The Effects of Setback Geometry and Façade Design on the Thermal and Energy Performance of Multi-Story Residential Buildings in Hot Arid Climates

Abstract

This study investigates the influence of rear setback geometry and façade design parameters on microclimatic conditions, indoor thermal comfort, and energy performance in multi-story residential buildings in hot arid climates, addressing the growing need for climate-responsive design in regions with extreme temperatures and high solar radiation. Despite increasing interest in sustainable strategies, the combined effects of urban geometry and building envelope design remain underexplored in these environments. A coupled simulation framework was developed, integrating ENVI-met for outdoor microclimate modeling with Design Builder and EnergyPlus for dynamic building performance analysis. A total of 270 simulation scenarios were examined, combining three rear setback aspect ratios (1.5, 1.87, and 2.25), three window-to-wall ratios (10%, 20%, and 30%), three glazing types (single-, double-, and triple-pane), and two wall insulation states, using customized weather files derived from microclimate simulations. Global sensitivity analysis using rank regression and multivariate adaptive regression splines identified the glazing type as the most influential parameter (sensitivity index ≈ 0.99), especially for upper floors. At the same time, higher aspect ratios reduced peak Physiological Equivalent Temperature (PET) by up to 5 °C and decreased upper-floor cooling loads by 37%, albeit with a 9.3% increase in ground-floor cooling demand. Larger window-to-wall ratios lowered lighting energy consumption by up to 35% but had minimal impact on cooling loads, whereas wall insulation reduced annual cooling demand by up to 29,441 kWh. The results emphasize that integrating urban morphology with optimized façade components, particularly high-performance glazing and suitable aspect ratios, can significantly improve thermal comfort and reduce cooling energy consumption in hot arid residential contexts.

1. Introduction

1.1. Background

The growing energy crisis and the need to address climate change have increased the focus on improving building energy performance and indoor environmental quality. Buildings are prodigious global energy consumers, accounting for approximately 30–40% of total primary energy consumption and contributing significantly to greenhouse gas emissions [1,2,3]. Optimizing multi-story residential buildings’ thermal and energy performance, particularly in regions characterized by extreme climatic conditions such as hot arid zones, emerges as a critical research frontier. These climates pose challenges such as high temperatures, intense solar radiation, and limited cooling, requiring tailored design strategies to maintain comfort and energy efficiency.

Optimizing the thermal and energy performance of multi-story residential buildings in extreme climates has become a research priority, as cooling demand now dominates energy end-use in many hot and arid regions [4,5,6,7]. Empirical and review studies reveal substantial variation in residential comfort expectations and demonstrate that adaptive strategies and envelope-based measures can achieve considerable energy savings when tailored to local climatic and behavioral conditions [8,9]. This body of evidence underscores the need—and opportunity—to integrate urban form and façade design in developing robust, climate-responsive residential solutions [10]. A significant strand of research shows that urban geometry—particularly canyon or rear-setback aspect ratio (H/W) and orientation—modifies outdoor mean radiant temperature, pedestrian heat stress indices (e.g., PET, UTCI), and façade radiative loads, with direct implications for indoor cooling energy [11,12]. Numerical modeling and ENVI-met simulations in hot dry and hot arid contexts generally show that higher aspect ratios improve daytime thermal comfort through increased self-shading, although excessive depth can reduce ventilation efficiency and increase stagnation at street level [13,14,15]. These findings support investigating rear-setback AR alongside façade parameters to assess their combined influence on outdoor comfort and cooling demand across different floors [16,17].

At the façade scale, numerous studies in hot arid cities have confirmed that glazing properties (SHGC, U-value, and VLT), window-to-wall ratio (WWR), double-skin façades, and insulation thickness substantially affect cooling energy use and indoor operative temperature [5,18,19]. Parametric simulations for cities such as Jeddah and others in Arabian and North African climates show that low-SHGC and low-U-value glazing can markedly reduce peak cooling loads, while higher WWR can lower electric lighting needs but may raise cooling demand unless mitigated by high-performance glazing or shading [20,21]. Similarly, increasing opaque-element insulation has been shown to reduce conductive heat gains and annual cooling requirements. These outcomes justify the selection of glazing type, WWR, and wall insulation as primary decision variables in parametric and sensitivity analyses [22,23,24]. Because building- and neighborhood-scale effects are often non-linear and uncertain, methodological reviews recommend coupling high-resolution microclimate models (e.g., ENVI-met) with dynamic building performance simulation and applying global sensitivity/uncertainty techniques such as PRCC, rank regression, MARS, or Sobol analysis to identify dominant drivers [25,26]. This methodological consensus supports the integrated ENVI-met and Design Builder/EnergyPlus approach adopted here, alongside global sensitivity analysis, to prioritize AR, glazing, WWR, and insulation across building floors.

Dynamic thermal simulation software is now an essential tool in building science for evaluating a building’s energy use and thermal performance throughout its life cycle [27,28]. These computational models enable detailed prediction, analysis, and optimization of design parameters to reduce energy consumption, improve indoor comfort, and mitigate environmental impacts [27,29]. A persistent challenge is the “energy performance gap” between simulated and actual outcomes, arising from simplifications, deterministic inputs, and omitting variability in occupant behavior and equipment operation. As van den Brom et al. [30] note, this gap reflects modeling limitations and uncertainties in real-world building behavior. Slight deviations in material properties, weather data, or internal loads can cause significant simulation errors [31]. To address this, researchers increasingly promote uncertainty-aware or probabilistic modeling that accounts for variations in occupancy, system operation, and local climate [32,33]. While the present study is not probabilistic, it reduces reliance on generic weather files and static occupancy assumptions by incorporating ENVI-met-derived local microclimate data and behavior-based schedules reflecting regional usage patterns, thereby narrowing the predicted–actual gap for hot arid residential buildings.

The global shift toward environmental stewardship and energy conservation reinforces the urgency of retrofitting existing buildings and optimizing envelope design in new construction [34]. In naturally ventilated or low-cooling-demand residences, indoor comfort depends primarily on effective envelope strategies and ventilation design. While retrofitting is crucial for existing structures, optimizing insulation thickness, WWR, and shape coefficient is vital for high performance in new projects. Numerous studies confirm that increasing insulation improves thermal resistance and lowers both cooling and heating loads [19,21,35]. Likewise, reducing WWR and optimizing shape coefficients further limits unwanted heat transfer and total energy use [36,37]. Advances in glazing technology have also yielded substantial cooling-energy savings in hot climates [20,37]. These findings affirm the need for a holistic approach to envelope design to achieve long-term energy sustainability.

Recent work in hot arid regions has examined the performance of multi-story residential buildings, which are especially susceptible to overheating and high cooling demands. Imessad et al. [38] showed that façade optimization, appropriate orientation, and solar control can reduce indoor temperatures and cooling loads in southern Algeria. Attia et al. [39] demonstrated the value of early-stage, simulation-driven decision making for envelope parameters in Middle Eastern climates. Mushtaha et al. [40] highlighted that integrating shading, natural ventilation, and insulation significantly enhances passive cooling. Al-Tamimi and Fadzil [41] emphasized the role of window design and shading depth in improving comfort and lowering peak cooling in desert environments. Collectively, these studies reinforce the importance of integrated simulation frameworks capable of evaluating envelope performance, vertical zoning, and microclimate interactions in multi-story residential design.

1.2. Significance of Sensitivity Analysis in Building Performance

Sensitivity analysis is a robust methodology for systematically evaluating how design parameters influence building performance. Its core utility lies in its ability to rigorously identify the critical factors that exert the most significant impact on system outputs, thereby providing invaluable insights for model simplification, robust quality assurance, and informed decision-making processes within the complex domain of building design and operation [42,43,44]. Sensitivity analysis minimizes the reliance on extensive and often expensive in situ measurements by methodically isolating and quantifying the influence of individual or interacting parameters. It mitigates the computational demands associated with exhaustive parametric studies. This analytical approach has found widespread application across diverse sub-domains of building science, including, but not limited to, design optimization [45,46], meticulous energy model calibration [47,48], comprehensive building stock assessment [49,50], strategic retrofit planning [39,51], and the critical analysis of climate change impacts on long-term building performance [52,53]. Furthermore, sensitivity analysis is frequently complemented by uncertainty analysis, which collectively aids in the quantitative assessment of risks associated with energy-saving measures and robustly supports evidence-based decision-making processes.

Sensitivity analysis is widely applied in building science. This method supports diverse applications, including the precise optimization of design configurations, the development of effective retrofitting strategies, the efficient management of building stock, and the crucial assessment of climate change impacts on both building energy efficiency and occupant thermal comfort [39,46,48,52,54,55]. Sensitivity analysis is often integrated seamlessly with advanced simulation tools and provides a systematic and iterative approach for prioritizing design decisions. By identifying the most influential parameters that govern thermal and energy performance, this methodology empowers designers to effectively target energy-saving measures and optimize indoor environments, leveraging comprehensive data derived from empirical observations and sophisticated simulation-based models [56].

Recent advancements in sensitivity analysis methodologies have substantially enriched building energy modeling. For instance, Goffart et al. (2018) meticulously evaluated the impact of various brick types on building cooling energy demand [57], while Yu et al. (2019) precisely identified key design parameters for WWR through comprehensive sensitivity studies [58]. Eisenhower et al. (2012) developed innovative sensitivity indices to pinpoint intermediate processes significantly influencing simulation uncertainties [59]. Spitz et al. (2014) employed the variance-based Sobol method, leveraging thousands of simulation runs, to rigorously identify the most significant factors affecting energy performance in a French experimental home [60]. Additional studies have extensively explored sensitivity analysis across various building types, climatic conditions, and methodological approaches, consistently highlighting its remarkable versatility. Hopfe and Hensen (2011) investigated the influence of different input parameters for office buildings [46], while Heiselberg et al. (2009) applied the Morris method to rigorously evaluate energy demands in Danish buildings [61]. Similarly, Heo et al. (2012) systematically ranked energy use intensity for Chicago’s commercial buildings by utilizing a comparable approach [62]. Furthermore, advanced techniques such as standardized regression coefficients (SRC) and Bayesian Gaussian models have been successfully employed to meticulously analyze energy consumption trends in educational institutions and office spaces [51,55]. These diverse applications underscore the robust utility of sensitivity analysis in providing actionable insights for optimizing building performance.

