Predictive model of surface temperature difference between green façades and uncovered wall in Mediterranean climatic area

Applied Thermal Engineering 163 (2019) 114406

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Predictive model of surface temperature difference between green façades and uncovered wall in Mediterranean climatic area

T

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Ileana Blanco, Evelia Schettini , Giuliano Vox Department of Agricultural and Environmental Science DISAAT – University of Bari, Bari, Italy

H I GH L IG H T S

G R A P H I C A L A B S T R A C T

green façades show lower surface • The temperature than the control wall. multiple linear regression is devel• Aoped to simulate thermal behaviour. regression is based on the climate • The conditions parameters. tool for the thermal ben• Aefitsprediction of the two green façades is provided.

A R T I C LE I N FO

A B S T R A C T

Keywords: Multiple linear regression analysis Pandorea jasminoides Rhyncospermum jasminoides Cooling effect Urban agriculture Building thermal performance

The thermal potential of vertical greenery systems in buildings can be fully explored through modelling. Models support designers in choosing between different technical solutions. This study analyses the cooling effect of two plants suitable for the Mediterranean area. A regression model simulating the difference of the wall external surface temperature between the wall covered with vegetation and an uncovered wall was developed. In order to overcome the gaps in literature, the model was fitted and validated on long period experimental data. It was based only on the use of climatic conditions as input variables, without making assumptions about the plants. Climatic data were grouped in solar radiation slots; the most significant predictors were selected for each slot. The adoption of this method allowed to obtain, during validation, coefficients of determination (R2) higher than 0.95 and low values of the root mean square error (0.4–0.6 °C). It was found that the vegetated walls recorded surface temperatures lower than the uncovered wall up to 7.7 °C in summertime. The results showed that the model developed with a statistical approach can efficiently be used for simulating the thermal effects of a green façade in a similar Mediterranean climate.

1. Introduction Nowadays the diffusion of the greening technology for more sustainable buildings is encouraged by the worldwide growing interest in urban green [1–3]. Urban Green Infrastructures (UGIs) are sets of manmade elements whose performance is influenced by built environment, climate conditions of the area and used plants [4,5]. Public and private

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green open spaces, planned and unplanned, such as remaining native vegetation, parks, gardens, street trees, sporting fields, golf courses, are classified as UGIs. Moreover, also engineered options such as greenery systems in a building as green roofs, green balconies, sky gardens, indoor sky gardens and vertical greening are UGIs [4,6–10]. The thermal effect of greenery systems on the microclimate of buildings is related to the climate conditions of the area, i.e. solar

Corresponding author. E-mail addresses: [email protected] (I. Blanco), [email protected] (E. Schettini), [email protected] (G. Vox).

https://doi.org/10.1016/j.applthermaleng.2019.114406 Received 18 February 2019; Received in revised form 10 June 2019; Accepted 16 September 2019 Available online 18 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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components that interact with the environmental conditions in a complex way and the energy balance in vertical greenery systems is related to many variables [35,36]. Thermal exchanges between the internal ambient, the building walls, the greenery components and the external ambient have to be evaluated [37]. The radiative, latent and convective heat transfer have to be considered together with the reduction of the solar radiation on the wall shielded by the vegetation. Some authors proposed models based on the electric-thermal analogy [38,39]. The evapotranspiration process requires special attention in thermal simulation models and the Penmann–Monteith equation was often used for quantifying the latent heat transfer [36,38–40]. Some models are based on a simplified quantification of evapotranspiration rate [41,42], others on the experimental definition of the transmissivity of the green layer [38]. In recent years, some research studies were aimed to develop thermal response models coupled with building energy simulation tools, validated against experimental data [43,44]. Most detailed models have made assumptions about different parameters [45]. Overall, models on vertical greenery systems which were developed with engineering methods are still scarce because of the complexity and because they need buildings detailed characteristics and thermal and physical properties of the green layer. Information such as leaf area index (LAI), solar reflectivity, transmissivity and absorptivity, stomatal resistance and aerodynamic resistance, coverage or view factors must be provided [44,45]. Conversely, statistical methods use large amount of measured data; they can have a satisfactory forecasting performance but they are not so complex to apply [6,46,47]. The temperature in the microclimatic layer of a green façade has been modelled by multi-parametric linear regression using experimental data on the solar radiation and on the ambient temperature [48]. The effect of an indirect green façade on the inlet air temperature of the ventilation system was modelled with a multi-parametric linear regression using the wind velocity, the relative humidity and the global solar radiation as independent variables [49]. Olivieri et al. [50] have expressed the need to use the statistical method for developing a performance predictive model of a vegetal façade based on the outdoor air temperature, relative humidity and horizontal solar radiation. Statistical models fitted on experimental data and using only climatic conditions as input variables bypass the necessity of providing specific data on the vegetation or of making assumptions on them. However, there is a lack of statistical models based on data relating to long periods of experimentation on different types of greenery systems. In this research, the systems under investigation, which allow greening a vertical surface, are two green façades [51–55]. Aim of the paper is to overcome the lack of data in literature by developing a statistical predictive model of the thermal performance in summer (from June to August) of two façades specially designed to be suitable in Mediterranean climate. They were made using evergreen climbing plants directly rooted in the ground. The plants climb on a structural support located at a small distance from the wall. The thermal performance of the green façades in summertime, period characterised by the highest external air temperature values, was analysed through the evaluation of the external surface temperature of the covered vertical walls in comparison to the uncovered control wall. A multiple linear regression model was built based on the data gathered during summer 2015. The regression model was validated with the data collected during summer 2016. Since vegetation layers interact with the environmental conditions in a complicated way, the influence of all the main climatic parameters of a site has been taken into consideration: temperature and relative humidity of the external air, wind speed and direction, solar radiation incident on a horizontal plane and on the vertical surface. It was not chosen in advance a restricted set of predictor variables. Climatic data were grouped in five solar radiation slots and for each slot the most useful predictors were filtered and their influence was defined. The application of this method facilitated the interpretation of the predictive models and led to better prediction

