A Morris sensitivity analysis of an office building ’ s thermal design parameters under climate change in sub-Saharan Africa

Sub-Saharan Africa faces severe overheating problems during hot periods due to substandardly constructed buildings and high-priced energy services. Global warming is expected to aggravate the situation. Although literature addresses the effects of climate change on buildings in different world regions, how it will impact the Sub-Saharan region is still being determined, particularly in terms of design parameters and how they will vary. This study assesses the influence of design parameters on the cooling energy demand of a small-scale office building in Lagos and Kano, Nigeria. A Morris sensitivity analysis was carried out to rank and compare the influence of different design parameters on energy consumption, determined using EnergyPlus for present-day typical weather and the SSP5-8.5 scenario. The future scenario was generated using the Future Weather Generator, a morphing tool. The results show that, in 2080, the cooling load will increase from 1551 kWh/a to 2612 kWh/a (68.4 %) in Kano and from 1931 kWh/a to 3093 kWh/a (60.1 %) in Lagos. The cooling load in Lagos will generally be higher than in Kano by 18.4 % (596 kWh/a). The results indicate that reductions in the thermal conductivity of the east wall and decreases in the solar absorptance of the east wall, roof, and west wall elements will be the most significant factors affecting cooling in Kano. In Lagos, reductions in the thermal conductivity of the east wall and decreases in solar absorptance of both the east wall and roof elements will be the most influential.