At its core, sensitivity analysis quantifies how variations in input parameters propagate through a building system to impact its performance outcomes. This method enables researchers to rigorously quantify the effects of discrete design variables on aggregate metrics such as energy consumption, occupant thermal comfort, and overall building operational efficiency [63]. Within the domain of building energy modeling, sensitivity analysis is routinely employed to explore the inherent variability in simulation results that arises from changes in input parameters, thereby serving as an indispensable tool for identifying influential factors, systematically minimizing uncertainties, and significantly improving the accuracy and reliability of energy model calibrations [64,65]. Consequently, it is essential to support informed decision-making processes by prioritizing variables that contribute most significantly to achieving holistic energy efficiency.

Sensitivity analysis methods are broadly categorized into two principal approaches: local and global. The distinction between these two lies primarily in how they explore the input parameter space and the type of insights they yield.

Global sensitivity analysis has gained considerable prominence recently due to its unparalleled ability to evaluate input uncertainties and their resultant impact across the entire parameter space. This comprehensive approach offers a holistic understanding of complex input–output relationships within a model, accounting for both individual parameter effects and their intricate interactions [66]. GSA enables researchers to derive highly reliable and generalizable insights for developing robust energy-saving solutions and design strategies by exploring the full range of plausible input values. However, this enhanced reliability often comes at the expense of higher computational demands, as it typically requires more model evaluations. Standard global techniques include the following:

• Variance-based methods (e.g., Sobol, Homma–Saltelli): These methods decompose the total output variance into contributions from individual input factors and their interactions, providing a quantitative measure of importance [2,3,67].
• Morris design and screening-based approaches: These methods efficiently identify influential factors through a series of local changes, offering a cost-effective way to screen out non-influential parameters [1,61,68].
• Regression analysis (e.g., standardized regression coefficients, rank regression): These techniques fit statistical models to the input–output data to quantify the relationship and identify significant predictors [69].
• Meta-modeling frameworks: These involve constructing simpler mathematical models (surrogates) that approximate the behavior of the complex building simulation model, allowing for more efficient sensitivity analysis [70].

Conversely, local sensitivity analysis examines the impact of uncertain input variables at a specific point or baseline scenario within the parameter space. These methods typically involve varying one input parameter at a time while holding all others constant at their nominal values. While computationally less intensive than global methods, local approaches inherently do not account for non-linear relationships or interactions between parameters, which significantly limits their ability to provide a holistic view of the parameter space [34]. Consequently, LSA is generally utilized for rapid evaluations of individual variables’ influence around a specific operating point but lacks the robustness and comprehensiveness required for a thorough and holistic sensitivity assessment, particularly in complex building systems where interactions are prevalent.

1.3. Research Gap and Aim of the Paper

Despite the extensive research in building energy performance and thermal comfort, a critical research gap persists in comprehensively understanding the intricate interplay between outdoor thermal variables and specific building envelope design parameters, particularly when considered this synergistically within hot arid climates. The existing literature frequently tends to compartmentalize investigations, focusing either on isolated outdoor microclimatic conditions or singular building envelope design parameters. This often overlooks the compounded and dynamic impact of their combined influence on overall building energy performance and crucial indoor thermal comfort metrics.

Furthermore, there is a distinct scarcity of in-depth investigations into the integrated influence of specific outdoor microclimatic factors, such as the rear setback aspect ratio, when concurrently considered with key internal envelope variables, including WWR, floor level, wall insulation characteristics, and glazing types. This research lacuna is particularly pronounced and consequential in the domain of multi-story residential buildings situated in arid regions, where the aforementioned factors critically and dynamically shape both energy efficiency profiles and internal thermal performance landscapes. The complexity of these interactions necessitates a multi-scalar approach, moving beyond single-variable analyses to capture the emergent behaviors of integrated urban and building systems.

To address this significant research gap and provide empirically validated, actionable insights, the current study sets forth the following primary objectives:

• Quantifying the individual and interactive effects of AR, WWR, GT, and wall insulation on T_o, cooling energy, and lighting energy consumption.
• Applying advanced global sensitivity analysis to identify the relative significance of these design parameters across different floor levels.

By systematically pursuing these objectives, this research seeks to significantly advance our understanding of the complex interplay between urban geometry, building characteristics, and their energy and thermal comfort implications.

2. Materials and Methods

The methodology adopted in this study integrates a multifaceted approach to systematically evaluating energy efficiency and thermal performance in building design, encapsulated within a four-step process. This framework ensures a holistic understanding of how external microclimatic conditions interact with internal building design parameters to influence overall performance.

2.1. Overall Study Framework

Figure 1 illustrates the general framework, which commences with the foundational step of simulating the outdoor microclimate. This is paramount for accurately understanding how external environmental conditions profoundly affect building performance, particularly within constrained urban geometries like rear setbacks. This step requires collecting key input data, including weather conditions, building material properties, soil profiles, and site location. All of these data points are critical for ensuring the fidelity and accuracy of the subsequent microclimate modeling. For this purpose, ENVI-met V5.5.1 software, a sophisticated computational fluid dynamics (CFD) tool specifically designed to assess the outdoor microclimate within the investigated rear setback, is utilized. Weather data was collected from the Aswan University weather station (HOBO U30). Incorporating field-collected meteorological observations into ENVI-met simulations requires a rigorous multi-step protocol to ensure model fidelity. Data acquisition from the Aswan University automated weather station yielded continuous air temperature measurements (±0.2 °C accuracy) and relative humidity (RH) (±3% accuracy) at 60-min intervals. These raw datasets underwent comprehensive quality assurance procedures, such as outlier detection using median absolute deviation thresholds. For ENVI-met compatibility, the processed data were restructured into a comma-separated (CSV) format with explicit header definitions (TIMESTAMP, TA, RH) and ISO 8601 datetime formatting [71]. The simulation framework employed full forcing boundary conditions, with the meteorological input file linked through the Boundary Condition Editor (v5.5.1). All of these data points are critical for ensuring the fidelity and accuracy of the subsequent microclimate modeling.

The second step centers on developing a highly detailed building energy simulation model. This model combines several data layers, as follows:

• Modified Weather Information: Crucially, this incorporates refined weather file data, specifically tailored and extracted from the outputs of the first microclimate simulation step, ensuring a dynamic and localized representation of external conditions.
• Occupant Behavior Profiles: Realistic occupancy schedules and activity patterns are incorporated to reflect actual building usage.
• Detailed Construction Features: Comprehensive specifications of all building envelope components (walls, roofs, and windows) are included.
• HVAC System Specifications: The design and operational characteristics of the heating, ventilation, and air conditioning (HVAC) systems are precisely defined.
• Lighting Equipment: Details of artificial lighting systems are integrated to assess their energy consumption.

This step primarily employs Design Builder v7.02.006, seamlessly integrating the powerful EnergyPlus v9.4 simulation engine. This combination comprehensively evaluates indoor thermal performance, the precise energy required for cooling, and the energy consumption attributed to artificial lighting.

The selection of ENVI-met v5.5.1 and Design Builder was deliberate and based on the complementary capabilities of the two tools. ENVI-met is well suited for high-resolution modeling of outdoor microclimatic conditions, including wind flow, radiation, and surface temperature distribution—factors critical in hot arid environments influenced by urban morphology. Design Builder, built on the EnergyPlus engine, offers advanced capabilities in building energy and thermal comfort simulation, supported by a vast body of validation literature. The ENVI-met and Design Builder combination provided the most integrated and practical framework for linking outdoor microclimate effects with indoor energy and comfort performance. This integrated approach also allowed for the creation of customized EPW weather files reflecting site-specific geometry, which is not possible using default weather datasets.

The critical decision variables are systematically identified and defined in the third step. These include intrinsic building envelope characteristics such as insulation properties, WWR, and GT. Crucially, the AR of the rear setback also serves as a pivotal decision variable. AR affects the microclimate by changing how sunlight and wind interact with the facades, influencing thermal comfort and energy use. While other decision variables primarily focus on the building facades separating interior spaces from the rear setback, the AR governs the overall microclimatic conditions of the outdoor space itself. The objective functions used to assess the impact of these decision variables include the operative temperature (T_o) for indoor thermal comfort and cooling and lighting energy for evaluating building energy efficiency. This study assessed operative temperature at the geometric center of each thermal zone, at a height of 1.1 m from the floor, corresponding to the seated occupant level, following ASHRAE 55 and ISO 7730 standards [72,73]. This location was selected as it represents the typical occupied zone within living spaces. It is important to note that Design Builder (EnergyPlus) calculates operative temperature by accounting for both the air temperature (T_a) and the mean radiant temperature (T_mrt), which is sensitive to surface temperatures and window-to-wall ratios. Therefore, variations in transparent versus opaque surfaces and internal surface temperatures were inherently reflected in the T_o calculations, reducing the risk of thermal comfort misrepresentation across different envelope configurations.

In defining the objective function, both T_o and T_a were included based on their respective roles in evaluating thermal comfort and thermal response. While T_o is a function of T_a and T_mrt, as specified in ISO 7726 [74], its inclusion was essential for assessing the perceived thermal comfort under occupied conditions. In contrast, T_a was retained in specific scenarios to capture variations in air-based thermal response, particularly under passive or free-running conditions, where airflow and envelope design changes directly affect zone temperature. Including both variables allowed the optimization framework to distinguish between occupant-experienced comfort and thermal dynamics driven by envelope geometry, without assigning duplicate weight to a single metric.

The fourth and final step involves a rigorous analysis of the relative impact of these identified variables on the building’s overall energy performance and indoor thermal comfort. A comprehensive global sensitivity analysis is meticulously conducted using two advanced statistical methods: rank regression (RR) and multivariate adaptive regression splines (MARS). These techniques help to assess how each variable affects performance and supports better design decisions for sustainable buildings. By understanding how the AR and other critical decision variables influence both the outdoor microclimate and the building’s internal energy dynamics, this framework provides a robust foundation for developing more sustainable and resilient architectural practices, particularly in challenging hot arid environments. Figure 2 presents the detailed framework of this study.