radiation, air temperature and relative humidity, wind velocity and direction. Besides, the vegetation type, plant position, plant height, coverage ratio, leaf area index (LAI), foliage (orientation, dimension, thickness and density), radiometric characteristics of the leaves (emissivity, reflectivity, absorptance and transmissivity), plant’s biological processes (photosynthesis, respiration and transpiration), and the growing medium (thickness, water content and density, substrate thermal properties) affect the thermal behaviour of the vegetation. The building itself and the surrounding built environment influence the thermal behaviour of UGI. Building characteristics, such as roof and wall construction materials, dimension, wall orientation and insulation level, and building indoor usage must be considered. The presence of UGIs will provide environmental benefits at building and urban scale [4,11]. UGIs contribute to improve urban climate reducing urban air temperature, extreme air and wall temperature values and thermal excursions on the building surface [7,12–15]. Urban greening can supply several ecosystem services such as improving aesthetically the place to live and work, removing airborne pollutants and improving air quality, enhancing storm-water management and water run-off quality, providing sound insulation and noise absorption [2,8,16,17]. UGIs improve the habitat for invertebrates, birds, weeds and plants promoting and increasing biodiversity. Moreover, UGIs mitigate the frequency and magnitude of the heat events due to urban heat island [18,19], reduce the ambient temperatures, improve human thermal comfort and decrease energy loads on building [7,8,11]. Nevertheless, in general, UGIs are one of the solutions that can be applied for positively influencing the urban heat island and for reducing the buildings’ demand for cooling energy. The most appropriate strategy should be assessed on a case-by-case basis also by considering the potentialities of different building types and high reflectivity materials and pavements surfaces [20,21]. The application of greening systems to the building envelope allows the improvement of the thermal performance of the building. Improving envelope energy performance is a suitable solution to increase energy saving [22,23]. Vertical surfaces of buildings constitute part of the building envelope that strongly condition the microclimate inside the building. Many experimental studies have been conducted on prototypes or real-scale constructions but they mainly concern short summer periods [11,24–26]. The performance of the greenery systems in cold months has been less investigated and it requires further investigations [11,27,28]. Data of tests carried out in real conditions are generally collected in short time making difficult the evaluation of the greening system performance and its extrapolation to other periods and climatic conditions. Another problem for the understanding of the scientific results is that some studies reported the maximum effect on temperature variations while other researchers reported the average temperature variations [29]. The most commonly reported parameter in estimating the thermal performance of green vertical systems is the wall external surface temperature. Comparisons between studies on surface temperature do not allow a complete evaluation of the thermal performance, because of the peculiarities in building construction properties [30]. Nevertheless, its analysis is useful in studying the effects produced by changing one parameter of the designed configuration; it allows comparing technical solutions having different plant species, water supplies and climate conditions. Solutions with different thickness of the air-gap created between the green layer and the wall, as in the case of indirect green façades, could also be analysed. Various models have been developed to fully explore the thermal potential of vertical greenery systems in buildings. Thermal response models were often not validated with real data [4,11,30]. The most of thermal simulation models on vertical greenery systems are based on the application of engineering methods [31]. The simplest way to analyse the thermal effect of vertical greenery systems is to focus only on their shading effect [32–34]. However, vegetative layers are living 2

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results. The developed statistical predictive model is useful for simulating the results of the application of the two green façades in a similar Mediterranean climate, using as input data only the climatic conditions. 2. Materials and methods 2.1. Experimental test The test took place at the experimental centre of the University of Bari in Valenzano (Bari), Italy, having latitude 41°05′N, longitude 16°53′E, altitude 85 m asl. The Mediterranean climate is a temperate climate, classified as Csa according to the Köppen-Geiger climate classification [56]. This climate has hot and dry summers, rainy winters and a solar radiation intensity that varies greatly with seasons. In order to simulate a vertical closure for civil buildings commonly used in the Mediterranean area, a vertical wall with perforated bricks joined with mortar was designed and realized. The total thickness of the masonry was 0.22 m. It was composed of a layer of bricks, 0.20 m thick, and a layer of plaster, 0.02 m thick, having a total thermal resistance R of 0.75 m2 K W−1 (following UNI EN 1745:2012 [57]). The masonry was characterised by a solar absorption coefficient (αs) equal to 42.1% and a long wave infrared emissivity coefficient (εLWIR) equal to 95.3%. Three wall prototypes in scale, each having a width of 1.00 m and a height equal to 1.55 m, were made facing south. On the backside of each wall, a sealed insulation structure was realized with sheets of expanded polystyrene. Each sheet of expanded polystyrene had a thickness of 0.03 m and R-value equal to 1.2 m2 K W−1. The presence of the insulating structure allowed evaluating only the thermal behaviour of the wall due to the plants and to the incident solar radiation. A blue shading net was placed onto the back structure to reduce the effect of the incident solar radiation. The walls were located in a wide open space with no shadow on the vertical surfaces deriving from external obstacles. The reciprocal shading between the three walls was negligible as it occurred only in short periods of time. The shading occurred when the solar radiation measured on a horizontal plane was low (Ihor < 200 W m−2). In this condition, the vegetation layers were not able to promote any thermal effect on the walls. Two walls were covered with vigorous evergreen climbing plants: one wall with Pandorea jasminoides variegated, the second with Rhyncospermum jasminoides. The third wall, used as control, was left uncovered. These plants have been selected for their remarkable propensity to grow by climbing on the wall, their vigorous growth and rapid development, and their excellent adaptation to the climatic conditions of the experimental area. The plants were transplanted on 18 June 2014. An iron net was placed 0.15 m far from the wall in order to provide a support for the climbing plants (Fig. 1). The drip irrigation method was used for all the plants and fertilization with N, P and K was performed.