Introduction
Nigeria and other sub-Saharan countries are more vulnerable to the effects of climate change than developed countries that have already begun implementing measures due to increasing air temperatures in all future scenarios [1].Consequently, energy operations within the built environment are partly impacted by global warming, leading to over 30 % of global energy consumption being attributed to maintaining indoor comfort [2].Fortunately, the building sector presents the highest potential for climate change mitigation compared to other sectors [3], offering potential savings of 42 % in operational energy, 35 % in greenhouse gas (GHG) emissions, and a 50 % reduction in raw material extraction [4].Achieving the climate change mitigation potential in the building sector is feasible through proper climate zoning considerations in building design.Identifying the connection between energy consumption and climate conditions can aid in making optimal decisions for climate-responsive buildings in various locations [5].
A significant number of empirical studies have been conducted since 2017 on the role of mitigation/adaptation measures to alleviate the impacts of climate change on building energy performance under various climate ranges worldwide.For example, in Brazil, studies utilizing sensitivity analysis methods indicate that natural ventilation, solar absorptance of the envelope, and thermal transmittance of the wall are crucial for the thermal and energy performance of low-cost housing in Belém and São Paulo [6].Similarly, while focusing solely on the trend for mitigation measures for the current climate in southern Brazil, the thermal transmittance and solar absorptance of the roof and the openings' ventilation parameters are essential for low-income housing [7].In a recent study on climate change mitigation in residential buildings in Brazil [8], simulation results show that the trend in the ideal thermal transmittances of the building envelope will vary across 30 different locations in present-day and future time frames.Specifically, the results emphasize that, compared to the present, in some locations, the ideal thermal transmittances will remain unchanged in the future.In other regions, they will shift dramatically from being at the highest range of U-values to being the lowest for future time frames.For the remaining regions, these values will decrease or stay relatively constant.
In the Netherlands, a study showed that most dwellings will not be affected much by future global warming [9].However, dwellings with poor ventilation, particularly those without good window solar protection mechanisms, are susceptible to overheating in the future.The study also found that increasing the ventilation rate of dwellings could reduce the overheating risk by 1.2 • C in future climate conditions and 2.3 • C in the worst climate scenario.One study on mitigation efforts on climate change for buildings in some Mediterranean regions suggested that an ideal thermal transmittance of the envelope elements in the present-day climate would not cause overheating in all the locations in the future [10].The results of another study in Luxembourg and Italy demonstrated that green roofs, as a measure of climate change mitigation, could cause a significant energy decrease, ranging from 20 % to 50 % for Esch-sur-Alzette in Luxembourg and from 3 % to 15 % for Palermo in Italy.It could also potentially lead to improved indoor comfort by causing a reduction of 2 • C-5 • C in the ceiling temperature when applied to the topmost floor of a building in both locations [11].Another study identified different passive cooling solutions in France, including optimizing the building envelope for the southern and northern regions under the future climate.For the northern regions, the optimal solutions will be well-insulated envelopes, small skylights, and roofs with high solar absorptance values.For the southern regions, the optimal solutions will be a non-insulated ground slab, a reflective cool roof, and large skylights to maximize both natural cooling potential at night and natural lighting.From the results, the optimum setpoint temperatures considering natural night ventilation are 18 • C and 26 • C. For a trade-off between energy demand and thermal discomfort for current and future climates, the study also suggests an albedo value of the solar reflectance of the cool roof be between 0.46 and 0.74 [12].Regarding predicting cooling measures as mitigation strategies for building stock in Switzerland, one study concluded that window shading and night ventilation are the most crucial measures, contributing to around 84 % cooling reduction [13].
In Asia, several mitigation measures are also documented in the literature.For example, passive solutions have shown that ventilative cooling, reflective and ventilated roofs, shading in windows, and roof insulation were the best passive measures for thermal comfort and energy consumption for a typical family dwelling under Pakistan's hot future climate [14].Contrary to findings in Cirrincione et al. [11], green roofs are the best mitigation measure, a study in Qatar concluded that adding expanded polystyrene to the envelope and having more energy-efficient windows are the most impactful [15].Additionally, another study exclusively investigated the synergy of green roofs and natural ventilation as mitigation measures for the future energy efficiency of buildings in Chongqing, China [16].Indeed, global warming would impact the choice of plant species in the green roof-natural ventilation strategy.However, with promising design alternatives based on the future climate, annual energy use in new buildings could be reduced by 12.2 %.In a sensitivity analysis study on the robustness of building parameters, after comparing them to Givoni building bio-climatic charts, the combination of solar protection strategies will reduce 56.7 % and 64.5 % in annual and peak cooling load, respectively, in response to future climate change for residential buildings in Hong Kong [17].Another study analyzed the impact of climate change on a reference building in several parts of China, and the result of a small sensitivity analysis showed that the most efficient passive design measures would be the construction type of walls, roofs, solar heat gain coefficient of the window, and window area [18].
Among the studies on climate change mitigation of buildings in the UK, the result of one recent study on overheating concluded that adaptive ventilation is potentially the key climate mitigation measure to enhance the robustness of thermal comfort in light of future climate change uncertainties for a post-retrofit dwelling in England [19].
Similarly, in the anticipated hotter and drier Iranian region in the Middle East due to climate change, another recent study [20] on ideal thermal transmittance suggested that mitigation strategies generally differ based on the climate region.The study concluded that in the central and northern Iranian regions (with low to high heating demand in the present), future ideal transmittance would be higher or lower than in the present-day climate.The study also suggested that for regions with already higher cooling needs in the present day, the lowest possible thermal transmittance for the building envelope is even more required in the future.
A recent study on different Australian climate zones quantified the climate potential of natural ventilation as an energy-saving and climate change mitigation measure under the present climate [21].The investigation revealed that under global warming with the required airspeed, the climate potential of natural ventilation could increase by 18 % [21].
Although not addressing future climate scenarios, some recent studies have attempted to enhance the identification of influential parameters for mitigation measures using machine learning techniques.For instance, a Bayesian adaptive spline surface surrogate model identified influential parameters for specific multiple time-scale periods (yearly, monthly, and hourly) in Tianjin, China [22].Similarly, focusing solely on the present-day climate, another study employing the Irish residential archetype compares the results of significant parameters obtained from a machine learning Feature Selection technique and sensitivity analysis [23].
Several studies have been conducted on measures and techniques for climate change mitigation under future conditions.However, in sub-Saharan Africa, only three studies were evident in the literature.The findings from one of the studies in South Africa on insulation as a mitigation measure under the future climate showed that a highly insulated building, compared to a poorly insulated one, causes a rise in energy consumption by 3.5 % and 11 % in the current climate and future conditions, respectively.However, a decrease of 0.73 • C in favor of an indoor thermal environment was observed in the current climate [24].Based on the study's findings, high insulation in buildings will generally not be favorable in southern African regions.Another notable study in sub-Saharan Africa used residential buildings as case studies in Kumasi and Ashanti in Ghana [25].Some adaptation and mitigation strategies were compiled to solve the impacts of climate change for both the present and the future.Although the study attempts to provide the collective potential of the mitigation strategies, it fails to comprehensively identify which measure is suitable for the future climate.The other study in Burkina Faso concluded that solar protective shading devices could lead to a 40 % reduction in cooling load [26].
Based on the literature discussed, the following knowledge gap and limitations were determined.1) Throughout most of the research studies mentioned above, investigations on climate change mitigation were only focused on the potential of either one or two thermophysical measures or a combination of other diverse measures, with none exclusively aimed at understanding the impact of a group of thermal properties and their comparison.2) Although a study in West Africa, close to Nigeria, analyzed the influence of diverse measures under climate change [25], those are unrelated to the thermophysical properties of the envelope.3) In all studies, the wall element, which forms a significant part of the building envelope, and window openings were addressed vaguely.Enclosed wall systems and windows were classified as a single element without categorization based on their orientations.Additionally, some studies only focused on the current climate [7,22,23].
This study will answer the following questions: "Will climate change require building practitioners to use different thermophysical properties for the building envelope in Nigeria?" Also, although Kano and Lagos are at a latitude below the Tropic of Cancer and above the Equator, which means that all faces of the building are exposed to solar radiation, "Should building practitioners account for each element orientation?"I. Tajuddeen and E. Rodrigues and, finally, "Are there meaningful similarities or differences to other regions?" We hypothesize that significant differences in the influence of the thermophysical properties of the elements in Kano (hot-dry) and Lagos (hot-humid) may be accounted for in the face of climate change, especially concerning the differences related to the wall surfaces.This hypothesis is substantiated in past studies where only climate zones in Nigeria with similarities could adopt the same strategies regarding the building wall elements [27]; the same phenomenon is also valid in other countries outside the sub-Saharan African regions [28][29][30].
The novelty of this study compared to similar studies in literature is summarized as follows.
• It exclusively assesses a large dimension of thermophysical properties of elements related to design parameters considering climate change.Therefore, in light of the absence of robust policies on climate change in Nigeria [31], this study holds significance in guiding policymakers and professionals in the building industry to establish a framework for mitigating the impact of climate change on Nigerian buildings.

