1 Introduction

During the hot period of the year, the human body activates defense mechanisms such as perspiration in order to maintain its temperature at normal bearable levels. The cooling system of the human body may begin to fail in case of high levels of temperature and humidity in the environment along with low wind speed. This causes thermal discomfort, which, in extreme cases, may lead to heat stroke. In general, when the human body receives a higher heat load than what it can remove into the environment, a sense of thermal discomfort is established. In almost half of the different settings around the world, the risk of mortality increased by between 1 and 3 % per 1 °C change in high temperature (Hajat and Kosatky 2010). Díaz et al. (2002) found that very hot weather is associated with high mortality levels, especially regarding persons over 65 years old. Muthers et al. (2010) compared the heat-related mortality during the summer of the year 2003 with other years and analyzed whether 2003 summer was exceptional in Vienna (Austria). Results showed that mortality increases significantly with thermal stress, but this increase attenuated in the last decades. Nastos and Matzarakis (2011) investigated whether there is any association between the daily mortality for the wider region of Athens, Greece and the thermal conditions, for the 10-year period 1992–2001. The findings extracted by the applied generalized linear models showed that statistically significant relationships (p < 0.01) between air temperature, human thermal indices, and mortality exist on the same day. The feeling of thermal discomfort due to high values of relative humidity and air temperature varies from person to person, influenced by age, sex, weight, used clothing, shading, existence of wind, activity, etc. (Moustris et al. 2009). As high risk groups are considered elderly people with serious health problems, infants, and people working under conditions allowing for the onset of heatstroke; namely, people working outdoors and under the effect of strong solar radiation (Matzarakis et al. 1999; Becker et al. 2003; Conti et al. 2005).

In the last decades, many various indices have been proposed in order to calculate the human thermal perception levels, such as the physiologically equivalent temperature (PET; Matzarakis et al. 1999; Mayer and Höppe 1987; Höppe 1999; Nastos and Matzarakis 2006, 2008a, b; Matzarakis and Nastos 2010) and the Universal Thermal Climate Index (Jendritzky et al. 2002; Fiala et al. 2011). Additionally, more simplistic discomfort indices had been proposed, such as the Cooling Power index (Siple and Passel 1945; Besancenot 1978; Tzenkova et al. 2003) and the Thom’s discomfort index (DI; Thom 1959).

It is of great consensus among the scientific community that heat stress combined with air pollution, especially in urbanized areas, affects human health and activities. Matzarakis and Mayer (1991) studied the thermal and air quality components of the urban climate in Athens, Greece during the summer heat wave of year 1987. For this purpose, they calculated and analyzed the predictive mean vote, PET as well as the Thom’s DI, during year 1987 summer heat wave over Athens, Greece. Nastos and Matzarakis (2008a, b) examined the effects of the daily minimum air temperature (T min) and human biometeorological variables, as well as their day-to-day changes, on sleep disturbances (SD) in the inhabitants of Athens, Greece. The extracted results suggested that a considerable increase in SD existed in 1994 compared to 1989. This was due to the many consecutive days with heavy thermal load (PET > 35 °C and T min > 23 °C) in 1994 compared to the lack of such days in 1989. Cohen et al. (2012) examined the daily and seasonal climatic behavior of various urban parks with different vegetation cover and its impact on human thermal sensation in the summer and winter in Tel Aviv, Israel. The results showed that an urban park with a dense canopy of trees has maximum cooling effect during summer and winter in daytime.

The use of artificial neural networks (ANNs) based on predictive models to thermal control strategies produced in many cases better results than mathematical and statistical models. The thermal comfort conditions were improved and there were in some cases significant energy savings (Moon and Kim 2010).

Santamouris et al. (1999) developed an ANN in order to model the heat island effect in the greater Athens urban area, Greece. Mihalakakou et al. (2002) applied ANN to simulate the heat island effect over Athens, Greece, using synoptic types as a predictor. Kostopoulou et al. (2007) compared multilinear regression analysis, canonical correlation analysis, and ANNs in order to simulate the maximum and minimum temperature in different seasons and areas over Greece. Chronopoulos et al. (2008) developed an application of artificial neural network models to estimate air temperature data in Greek areas with sparse network of meteorological stations. Moustris et al. (2009) developed ANNs in order to forecast 24 h in advance the discomfort levels due to the combination of air temperature, air humidity, and wind speed during the hot period of the year at representative locations of Athens city, Greece. Moustris et al. (2010a) applied ANNs to forecast the discomfort levels for the next three consecutive days, as well as the number of consecutive discomfort hours during the day using air temperature, air humidity, and wind speed in the greater Athens area, Greece. Gobakis et al. (2011) developed a model for urban heat island prediction using ANN techniques. Finally, Chronopoulos et al. (2011) presented an ANN model-based approach to assess bioclimatic conditions in remote mountainous areas, in the mountainous area of Samaria Forest canyon, Greece, using a relatively limited number of microclimatic data from easily accessible meteorological stations.

The aim of this work is to investigate the ability of ANN models to predict the comfort–discomfort levels within the greater Athens area (GAA). For this reason, numerous ANN models were developed, and the multiple criteria analysis (MCA) technique was applied in order to choose the best ANN architecture.