Fig. 1. The experimental walls; the right one is greened with Rhyncospermum jasminoides, the central one with Pandorea jasminoides variegated and the left one is the control wall (uncovered).

of ± 0.15 °C (Tecno.EL s.r.l. Formello, Rome, Italy). Solar radiation in the wavelength range 0.3–3 μm both normal to the wall and on a horizontal plane was measured by means of pyranometers with an accuracy of 10 W m−2 (model 8–48, Eppley Laboratory, Newport, RI, USA). Wind speed and direction were measured by a Young Wind Sentry anemometer with an accuracy of 0.5 ms−1 and of ± 5°, respectively (Young Company, Traverse City, MI, U.S.A). The climatic parameters were measured throughout the experimental test with a frequency of 60 s; their average values were calculated every 15 min and recorded by a data logger (CR10X, Campbell, Logan, USA). Plant Leaf Surface Index (LAI) measurements were taken with an AccuPAR PAR/LAI Ceptometer (model LP-80, Decagon Devices Inc., Pullman, WA, USA). LAI varies throughout the year from 2 to 4 for Rhyncospermum jasminoides, and from 1.5 to 3.5 for Pandorea jasminoides variegated. These values ranged from a minimum to a maximum, due to a modest loss of foliage in winter, although the plants were evergreen. Analysis of variance (ANOVA) was performed by using CoStat software (CoHort Software, Monterey, CA, USA). 2.3. Climate conditions of the experimental field during 2013–2015 A preliminary study of the climate parameters of the site was carried out. The study was realized in order to define the experimental conditions. In the period January 2013 – December 2015, the external air temperature values, at the experimental field, ranged from −1.4 °C to 41.4 °C. The yearly cumulative solar radiation on a horizontal plane varied in the range 4891–5327 MJ m−2. The monthly value of cumulative solar radiation on a horizontal plane varied from 143 MJ m−2, recorded in January 2014, to 802 MJ m−2, recorded in July 2015. The annual cumulative solar radiation on the south facing vertical wall varied in the range 3515–3759 MJ m−2; the monthly value ranged from 209 MJ m−2 (January 2014) to 397 MJ m−2 (September 2013).

2.2. Data acquisition Temperature and relative humidity of the external air, wind speed and direction, surface temperature of the wall on the external plaster exposed to the solar radiation, solar radiation on a horizontal plane and solar radiation incident on the vertical surface were acquired during the test. The solar radiation on a horizontal plane is a reference parameter useful for comparing the climate of different areas. Solar radiation on the vertical wall is the portion of solar radiation incident on the south facing green façades. External air temperature and relative humidity were measured by a Hygroclip-S3 sensor with an accuracy of ± 0.1 °C and ± 0.8%, respectively (Rotronic, Zurich, Switzerland). It was adequately shielded from solar radiation. Temperature of the plaster surfaces exposed to solar radiation was measured using thermistors having an accuracy

2.4. Multiple linear regression analysis Data can be statistically analysed and modelled by means of a statistical regression analysis. Regression analysis is a methodology to investigate the functional equation between a dependent variable or response and the variables that influence the response, known as independent or predictor or influence variables [46,47]. In relation to the 3

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variables; k is the number of regression coefficients; yi are the observed n data, y¯ is the mean value of yi, ∑i = 1 (yi − yi )̂ 2 is the sum of squared n 2 errors and ∑i = 1 (yi − y ) is the total sum of squares. The R2 is a measure of how much variation of the response variable is explained by every predictive variables dataset at time t. It represents the percentage of variability in the independent variable that is explained when considering as if all predictor variables in the model affect the response variable. A high value of the R2 means that the predictors account for a great amount of variability in the independent variable. The coefficient of determination R2 ranges between 0 and 1. When R2 is close to 1 then most of the variation of the observed values can be explained by the model [58]. Even with a high value of R2, a more detailed analysis is needed to ensure that the model can be used to describe the observed data and to predict the response for another set of data different from the one used to generate the model [47]. The Radj2 indicates how well terms fit a curve or line, but it is adjusted for the number of terms in a model. The Radj2 gives the percentage of variability explained by only those predictor variables that really affect the response variable. Adding more useless variables to a model, the Radj2 will decrease. Adding more useful variables, the Radj2 will increase. The Radj2 will always be less than or equal to the R2 for large datasets. Radj2 can be positive or negative. The RMSE is a standard statistical metric that measures the scatter in the data around the model. It indicates how concentrated the data is around the line of best fit; it measures how accurately the model predicts the response. The RMSE is the most important criterion for fit if the main purpose of the model is prediction and for describing uncertainty. The smaller RSME the better is the model’s performance [58]. A small RMSE implies that the sample is accurate and precise. Meteorological and surface temperature data recorded during summer 2015 at the experimental field were analysed and a multiple linear regression model was fitted on 2015 data. The model estimates the difference between the external surface temperature of the control wall and of the green façade. Then the model was used to predict the behaviour of the green façade during summer 2016. The validation of the model was done by comparing the data observed during summer 2016 and the data predicted with the model. The predicted data (ŷtp) were obtained by Eq. (1), using the predictor variables measured in 2016. The regression parameters where obtained with the data recorded in 2015.

number of predictor variables, simple linear regression has only one predictor variable while multiple linear regression has more than one predictor variable. The univariate linear regression analysis models the connection among variables by fitting a linear equation to the data. The linear fitting of multiple linear regression analysis is attempted by keeping constant all but one of the predictor variables [47]. Regression models are influenced by number of input parameters, kind of data, time interval, forecasting temporal horizon [46]. In this paper the multiple linear regression technique was used to forecast and model time series. The response variable that was analysed is the difference between the external surface temperature of the control wall and the surface temperature of the wall covered by the plant. The response variable at time t is coded as yt. The external climate conditions were used as predictors variables: external air temperature and relative humidity, horizontal and vertical solar radiation, wind velocity and direction. The multiple linear autoregressive model used in this research is:

