertainty quantification of ground reflected irradiance
is demonstrated, which marks the starting point of this Ph.D. research.
The paper tends to propose a methodology through which,~ evaluation of
the reliability of shading devices during the cooling season is
facilitated.

\section*{Data description}

{\label{585559}}

Since the typical weather data present a long time average of climate
parameters, therefore it is possible that some critical weather changes
are ignored. ~For instance, Europe experienced two heat waves in during
the last decades. An extreme one in 2003 and another in 2015. Studies
show that unqualified building design had a significant role in the
amount of damages. The required values of solar irradiation are
extracted from the 5 years of weather data in Milano. Global, direct
normal and diffuse irradiance from 2012 till 2016 are the main source of
data used in the simulations.

\section*{Methodology}

{\label{872088}}\par\null

Until a decade ago, uncertainties were divided into two major categories
based on the natures of their source: epistemic and aleatory. Epistemic
uncertainty concerns phenomenon, on which we have imperfect knowledge.
This type of~ uncertainty is reducible through repeated measurements of
the~uncertain~ phenomena. Meanwhile, aleatory uncertainty is related to
lack of knowledge and cannot be explained by a distribution as scarce
data are available regarding the pattern of their
occurrence~\cite{Kiureghian_2009}. However, the concept of uncertainty has
been recently approached by three main perspectives i.e. randomness
(probabilistic), fuzziness (Possibilistic), and uncertain (neither
probabilistic nor possibilistic) theory~\cite{Dubois_2001}.~

Uncertain parameters of related to solar radiation in street canyon\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Parameters & Nature of uncertainty & Suitable approach\tabularnewline
\midrule
\endhead
Diffuse solar irradiation & Epistemic & Probability\tabularnewline
Ground reflectance & Epistemic & Probability\tabularnewline
Vegetation & Aleatory & Possibilitic\tabularnewline
\bottomrule
\end{longtable}

Regarding the associate the uncertainty in indecent solar radiation, the
following framework (Fig.3) will follow during this Ph.D.
research.~However, the present paper will provide a practice on the
associate the uncertainty on ground reflectance within the urban
~contextand impact on building design strategies (Fig. 5).\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Frame-1/Frame-1}
\caption{{Framework to quantify uncertainty in incident solar radiation on the
building envelop
{\label{605817}}%
}}
\end{center}
\end{figure}

The value of monthly ground reflectance is considered as 0.2 in the
standard simulations. This value is resulted from the combination of
ground reflectivity of pervious and impervious surfaces and based on
equation (1):

\begin{equation}
\rho_{\text{GR}}=\rho_{GR\_p}f_{GR\_P}+\rho_{GR_{\text{imp}}}(1-f_{GR\_P})\nonumber \\
 \end{equation}

where P\textsubscript{GR} is ~ground reflectance, P\textsubscript{GR\_P}
and P\textsubscript{GRimp} refer to road pervious and impervious
f\textsubscript{Gr\_P~}is road area function. Moreover, the ground
reflectance value is affected by ground surfaces cover by snow
situation~\cite{Clarke_2002}. Since this study is only focused on the
cooling season (for shading design purposes), the effect of snow is
ignored in the presented calculations. The range of uncertainty in
ground reflectance is extracted from Sun et al.~\cite{Sun_2013}.
According to this study, the range of ground reflectance could vary
between 0.05 and 0.45 with a center point of 0.25. This value can be
represented through a triangular probability distribution displayed in
Fig.4 .

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/2017-05-29-(1)/2017-05-29-(1)}
\caption{{The distribution of ground reflectance variation
{\label{967830}}%
}}
\end{center}
\end{figure}

The next step in uncertainty analysis is to make different samples from
the existing distribution. Choosing the~ most appropriate sampling
method and size of the samples has an important role in uncertainty
based~ analysis, as it should be large enough to provide accurate
results \cite{wang2014monte}. Indeed, the~ input covers the entire range
of space, in order to guarantee that the samples~ are reliable
representatives of the entire uncertain space~\cite{Saltelli_2007}.

The Latin Hypercube Sampling method is selected for this step. Regarding
that, the number of ~20 random samples from each year of climatic data
between 2012-2016 is considered. This resulted in an overall sum of 100
annual simulations (8760 hours) of incident solar radiation on the
surface of a vertical wall facing south. The simulations were handled
with JePlus simulation manager. As mentioned before, this study is only
focused on the cooling season, which for Milan city starts from the
first of July and endson the 9th of September~\cite{Dongellini_2015} . ~

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Frame-2-2/Frame-2-2}
\caption{{The proposed method to assessing the impact of uncertainty embedded in
ground reflected radiation
{\label{448851}}%
}}
\end{center}
\end{figure}

\section*{Results and discussions}

{\label{118355}}

The total hourly values for incident solar radiation on building
envelope is extracted from the result of simulations. In order to study
on the impact of uncertainty in ground reflectance, the 1st to the 99th
percentile of incident solar radiation for each hour of a day is
presented in Fig. 6(Up).