2 Data and methodology

The GAA is located in a small peninsula at the southeast part of the mainland of Greece (Fig. 1). It covers an area of 450 km2 and is surrounded by mountains of moderate height (400–1,500 m) at the east, west, and north sides while the sea (Saronikos Gulf) lies at the south side. Small openings to the north, northwest, and northeast, connect the GAA with the Greek mainland (Paliatsos and Nastos 1999; Theoharatos et al. 2010). During the last decades, the expansion of the city of Athens established the so-called urban heat island (Philandras et al. 1999), which acts synergistically with the incidence of heat waves (Matzarakis and Nastos 2010), exacerbating the thermal perception of the inhabitants. Therefore, higher thermal conditions combined with the atmospheric pollution, has an explicit effect on people’s health and the quality of living (Moustris et al. 2010b). The issue of human thermal sensation in various outdoor areas of a city has drawn rather limited attention in the research field (McGregor et al. 2002; Spagnolo and de Dear 2003; Moustris et al. 2009). Most of the comfort–discomfort studies are conducted in indoor conditions such as vehicles, offices, and residential buildings (Shimizu and Jindo 1995; Atthajariyakul and Leephakpreeda 2005; Moon et al. 2009).

Fig. 1
figure 1

The map of Greece and the GAA (upper panel), and the location and the altitude of the hydrometeorological network stations within the GAA (lower panel)

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In this work, for the investigation of comfort–discomfort levels, the Thom’s DI was used (Thom 1959). This is due to the fact that DI is a very simple discomfort index, as well as the availability of meteorological data covering the examined area (air temperature and relative humidity) and their low variability. The Thom’s DI refers to a human being indoors in a state of relaxation without having any vigorous physical activity and dressed in light clothing. In order to calculate DI, values of air temperature and relative humidity have to be used and this is the main reason why DI is one of the most frequently used discomfort indices worldwide. For these two meteorological parameters, there are available measurements from many places all over the world covering significant time series of data. The weaknesses of DI is that it does not take into account many other parameters, which have a great influence on the energy balance of the human body such as the short and long wave radiation, wind speed, metabolic rate, age and sex, activity of the person, etc.

The equation that is used for the calculation of the DI (Giles et al. 1990; Tzenkova et al. 2003) is :

$$ {\hbox{DI}} = {0}{.4} \times \left( {T + {T_w}} \right) + {4}{\hbox{.8 in }}^\circ {\hbox{C}} $$

or

$$ {\hbox{DI}} = T - \left( {055 - 00055 \times {\hbox{RH}}} \right) \times \left( {T - 14.5} \right){\hbox{i}}{{\hbox{n}}^{^\circ }}{\hbox{C}} $$

where, T is the air temperature (degree Celcius), T w is the wet bulb temperature (degree Celcius), and RH is the relative humidity of the air (percentage). This is an easily used and calculable bioclimatic index. It can accurately describe only the thermal comfort–discomfort during the hot period of the year. The values of the DI and the sense of thermal comfort–discomfort of the population are depicted in Table 1.

Table 1 Values of DI and the corresponding thermal sensation (Giles et al. 1990)
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The meteorological variables which were used in this work have been recorded by the Hydrological Observatory of Athens, operated by the National Technical University of Athens. It is an evolution from the hydro-meteorological network METEONET of the Laboratory of Hydrology and Water Resources Management of the National Technical University of Athens (METEONET 2011). The meteorological variables concern hourly values of air temperature (degree Celcius) and relative humidity (percentage) and cover the 5-year period 2006–2010.

These meteorological data were provided by eight fully automatic telemetric hydrometeorological stations installed within the GAA. Concretely, the eight regions are: Ano Liossia, Galatsi, Ilioupoli, Mandra, Menidi, Penteli, Pikermi, and Psittalia. These regions are depicted in Fig. 1 (lower panel).

Ιn order to predict the maximum daily value of the DI for the next 3 days along with the number of consecutive hours during the day where DI ≥ 24οC (over 50 % of the population feels discomfort due to hot) for each one of the eight examined stations areas, numerous ANN models were created.

At first, the appropriate number of input variables that were used for the training of the ANN models was defined. The trial-and-error approach was used in order to decide for the best ANNs architecture. The input parameters for the ANN models training are depicted in Table 2.

Table 2 Input data for the ANN models training
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Afterwards, the appropriate number of the previous days that were used as input data to the ANN model was defined. This was done by using the trial-and-error technique. Moustris et al. (2010a) have used data of the six previous days to feed an ANN model in a similar model. Therefore, this is the number of days that this ANN model is initially tested. Adding and removing days and comparing the results provide the most accurate forecast. The results of these models are evaluated by the coefficient of determination. This statistical index is selected because it is the most widely used in the literature to evaluate similar models (Comrie 1997; Karul et al. 2000; Antonic et al. 2001; Yang and Kim 2004; Jiang 2008; Tseliou et al. 2010; Pelliccioni et al. 2010). Moreover, it is possible to compare models by using this statistical index among models that have the same or similar complexity (Dreyfus 2005). For this reason, only one parameter changes when a model is compared to another. This can be the number of neurons, hidden layers, epochs, etc.