yt = β0 + β1 yt − 1 + β2 x1, t + β3 x2, t + β4 x3, t + β5 x 4, t + β6 x5, t + β7 x 6, t + εt (1) where: the response variable yt is the difference between the external surface temperature of the control wall and of the green façade at time t; t = 1, …, n (n = 8832), with a time sample of 900 s, extends from June to August 2015. The predictor variable yt-1 is the difference between the external surface temperature of the control wall and of the green façade at time t-1; xj,t are the weather predictor variables at time t, with j = 1, … , 6. The value j = 1 refers to the external air temperature, j = 2 to the horizontal solar radiation, j = 3 to the external air relative humidity, j = 4 to the wind velocity, j = 5 to the wind direction and j = 6 to the vertical solar radiation. βl, with l = 0, …, 7, are the regression parameters of the model; β0 is the intercept. εt is the error standing for the difference between the predicted data and the observed data. The weather predictor variables at time t-1 were evaluated through correlation analysis. They were excluded due to the high correlation with the value at time t. The objective of the regression model was to minimize the sum of squared errors by varying the coefficient βl. The Regression Tool in Excel’s Data Analysis add-in was used to obtain the estimated regression parameters (βl ) with the Least Squares Method. The backward selection method was used for selecting the variables in the regression model. All the candidate variables were initially used in the model. Subsequently, the least significant variable was removed at each step, until only significant variables remained. The fitted values (ŷt) were obtained by using the βl values in Eq. (1). The error (εt) is the difference between the observed data (yt) and the fitted data (ŷt):

yt = y^t + εt

3. Results and discussion 3.1. The measured wall temperature The monthly values of the external surface temperature recorded on the uncovered control wall during 2016 are shown in Fig. 2 by multiple box-plots [59]. The median ranged from 7.1 °C to 25.5 °C. Ignoring the outlier values, maximum values were recorded around 41.1 °C and minimum values close to −0.6 °C. Concerning the warmest period in the summer 2016, from June to August, the external surface temperatures recorded on the control wall were characterized by a high variability and the median was in the range 22.3–25.5 °C. The period from June to August recorded surface temperature peaks on the control wall over 37.8 °C, neglecting the outlier values. The other warm months were characterised by maximum values of about 31.8–32.8 °C. Thus, the mitigation of the wall surface temperature due to the presence of the plants was analysed for June, July and August when the cooling effect is expected to be more effective. A value of the horizontal solar radiation of 200 W m−2 was found by Vox et al. [60] as a threshold value for arousing a cooling effect by the green façades on the wall external surfaces. One-way ANOVA analyses at a 95% probability level were carried out for every month of the analysed period with the aim of comparing the average values. Duncan's test was applied with a significance level

(2)

The fitted values were obtained considering, for the set of predictor variables, one of the n observations. Three parameters can be used to measure the quality of the fitting of the multiple linear regression model: the coefficient of determination (R2), the adjusted coefficient of determination (Radj2) and the rootmean-square error (RMSE). In this research, these parameters for the model proposed are defined as: n

R2 = 1 −

∑i = 1 (yi − yi )̂ 2 n

∑i = 1 (yi − y )2

2 Radj = 1 − (1 − R2)

n−1 n−p−1

(3)

(4)

n

RMSE =

∑i = 1 (yi − yi )̂ 2 n−k

(5)

where n is the number of observations; p is the total number of the 4

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Fig. 2. External surface temperature of the control wall during 2016.

Table 1 Monthly average of the daily maximum difference value between the surface temperature recorded on the control wall and on the green walls; average daytime temperature variation with solar radiation on a horizontal surface higher than 200 W m−2. Data recorded in 2016.

Rhyncospermum jasminoides Pandorea jasminoides variegated Control wall

Average of the maximum reduction of the covered walls surface temperature versus the control wall (°C)

Average variation of the wall external surface temperature during daytime; solar radiation on a horizontal surface ≥ 200 W m−2 (°C)

June

June

a

July a

August a

b

July c

August

5.1 5.1a

5.8 5.6a

5.9 5.5a

7.1 8.1b

7.9 9.1b

6.7b 7.9b

–

–

–

12.4a

14.1a

12.9a

a–c

Average values of the temperature in a column (i.e. for a specific month) with a different superscript letter statistically differ at P < 0.05 using Duncan’s test.

Table 2 Maximum difference value between the surface temperature recorded on the control wall and the surface temperature recorded on the green walls; maximum daytime temperature variation considering solar radiation on a horizontal surface higher than 200 W m−2. Data recorded in 2016.

Rhyncospermum jasminoides Pandorea jasminoides variegated Control wall

Maximum reduction of wall external surface temperature versus control wall (°C)

Maximum range of wall external surface temperature during daytime; solar radiation on a horizontal surface ≥ 200 W m−2 (°C)

June

July

August

June

July

August

6.5 6.6

7.0 6.7

7.7 7.7

10.9 12.3

10.4 12.0

11.8 13.4

17.5

16.9

18.4

wall external surface temperature (Table 1). It was calculated as the difference between the highest temperature and the lowest temperature registered each day during daytime, when solar radiation on a horizontal surface was higher than 200 W m−2. In June and August no significant difference was reported between the two plants for the temperature variation. During July, that was the hottest month,

equal of 0.05. Table 1 shows the monthly average of the daily maximum difference between the surface temperature recorded on the reference wall and the surface temperature recorded on the green walls in 2016. No significant difference was recorded between the two plants. Significant differences were recorded between the green walls and the control wall for the monthly average of the daily variation of the 5

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control wall rose almost in synch with the solar radiation values in a more accentuated way than the temperature of the external side of the walls screened by the plants. During the daytime, with the solar radiation on a horizontal surface higher than 200 W m−2, the external surface of the control wall was characterized by temperature values always higher than the ones regarding the wall external surface of the green façades. The green layer induced the mitigation of the temperature of the walls external plaster. The wall surface temperature of the green façades reached the maximum value always at least 1 h later than when the maximum value of the wall surface temperature of the control wall was recorded. The thermal insulation effect of the green façades was registered during night, but this behaviour is not desirable in summer. After sunset and at nighttime, the temperatures on the external wall of the green façades started to rise above those on the control wall with a maximum difference of 2.0 °C. The air-gap temperatures always followed the hourly evolution of the external ambient air temperature (Figs. 3–5). The air-gap temperatures often remained below the external ambient air temperature mainly for Rhyncospermum jasminoides. It is in agreement with the findings of Chen et al. [24] and Pérez et al. [62], which assessed the ability of the green façades to create a behind-green layer microclimate, characterized by lower air temperature than the external one during daytime in summer sunny days.