Methodology
We addressed the steps in the following study framework to answer the above questions and test the hypothesis (Fig. 1).We first identified the present-day climate regions in Nigeria and selected Lagos and Kano because these were the most representative of contending harsh climatic regions.To evaluate the office energy performance, we retrieved weather data in hourly resolution corresponding to a typical meteorological year (TMY) from 2007 to 2021.Next, a morphing technique was used to generate future weather suitable for building energy simulation.
This technique statistically transforms the present-day climate to match future climate projections for SSP5-8.5.Then, parametric simulations were conducted to understand the energy performance of the building based on the annual cooling load indicator and to conduct a statistical sensitivity analysis to rank several envelope design parameters.

Present-day climate
Nigeria falls within 10 • 00′ N and 8 • 00' E geographical coordinates, with tropical characteristics and a wide climate variation.The warmhumid characteristic is intense along the coastal line, especially at night (e.g., Lagos), and the maximum temperatures range around 32 • C [32].Like West Africa and other tropical regions, Nigeria experiences two climate seasons: the wet season, approximately from April to October, and the dry season, from November to March.During the onset of the wet season in spring, heavily influenced by an air mass originating from the South Atlantic Ocean around March to April, maximum temperatures can soar to as high as 44 • C in the Northern part of the country, exhibiting a typical hot-dry characteristic, as seen in Kano.The dry season is typically accompanied by a mass of dusty air from the Sahara Desert [32].This study selected two examples of extreme warm-humid and hot-dry zones in Nigeria for analysis, as already categorized by ASHRAE 169 [33] (Fig. 2).This selection is justified as both Lagos and Kano have a significant portion of the population and represent some of the most challenging climates in Nigeria, providing a broader perspective on the climate change trend.

Future climate
For future weather data, we adopted the SSP5-8.5 to plan for the worst-case scenario since it represents a future where global warming may exceed 2 • C.This scenario envisages global economic growth driven by natural gas, oil, and coal burning [34].Resources are allocated to adapt to climate change with minimal efforts to reduce emissions, resulting in a projected warming of 3.3 • C to 5.7 • C by the end of the 21st century [34] compared to 1950, when radiative forcing is expected to reach 8.5 W/m 2 [35].
We used the Future Weather Generator Tool to morph present-day hourly weather to match future climate projections [36].This tool uses EC-Earth3 climate data for the monthly variable changes.

Office building
The office building is a multi-thermal zone model, and the simulation Fig. 1.Study concept framework.

I. Tajuddeen and E. Rodrigues
was run in EnergyPlus.We used the small office building template from ASHRAE 189.1-Standard [37], which closely aligns with the ASHRAE 169 [33] climate zones of the regions under investigation.This template includes typical space types, their operation schedules, and construction details, such as thermophysical properties of the envelope and building components.

Functional program
Fig. 3 depicts the office layout, which has a volume of 200 m 3 (length of 10 m, breadth of 5 m, and height of 4 m), comprising one large room (25 m 2 ) to potentially accommodate at most two occupants and two smaller rooms (12.5 m 2 ) for one occupant each.Office space is intended for small private businesses as small and medium-scale enterprises are rapidly growing in big cities in Nigeria, and this trend is expected to continue in the future.This study focuses only on primary thermal zones where occupants spend most of their hours during working periods.

Construction and materials
We set the boundary conditions of all the external walls and roof to outdoors and the boundary condition of the floor to the ground.Since the temperature beneath the ground is always stable and colder than surfaces above it, the temperature of the ground in contact with the building surface was assumed to be 21 • C during the hotter months of the year and 20 • C during the wetter and colder months of the year.
In terms of construction and materials, Table 1 displays the layers of each construction and their thermal properties.The external door has one more layer than the interior doors, comprising a dense metallic material with high thermal conductivity for security purposes.The internal doors are lighter, with the structural layers serving as the finished layers.The internal wall is a simple brick wall with finishing on both sides.
The thermophysical properties that vary are presented in Table 2.The window area is approximately 10 % of each office room's exterior wall.Each window is a single pane construction with U-value and SHGC varying between 0.8 W/m 2 ⋅K and 5.4 W/m 2 ⋅K and 0.36 to 0.87, respectively.In this study, the ground floor does not have an insulation layer corresponding to common construction practices in Nigeria.However, its structural layer was varied to understand any thermal changes between the immediate ground and the floor.It is worth mentioning that the varying parameters are based on the thermophysical properties of abstract construction methods and the building elements of a conventional building.This means that only one layer for each varying building element was considered.Since this study aims to predict the future sensitivity of construction elements, it could be assumed that a greater variety of building elements and their uncertain layers will be available.

Internal gains
Based on ASHRAE 189.1-Standard [37], lights were set to 10.06 W/m 2 , electric equipment to 7.6 W/m 2 , and the metabolic rate of an office activity level to 58 W/m 2 .One person is assumed to occupy each small office, and two are in the larger room.The schedules for artificial lighting, occupancy, and electric equipment are for typical working hours (8:00 a.m. to 12:00 p.m. and 1:00 p.m. to 4:00 p.m.).