2.2. Investigated Area and Study Model

The geographical focus of this study is Aswan City, situated in southern Egypt, precisely located at a latitude of 24.0861° N and a longitude of 32.8989° E, with an average altitude of 194 m above sea level. Aswan is characterized by a hyper-arid climate, classified as a hot desert climate (Köppen BWh), which is representative of many regions globally facing significant thermal and energy challenges in the built environment. This climate is defined by extremely high ambient temperatures, often ranging from an average daily minimum of 25 °C in cooler months to a scorching average daily maximum exceeding 42 °C in the peak summer months (specifically June and July), coupled with minimal annual rainfall, typically less than 1 mm [75]. The region experiences intense solar radiation throughout the year, clear skies, high direct normal irradiance, and significant diurnal temperature fluctuations. These climatic characteristics render Aswan an ideal and highly relevant case study for investigating building performance under severe hot arid conditions, where cooling demands are paramount and passive cooling strategies are critically important.

This research utilizes a representative multi-story residential building model in the Al-Aqqad district of Aswan City. This district is characteristic of contemporary urban developments in the region, featuring densely packed residential blocks with varying building heights and narrow interstitial spaces. The chosen building is a five-story structure, a common typology for residential developments in urban Egyptian contexts, designed to accommodate two independent 75 m² flats per floor, resulting in a total floor area of approximately 160 m² per story, including shared staircases and circulation areas. Each floor maintains a standard height of 3 m.

This study’s critical design feature and focus is the rear setback, representing the open space or void between the examined building and an adjacent hypothetical building. This setback is consistently maintained at a width of 8 m, with the studied building positioned 4 m from its property line. This specific urban geometry creates a distinct microclimatic zone, often referred to as an urban canyon or courtyard-like space, where the surrounding building envelopes modulate solar access, wind flow, and radiative exchange [76]. The interaction within this setback is particularly interesting, as it directly influences the thermal comfort of occupants in rooms overlooking this space and significantly impacts the building’s overall energy balance, primarily through shading and ventilation effects. The baseline WWR for the building’s facades, particularly those overlooking the rear setback, is 10%. This value serves as the initial condition for the parametric variations explored in this study. The building model’s internal construction features, including wall compositions, roof specifications, and window glazing properties, are detailed in subsequent sections, forming the basis for the energy performance simulations. The typical architectural plan of the examined building, illustrating its spatial organization and dimensions, is presented in Figure 3. This plan provides a visual reference for the building’s layout and relationship with the rear setback area, which is central to microclimate and energy analyses.

2.3. Outdoor Aspect Ratio Configurations

This study meticulously examines the impact of varying ratios on outdoor microclimate conditions and the subsequent influence on thermal comfort within the rear setback area. The aspect ratio (AR), defined as the ratio of the building height (H) to the width (W) of the urban canyon or setback, is a crucial geometrical parameter that profoundly affects solar access, daylight penetration, radiative heat exchange, and wind flow patterns within these spaces [77]. For this research, the width of the rear setback (W) is consistently maintained at 8 m. At the same time, the building height (H) is systematically varied to establish three distinct AR configurations, representing a range of typical urban densities and shading potentials found in contemporary architectural designs, particularly relevant to the Egyptian context. These configurations are designed to provide a comprehensive understanding of how urban geometry modulates microclimates in hot arid environments, as follows:

Case 1 (C1): Low AR: The building height is 12 m, resulting in an aspect ratio (H/W) of 1.5. This configuration represents a relatively open urban canyon, allowing for greater solar penetration for longer durations, particularly on lower floors, and potentially higher wind speeds, depending on prevailing directions.

Case 2 (C2): Moderate AR (Current Case): The building height is 15 m, yielding an aspect ratio (H/W) of 1.87. This case serves as the baseline, representing the existing configuration, and offers a balance between solar exposure and shading. It allows for a comparative analysis of how deviations to lower or higher ARs impact microclimatic conditions.

Case 3 (C3): High AR: The building height is increased to 18 m, resulting in an aspect ratio (H/W) of 2.25. This configuration represents a more enclosed urban canyon, which is expected to significantly enhance self-shading effects on facades and ground surfaces within the setback, thereby reducing direct solar radiation and potentially mitigating heat accumulation. However, this may have potential implications for daylighting and ventilation at lower levels.

These three investigated cases are systematically summarized in

Table 1. The rear setback AR configurations.

Abbreviations	AR (H/W)	Section
C1	1.5
		H = 12 m, W = 8 m
C2 (current case)	1.87
		H = 15 m, W = 8 m
C3	2.25
		H = 18 m, W = 8 m

, providing a clear overview of the AR variations and their corresponding building heights relative to the fixed setback width. The selection of these specific AR values is crucial for evaluating their distinct impacts on pedestrian-level thermal comfort and overall energy performance, as they determine the duration and intensity of solar exposure and the prevailing airflow characteristics within the urban canyon.

2.4. Sensitivity Analysis Framework: Objectives and Decision Variables

A comprehensive sensitivity analysis framework was developed to address this study’s multifaceted research objectives. Two global sensitivity analysis methods were employed to assess the influence of design variables on thermal and energy outcomes: rank regression and multivariate adaptive regression splines. RR was used to identify monotonic relationships between inputs and outputs, while MARS captured potential non-linear effects and variable interactions. This dual-method approach enhances the robustness and reliability of the findings by providing complementary perspectives on the input–output relationships, exploring the entire input factor space rather than relying solely on local derivatives at a single data point [77,78]. As depicted in Figure 4, this framework’s core components are the clearly defined objective functions and the systematically varied decision variables.

2.4.1. Objective Functions

This study addresses several critical aspects of energy efficiency and thermal comfort pertinent to building design in hot arid regions. The primary objective functions selected for evaluation are as follows:

• Given the extreme heat and prolonged hot seasons characteristic of arid climates, minimizing the energy required to maintain acceptable indoor thermal comfort levels is paramount. This objective quantifies the total electrical energy consumed by the HVAC (heating, ventilation, and air conditioning) system for cooling purposes over a specified period. It is directly influenced by internal heat gains (occupants, lighting, and equipment), solar heat gains through glazing, and heat conduction through the opaque envelope. Optimizing architectural design strategies to lower these cooling demands is fundamental for achieving energy sustainability and reducing operational costs in such environments [79,80].
• This objective quantifies the electrical power needed for artificial illumination within the building spaces. Its assessment focuses on factors such as the installed lighting intensity, the efficiency of lighting technologies (e.g., LED vs. fluorescent), and the duration and patterns of artificial lighting usage. The goal is to optimize design parameters (e.g., WWR, GT) to maximize natural daylight utilization, thereby reducing reliance on artificial lighting and consequently minimizing energy consumption and associated environmental impacts [12,81].
• As a central parameter in evaluating indoor thermal comfort, the operative temperature provides a more comprehensive and accurate measure of an occupant’s thermal experience than air temperature alone. T_o integrates the effects of both T_a and T_mrt, weighted by the air velocity, as defined by:

$$To={\displaystyle \frac{\left(\right(Ta\ast hc)+(Tmrt\ast hr\left)\right)}{(hc+hr)}}$$

where $hc$ is the convective heat transfer coefficient and $hr$ is the radiative heat transfer coefficient. This metric is crucial for designing interior spaces that effectively balance energy efficiency with human comfort, particularly in conditions where radiant heat sources (e.g., hot surfaces, solar radiation through windows) significantly influence perceived temperature [82]. Assessing this helps to ensure that strategies to reduce energy consumption do not inadvertently compromise occupant well-being.

2.4.2. Decision Variables

This study systematically investigates the impact of four key building design variables and the inherent variation due to floor level on cooling energy consumption, lighting energy consumption, and operative temperature in hot arid climates. The parametric ranges for these variables were carefully selected to represent realistic design choices and comply with relevant building codes where applicable.

• AR: As detailed in Section 3.3, the AR of the rear setback is investigated through three distinct cases (C1: 1.5, C2: 1.87, and C3: 2.25). This variable is critical because it simultaneously influences both the outdoor microclimate (modulating solar access, shading patterns, and wind flow) and, consequently, the indoor thermal comfort and energy demand of the building’s facades overlooking the setback [83]. Higher ARs generally lead to increased self-shading and reduced solar exposure to lower facade sections, while lower ARs result in more open spaces with greater solar penetration.
• WWR: The WWR is evaluated at three discrete percentages: 10%, 20%, and 30%. This ratio represents the proportion of glazed area to the total external wall area. WWR is a crucial architectural parameter that significantly influences both solar heat gain (and, thus, cooling loads) and the availability of natural daylight within interior spaces [84]. The selected percentages adhere to typical design practices and consider Egypt’s energy code restrictions.
• GT: Three distinct glazing configurations are assessed based on their thermal and optical properties, as described in Table 2. The choice of glazing type is critical for managing heat transfer across the building envelope, directly impacting cooling loads and indoor comfort. These properties were utilized in the Design Builder simulations to model energy performance accurately.

Table 2. Thermal and optical properties of single-, double-, and triple-pane glazing configurations.

Glazing Type	U-Value (W/m2·K)	SHGC	VLT
Single pane	~5.8	0.85–0.90	0.88–0.90
Double pane	~2.8	0.70–0.80	0.80–0.85
Triple pane	~1.8	0.60–0.70	0.75–0.80

Note: (U-value) is the thermal transmittance, (SHGC) is the solar heat gain coefficient, and (VLT) is the visible light transmittance.

Table 2. Thermal and optical properties of single-, double-, and triple-pane glazing configurations.

Glazing Type	U-Value (W/m2·K)	SHGC	VLT
Single pane	~5.8	0.85–0.90	0.88–0.90
Double pane	~2.8	0.70–0.80	0.80–0.85
Triple pane	~1.8	0.60–0.70	0.75–0.80

Note: (U-value) is the thermal transmittance, (SHGC) is the solar heat gain coefficient, and (VLT) is the visible light transmittance.

• Wall insulation: This study compares two primary wall configurations for the building envelope, as follows:

• Uninsulated: Comprising a 16 cm thick brick wall with internal and external cement plaster layers (0.02 m cement plaster + 0.12 m brick + 0.02 m cement plaster). This represents a standard traditional construction method with limited thermal resistance in the region. The U-value for this uninsulated wall is approximately 1.6 W/(m²⋅K).
• Insulated: Comprising a 33 cm thick wall incorporating 5 cm foam insulation (0.02 m cement plaster + 0.12 m brick + 0.05 m foam insulation + 0.12 m brick + 0.02 m cement plaster). This represents a significantly improved thermal envelope. The U-value for this insulated wall is approximately 0.4 W/(m²⋅K), demonstrating its superior thermal resistance in mitigating heat transfer from the harsh external environment.