Rhyncospermum jasminoides showed the lowest temperature variation (7.9 °C). This value was statistically different from the variation recorded both for the wall covered with Pandorea jasminoides variegated and for the control wall. In August, the following maximum daytime temperature variation were recorded: 11.8 °C for Rhyncospermum jasminoides, 13.4 °C for Pandorea jasminoides variegated and 18.4 °C for the control wall (Table 2). The variations were evaluated when solar radiation on a horizontal surface was higher than 200 W m−2. The highest maximum reduction value between the surface temperature measured on the control wall and on the green wall was recorded in August: 7.7 °C for both Rhyncospermum jasminoides and Pandorea jasminoides variegated (Table 2). During a summer month in Thessaloniki’s climatic conditions, characterised by warm temperate humid climate, Eumorfopoulou and Kontoleon [61] reported that the maximum temperature reduction of the exterior surface of a plant-covered east-facing wall varied in the range 1.9–8.3 °C, with an average of 5.7 °C. Pérez et al. [11] assessed a reduction from 1.7 °C to 13.0 °C of the external surface temperature of a wall covered with traditional green façades during summertime in a warm temperate climate region. Susorova et al. [25] reported that the presence of vegetation on the façade in a hot summer continental climate caused an average decrease of the temperatures, on brick infills external surface, from 1.0 °C to 9.0 °C during summer. The daily thermal behaviour of the walls is shown in Figs. 3–5. One day for month was chosen: two typical sunny days (Figs. 3 and 5) and one cloudy day (Fig. 4). The temperature of the external air, of the surface of the external side of the three walls exposed to solar radiation, of the air gap between the vegetation and the wall, and the solar radiation on a horizontal plane are shown. In the morning, the temperature of the external surface of the

3.2. Regression analysis results The regression model estimated the difference of temperature between the control wall without vegetation and the green wall at time t. It was built based on the data measured in the period June-August 2015 at the experimental field.

Fig. 3. External surface temperature of the three walls, air gap temperature between the vegetation and the wall, external air temperature and solar radiation on a horizontal plane for a sunny day, 18/06/2016. 6

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Fig. 4. External surface temperature of the three walls, air gap temperature between the vegetation and the wall, external air temperature and solar radiation on a horizontal plane for a cloudy day, 17/07/2016.

radiation); unlike β3 , β7 is always significant for every Ihor. The dependency on the external air relative humidity variable is highlighted by the coefficient β4 . The positive values for β4 mean that the higher the humidity, the greater the dependent variable ŷt. The dependency on the wind velocity variable is highlighted by the coefficient β5 while on the wind direction by the coefficient β6 . As expected, the lowest dependence of the wind velocity variable results for Ihor < 200 W m−2, from sunset to sunrise when the wind has generally calmed down compared to other hours of the day. Tables 4 and 5 also show the parameters of quality analysis. It can be noted that the coefficients R2 and Radj2 are very high, with values higher than 0.94, for all the radiation slots and for both the green walls. R2 and Radj2 show the goodness of the fit by the trained models. In this case, they have similar values due to the large datasets being used. The RMSE values indicate that the scattering around the model is low. The predictive statistical models described by Olivieri et al. [50] concern a green façade covered with sedum and a wall characterised by metal finish; they are characterized by values of R2 varying between 0.63 and 0.87. The multi-parametric linear regression model of the temperature in the microclimatic layer of an indirect green façade proposed by Suklje et al. [48] was characterized by a value of R2 equal to 0.86. A multiple regression model becomes more effective by adding a significant variable to it, while the addition of an unimportant variable can make the model worse. Thus, in order to analyse the importance of the individual regression coefficients, the Student t test was applied. The t-value represents the test statistic for the Student t test. The tvalues test the hypothesis that the coefficient is different from 0. The

Due to the great amount of heterogeneous data and to the variable thermal performance of the green walls through the different hours of the day, the observed data related to summer 2015 were grouped in 5 solar radiation slots. They were characterized by intervals of solar radiation on a horizontal surface (Ihor) as shown in Table 3. A regression model for each green wall and for each Ihor was developed. The predictor variable yt-1 is the previous value that was measured for yt. Regression coefficients and quality parameters of the models are shown in Tables 4 and 5. A regression coefficient βl measures the partial effect of the predictor variable xj,t on ŷt holding the other predictor variables fixed. This interpretation is not valid, of course, for the intercept β0 . The value of the coefficients βl is characterised by measurement unit, thus these coefficients cannot be compared to each other. Therefore, the coefficients βl cannot be assumed as indicators of the importance of the predictor variable in the explanation of the variability of ŷt. When a coefficient βl is not provided, it means that the influence of the related predictor weather variable on the difference of temperature between the control wall without vegetation and the green wall is not statistically significant at a 99.9% probability level. The coefficient related to the external air temperature predictor variable (β2 ) is significant for every Ihor except Ihor 600-800 for the green wall covered with Rhyncospermum jasminoides. The positive values for β2 mean that the higher the external air temperature, the greater the difference of temperature between the control wall without vegetation and the green wall. The coefficients that explain the dependency of the solar radiation variable are β3 (horizontal solar radiation) and β7 (vertical solar 7

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Fig. 5. External surface temperature of the three walls, air gap temperature between the vegetation and the wall, external air temperature and solar radiation on a horizontal plane for a sunny day, 28/08/2016.