HVAC system
For the HVAC, a Fan Coil HVAC Template was set in each zone, with a Chiller for cooling and a Boiler for heating.The thermostat was set to maintain a cooling setpoint of 26 • C and a heating setpoint of 18 • C.An occupancy typical of an office was used, which operates from 8:00 a.m. to 4:00 p.m. but excludes 12:00 p.m. to 1:00 p.m. (which represents break hours).The operation schedule excluded weekends and any observed national holiday of the calendar year.The HVAC had an outdoor airflow rate of 0.00944 m 3 /s per person in all three zones.In order to simulate opening windows to vent the rooms, ventilation of 2 air changes per hour was set to occur when the outdoor dry-bulb temperature was below 26 • C and indoor air temperature was at least 2 • C higher than the outdoor dry-bulb temperature.Lastly, a constant infiltration rate of 0.0000756 m 3 /s/m 2 was set.
We considered the following energy components: cooling coil total cooling energy (in cooling mode), chiller electricity energy (in cooling mode), fan electricity energy (associated with cooling and heating mode), pump electricity energy (heating-related pump), and boiler natural gas energy (heating mode).These components are calculated for a whole year.

Sensitivity analysis
The Morris Global Sensitivity statistically uses the elementary effects to capture the influence of different variables to provide the option to identify model parameters based on either being negligible/slight influence, linear/additive, or non-linear/second order.To extract the sensitivity of the design variables, we initially developed a design of experiments for Morris, where we considered 12 trajectories (r) and eight levels of variations (p) of the variables to allow the elementary effects to understand the variables' behavior.Given 29 analyzed parameters (k), the Morris original sampling recommends using different r trajectories of k + 1 points in the sampling space, thereby having k elementary effects.Therefore, the number of observations in the sample is defined by n = r × (k +1) (i.e., with 29 parameters k, and 12 trajectories r, each sample has 360 parametric simulations).Following Morris's recommendation [38], the change step is 4 for 8 intermediate values of the parameters.Since we are considering two climate regions (Kano and Lagos), each with a present-day climate and SSP5-8.5 2080, we concluded 1440 parametric simulations.
Following this, we demonstrate the Morris method by defining an experimental region ω, representing a k dimensional space with p levels, where each independent parameter x i can assume a value in the interval , enabling parameters to be considered concurrently, and allowing them to be easily transformed from their original values to a unit hypercube by input normalization.Considering the independent parameters (x i ), where i varies from {1,2,…,k}, in p levels in the region ω, for each value of x, the i th elementary effect is defined as follows in equation (1): Where Δ is a value between , having p as the number of levels in ω; x is each selected value in ω; y is the analyzed model, which uses X as input variables; d i (X) is the elementary effect from the i th variable in the function y.
Considering r number of trajectories, k movements are made onefactor-at-a-time to calculate the i th elementary effects defined by d i ( X j ) .After that, equations (2), (3), and (4) are used to determine the Morris indices u, u * , and σ.
Where i is a variable; r is the number of sample paths; j is each path in the sample space of each parameter i; u i is the mean of the elementary effects of the parameter i; u * is the mean, in absolute value, of the elementary effects of the parameter i; σ i is the standard deviation of the elementary effect of the parameter i; is the elementary effect of the ith parameter in path j.
A different sensitivity index was proposed to improve Morris's original sampling approach [39].This sensitivity index is denoted by u * and σ i .Based on this, we only considered u * and σ i in this study, and not u i , to rule out the negative values.
With u * , negligible or few influential parameters are defined as against the most influential parameters, and with the joint of u * and σ i , the linearity or the second order influence is defined.A comparison of the mean allows the understanding of parameters with the most influence.A higher mean represents a higher influence.Similarly, the σ i allows a better understanding of parameters with non-linear behavior.In other words, those parameters interact with others before they cause an influence (second-order effect).Again, the ratio of the σ i and u * determines monotonicity.In a monotonic relationship, an increase in the independent parameter causes a direct increase in the dependent parameter (a positive monotonicity) [6].

Present-day and future climates
Since the energy indicators strictly depend on the climate, it is necessary to provide climate analyses of the two regions based on the outcome of the morphing.This will allow an in-depth understanding of the region's dynamics and extent of hotness or humidity, spanning from the present day to future SSP5-8.5 2080.
By comparing the climate variables under the present-day climate of both regions in Fig. 5, it can be observed that Kano, the hot-dry region, has higher dry-bulb temperature and solar radiation values but lower dew point temperature than Lagos (hot-humid).This is especially visible across the dry seasons where it is at peak, with present-day climate in Kano having the following averages: dry-bulb temperatures approximately between 30 Similar to present-day climates, in SSP5-8.5 2080, lower dry-bulb temperatures and solar radiation are observed in Lagos than in Kano.However, the dew-point temperature is higher.Therefore, more evaporation and higher relative humidity are expected.Fig. 6 shows that Kano will have higher values of dry-bulb temperature and diffuse radiation than Lagos in the future.The peak dry-bulb temperature in Kano is about 38 • C, and diffuse radiation ranges from 150 Wh/m 2 to 300 Wh/ m 2 .
In comparison, the peak dry-bulb temperature in Lagos is around 33 • C, and diffuse radiation is between 180 Wh/m 2 and 270 Wh/m 2 .In Fig. 6, Lagos's peak dew point temperature is above 27 • C and higher than in Kano.The peak dew-point temperature across all months in Lagos is relatively stable.Conversely, the peak dew-point temperature in Kano is 26 • C, which is not relatively stable across all months like in Lagos, occurring only in the warm months and finally dropping to less than 5 • C in the colder months.
It is also important to note the monthly differences between the variables of the SSPs in both regions and the variables of their respective present-day climates.Generally, based on the temperature differences between the SSP5-8.5 and present-day climate, it was clear that Kano has more differences in the dry-bulb temperature compared to Lagos.However, while horizontal diffuse radiation is higher for the Kano SSP5-8.5 2080 than Lagos SSP5-8.5 2080, the differences in the SSP5-8.5 2080 and present-day climate are more pronounced in Lagos than in Kano.Similarly, while dew-point temperature and relative humidity are higher in Lagos than in Kano (Fig. 6), the differences between the SSP and present-day climate are greater in most of the months in Kano.These two instances mean that, in the present time, the solar radiation in Kano is already high, attaining its peak, and will only increase slowly in the future, the same way that the relative humidity and dew-point  temperature have already risen close to their peak in the present time in Lagos, and will only increase gradually in the future.