The presence and thickness of insulation are primary determinants of the opaque envelope’s thermal resistance, directly influencing conductive heat gains and losses, thereby playing a pivotal role in maintaining indoor thermal comfort and reducing energy consumption for cooling [85].

• Floor Level: While not a design choice, the floor level (ground floor, 1st, 2nd, 3rd, 4th, and 5th) is an independent variable within the multi-story building that significantly affects thermal performance due to variations in solar exposure, shading from adjacent buildings or self-shading, wind patterns, and internal heat gains. Higher floors typically experience greater solar radiation exposure and exhibit different air flow dynamics than lower floors within an urban canyon. Analyzing performance across different floors provides crucial insights into vertical thermal stratification and informs floor-specific design considerations.

A comprehensive parametric study was conducted, systematically combining these decision variables. The AR cases investigated (C1, C2, and C3) were evaluated for both wall insulation scenarios (with and without insulation), each with variations in WWR (10%, 20%, and 30%) and GT (single-, double-, and triple-pane). This meticulous combination resulted in a total of 3 (AR cases) × 2 (insulation states) × 3 (WWR options) × 3 (GT options) = 54 unique building configurations. Furthermore, given that the performance of each configuration was assessed across multiple floor levels (up to six floors for C3), the total number of distinct simulation scenarios evaluated grew significantly, generating a robust dataset for the subsequent sensitivity analysis.

Table 3. Investigated cases for parametric study.

AR Case	Wall Insulation	WWR Range (%)	Glazing Types
C1 (1.5)	Without/With	10, 20, 30	Single, Double, Triple
C2 (1.87)	Without/With	10, 20, 30	Single, Double, Triple
C3 (2.25)	Without/With	10, 20, 30	Single, Double, Triple

provides a detailed summary of these investigated cases, delineating the combinations of AR cases, wall insulation states, and the parametric variations in WWR and GT.

2.5. Outdoor Microclimate Simulation

The initial phase of this study involved a meticulous and thorough analysis of the impact of varying ARs on external thermal performance within the rear setback area. This analysis was conducted for the three predefined cases: C1 (AR = 1.5), C2 (AR = 1.87), and C3 (AR = 2.25), as detailed in Section 3.3. A hybrid approach was employed to comprehensively understand the microclimatic conditions, combining robust field measurements with advanced numerical simulations. Although this research focused on a single residential building, ENVI-met was used to capture the localized microclimatic variations induced by different rear setback configurations, significantly affecting the building envelope’s environmental conditions. One key objective was to extract site-specific weather data—including air temperature, relative humidity, and wind speed—at various building heights corresponding to each floor level. These microclimatic outputs were essential for creating customized weather files, which were then used as inputs in the Design Builder simulation to enhance realism and accuracy. While Design Builder and EnergyPlus offer robust capabilities for simulating indoor thermal and energy performance, they do not model the external urban microclimate influenced by building morphology. ENVI-met filled this gap by enabling the spatial analysis of outdoor environmental parameters, making it a necessary component of the coupled simulation framework used in this study.

2.5.1. ENVI-Met Model Setup and Simulation Protocol

Numerical simulations of the urban microclimate within the rear setbacks were performed using ENVI-met V5.5.1 software. ENVI-met is a widely recognized and validated three-dimensional (3D) computational fluid dynamics (CFD) modeling tool designed explicitly for microclimatic applications in urban environments. Professionals and researchers extensively utilize it in urban planning, landscape architecture, civil engineering, and urban climate studies because it can simulate complex interactions between surfaces, vegetation, and the atmosphere. The software operates based on a non-hydrostatic microclimate fluid dynamics model, solving Reynolds-Averaged Navier–Stokes (RANS) equations to simulate atmospheric flow, heat transfer, and moisture transport near the ground surface. This allows for the assessment of key meteorological parameters, including air temperature (Ta), relative humidity (RH), wind speed (V), and mean radiant temperature (T_mrt) at high spatial and temporal resolutions [86].

The case study building’s 2D footprint was initially created using AutoCAD 2025 software for the ENVI-met simulations. This 2D plan was converted into a bitmap format (.bmp) and meticulously imported into the ENVI-met graphical user interface (ENVI-met Spaces) for digitization and 3D model generation. The digitization process involved defining the precise geometry of the buildings, the rear setback, and the surrounding urban environment within a defined grid system. The simulation domain was set with dimensions of x = 50, y = 50, and z = 40 grid cells, with a spatial resolution (grid-scale) of x = 2 m, y = 2 m, and z = 2 m. This resolution was chosen to capture fine-scale microclimatic variations within the setback while balancing computational feasibility.

Meteorological data for the simulations were collected from the Aswan University weather station (HOBO U30 data logger) for the specific study period. These inputs, along with detailed building material specifications (e.g., thermal properties of plaster, brick, and concrete) and soil profiles (loamy soil and concrete pavement for the ground surfaces), were precisely incorporated into the ENVI-met model before running the simulations. Due to the inherent computational intensity and time required for high-resolution CFD simulations, ENVI-met is typically unsuitable for year-long or long-term dynamic simulations. Instead, it was strategically utilized to simulate a representative critical day: 2 July 2023. This day was identified as one of the hottest days of the year in Aswan, making it ideal for analyzing peak thermal stress conditions. To minimize potential inaccuracies arising from initial model stabilization and to ensure a comprehensive analysis of the diurnal environmental conditions, each simulation was initiated four hours before the target day (i.e., beginning on 1 July 2023, at 8:00 p.m.) and extended for a total duration of 28 h (until 2 July 2023, at 11:00 p.m.). This extended simulation period allowed the model to reach a stable state and provided a complete diurnal data cycle for the target day.

The simulation protocol systematically involved running ENVI-met for the three distinct AR cases (C1, C2, and C3). For each case, meteorological parameters—including Ta, RH, V, and Tmrt—were extracted at various points within the rear setback, including different heights, to understand vertical stratification. This systematic data collection at each floor level was essential to capture the variations and changes influenced by the AR parameters investigated.

Table 4. ENVI-met simulation input data summary.

Parameter	Value
Number of main area grid boundaries	X = 50, y = 50, z = 40
Soil profile for all grids	Loamy soil and concrete pavement, light
Grid-scale	x = 2, y = 2, z = 2
Wall material	Plaster, brick wall, plaster
	Thickness of layers (m) = (0.02, 0.12, and 0.02)
	Albedo = 0.4
Roof materials	Reinforced concrete
	Thickness = 0.2 m, Albedo = 0.3
Simulation date	2nd of July
Start wind speed at 10 m height (m/s)	2
Start wind direction (°)	90 from the north
Max air temperature (°C)	42.29
Min air temperature (°C)	25.80
Initial specific humidity of the atmosphere (g/Kg)	8
Max relative humidity (%)	36.5
Min relative humidity (%)	14.80

presents a detailed summary of the key input data utilized in the ENVI-met simulations. The meteorological inputs, derived from Aswan’s observed climatic conditions, formed the simulation process’s foundation. Additionally, human biometeorological parameters (though primarily used in Rayman for PET calculation, their relevance for ENVI-met’s comprehensive modeling is noted) and precise building material properties were integrated as essential inputs to ensure accurate and reliable simulation results.

Following the ENVI-met simulations, the outputs, specifically T_a, RH, V, and T_mrt, were used as input data for Rayman software (version 1.2). Rayman is a specialized biometeorological tool designed to calculate various thermal comfort indices, with PET being one of the most widely used and appropriate indices for outdoor thermal comfort assessment [87,88]. This integration allowed for a comprehensive evaluation of PET, which quantifies the thermal sensation experienced by individuals in the outdoor environment of the rear setbacks under varying microclimatic conditions. Through this systematic and scientifically rigorous approach, this study establishes a robust framework for analyzing and understanding the thermal comfort conditions within rear setbacks, providing a nuanced perspective on the influence of urban geometry.

2.5.2. Field Measurements for Meteorological Data

To validate the simulation model, experimental measurements were carried out at a central point within the rear setback area throughout the day. The primary aim was to compare the outdoor simulation results with the field data collected. The measurements were recorded on 2 July 2023, at hourly intervals. The air temperature and relative humidity were recorded at 1.5 m from the ground in the middle of the rear setback. A HOBO U12 data logger was utilized for this purpose, housed in customized solar radiation shields to ensure precise measurements while minimizing the impact of direct sunlight, as depicted in Figure 5. The data logger was configured to record Ta and RH at one-hour intervals over 24 h [14].

2.5.3. Verification of Study Model Accuracy

The accuracy and reliability of any simulation model are paramount for the credibility and generalizability of its findings. Therefore, rigorous validation was undertaken to compare the simulated outdoor microclimate data from ENVI-met against the actual field measurements collected from the HOBO U12 device. This validation focused on key meteorological parameters, including air temperature and relative humidity, critical indicators of outdoor thermal conditions. Figure 6 presents the model validation in terms of Ta and RH.

The comparison involved plotting the hourly measured data against the hourly simulated data for 2 July 2023. To quantitatively assess the agreement between the simulated and measured values, several widely accepted statistical metrics were employed, as follows:

• Root Mean Square Error (RMSE): RMSE quantifies the average magnitude of the errors. It is calculated as:

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\left(S_i-M_i\right)}^2}$$

where $S_i$ is the simulated value, $M_i$ is the measured value, and $N$ is the number of data points. A lower RMSE indicates better model accuracy.

• Coefficient of Determination (R²): R² represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It indicates how well the simulated data fits the measured data. It is calculated as:

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^N{\left(S_i-M_i\right)}^2}{\sum _{i=1}^N{\left(S_i-\overline{M}\right)}^2}}$$

where $\overline{M}$ is the mean of the measured values, and an R² value closer to 1 indicates a strong correlation and good agreement between the simulated and measured data.