value of ŷt-1 equal to the average of yt for summer 2015. yt are shown in Figs. 6 and 7 for a long Measured yt and calculated  period of clear sky. As shown in Fig. 6, the maximum difference between the external surface temperature of the control wall and of the green wall covered with Pandorea jasminoides variegated was 6.1 °C and 5.9 °C for the simulated values and the measured values, respectively. The highest negative difference between the external surface temperature of the control wall and of the green wall was −1.8 °C and −2.3 °C for the simulated values and the measured values, respectively. Concerning the Rhyncospermum jasminoides (Fig. 7), the maximum difference between the external surface temperature of the control wall and the green wall was 6.0 °C and 6.8 °C in the case of the simulated values and of the measured values, respectively. The highest negative difference between the external surface temperature of the control wall and of the green wall was −1.6 °C and −1.8 °C for the simulated values and the measured values, respectively. Fig. 8 shows the correlation analyses for the simulated results and experimental results. The coefficients of determination (R2) were 0.95 and 0.98 for the wall covered with Pandorea jasminoides variegated and for the one covered with Rhyncospermum jasminoides, respectively. For both cases, the determination coefficients show a good agreement between the simulated results and the experimental results because they are approaching 1. For the wall covered with Pandorea jasminoides variegated, the simulated and experimental data deviate by maximum 2.1 °C. The average absolute difference and the standard deviation between the numerical predictions and the experimental measurements were both

Table 3 Solar Radiation slots used in the regression model. Solar Radiation on a horizontal surface Ihor Ihor Ihor Ihor Ihor

200 200-400 400-600 600-800 800

Ihor < 200 W m−2 200 ≤ Ihor < 400 W m−2 400 ≤ Ihor < 600 W m−2 600 ≤ Ihor < 800 W m−2 Ihor ≥ 800 W m−2

coefficient with the highest t-value identifies the most important variable. The t-values connected to the individual regression coefficients are presented in Tables 6 and 7. In both green façades the coefficients related to the variable vertical solar radiation x6,t show high t-values. Thus x6,t confirms to be the parameter with the greatest influence on the dependent variable, particularly for Ihor > 400 W m−2, in addition to yt-1, as expected. 3.3. Use of the predictive model in the case study The predictive model was calibrated using the data recorded during summer 2015. The model was used to simulate the difference between the surface temperatures of the walls during summer 2016. External air temperature and relative humidity, solar radiation, wind velocity and direction were used as model input. In the predictions, the response variable in the previous time period ŷt-1 becomes one of the predictor variables for calculating ŷt. The procedure starts by using as input a 8

Ihor Ihor Ihor Ihor Ihor

800

600-800

400-600

200-400

200

−0.368 −0.443 −0.549 −0.249 −0.626

β0

0.002 0.006 0.009 – 0.009

– – – 0.0003 0.0004

External solar radiation horizontal

External Air Temperature

Difference between the external surface temperature of the control wall and of the green façade at time t-1 0.899 0.907 0.917 0.917 0.911

x2,t

β3

x1,t

β2

yt-1

β1

0.002 0.001 0.003 0.002 0.003

External Air relative Humidity

x3,t

β4

0.010 – – −0.055 −0.051

Wind Velocity

x4,t

β5

9

Slot of solar radiation

Ihor Ihor Ihor Ihor Ihor

800

600-800

400-600

200-400

200

0.890 0.804 0.862 0.870 0.884

Difference between the external surface temperature of the control wall and of the green façade at time t-1

Weather predictors variables

β1

yt-1

−0.486 −0.560 −0.904 −0.496 −0.642

β0

Predictor variable to whom the regression coefficient is related

Quality model parameters

Estimated Regression coefficient

−0.001 -

External solar radiation horizontal

External Air Temperature

0.004 0.014 0.021 0.013 0.015

x2,t

β3

x1,t

β2

0.002 0.004 -

External Air relative Humidity

x3,t

β4

0.011 −0.041 −0.064 −0.065

Wind Velocity

x4,t

β5

Table 5 Estimated regression coefficients and quality model parameters for the green wall covered with Pandorea jasminoides variegated, for the summer period 2015.

Slot of solar radiation

Quality model parameters Predictor variable to whom the regression coefficient is related Weather predictors variables

Estimated Regression coefficient

Table 4 Estimated regression coefficients and quality model parameters for the green wall covered with Rhyncospermum jasminoides, for the summer period 2015.

0.0004 −0.0004

Wind Direction

x5,t

β6

0.0002 0.0003 – – −0.0007

Wind Direction

x5,t

β6

0.002 0.004 0.002 0.002 0.003

External solar radiation vertical

x6,t

β7

0.002 0.001 0.001 0.001 0.002

External solar radiation vertical

x6,t

β7

0.94 0.96 0.97 0.99 0.99

R2

0.99 0.99 1.00 1.00 0.99

R2

0.94 0.96 0.97 0.99 0.99

Radj2

0.99 0.99 1.00 1.00 0.99

Radj2

0.14 0.20 0.21 0.15 0.15

RMSE

0.06 0.11 0.11 0.12 0.13

RMSE

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Table 6 t-values for the estimated regression coefficients for the green wall covered with Rhyncospermum jasminoides, for the summer period 2015. t values Estimated Regression coefficient

β0

β1 yt-1

β2 x1,t

β3 x2,t

β4 x3,t

β5 x4,t

β6 x5,t

β7 x6,t

−26.336 −6.698 −9.322 −7.983 −8.408

466.193 191.256 371.770 425.351 292.250

4.655 3.406 5.651 5.889

9.372 10.905

23.691 3.708 6.336 4.849 6.399

10.345 −12.657 −11.038

11.364 4.382 −8.080

24.935 6.734 18.851 26.254 26.379

Predictor variable to whom the regression coefficient is related Slot of solar radiation

Ihor Ihor Ihor Ihor Ihor

200 200-400 400-600 600-800 800

Table 7 t-values for the estimated regression coefficients for the green wall covered with Pandorea jasminoides variegated, for the summer period 2015. t values Estimated Regression coefficient