Distribution of energy indicators
Fig. 7 shows the normal and log-normal distributions of the energy outputs based on Morris's factorial sampling of the input parameters.The normal distributions are much more dominant in all the samples than in Kano's present-day samples.The log-normal distribution could be seen in all the heating energy outputs except Kano SSP5-8.5 2080, while for Lagos SSP5-8.5 2080, heating energy has zero values and, therefore, no distribution.The normal distribution of the outputs suggests that the sample size (using 12 trajectories) has appropriately sampled the entire parameter space of the input.In the computational design of the experiment, the deviation from the mean of the output represented by the normal distribution is strongly correlated to the range of the input parameters (uniformly distributed in this study) [41].The distribution of outputs in Fig. 7 corresponds to the distribution of the outputs in the uncertainty analysis studies [7,42], where the authors used Latin Hypercube Sampling, for which the dominant input parameters are uniformly and discretely distributed thermal properties of construction elements.Similarly, a study found ten trajectories sufficient for the robust ranking of building energy input parameters in a Morris sensitivity analysis study [43].This, therefore, underscores the efficiency of the Morris sampling technique.It must be noted that other studies using a Morris sensitivity analysis, for example, Nunes et al. [6] and Menberg et al. [43], only focused on the robustness of the elementary effects in ranking input parameters and did not report the output distribution based on its sampling.Furthermore, for the distribution of output ranges in Kano, as shown in Fig. 8, the average annual cooling energy for the 360 simulations is higher in the future SSP5-8.5 2080 than in the present-day climate.The average annual cooling energy for Kano SSP5-8.5 2080 is 2612 kWh/a, and each annual cooling energy from the simulation varies between kWh/a and 4095 kWh/a.For present-day climate, the average sum is 1551 kWh/a, and annual cooling energy varies between 950 kWh/a and 2832 kWh/a.The increase in cooling loads of the average sum of the simulations from the present-day climate to the extreme future SSP5-8.5 2080 is 1061 kWh/a (68.4 %).Although the average sum of the same 360 simulation results for SSP5-8.5 2080 for the heating energy is 1.35 kWh/a, and varies between zero and 3.47 kWh/a.As should be expected, this average is lower than the value in the equivalent presentday climate.The average sum of the heating energy of the present-day climate is 8.00 kWh/a, while the values vary between 3.56 kWh/a and 15.10 kWh/a.
Similarly, Fig. 8 further shows the differences in cooling load under Lagos for the present-day climate and the SSPs.In comparison with Kano, notice that the cooling loads in Lagos are a bit higher, mainly due to consistent levels of high humidity and dew-point temperature throughout the months of the year than in Kano (Figs. 5 and 6), forcing more energy to be expended on cooling.
The cooling energy for the average sum of the 360 simulation results of each sample and variation of values under Lagos are summarized as follows: for the SSP5-8.5 2080 sample, again being the highest, the average annual cooling energy is 3093 kWh/a, while annual value of each cooling energy varies within 2262 kWh/a and 4747 kWh/a; for the present-day climate sample, the average sum of the cooling energy is 1932 kWh/a while each annual cooling energy varies within 1376 kWh/ a and 3123 kWh/a.In this case, the increase in cooling load from the present-day climate to the 2080 SSP5-8.5 timeframe is 1161 kWh/a (60.1 %).Just like the case of Kano, in contrast to the cooling energy, the heating energy for the present-day climate is higher than SSP5-8.5 in Lagos.The average sum of heating energy in the SSP5-8.5, the values are zero.Conversely, the average sum of heating energy in the present-day climate for Lagos is 0.005 kWh/a, and each annual value of the heating energy varies from zero to 0.005 kWh/a.In summary, while there will be no heating requirement in SSP5-8.5 2080 in Lagos, there will be minimal heating needs in Kano during the cold and dry wind periods.Consequently, the difference between the samples' average sum of cooling energy in the extreme in Lagos and Kano is 481 kWh/a (18.4 %).

Morris elementary effects
To better understand the overall statistical relationship among the independent parameters, the construction elements are categorized to allow a clearer understanding of any thermal property that influences the cooling energy.The 29 parameters in this study are then categorized so that large colored points represent the active thermal properties, while small, grey-colored points represent the remaining inactive parameters.For a better understanding of the results in this section, it is recommended that the reader has a clear understanding of the statistical linear/monotonic and non-linear/non-monotonic relationships, as well as the definition of mean/absolute mean and standard deviation concerning influential/non-influential parameters and the second influence effect, as respectively described in Section 2.4.