The validation results indicated a strong correlation between the ENVI-met simulated data and the field measurements. Specifically, for T_a, the RMSE was 1.2 °C, and the R² value was 0.92. For RH, the RMSE was 3.1, and the R² value was 0.98. These statistical results demonstrate a high level of accuracy and agreement, well within the acceptable ranges for microclimate modeling studies [77]. The low RMSE and high R² values confirm that the ENVI-met model accurately captures the diurnal variations and magnitudes of air temperature and relative humidity in the hot arid environment of Aswan. This robust validation provides a solid foundation for the credibility of the subsequent microclimatic analyses and their integration into the building energy simulations.

2.6. Indoor Building Energy Simulation

Following the detailed outdoor microclimate simulations and their rigorous validation, the subsequent crucial phase of this study involved conducting comprehensive indoor building energy simulations. This step was performed using Design Builder v7.02.006, a sophisticated graphical user interface for the powerful EnergyPlus v9.4 dynamic thermal simulation engine [89].

2.6.1. Building Model Setup and Integration of Microclimate Data

The core of the indoor simulation involved developing a highly detailed 3D geometric model of the representative multi-story residential building within Design Builder. As described in Section 3.2, the building geometry was precisely replicated, including all thermal zones (residential flats, staircases, and corridors) on each of the five floors. A critical aspect of this integrated approach was localized microclimatic data from ENVI-met simulations. Hourly meteorological parameters, including air temperature, relative humidity, and wind speed, were obtained from ENVI-met simulations for 2 July 2023, with vertical resolution corresponding to each floor level and architectural configuration (C1–C3). The simulation outputs underwent systematic processing involving (1) data standardization into a CSV template, (2) quality control verification, and (3) conversion to the EnergyPlus Weather (EPW) format using the Elements Weather Converter utility. This methodology enabled precise substitution of conventional weather data with microclimate-specific values while maintaining EPW file structure integrity. The resultant customized EPW files, uniquely characterizing the microclimatic conditions of each rear setback configuration, were subsequently implemented as boundary conditions in Design Builder energy modeling. This approach represents a significant methodological advancement over conventional practices by (i) capturing height-dependent atmospheric variations, (ii) accounting for building-induced microclimate modifications, and (iii) providing temporally resolved (hourly) environmental inputs that reflect actual building surroundings rather than regional airport weather data [76]. The implementation demonstrates a 23–28% improvement in thermal load prediction accuracy compared to standard weather files in preliminary validation studies.

2.6.2. Building Characteristics and Internal Loads

To ensure the fidelity of the simulations, the residential building model was configured with realistic material properties and operational schedules typical of Aswan’s urban context.

Table 5. Summary of building parameters, simulation settings, and output variables for energy and thermal performance analysis.

Category	Details
Construction Materials	Walls: Uninsulated brick wall (U-value ≈ 1.6 W/(m2·K)) and insulated wall with 5 cm foam insulation (U-value ≈ 0.4 W/(m2·K)). Roof: Reinforced concrete (0.2 m thickness, U-value ≈ 2.0 W/(m2·K)). Floors: Ceramic tiles followed by two layers of cement mortar and sand (U-value ≈ 5.47 W/(m2·K). Windows: Single-, double-, and triple-pane glazing with specific U-values, SHGCs, and VLTs for each WWR (10%, 20%, and 30%).
Internal Loads	Occupancy: Density of 0.05 people/m2; 100 W/person (sensible heat); and 60 W/person (latent heat). Lighting: Power density of 8 W/m2; typical usage schedules. Equipment: Power density of 5 W/m2; schedules aligned with occupancy patterns.
HVAC System	A split-type air conditioner, COP = 3.2, absorbed power = 1200 W per unit, cooling setpoint of 24 °C, and heating setpoint of 20 °C, was used.
Ventilation	Natural ventilation is based on minimum air change rates for health and indoor air quality. Windows are assumed to be closed during mechanical cooling. Infiltration rates accounted for uncontrolled air leakage.
Simulation Period	Hourly ENVI-met data for 2 July was integrated into the July segment of the EPW file for peak summer conditions.
Output Variables	To: Hourly temperatures are used to assess thermal comfort. Cooling Energy Consumption: Annual cooling energy (kWh) for the building, disaggregated by floor. Lighting Energy Consumption: Annual lighting energy (kWh) to evaluate daylighting and WWR impacts.
Infiltration rate	0.7 ACH

summarizes the building parameters, simulation settings, and output variables used in this study.

The energy simulation incorporated fixed schedules based on Egyptian household behavior patterns, accounting for occupancy, lighting, appliance use, and HVAC operation. Demographic data [90] informed the assumption of five occupants per unit, with working-age residents (22–60 years) typically absent during weekday work hours (08:00–15:00) but present during evenings and weekends. The schedule accounted for Egypt’s Friday–Saturday weekend and incorporated major Islamic and national holidays, despite the lunar calendar variability in Islamic observances. The residential units were assumed to be fully electric, consistent with standard practice in multi-story housing developments in Upper Egypt, where natural gas infrastructure is typically not provided in apartment units. Accordingly, the model excluded gas-based equipment (e.g., gas stoves or heaters) and instead incorporated electric alternatives. The building’s equipment inventory included refrigerators, washing machines, televisions, water heaters, ceiling fans, lighting fixtures, and kitchen appliances such as electric ovens, microwaves, kettles, and blenders. Each appliance was assigned a representative power rating and operational schedule based on local usage behavior and validated literature sources. Appliance-specific load characteristics, including continuous, intermittent, and peak-use patterns, were captured to simulate their thermal impact and electricity consumption. Lighting power densities followed space-specific values (living rooms: 17 W/m²; bedrooms: 13 W/m²; other spaces: 9 W/m²) derived from empirical studies [91], while appliance loads included realistic heat gains from household devices. HVAC operation was synchronized with occupancy patterns using appropriate cooling/heating setpoints to maintain thermal comfort thresholds. Residential appliance energy consumption exhibits a bimodal distribution characterized by either high-wattage/short-duration or low-wattage/long-duration operation patterns. Continuous loads (380–150 W) persist throughout the day for essential refrigeration and ventilation, while intermittent high-power devices (1800–1100 W) operate in brief pulses (<0.1 h) for specific tasks. Moderate-power appliances (300–60 W) demonstrate intermediate usage durations (0.05–2 h), primarily supporting domestic chores and entertainment. The observed load characteristics reflect typical household energy behaviors, where thermal loads from electrical equipment significantly influence indoor environmental conditions and aggregate power demand profiles. This operational paradigm aligns with established residential energy use patterns in similar climatic contexts [91]. This comprehensive scheduling framework ensures that the simulation accurately captures the temporal variations in energy use characteristic of Egyptian residential buildings.

To ensure accurate modeling of HVAC energy consumption, the absorbed electrical power and the coefficient of performance (COP) of the air conditioning system were explicitly defined. A split-type air conditioning unit was assumed for each apartment, with an average cooling COP of 3.2, consistent with typical efficiency levels for residential systems operating in hot climates. These values were integrated into the DB system templates for realistic equipment performance. Regarding air infiltration, a constant rate of 0.5 ACH (Air Changes per Hour) was assumed for occupied zones, representing a moderately air-tight construction standard. This assumption aligns with the mid-range values reported in previous studies for naturally ventilated apartments in Egypt. Infiltration was modeled using the infiltration rate in DB. To ensure adequate indoor air quality (IAQ), the baseline ventilation strategy follows recommendations from ISO 17772-1:2017, which outlines the minimum airflow requirements based on occupancy and pollutant loads [92]. Cooling temperature setpoints were set at 24 °C during occupied hours and allowed to float up to 28 °C during unoccupied periods. These values were chosen based on Category II indoor environmental quality (IEQ) criteria, as defined in ISO 17772-1:2017 and EN 16798-1:2019, which are suitable for residential applications and ensure acceptable thermal comfort for the majority of occupants [93]. Although less relevant in this climate, heating setpoints were set at 20 °C for completeness and consistency.

2.6.3. Output Variables and Data Collection

For each of the 54 unique building configurations (as detailed in Table 2), and for each floor level, Design Builder generated hourly and annual simulation results for the defined objective functions, as follows:

• T_o: Hourly operative temperatures were extracted for representative zones on each floor to assess indoor thermal comfort.
• Cooling Energy Consumption: Annual cooling energy consumption (kWh) was calculated for the entire building and disaggregated by floor to assess vertical distribution, with the HVAC system’s energy use analyzed alongside indoor thermal parameters such as Ta, RH, and T_o. The monthly energy consumption for July was estimated by scaling the July 2nd simulation results using Cooling Degree Hours (CDHs). This was achieved through cross-multiplication of monthly CDHs, and annual energy consumption was determined by summing the CDHs for all months, providing a precise evaluation of energy performance. This study examined the effects of design variables—AR, WWR, GT, and wall insulation—on total cooling energy, lighting energy, and overall energy consumption across 270 modeled cases with and without insulation. Simulations were conducted using Design Builder, with outputs systematically stored in 270 Excel files for comprehensive analysis, ensuring an accurate assessment of parameter impacts on energy efficiency and thermal comfort.
• Lighting Energy Consumption: Annual total lighting energy consumption (kWh) was collected to assess the impact of daylighting and WWR variations.

This extensive dataset formed the basis for the subsequent global sensitivity analysis, enabling a detailed investigation into the individual and interactive effects of the architectural design parameters on the building’s energy performance and thermal comfort.

2.7. Validation of the Energy Model and Sensitivity Analysis

The scientific rigor and reliability of the simulation results are intrinsically linked to the validation of the computational models employed. This section details the approach to validating the Design Builder model and provides a comprehensive overview of the global sensitivity analysis techniques utilized.

2.7.1. Validation of the Design Builder Model

This section validated the energy simulation model by comparing measured and simulated monthly energy consumption data, as illustrated in Figure 7a,b. A linear regression analysis resulted in the equation (y = 1.2906x − 124.99), with a coefficient of determination (R²) of 0.989, indicating a strong correlation between the measured and simulated values. The high R² value confirms the model’s ability to accurately represent energy consumption patterns, with only minor deviations observed during peak consumption months (June–August). These regression results establish a robust linear relationship, demonstrating the model’s reliability in predicting building energy performance. Consequently, the validated model is well suited for evaluating energy efficiency and optimizing building performance in similar climatic and architectural contexts.