β0

β1 yt-1

β2 x1,t

β3 x2,t

β4 x3,t

β5 x4,t

β6 x5,t

β7 x6,t

−13.521 −6.977 −6.761 −10.072 −11.774

178.666 85.741 115.316 256.513 228.438

4.761 4.978 6.138 8.827 9.376

– −7.116 – – –

10.545 – 5.220 – –

4.734 – −5.317 −12.855 −12.434

10.236 – – – −4.573

12.177 10.472 15.423 48.355 46.329

Predictor variable to whom the regression coefficient is related Slot of solar radiation

Ihor Ihor Ihor Ihor Ihor

200 200-400 400-600 600-800 800

Fig. 6. Comparison between the model output (predicted values) and measured values for the wall covered with Pandorea jasminoides variegated, 9–15/08/2016.

model regarding Pandorea jasminoides variegated and Rhyncospermum jasminoides, respectively. These values show the good agreement between the simulation results and the experimental measurements and are comparable with the results of the validation of the analytical models presented by Susorova et al. [41], Djedjig et al. [43], Scarpa et al. [39], Dahanayake and Chow [44], Suklje et al. [45], He et al.

equal to 0.4 °C. Concerning the wall covered with Rhyncospermum jasminoides, the simulated and experimental data deviate by maximum 1.7 °C. The average absolute difference and the standard deviation between the model predictions and the experimental data were 0.4 °C and 0.3 °C, respectively. The RMSE was 0.6 °C and 0.4 °C for the validation of the 10

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Fig. 7. Comparison between the model output (predicted values) and measured values for the wall covered with Rhyncospermum jasminoides, 9–15/08/2016.

Fig. 8. Comparison of simulated and measured difference between surface temperature of the control wall and the wall covered with Pandorea jasminoides variegated (a) and Rhyncospermum jasminoides (b), 9–15/08/2016.

it into a building simulation software (TRNSYS). The results were validated through experimental comparisons during one summer month with an outdoor reduced scale building having a west-oriented green wall. The average difference between the numerical predictions and the experimental measurements of the green wall surface temperature in August was 0.22 °C for the vegetated façade with a mean-root-square error of 1.42 °C. Scarpa et al. [39] developed a living wall mathematical model that was able to account for different features of living walls. The model validation was carried out through the comparison with field

[63]. Susorova et al. [41] studied the thermal effects of plants on heat fluxes through building external walls by means of a self-developed mathematical model of a green façade. The model was experimentally validated taking into consideration a bare wall and a green façade with P. tricuspidata, south exposed, on a real building in Chicago, USA. The comparison of the measured and modelled exterior surface temperatures for the vegetated façades showed R2 values equal to 0.96 on a sunny day and 0.86 on a cloudy day. Djedjig et al. [43] developed a green envelope model and integrated 11

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substitute of the energy simulation models for buildings characterized by constructive characteristics typical of the investigated Mediterranean area.

measurements realized during a summer and a winter week. Two different kinds of living walls, one with closed air cavity and grass and the other one with open air cavity and a vertical garden were evaluated. The maximum difference between the simulated and the field data of the external surface temperature of the living wall during the summer week was 1.0 °C. The RMSE for the living wall with the open air cavity was 1.1 °C and 0.4 °C during the summer and winter validation period, respectively. The RMSE was 0.5 °C during both the summer and winter validation period, for the living wall with the closed air cavity. A self-developed mathematical model integrated into EnergyPlus building simulation program was used by Dahanayake and Chow [44] for analysing the impact of living walls on building energy performance. The simulation results regarding the exterior surface temperature were validated against two experimental studies carried out on living walls in a summer month and in the period June-September respectively. The agreement of simulated results with experiment results was assessed by means of a correlation analysis showing R2 values of 0.88 and 0.80 for each experimental study, respectively. Suklje et al. [45] proposed a modelling approach that considers the vertical greenery system as a homogeneous layer with apparent thermophysical properties. The model was validated on the period July-August against the data that were generated for an indirect green façade in summer conditions by using a validated thermal response model developed in a previous study [64]. It was shown that outer surface temperature of the building envelope differed by maximum ± 1.1 °C, with standard deviation equal to 0.3 °C, from the calculated data. He et al. [63] investigated the thermal performance of living wall system by developing a coupled heat and moisture transfer model. Model output parameters were compared with field data, measured in a summer and a winter week, in order to validate the accuracy of the model. The analysis on the exterior surface temperature of living wall structure layer showed an RMSE of 0.15 °C both in summer and winter conditions.