Present-day climate.
In Fig. 9, under the roof category, solar absorptance appears to be the most influential thermophysical parameter.This means that a change in the solar absorptance value could lead to a variation of around 300 kWh/a in cooling.The solar absorptance further depicts a strong positive monotonic relationship.The next influential thermophysical parameter is the thermal conductivity, which is non-linear.The thermal capacity and density are also non-linear/nonmonotonic and have little influence compared to the solar absorptance.
Regarding the floor category, thermal conductivity stands out as the most influential parameter.It exhibits both monotonicity and linearity.However, there is a negative correlation (negative monotonicity) between thermal conductivity and cooling energy.This indicates that decreasing the thermal conductivity of the floor results in an increase in cooling energy since the ground functions as a heat sink due to its lower temperatures.This relationship explains the negative monotonicity and the significant impact of the floor on cooling energy.Furthermore, density and specific heat capacity are not influential under this category.
Under the north and south wall categories, virtually all the thermophysical parameters are non-influential, although the solar absorptance has a slightly monotonic relationship.Simultaneously, thermal conductivity, specific heat capacity, and density could be described as non-influential.
The thermal conductivity and solar absorptance follow a similar trajectory in the west and east wall categories.Solar absorptance leads, with thermal conductivity following suit in both categories.The primary distinction lies in the solar absorptance being nearly monotonic on the west wall and east wall, while thermal conductivity is nearly monotonic on the east wall, and both are non-linear on the west wall.Furthermore, thermal capacity and density function as non-linear parameters in both categories, with thermal capacity exerting a subtle influence.These nonlinear parameters indicate that alterations in their values will reduce cooling energy at certain points and increase it at others.
Finally, the SHGC appears to be slightly more influential than the thermal transmittance parameter for the east, west, and south window categories.The SHGC exhibits a strong monotonic trend in the east  window category but not in the south and west window categories.
3.3.1.2.Future scenario.Fig. 10 illustrates all the categories of construction elements and the influences of thermophysical properties from each element.Solar absorptance is the most influential parameter for the roof category, followed by thermal conductivity.Solar absorptance exhibits a strong monotonic and linear relationship, while thermal conductivity exhibits an almost monotonic behavior.Specific heat capacity and density are the least influential parameters and are non-linear.
Furthermore, regarding the influence of the thermophysical properties under the floor category in Fig. 10, thermal conductivity is the only influential but negatively monotonic parameter, signifying a very high absolute mean value (~750 kWh/a).Density and specific heat capacity are non-linear and could be considered non-influential.For the influences on cooling energy in the north, south, west, and east wall categories, the solar absorptance is ranked next to the thermal conductivity.This is opposite to the statistical dispersion in the roof category, where the solar absorptance is strongly monotonic and most influential.Lastly, while the SHGC is slightly influential and monotonic in the east window category, neither the SHGC nor the thermal transmittance significantly influences the south and west categories.

3.3.2.1.
Present-day climate.Fig. 11 illustrates the influences of thermophysical properties on cooling energy under different categories of elements in the present-day climate in Lagos.Solar absorptance is the most influential thermal parameter in the roof category, followed by thermal conductivity, specific heat capacity, and density.There is a slight technicality in the influence of thermal conductivity and specific heat capacity in the roof categories in the present day.By closely examining the graph in these two categories, it is evident that the absolute mean values of specific heat capacity and thermal conductivity are small (Table 3), but they hold some qualities of significance.For example, on the one hand, they possess a high standard deviation value, providing an advantage and allowing them to interact with other parameters to cause influence.On the other hand, their non-monotonicity adds complexity, making it challenging to understand their proportionate changes to cooling energy.This complexity is the reason why they may not be termed influential parameters.
Thermal conductivity is the most influential parameter for the floor category, while the others are non-influential.In the north and south wall categories, solar absorptance and thermal conductivity are slightly influential and exhibit some monotonic behavior.For the west category, the solar absorptance of the elements is the most influential, while in the east category, both solar absorptance and thermal conductivity share almost equal influences.They both show tendencies of monotonic behavior with cooling energy, albeit with a greater margin of influence in the east wall category than the west wall category (Fig. 11).Finally, in this section, the impacts of SHGC and window thermal transmittance behaviors on cooling energy are negligible across all elements' orientations.3.3.2.2.Future scenario.Fig. 12 depicts the elementary effects of the thermophysical properties of any construction element under SSP5-8.5 2080.In the roof category, solar absorptance and thermal conductivity are the most influential thermophysical properties, followed by the specific heat capacity and density, which are non-influential and nonlinear.It is important to clarify the seemingly contentious situation, where, in a few instances, the parameters in SSP5-8.5 show a lower proportion of the absolute mean value than those in a present-day climate.This partially occurs due to the lower intensity of solar radiation across several months, as discussed in Section 3.1.This results from higher relative humidity due to higher temperatures in the future (especially in Lagos with high dew point temperatures and relative humidity throughout the year), causing more saturation and evaporation accompanied by lower sky cover, leading to greater variations in the values of direct normal and diffuse radiations among the climates.These effects could decrease the absolute mean value of a parameter in the future since these thermophysical properties are heat-dependent from the atmosphere.
In the floor category, thermal conductivity is the influential parameter.Not all parameters have a significant impact for the north and south wall categories, while thermal conductivity and solar absorptance are the influential factors for the west and east walls.Finally, the SHGC and thermal transmittance of the windows do not exhibit any effect in all scenarios.