The primary statistical metrics used for quantitative validation, as recommended by ASHRAE Guideline 14-2023 for validation of building energy models, included the following:

• Coefficient of Variation of the Root Mean Square Error (CV (RMSE)): Based on the comparison between simulated and measured monthly energy consumption, the calculated CV (RMSE) was 7.85%. According to ASHRAE Guideline 14, a CV (RMSE) of less than 15% for monthly calibration is acceptable. Therefore, the obtained CV (RMSE) indicates that the model demonstrates a high level of accuracy and is well calibrated for evaluating energy performance under similar conditions [94].
• Normalized Mean Bias Error (NMBE): NMBE indicates the average bias of the simulated data relative to the measured data. A positive NMBE means that the model generally overpredicts, while a negative value underpredicts. Based on the simulation results, the calculated NMBE was +4.20%, indicating a slight overall overestimation of energy consumption by the model. According to ASHRAE Guideline 14, an NMBE within ±5% is acceptable for monthly data calibration. Thus, the model is considered well calibrated and suitable for evaluating building energy performance [94].

The validation results for the annual cooling energy consumption of the baseline model against reliable local energy consumption data (or the adapted ASHRAE benchmark results, adjusted for local material properties) showed a CV (RMSE) of less than 15% and an NMBE within ±5, alongside an R2 value exceeding 0.95. These values confirm that the Design Builder/EnergyPlus model, when integrated with the specific microclimatic EPW files, provides a highly accurate and reliable representation of the building’s energy performance in the hot arid climate of Aswan. This robust validation ensures that the subsequent parametric and sensitivity analyses are based on a credible and well-calibrated simulation environment.

2.7.2. Global Sensitivity Analysis Techniques

The comprehensive dataset generated from the 54 unique building configurations evaluated across multiple floor levels provided the necessary input for performing the global sensitivity analysis in this study. The analysis used two advanced, non-linear, and non-parametric global sensitivity methods: rank regression and multivariate adaptive regression splines. These methods were specifically chosen for their ability to handle complex, potentially non-monotonic relationships between input variables and outputs, as well as to identify the importance of individual variables and their interactions across the entire input space, without making a priori assumptions about the underlying distribution of inputs or linearity of relationships [79]. The analyses used custom scripts developed in a statistical computing environment (e.g., Python 3.13.2 with scikit-learn or R with earth and relaimpo packages).

• Rank Regression Analysis

RR is a non-parametric global sensitivity analysis method that quantifies the strength and direction of monotonic relationships between the input parameters and the simulated outputs. In this study, for each objective function (T_o, cooling energy consumption, and lighting energy consumption), the simulated outputs and the corresponding input parameters (AR, WWR, GT, wall insulation, and floor level) were transformed into their respective ranks before performing a regression analysis. This transformation renders the method robust to outliers and effective for identifying influential variables even in non-linear, monotonic relationships. The sensitivity index was derived using Partial Rank Correlation Coefficients (PRCCs). For each input variable, the PRCC was computed, which measures the correlation between the ranked output and an individual ranked input after removing the linear effects of all other ranked inputs. A higher absolute value of the PRCC indicates a stronger unique influence of that variable on the output, providing insights into its contribution to the variability observed in the simulation results.

b.

Multivariate Adaptive Regression Splines

MARS is a powerful non-parametric regression technique utilized explicitly in this study to model complex, non-linear relationships between the input parameters and the objective functions, including high-order interactions, without requiring explicit specification of the functional form [95,96]. The MARS model was constructed using the same comprehensive dataset of input parameters and their corresponding simulated objective function values. The algorithm automatically identified and generated piecewise linear basis functions (hinge functions) to approximate the underlying, potentially non-linear, relationships observed in the simulation data. This process involved a forward stepwise procedure to add basis functions that improve the model fit, followed by a backward pruning pass to remove less significant terms and prevent overfitting. Sensitivity indices were extracted from the final MARS model. These indices quantify the relative importance of each variable (and their interactions) by measuring the reduction in the Generalized Cross-Validation (GCV) error or similar criteria when that variable is included in the model. This allowed for the identification of both main effects and complex interaction effects that influence operative temperature, cooling energy, and lighting energy consumption.

This study leverages their complementary strengths by applying RR and MARS. RR provided efficient initial screening for influential variables and validated monotonic trends across the parameter space. At the same time, MARS offered a deeper insight into the potentially non-linear and interactive behaviors often characteristic of complex building performance phenomena. The consistent findings from both methods enhance the scientific credibility and robustness of the sensitivity assessment, providing a reliable quantification of the relative importance of AR, WWR, glazing type, and wall insulation on the key performance indicators across various floor levels in the specified hot arid climate.

3. Results

This section meticulously presents and discusses the comprehensive simulation results derived from the integrated microclimate and building energy models, complemented by the findings from the global sensitivity analyses. The aim is to systematically elucidate AR’s, WWR’s, GT’s, and wall insulation’s intricate impacts on outdoor microclimatic conditions, indoor thermal comfort, and energy consumption in multi-story residential buildings in Aswan’s hot arid climate. The results are presented in a structured format, starting with the outdoor microclimate, then indoor thermal performance and energy consumption, and concluding with the sensitivity analysis, which quantifies the relative importance of each design parameter.

3.1. Thermal Performance Analysis

This subsection integrates the analysis of outdoor microclimate and indoor thermal comfort, focusing on how various architectural design parameters influence air temperature, relative humidity, wind speed, PET, and T_o.

3.1.1. Air Temperature and Relative Humidity Performance

This section examines the spatial and temporal distributions of air temperature (T_a) and relative humidity in both indoor and outdoor environments across three aspect ratio configurations (C1: 1.5, C2: 1.87, and C3: 2.25) and six vertical levels (ground to fifth floor) in Aswan’s hot arid climate. Emphasis is placed on thermal differentials (ΔT) and RH trends to assess the impact of design parameters on building thermal performance. Microclimate simulations using ENVI-met v5.5.1 captured the thermal behavior within the rear setback at pedestrian height (1.5 m), showing that diurnal Ta followed expected solar patterns, reaching 41.5 °C around 14:00 and cooling to 27 °C by 18:00, as shown in

Table 6. Average of Ta and RH analysis across different floors and proposed cases.

Floors	Proposed Cases	Ta avg (°C)				ΔT (K)		RH avg (%)
		Outdoor		Indoor				Outdoor		Indoor		ΔT
GF	C1	35.1		37.0		−1.9		21.8		19.8		2.0
	C2	35.0		37.0		−1.9		21.8		19.8		2.0
	C3	35.0		37.4		−2.3		21.8		19.4		2.4
1st	C1	35.1		37.0		−1.9		21.8		19.8		2.1
	C2	35.1		38.0		−3.0		21.7		18.7		3.0
	C3	35.1		38.0		−2.9		21.7		18.7		3.0
2nd	C1	35.1		38.3		−3.1		21.6		18.5		3.2
	C2	35.1		35.2		−0.1		21.7		21.7		0.0
	C3	35.1		37.9		−2.8		21.6		18.7		2.9
3rd	C1	35.2		43.5		−8.3		21.6		14.1		7.5
	C2	35.1		38.2		−3.0		21.6		18.6		3.0
	C3	35.1		37.9		−2.8		21.6		18.8		2.8
4th	C2	35.2		43.6		−8.4		21.5		14.0		7.6
	C3	35.1		38.1		−3.0		21.5		18.6		3.0
5th	C3	35.2		43.4		−8.2		21.5		14.2		7.3
		−8.5 °C					−0.08 °C	−0.02%					7.5%
		35 °C					44 °C	14%					21.7%

. The aspect ratio significantly influenced these conditions due to varying shading effects. Notably, the highest AR case (C3) reduced peak temperatures by nearly 5 °C compared to the lowest AR (C1), confirming the findings of previous research on the role of urban geometry in moderating microclimates [12,81,85].

Parallel simulations conducted with Design Builder revealed a distinct vertical thermal stratification inside the building. Higher floors were consistently warmer due to intensified solar exposure and cumulative heat gains. For instance, in the uninsulated C1 case with single-pane glazing and a 30% window-to-wall ratio, the third-floor experienced peak indoor temperatures of 43.83 °C, while the ground floor remained around 38.5 °C—a vertical difference of 5.33 °C. This gradient emphasizes thermal management challenges in multi-story buildings subjected to high solar loads. Comparative performance among the three ARs indicated that the mid-range configuration (C2) offered the most balanced thermal behavior, particularly on mid-level floors. The second floor, for example, recorded a negligible temperature differential (ΔT = −0.1 K), reflecting improved thermal regulation. Interestingly, although the C3 configuration significantly lowered upper-floor temperatures due to increased shading, it led to a 9.3% rise in cooling loads on the ground floor. This effect, likely caused by reduced air circulation in deeper, canyon-like spaces [15,97,98], highlights the complex interplay between shading and ventilation in urban form design.

Relative humidity patterns exhibited an inverse relationship with temperature. The lower floors maintained higher RH levels (e.g., 19.82% on the ground floor in C1), while the upper floors saw pronounced reductions (e.g., 14% on the fourth floor in C2). Integrating high-AR geometries with insulated walls proved beneficial in stabilizing RH by reducing conductive heat transfer. Figure 8 illustrates the average Ta and RH variations across floor levels and AR configurations. While the outdoor temperatures remained relatively stable, the indoor temperatures rose with elevation, reaching extreme values on the upper floors of C1 and C3 due to solar gain and limited ventilation. Conversely, RH declined with height, indicating elevated moisture loss and airflow effects. These observations underscore the significant influence of building height, solar radiation, and ventilation strategies on indoor thermal and humidity profiles, consistent with findings from previous studies on urban design optimization in hot climates [15,76].

Table 7. Thermal distribution in the rear setback area.

Cases	10:00 a.m.	12:00 p.m.	2:00 p.m.	4:00 p.m.	6:00 p.m.
C1
C2
C3

summarizes the simulation results assessing the spatial distribution of air temperature within a rear setback zone at pedestrian height (1.4 m) under peak summer conditions. Temperature data were extracted at selected time intervals—10:00, 12:00, 14:00, 16:00, and 18:00—to capture diurnal thermal variation. The findings indicate a typical diurnal temperature cycle, with Ta steadily increasing from early morning, reaching a maximum of 41.5 °C at 14:00 due to intense solar radiation, then progressively decreasing into the evening. The observed temperatures fluctuated between 27 °C and 41.5 °C throughout the day. These results emphasize the critical role of solar geometry and AR in shaping microclimatic heat distribution across urban setback areas.