This Figure is suitable for assessing the performance of different
shading strategies, as it displays the frequency of occurrence based on
the magnitude of the power.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/2017-05-29-(2)/2017-05-29-(2)}
\caption{{Up: Cumulative distribution of hourly values of incident solar
radiation. Down: The heat map of percentile of hourly values of incident
solar radiation
{\label{525215}}%
}}
\end{center}
\end{figure}

\subsection*{Case 1. Automatic Shade}

{\label{895248}}

In the first case study, we consider an automatic rolling shade, which
closes when the incident solar radiation on the wall exceeds 300
W/m\textsuperscript{2}. Figure 6 displays the frequency of incident
radiation when the shading is installed. It is observed that the shading
system will be active from 10:00 a.m. to 4:00 p.m. However, at 10:00 am,
it will be only active 20\% of the time, and at 4:00 p.m. less than 10\%
during summer (Fig. 7 -Up). Meanwhile, the main activity of the shading
system will be from 11:00 a.m. to 3:00 p.m., where the shades will be
closed approximately 50\% of the time. Such pattern may be unreasonable
for schools and offices which require adequate daylight throughout the
day, while also affects the electric energy consumption by requiring
extended lighting hours during midday.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig-Sc1/Fig-Sc1}
\caption{{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Up: Evaluating the performance~ of
shading strategy with the threshold 300 (K/m\textsuperscript{2}). Down:
Assessing~ the~~~~ performance of fixed strategy in lower (red line)~
and upper limit (black line)
{\label{712881}}%
}}
\end{center}
\end{figure}

\subsection*{Case 2. Fixed Horizontal
Shade}

{\label{292806}}

In the second case study, we consider a fixed shade that is installed to
block radiation during the cooling season in Milan, i.e. June 1st to
September 15th. We would like the dimension of the shading to be so that
it would start blocking radiation from 10:00 am June 1st when the 5
years median of incident radiation on the surface is 360
W/m\textsuperscript{2}. In this case, we are eliminating direct and
diffuse solar radiation when the solar altitude reaches 49 degrees,
however, we will keep the reflected radiation from the ground. Fig. 8
displays the incident radiation on the wall when the horizontal shading
is deployed. It is observed that the designed shading cannot adequately
block the radiation, as we have values higher than 500
W/m\textsuperscript{2}. This is due to the fact that in September the
solar elevation is low; however, the incident radiation can reach as
high as 500 W/m\textsuperscript{2}. Therefore, we decreased the
threshold of solar altitude to 38, where it can block the direct solar
radiation for approximately 99\% of the time during the cooling season
(Fig. 9).\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/image8/image8}
\caption{{Incident solar radiation on the south wall for a solar elevation of 49
degrees.%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/image9/image9}
\caption{{Incident solar radiation on the south wall for a solar elevation of 38
degrees.%
}}
\end{center}
\end{figure}

\section*{Conclusion}

{\label{642085}}

The impact of uncertainty in ground reflectance is practiced in this
study. This value in EnergyPlus is considering as average monthly equal
0.2. However, according to literature, this value can be varied between
0.05 and 0.45. Regarding this analysis, two different scenarios are
evaluated. The first scenario considers a controlled shading strategy
and second one assessing the performance of a fix shedder. The total
amount of incident solar radiation on the building envelope with the
respect of ground radiation uncertainty is evaluated. The uncertainty in
ground reflectance is propagated on the building energy model and the
analysis is performed for 5 years of weather conditions. In order to
propagate this uncertainty, different sets of samples are generated with
Monte Carlo sampling. The results provide a better overview of the
performance of each scenario, especially, on the lower and upper limits
of shading performance also the frequency of incident solar radiation
for each hour of a day.

This kind of analysis will be useful for designers to provide a more
confidence performance of proposed shading strategies. Also, this
analysis can use for analysis related to solar heat gains and inside
comfort conditions. This analysis could be used to reduce the
performance gap between reality and building energy simulations. As
observed in scenario 2.

\section*{The future work}

{\label{140656}}

The future work of this study will be composed of following~ tasks:~~~~~

\begin{itemize}
\tightlist
\item
  ~ Uncertainty quantification of different types of vegetation ( based
  on height, shape, density, etc.) and their impact on the shading
  factor, and the amount of reflected solar radiation from ground.~
\item
  ~ Quantifying the variation in diffuse solar radiation based on
  different climatic stations in various locations of a city, as well as
  multiple years.
\item
  Modeling an urban geometry with DART tool and incorporating the
  earlier results with the input data of the tool and quantifying the
  incident solar radiation on the building surfaces.~~
\item
  Applying the previous steps on different shading strategies for
  assessing the reliability of each design choice, and creating
  comparative graphs based on the performance of each shading strategy.
\end{itemize}

\par\null

\section*{Acknowledgements}

{\label{770862}}

This research is conducted by the~ support of a doctoral scholarship
granted by Fondazione Fratelli Confalonieri. Moreover,~ the weather data
using in this study is provided by Osservatorio Meteo Milano Duomo.

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