Significance of influential parameters
Compared to other global sensitivity analysis techniques, the Morris elementary effect provides absolute non-dimensionless values of u to the u * and σ, contributing to shifting the average cooling loads and causing variation, respectively.Among the several absolute mean values in Tables 3 and it would be more engaging to pay attention to the significance of parameters that lie around being monotonic, influential, and, most importantly, positively correlated to cooling energy.The simple reason for this is markedly due to their variations, which cause a corresponding change to any average cooling energy in the same direction, even though not at a constant rate (due to the monotonic effect).In that case, it is possible to explore the extent of the significance of these parameters on the average cooling energy values to gain further knowledge on whether these are worthy of optimization since the overall aim of sensitivity analyses is to know what elements to optimize.
Therefore, based on Fig. 13, we can see the proportions of the selected parameters (X) as they contribute relatively to the potential shift in the average cooling energy (CE) for all climate scenarios.Upon normalization of the proportions against their respective average cooling energy, the following contributions of the parameters causing this shift are observed: in Kano's present day, the roof solar absorptance (X 7 ) causes the biggest change of 19.8 %, and in the SSP5-8.5 2080 scenario, the east wall thermal conductivity (X 16 ) causes the highest change of 17.5 %.Similarly, in Lagos, X 7 causes a change of 13.9 %, and X 16 causes a 16.7 % change in the present day and SSP5-8.5 2080, respectively.Among the hundreds of parameters that influence cooling energy in buildings (regardless of thermal properties), it is fair to conclude that the percentages above of the influential parameters significantly impact the cooling loads in this study.
Furthermore, it is interesting to note that the percentages of significance of the influential thermal properties normalized with cooling energy are becoming less important in Kano but more important in Lagos as the climate becomes warmer.However, based on Fig. 13, the summation of influential parameters for a given average cooling load could still appear significant.It is impossible to add the proportions of these parameters to define an overall influence on any cooling load, as that could result in misleading conclusions.The reason behind this is practical.As can be seen, Table 3 shows that the parameters possess nonzero sigma values, declaring them as non-additive/non-independent since they could potentially interact with each other.Therefore, before reaching conclusions on whether they are more significant as they appear based on the percentages in Fig. 13 and/or whether the significance would decrease in the future under warmer periods, a future variance-based sensitivity analysis would help determine which parameters are paired in synergistic interactions (where the presence of one enhances the other) or antagonistic interactions (where the presence of one inhibits the other); and what the actual proportions are after the interactions.

Discussion
Relative to the elementary effects of Morris sensitivity analysis discussed above, the relationship between some thermal properties and cooling energy in this study has important similarities and differences compared to other studies (Table 4).For example, the thermal capacities of elements in the present and future in this study have a non-linear relationship with cooling energy (except for Lagos in the present day), similar to the studies in Brazilian climates found in Belém, São Paulo [6], and Florianópolis [7].Furthermore, the non-linearity of the thermal capacity in this work is associated with the extremely warmer climates of the study areas, which will become even more exacerbated in the future.In practical terms, this could mean that, in very warm climates, there is a strong diurnal temperature change.In other words, nighttime and daytime temperatures are significantly different.Therefore, during the daytime, when the temperature is very high, and as the thermal capacity of the element (thermal mass) is assumed to increase, it allows the gradual absorption of heat from the indoor space, cooling the indoor environment, thus leading to a decrease in cooling energy.However, because the thermal mass has absorbed heat during the daytime, it tends to release the heat back to the same space at night, causing an increase in cooling energy.This phenomenon results in non-linear behavior.Assuming that the thermal capacity of an element is the most influential parameter on cooling energy, professionals or policymakers may want to provide mechanisms to flush out the heat absorbed by the increased thermal mass element at nighttime, allowing the element to lose heat Fig. 11.Elementary effects of thermal properties on cooling energy under present-day climate in Lagos.[44].This may be achieved through its interaction with other design parameters (which is not within the scope of this study), thereby reducing cooling energy to counteract its non-linearity with cooling energy.
This study noted another important observation regarding the relationships between floor thermal conductivity and cooling energy.Compared to other thermal properties, the floor conductivity shows a high absolute mean value (Table 3); however, it negatively correlates with cooling energy.This is similar to other studies in less warm climates [6,7] where the floor U-values exhibit a negative trend in cooling energy and tend to increase in that trend.In warmer climates, the ground tends to be colder than the layers above compared to colder climates; therefore, decreasing the thermal conductivity of the floor (i.e., having a highly insulated floor) could prevent a portion of the trapped heat in the indoor space from being transferred to the ground, as the ground serves as a heat sink, thus increasing cooling energy.This suggests that focusing on decreasing the thermal conductivity of the floor is not crucial in warmer climates.
Additionally, there are other similarities in some thermal properties among studies.For example, positive monotonicity exists between cooling energy and thermal conductivities in the Kano and Lagos climate scenarios and the elements' U-value in the Belém climate scenarios.In contrast, non-linearity exists between cooling energy and elements' Uvalue in São Paulo climate scenarios [6].It is possible to compare the statistical trend of the thermal conductivities in this study and U-values in other studies on cooling energy since decreasing the values of both parameters decreases cooling energy.Again, the trend in the influence and monotonicity of solar absorptance of the roof on cooling energy in present-day Kano and Lagos is similar to the cooling energy in the Florianópolis climate in another study [7].Another interesting comparison is that in this study and other studies [6,7] with a small proportion of window-to-wall ratios (WWR), the SHGC and window U-value were non-influential on cooling energy; conversely, in the study [42] with a large proportion of WWR (70 %-80 %), the SHGC appeared most influential on cooling energy, and both window U-value and SHGC appeared most influential on heating energy [17,42].
Consequently, the statistical relationships of thermal properties in this study provide an inference to the hypothesis that thermal properties of elements can vary differently or similarly under various climates, construction, and building types.This implies that some similarities in design parameters may exist in regions with common climate features.However, significant differences are more prominent, suggesting that a sensitivity analysis is needed to explore specific design options.
This study presents three main limitations.First, the study only assumed abstract constructions, where the entire element's thermophysical properties were modeled as a single layer.This decision was made to prevent dependent variables from producing biased results in sensitivity analysis.However, this simplification overlooks the positioning of the insulation and thermal mass layers, which may impact energy performance.Therefore, other approaches like uncertainty analysis could be conducted to understand the complex uncertainties in positioning the construction elements' layers in the future.Second, a single small building prototype was used for analyses in both climates, implying that the findings of this study cannot be generalized for all buildings; other building typologies and sizes need to be investigated to minimize climate change's impact on the entire building stock.Finally, the morphing of typical meteorological years incorporates its limitations, such as introducing the effects of climate change independently between variables [45], underestimating the effects of climate change on coastal locations due to some of the location's cell points falling on the sea [46], and misrepresenting extreme weather events in duration and frequency [36].I. Tajuddeen and E. Rodrigues