Acknowledgements The contribution to programming and conducting this research must be equally shared between the Authors. This work was supported by the Italian Ministry of Economic Development [“Piano triennale della Ricerca 2015-2017 nell’ambito del Sistema Elettrico Nazionale, Progetto D.1 ‘Tecnologie per costruire gli edifici del futuro’, Research activity: “Analisi di tecniche di raffrescamento sostenibili applicabili in edifici civili e in edifici serra”, Piano Annuale di Realizzazione (PAR) 2017“, Accordo di Programma Ministero dello Sviluppo Economico – ENEA]. References [1] U. Berardi, A. GhaffarianHoseini, A. GhaffarianHoseini, State-of-the-art analysis of the environmental benefits of green roofs, Appl. Energy 115 (2014) 411–428, https://doi.org/10.1016/j.apenergy.2013.10.047. [2] R. Fernandez-Cañero, T. Emilsson, C. Fernandez-Barba, M.Á. Herrera Machuca, Green roof systems: A study of public attitudes and preferences in southern Spain, J. Environ. Manage. 128 (2013) 106–115, https://doi.org/10.1016/j.jenvman.2013. 04.052. [3] M. Santamouris, Cooling the cities – A review of reflective and green roof mitigation technologies to fight heat island and improve comfort in urban environments, Sol. Energy 103 (2014) 682–703, https://doi.org/10.1016/j.solener.2012.07.003. [4] B. Raji, M.J. Tenpierik, A. van den Dobbelsteen, The impact of greening systems on building energy performance: A literature review, Renew. Sustain. Energy Rev. 45 (2015) 610–623, https://doi.org/10.1016/j.rser.2015.02.011. [5] A. Gagliano, M. Detommaso, F. Nocera, G. Evola, A multi-criteria methodology for comparing the energy and environmental behavior of cool, green and traditional roofs, Build. Environ. 90 (2015) 71–81, https://doi.org/10.1016/j.buildenv.2015. 02.043. [6] D. Erdemir, T. Ayata, Prediction of temperature decreasing on a green roof by using artificial neural network, Appl. Therm. Eng. 112 (2017) 1317–1325, https://doi. org/10.1016/j.applthermaleng.2016.10. [7] B.A. Norton, A.M. Coutts, S.J. Livesley, R.J. Harris, A.M. Hunter, N.S.G. Williams, Planning for cooler cities: A framework to prioritise green infrastructure to mitigate high temperatures in urban landscapes, Landsc. Urban Plan. 134 (2015) 127–138, https://doi.org/10.1016/j.landurbplan.2014.10.018. [8] R.W.F. Cameron, J.E. Taylor, M.R. Emmett, What’s “cool” in the world of green façades? How plant choice influences the cooling properties of green walls, Build. Environ. 73 (2014) 198–207, https://doi.org/10.1016/j.buildenv.2013.12.005. [9] E. Schettini, I. Blanco, C.A. Campiotti, C. Bibbiani, F. Fantozzi, G. Vox, Green control of microclimate in buildings, Agric. Agric. Sci. Procedia 8 (2016) 576–582, https://doi.org/10.1016/j.aaspro.2016.02.078. [10] E. Schettini, C.A. Campiotti, I. Blanco, G. Vox, Green façades to enhance climate control inside buildings, Acta Hortic. 1227 (2018) 77–84, https://doi.org/10. 17660/ActaHortic.2018.1227.9. [11] G. Pérez, J. Coma, I. Martorell, L.F. Cabeza, Vertical Greenery Systems (VGS) for energy saving in buildings: A review, Renew. Sustain. Energy Rev. 39 (2014) 139–165, https://doi.org/10.1016/j.rser.2014.07.055. [12] C.L. Tan, N.H. Wong, S.K. Jusuf, Effects of vertical greenery on mean radiant temperature in the tropical urban environment, Landsc. Urban Plan. 127 (2014) 52–64, https://doi.org/10.1016/j.landurbplan.2014.04.005. [13] G. Vox, I. Blanco, C.A. Campiotti, G. Giagnacovo, E. Schettini, Vertical green systems for buildings climate control, Proc. 43rd Int. Symp. Agric. Eng. Actual Tasks Agric. Eng. Opatija, Croat. 2015 (2015) 723–732 24-27 Febr. (accessed June 5, 2019). [14] I. Blanco, E. Schettini, G. Scarascia Mugnozza, C.A. Campiotti, G. Giagnacovo, G. Vox, Vegetation as a passive system for enhancing building climate control, Acta Hortic. 1170 (2017) 555–562, https://doi.org/10.17660/ActaHortic. 2017. 1170.69. [15] C.A. Campiotti, E. Schettini, G. Alonzo, C. Viola, C. Bibbiani, G. Scarascia Mugnozza, I. Blanco, G. Vox, Building green covering for a sustainable use of energy, J. Agric. Eng. 44 (2013) 253–256, https://doi.org/10.4081/jae.2013.292. [16] M. Köhler, P.H. Poll, Long-term performance of selected old Berlin greenroofs in comparison to younger extensive greenroofs in Berlin, Ecol. Eng. 36 (2010) 722–729, https://doi.org/10.1016/j.ecoleng.2009.12.019. [17] D.B. Rowe, Green roofs as a means of pollution abatement, Environ. Pollut. 159 (2011) 2100–2110, https://doi.org/10.1016/j.envpol.2010.10.029. [18] T. Karlessi, M. Santamouris, A. Synnefa, D. Assimakopoulos, P. Didaskalopoulos, K. Apostolakis, Development and testing of PCM doped cool colored coatings to mitigate urban heat island and cool buildings, Build. Environ. 46 (2011) 570–576, https://doi.org/10.1016/j.buildenv.2010.09.003. [19] I. Jaffal, S.-E. Ouldboukhitine, R. Belarbi, A comprehensive study of the impact of green roofs on building energy performance, Renew. Energy 43 (2012) 157–164, https://doi.org/10.1016/j.renene.2011.12.004.

4. Conclusion Building design requires nowadays the use of energy performance simulation models. A predictive model for the estimation of the difference of temperature between an uncovered wall and vegetated walls was developed. Unlike the models developed so far, this research provided a model based on the statistical approach fitted and validated on data of a long period of experimentation. It used only external climate conditions as input variables, without making assumptions or providing very detailed data on the different parameters of the plants, as in the case of engineering models. External climate conditions were used as predictors and input of the model: external air temperature and relative humidity, horizontal and vertical solar radiation, wind velocity and direction. The data measured in the summer 2015 were used to build the model. Data were grouped in 5 solar radiation slots in order to facilitate the interpretation of the predictive models. The most significant predictors were selected for each slot. The developed overall model refers to green façades covered with Pandorea jasminoides variegated and Rhyncospermum jasminoides. The model was validated by comparing the data of the surface temperatures measured in the summer 2016 with the data obtained by the model, using the climatic data of 2016 as model input. The adoption of this method to build the global model allowed to obtain, in validation, good results with coefficients of determination (R2) higher than 0.95. A maximum standard deviation equal to 0.4 °C between the numerical predictions and the measurements was recorded. The difference of temperature between the uncovered and the vegetated wall was the model output as it is the achievable benefit with a green wall. The research showed that the model can be used for the prediction of the thermal benefit of the green façades in the Mediterranean area during summer, by adopting a new dataset of weather conditions. The results indicate that in early design phases the statistical models can be a valid 12

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