3.1.2. Physiological Equivalent Temperature (PET) (Outdoor) and Operative Temperature (T_o)

These thermal comfort indices offer a holistic evaluation of thermal perception in indoor and outdoor environments. During indoor simulations, the cooling setpoint was consistently maintained to ensure controlled scenario comparisons.

• Outdoor PET Variation with AR: The PET, which synthesizes multiple meteorological variables to reflect perceived thermal stress outdoors, was analyzed at pedestrian height (1.5 m). As shown in Figure 9, configuration C1 (AR = 1.5) consistently exhibited the highest PET values during early afternoon hours, indicating severe thermal discomfort due to elevated air temperatures and intense direct solar exposure. In contrast, C3 (AR = 2.25) achieved the greatest reduction in peak PET, recording values of around 60 °C, approximately 5 °C lower than those of C1. This result highlights the effectiveness of higher AR configurations in creating self-shaded environments and mitigating radiant heat loads. The reduction in PET is primarily attributed to decreased Ta and mean radiant temperature (T_mrt), despite marginally reduced wind speeds, emphasizing the critical role of urban form in enhancing outdoor thermal comfort in arid climates [13,99,100].
• T_o and Key Influences: T_o, which accounts for both air temperature and mean radiant temperature, is a reliable indicator of indoor thermal perception. Across all AR scenarios, a consistent vertical thermal gradient was observed, with the upper floors experiencing higher temperatures due to greater solar exposure and reduced shading. In the uninsulated C1 scenario (30% WWR, single pane glazing), the third floor peaked at 43.83 °C, while the ground floor remained at approximately 38.5 °C. This stratification stems from the intensified radiant heat on the upper levels and limited facade protection.

• AR Effects on Indoor T_o: Although AR primarily governs outdoor microclimate conditions, its influence on facade exposure indirectly affects indoor T_o. The intermediate AR configuration (C2 = 1.87) provided the most favorable thermal conditions on the mid-level floors, such as 35.2 °C on the second floor, balancing solar shading and airflow. Meanwhile, C3, while beneficial for upper-floor shading, may restrict ventilation at lower levels due to deeper canyon effects, potentially elevating heat retention if airflow is not adequately managed.
• WWR Influence on Indoor T_o: An increase in window-to-wall ratio from 10% to 30% generally rises indoor T_o, particularly in buildings lacking insulation or advanced glazing systems, due to enhanced solar gains. However, the negative impact is considerably lessened when high-performance glazing is employed.
• Glazing Type as a Dominant Factor: Among the tested parameters, GT had the most pronounced effect on the upper floor T_o values, correlating with increased solar gains through fenestration. The transition from single- to double- or triple-pane systems led to notable reductions in T_o by limiting solar heat gain and thermal conductivity. This finding affirms the essential role of efficient glazing in maintaining indoor comfort in hot climatic zones [20,21].
• Wall Insulation Benefits: Incorporating thermal insulation into building envelopes (U-value reduction from 1.6 to 0.4 W/(m²·K)) significantly lowered indoor T_o by minimizing conductive heat transfer. When combined with advanced glazing and optimized AR configurations, insulation provided synergistic benefits, enhancing the building’s overall thermal performance.

3.2. Building Energy Performance Analysis

This subsection presents the simulation results for annual cooling and lighting energy consumption, providing a quantitative assessment of the energy implications of varying architectural design parameters.

3.2.1. Annual Cooling Energy Consumption

In Aswan’s hot arid climate, annual cooling energy constitutes the primary energy end-use in multi-story residential buildings, with consumption patterns highly sensitive to architectural design variables.

• The aspect ratio significantly influences cooling energy requirements by modulating solar exposure and shading efficiency. The lower AR configuration (C1) consistently exhibits higher energy demand, particularly on the upper floors. Conversely, the higher AR case (C3) demonstrates notable reductions in upper-floor cooling loads—up to 37% compared to C1—primarily due to enhanced self-shading and mutual shading between adjacent structures, as depicted in Figure 10. However, this configuration also shows a modest increase in ground-floor cooling demand (approximately 9.3%), likely resulting from diminished air movement and reduced ventilation efficacy within deeper urban canyons, which hinder heat dissipation [13,100].
• An increase in WWR correlates with elevated cooling energy use, driven by greater solar heat gains through fenestration. This impact is significantly reduced when high-performance glazing and effective wall insulation are employed, indicating that larger window areas can be accommodated if paired with energy-efficient envelope components.
• Glazing type is a dominant factor in shaping cool energy consumption. Transitioning from single-pane to double- or triple-pane glazing results in substantial energy savings due to reduced solar heat gain and thermal transmission. In optimized scenarios, adopting triple-pane glazing—characterized by low solar heat gain coefficient (SHGC) and U-values—can reduce annual cooling loads by up to 29,441 kWh, underscoring its critical role in thermal performance enhancement.
• Thermal insulation of opaque surfaces significantly lowers cooling energy consumption by limiting heat conduction from the exterior. Across all tested configurations, insulated walls consistently contribute to lower cooling demands, reinforcing the necessity of envelope optimization in hot climates.

Our simulations’ elevated cooling energy demands (Figure 10) align with established benchmarks for residential buildings in Aswan’s extreme climate, where summer temperatures routinely surpass 40 °C. Comparative data from Upper Egypt [34,101] and analogous hot arid regions demonstrate typical annual cooling consumption between 70 and 100 kWh/m², with variations attributable to three key factors: (1) building envelope thermal properties, (2) HVAC system coefficients of performance, and (3) magnitude of internal heat gains from occupants and appliances.

3.2.2. Annual Lighting Energy Consumption

Lighting energy demand in residential buildings is directly influenced by natural daylight availability, which is governed primarily by the WWR and further modulated by glazing type and building geometry, particularly the aspect ratio.

• Effect of WWR: Increasing the WWR from 10% to 30% led to a noticeable reduction in annual lighting energy consumption by approximately 28–35%, depending on the floor level and orientation. For instance, in the C2 configuration, lighting energy dropped from 2470 kWh/year at 10% WWR to 1765 kWh/year at 30% WWR on the second floor, due to improved daylight penetration. However, the trade-off includes increased cooling loads, especially if high-performance glazing is not implemented.
• Influence of GT: While primarily selected for thermal control, glazing systems also impact daylighting through their visible light transmittance (VLT). Single-pane clear glass typically has VLT values of around 80–90%, while triple-pane low-e glazing may have VLT values of around 60–70%. Simulations indicate that switching from low-VLT (60%) to high-VLT (80%) glazing can reduce lighting energy by up to 12% annually, with minimal impact on cooling savings if advanced coatings are used. For example, in a C1 scenario with 30% WWR, annual lighting energy fell from 2120 kWh to 1870 kWh when high-VLT glazing was used.
• Impact of AR: Higher AR configurations (e.g., C3 = 2.25) result in increased self-shading, particularly on lower floors, which can reduce indoor daylight levels. This effect was quantified by a 15–22% increase in lighting energy demand on the ground and first floors of C3 compared to C1. For example, lighting energy on the ground floor of C3 reached 2350 kWh/year, compared to 1910 kWh/year in C1. This demonstrates a design trade-off, where improved thermal comfort via shading may come at the cost of higher lighting demand.
• Wall Insulation Consideration: As expected, wall insulation has no measurable impact on lighting energy, since it only affects thermal performance and not visible light transmission. Lighting consumption remained unchanged—within a margin of ±2%—between insulated and uninsulated wall cases.

3.3. Sensitivity Analysis Results

The sensitivity analysis conducted using the two mentioned methods, RR and MARS, examines the influence of three key variables on the building’s energy consumption and indoor thermal performance: AR, WWR, and GT. The results are divided into two sections, without insulation and with insulation, and focus on three function objectives: cooling energy, lighting energy, and T_o. In the rank regression analysis without insulation, AR significantly affects cooling energy, particularly on higher floors (F3, F4), with a sensitivity index value of 0.5567 on F4 indicating a notable impact. WWR shows a negligible effect on lighting energy, with values close to zero. GT has a substantial effect on T_o, especially on F4, where the value reaches 0.9999, reflecting a major influence of GT on indoor temperature. With insulation, the impact of AR on cooling energy decreases, though it remains noticeable on the higher floors. The effect of WWR on lighting energy remains minimal, and GT continues to strongly influence T_o on the upper floors (Figure 11).

In the MARS analysis, the sensitivity indices reveal the impact of various design variables on cooling energy, lighting energy, and T_o across different cases. Without insulation, the AR and WWR show significant sensitivity to cooling energy, particularly on higher floors (F3, F4), with AR reaching a sensitivity index of 0.1846 and WWR reaching 0.0983 on F4. Conversely, WWR exhibits a negligible sensitivity index for lighting energy, with values close to zero in most cases. GTs demonstrate a substantial sensitivity index for T_o, particularly on upper floors (F4), where its value reaches 0.9873, indicating a strong influence of GT on indoor temperature regulation. When insulation is introduced, the sensitivity indices for AR and WWR on cooling energy decrease but remain noticeable on higher floors (F3, F4). The sensitivity of WWR to lighting energy remains minimal, with values close to zero, while GT continues to exhibit a high sensitivity index for T_o, particularly on upper floors. These trends, as illustrated in Figure 12, emphasize the role of insulation in mitigating the impact of AR and WWR on cooling energy, while GT retains its influence on indoor thermal conditions.

In the case of no insulation, the comparison between RR and MARS highlights similarities and slight differences in sensitivity analysis results. For cooling energy, RR indicates a strong sensitivity index for the AR, particularly on higher floors, with a value of 0.5567 on F4. The WWR also shows some influence, but its sensitivity index is less pronounced. Similarly, MARS identifies a significant sensitivity index for AR on cooling energy, with lower values, such as 0.1846 on F4, and a more evenly distributed sensitivity index for WWR across floors. Both methods confirm that WWR has a negligible sensitivity index for lighting energy, with values close to zero across all floors.

Regarding T_o, rank regression reveals a high sensitivity index for GT, particularly on higher floors, with F4 showing a GT value of 0.9999. MARS also identifies GT as a significant influencing factor, but with slightly lower sensitivity values, such as 0.9873 on F4. Both methods agree that AR significantly impacts cooling energy, WWR minimally affects lighting energy, and GT strongly influences T_o, especially on higher floors. However, rank regression generally produces higher sensitivity indices, potentially overestimating the influence of variables such as AR and GT, while MARS provides more conservative and balanced results. These findings are illustrated in Figure 13.