Conclusion
This study compares the present-day and future cooling needs of two contending harsh climates in Nigeria.We used the Morris sensitivity analysis to capture the influences and the complex non-linear behavior of some thermal properties under elements' categories to understand areas that require urgent attention to mitigate the effect of climate change on cooling energy demand.Regarding the research questions at the beginning of this study, we confirmed that practitioners must account for the different thermal properties of elements in the face of climate change in tropical and subtropical regions and must not assume that elements in similar regions behave entirely the same.The results also confirmed that even the behavior of thermal properties of the same element under the same region can unpredictably vary either linearly or non-linearly relative to its orientations.Therefore, due to the potential climate change challenges that will worsen in the future, especially in extremely warmer climates in many tropical and subtropical regions, these findings have a broader impact with a high degree of confidence compared to similar warm climates worldwide.The methodology can be replicated in other regions to identify their peculiar sensitive parameters to combat climate change in the built environment.
The specific contributions of this study to existing findings in the literature are summarized as follows.
• Generally, building elements in regions with similar climates will behave similarly but differently regarding their thermal properties.This underscores the importance of exploring their sensitivity under various climate change scenarios.
• The results of this study suggest that the non-linearity and secondorder influence of elements' thermal capacity in most warm climates will increase in the future.• Our study identified a significant negative trend in floor thermal conductivity affecting cooling energy in extremely warm climates.This implies that in regions with slightly lower temperatures, where floor U-values currently show a milder negative trend, this pattern could amplify, resulting in a more pronounced negative effect on cooling energy.• For the future hot-dry climate (Kano), the cooling energy needs may be reduced by decreasing the thermal conductivities of the roof and east wall elements and decreasing the solar absorptance of the east wall element.• In the future hot-humid climate (Lagos), reducing the thermal conductivity and solar absorptance of the east wall and the roof's solar absorptance will decrease cooling energy needs.• In practical terms, the parameters considered influential in this study are important in the wide range of all parameters affecting overall cooling energy variation.• The warm climates in present-day Nigeria will become even warmer in the future.This increase in warmth will raise the cooling energy usage by 64.8 % and 60.1 % in Kano and Lagos, respectively, aligning with the existing trend.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Previous studies r = 12 -Nvent, envelope SAB, wall U-value [7] LSA r = 80 -Window area vent, roof SAB, Roof U-value [17] BBCC _ r = 8 -SHGC, wall SAB, OPF [43] SRC, Sobol _ r = 10 -Set point temperature, envelope U-value [40] Higher-order-analysis r = 10 -Set point temperature, building aspect ratio LSA: local sensitivity analysis, BBCC: building bioclimatic chart, SRC: standard regression coefficient, OPF: overhang projection factor.
I. Tajuddeen and E. Rodrigues

Fig. 2 .
Fig. 2. Nigerian Climate Zone Map according to ASHRAE 169 showing the two regions analyzed in this study.
• C and 32 • C, diffuse solar radiation varying between 114 Wh/m 2 to 270 Wh/m 2 and peak dew point temperature of about 21 • C. The dew point significantly drops to around 2 • C in the cold season; hence, very slight relative humidity values are expected.In comparison, Lagos has between 28 • C and 29 • C as the peak dry-bulb temperature during the dry season and more relatively stable dew temperature values across all the months, varying between 20 • C and 26 • C.This amounts to more humidity and underscores the reason for lower diffuse solar radiation varying between 95 Wh/m 2 and 190 Wh/ m 2 across all the months.

Fig. 5 .
Fig. 5. Comparison of present-day climate daily variables in (a) Kano and (b) Lagos.

Fig. 7 .
Fig. 7. Distribution of energy indicators for (a) present-day and (b) future climate in Lagos and (c) present-day and (d) future climate in Kano.

Fig. 9 .
Fig. 9. Elementary effects of thermal properties on cooling energy under present-day climate in Kano.

Table 1
Thermal properties of construction elements based on ASHRAE 189.1-Standard.

Table 3
Morris indices under different climate scenarios.

Table 4
Comparison of Morris sensitivity analysis of the present study and some recent studies in the literature.