In the case of insulation, the comparison between RR and MARS demonstrates a reduction in the sensitivity index of the AR on cooling energy. However, its influence remains noticeable on higher floors. RR indicates that AR continues to impact cooling energy, with a sensitivity index of 0.5711 on F4, while the WWR shows a minor sensitivity index. Similarly, MARS identifies a reduced sensitivity index for AR on cooling energy, with lower values such as 0.1821 on F4, and a diminished sensitivity index for WWR. For lighting energy, both methods confirm that WWR has a minimal sensitivity index, with values close to zero, even with insulation. Regarding T_o, RR highlights that GT remains a significant factor, with F4 showing a sensitivity index of 0.9997. MARS also confirms the strong influence of GT, though with slightly lower sensitivity index values, such as 0.9955 on F4. Overall, the sensitivity indices for AR and WWR on cooling energy are reduced when insulation is considered; however, GT maintained the highest sensitivity index across both RR and MARS methods for T_o, confirming its central role in thermal performance. RR yields higher sensitivity index values than MARS, providing a more balanced and conservative analysis. All of these results are depicted in Figure 14.

Table 8. Sensitivity indices from RR and MARS for key design parameters on the upper floor (F4), comparing their impact on cooling, operative temperature, and lighting energy under insulated and non-insulated conditions.

Wall Insulation	Parameter	Output Variable	RR Index	MARS Index
Without insulation	AR	Cooling Energy	0.5567	0.1846
	WWR	Cooling Energy	0.1205	0.0983
	GT	Operative Temperature	0.9999	0.9873
With insulation	AR	Cooling Energy	0.5711	0.1821
	WWR	Lighting Energy	~0.0001	~0.0000
	GT	Operative Temperature	0.9997	0.9955

summarizes the sensitivity indices for key variables using RR and MARS to provide a more precise comparison of the influence rankings derived from both techniques. The consistency in identifying GT as the dominant factor for operative temperature across both methods strengthens the reliability of the findings. At the same time, minor variations in AR and WWR rankings reflect method-specific sensitivity to interaction effects.

4. Discussion

This study examined the combined influence of rear setback ratio, WWR, glazing type, and occupancy patterns on energy performance and thermal comfort in a multi-story residential building under hot arid climatic conditions. While the roles of WWR and glazing have been investigated in previous works, the novelty of this research lies in integrating rear setback geometry and vertical stratification into the energy simulation, offering a deeper understanding of how urban form and façade decisions interact.

The simulation results revealed that glazing type was the most influential parameter, particularly affecting the upper floors, where the operative temperature showed a sensitivity index as high as 0.99. This aligns with the findings of Alwetaishi [102], who emphasized the significant impact of window glazing on indoor comfort in arid regions. However, our study adds a new dimension by showing that thermal response varies by floor level, highlighting the vertical heterogeneity of energy performance. For instance, triple glazing on the fifth floor resulted in a 15% reduction in peak operative temperatures. At the same time, the same intervention had a minimal effect on the ground floor due to limited solar exposure and airflow.

The AR of the rear setback was another critical factor influencing microclimate and building performance. Increasing the setback depth (AR from 1.5 to 2.25) reduced PET by up to 5 °C at pedestrian level, improving outdoor comfort in semi-enclosed rear spaces. Simultaneously, this change resulted in a 37% decrease in cooling loads on upper floors, likely due to enhanced convective airflow and reduced radiant heat gains. These findings are in agreement with those of Nasrollahi et al. [11], who reported that urban morphology significantly affects microclimate conditions in arid cities. However, our results also showed that deeper setbacks slightly increased cooling loads on the ground floor by approximately 9.3%, possibly due to reduced shading from neighboring walls and greater surface exposure. This nuanced result suggests the need for floor-specific design strategies, particularly in densely built environments.

The WWR was also evaluated in three configurations (10%, 20%, and 30%). As expected, higher WWR reduced lighting energy by up to 35%. However, increasing WWR had a relatively small impact on cooling demand compared to that of glazing type, confirming the results of previous research by Alkhatatbeh et al. [103], who reported that WWR alone cannot offset thermal loads without appropriate shading or glazing optimization.

Occupant behavior, including occupancy schedules, appliance use, and HVAC operation, significantly shaped the building’s energy profile. The model incorporated realistic Egyptian household routines, including intermittent high-load devices and continuous low-load equipment. These internal gains were particularly influential in increasing cooling loads during the afternoon peak period (13:00–16:00). This pattern is consistent with the load profiles reported by El-Shorbagy et al. [104] for residential buildings in Egypt.

A significant methodological contribution of this study is the coupled simulation approach, integrating ENVI-met for microclimate modeling and Design Builder for indoor energy analysis. This enabled the generation of customized weather files that reflect the actual environmental conditions across different setback geometries. Unlike typical simulations using generic EPW files, this approach captured spatial variations in outdoor air temperature and wind speed, directly influencing indoor thermal behavior. This is especially relevant in hot arid regions, where urban geometry significantly shapes airflow and radiant heat exchange.

To ensure the validity of the thermal comfort evaluations, the building thermal loads were assessed using EnergyPlus’s internal heat balance algorithms, accounting for dynamic interactions between solar gains, envelope transmittance, internal loads (lighting, equipment, and occupancy), and ventilation rates. The cooling and heating systems were sized using the EnergyPlus auto-sizing function, which computes required capacity based on peak thermal loads for each thermal zone under design-day conditions. This approach ensures that system under-sizing does not bias the indoor operative temperature outputs.

The relatively high operative temperature values observed in some cases were not due to insufficient HVAC capacity. Instead, they reflected the impact of architectural variables such as high window-to-wall ratios, glazing types with elevated solar heat gain coefficients, and the modulation of rear setback geometry. These design parameters influence solar exposure and internal radiant temperatures, which are factored into the operative temperature calculation. Furthermore, it is essential to note that the thermal comfort thresholds were interpreted according to ISO 17772-1:2017 [92], which defines acceptable ranges for Categories I–III. Some operative temperature values exceeding Category II may still fall within Category III, especially in highly sun-exposed upper zones. This simulation framework aims to reveal the influence of passive design strategies and façade geometry on energy use and comfort outcomes, independent of mechanical system limitations.

Finally, the sensitivity analysis using multivariate adaptive regression splines confirmed that the glazing type and setback aspect ratio were the most influential parameters affecting cooling energy and operative temperature. These insights offer practical guidance for urban designers and architects in similar climatic regions. In contrast to studies focusing solely on envelope design or passive cooling, this research demonstrates the need for an integrated approach that accounts for both microclimatic context and occupant dynamics.

5. Limitations

Although HVAC systems were auto-sized using EnergyPlus to match peak zone loads, we acknowledge that certain zones exhibited elevated operative temperatures and relative humidity levels that, in a few cases, exceeded ISO 17772-1 Category II thresholds. These outputs may be partially influenced by the thermal inertia of the building, internal load profiles, or assumptions regarding infiltration and equipment performance. While we attribute most thermal variations to architectural parameters such as WWR, glazing, and setback geometry, it is possible that dynamic load spikes during peak summer hours briefly exceeded the available capacity, especially in top-floor zones. Furthermore, the relative humidity levels were not actively controlled in the simulation, which may have contributed to comfort deviations in some cases. These factors represent methodological limitations that future studies may overcome by including dynamic HVAC control strategies, dehumidification systems, and equipment redundancy.

Another limitation relates to the simulation of indoor relative humidity. While RH values were generated dynamically based on internal heat gains, infiltration, and moisture transfer processes, no active humidity control systems (such as humidifiers or dehumidifiers) were modeled. As a result, the indoor RH levels reported in Figure 8, particularly during cooler or low-occupancy periods, occasionally fall below the recommended comfort range of 40–60% specified in ISO 17772-1 and EN 16798-1. This may be attributed to dry outdoor air infiltration, limited internal moisture generation, and the absence of humidification strategies. Although RH was not a primary objective of this study, we acknowledge that low humidity can negatively affect occupants’ comfort and perceived indoor air quality. Future studies should incorporate active RH control mechanisms or sensitivity analysis on moisture loads to more accurately assess comfort conditions in hot arid climates.

6. Conclusions

This study provides a comprehensive, empirically validated analysis of how urban geometry and façade design parameters influence microclimate conditions, thermal comfort, and energy performance in multi-story residential buildings situated in hot arid climates, using Aswan, Egypt, as a representative case study. By integrating ENVI-met microclimate simulations, Design Builder energy modeling, and two advanced global sensitivity techniques (RR and MARS), the research quantifies the relative impact of rear setback AR, WWR, GT, and wall insulation on critical performance metrics, including cooling and lighting energy consumption and T_o.

The results show that glazing type strongly affects indoor thermal comfort, especially on upper floors, making it a key factor in cooling performance. AR significantly influenced outdoor thermal comfort and cooling energy demand, particularly at upper levels, where a high AR (2.25) reduced the peak cooling loads by up to 37% but slightly increased ground-floor demand due to reduced ventilation. WWR strongly influenced lighting energy use but only marginally affected thermal performance, while wall insulation consistently enhanced energy efficiency by lowering conductive heat gains.

This study fills a research gap by showing how urban form and façade design interact under real microclimate conditions, often overlooked in past work. By linking outdoor microclimate simulations with customized weather files for indoor energy modeling, this work demonstrates the necessity of integrating micro-scale environmental data into building performance assessments in arid zones. This study’s limitations include its focus on a singular urban form, idealized occupancy, and HVAC assumptions. While these choices ensured simulation clarity and computational feasibility, future research should explore a broader range of urban morphologies, passive cooling techniques, material aging effects, and stochastic occupant behavior. Additionally, incorporating economic analysis could support cost–benefit evaluations of the proposed design interventions. The findings offer actionable strategies for architects, urban planners, and policymakers to enhance thermal comfort and reduce energy consumption in arid climates. Prioritizing high-performance glazing, optimizing setback ARs, incorporating robust insulation, and carefully balancing WWR can lead to substantial energy savings and improved occupant comfort, contributing meaningfully to climate-responsive and sustainable building design.