Finally, MCA was used in order to select the most accurate ANN models with the aid of the coefficient of determination of each model. MCA is a useful tool for addressing some of these challenges involved in the evaluation of models that include many parameters. The ranking methodology was used. It is a simple method that involves assigning each decision element a rank that reflects its perceived degree of importance relative to the decision being made. The decision elements can then be ordered according to their rank (first, second, etc.). Ranks are assigned according to the following nine-point scale (Mendoza et al. 1999):

  1. 1

    ➜ Weakly important

  2. 3

    ➜ Less important

  3. 5

    ➜ Moderately important

  4. 7

    ➜ More important

  5. 9

    ➜ Extremely important

The ranking is then multiplied by the coefficient of determination (R 2) of each criterion, and the sum is the total score of each model (MCA score). Each model has six criteria to be evaluated. The first three are the value of the DI for the first, second, and the third day. The other three are the number of consecutive hours with high thermal discomfort levels during the day for the first, second, and the third day. The ranking given to these criteria is depicted in Table 3. The ranking was selected according to the above nine-point scale.

Table 3 MCA ranking to the ANN models forecasting parameters.
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The initial ANN model was a multilayer perceptron (MLP) with one hidden unit consisting of 11 processing elements (PEs). Both hidden and output layer use momentum as learning rule with step size = 1.0, momentum = 0.7 and the activation function tanhaxon, which is given by the equation (Bishop 1995):

$$ \tan \,h(x){ = }\frac{{{e^x} - {e^{{ - x}}}}}{{{e^x} + {e^{{ - x}}}}} $$
(2)

The number of epochs was set to 1,000, and the weights updated to batch. The steps that are followed to construct the final ANNs model are described below. It should be noted that the models with the highest MCA score proceed to the next step each time.

  1. 1.

    Selection of the input variables used for the training of the ANN models. All and some of the variables are tested as inputs.

  2. 2.

    Selection of the number of the previous days used for input data. Six days are initially tested. Then, the number of days decreases until a lower MCA score is achieved. Afterwards, the number of days increases until a lower MCA score is achieved.

  3. 3.

    Selection of the number of hidden layers. One hidden layer is initially tested and then one more unit is added each time.

  4. 4.

    Selection of the number of epochs. One thousand epochs are initially tested and then increase by 1,000 each time.

  5. 5.

    Selection of the number of the PEs in the hidden layers. In this step, genetic algorithms (GA) are used in order to define the optimum number of PEs because manually testing would be much more time consuming (Ceravolo et al. 2009).

  6. 6.

    Selection of the best type of neural networks. The MLP, generalized feed forward networks (GFFN), and time-lag recurrent networks (TLRN) type of neural networks were tested.

The result of the above steps was the selection of the best of the numerous ANNs developed models. These models were trained with data concerning the period 2006–2009 and then were tested on the data of year 2010. It should be noted that data of year 2010 are absolute unknown to the trained ANN model.

The predictions of the ANN models were compared to the real-observed ones and evaluated by using statistical methods and indices (Ma and Iqbal 1983; Elbir 2003; Shahi et al. 2009; Velten 2009). The accuracy of the models was evaluated by R 2, the Index of Agreement (IA), the mean bias error, the mean absolute bias error, and the root mean square error. The prediction of the exceedances (according to the DI thresholds), was evaluated by the true predicted rate (TPR), false-positive rate, false alarm rate, and success index (SI; Nunnari et al. 2004; Papanastasiou et al. 2007).

3 Results and discussion

At first, the number of the inputs that were used for the training of the ANN model was defined. The trial-and-error approach was used. The initial input and output data are those presented in Table 2.

The initial ANN model 1 was a MLP with one hidden layer consisting of 11 PEs or artificial neurons. The 20 % of the training data were used for the cross-validation method (Moustris et al. 2010a). Both hidden and output layer use the momentum as learning rule with step size = 1.0, momentum = 0.7, and the activation function is the tanhaxon. The number of epochs was set to 1,000 and the weight updated to batch. Data from the five previous days were used to train the network and produced results. In ANN model 1, all the input parameters have been used to train the network while in the ANN model 2, the station’s number and the month’s number have not been used (Table 2). The accuracy of each model was expressed by the R 2 and the results are depicted in Table 4. ANN model 2 achieves a higher MCA score and clearly outperforms the ANN model 1. Therefore, the input parameters station number and month number were not being used as input parameters.

Table 4 Coefficient of determination (R 2) and MCA score for different input data
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Then, the number of the previous days that were used as input data to the ANN model was tested. The structure of ANN model 2 was used. The trial-and-error technique was applied. By adding one extra day each time to the training data of the ANN model, it is possible to find the number of days where the MCA score is maximized.

The following models were tested:

  • ANN model 2 (data from five previous days)

  • ANN model 3 (data from six previous days)

  • ANN model 4 (data from seven previous days)

The results are presented in Table 4. The ANN model 3 achieves the maximum MCA score; therefore, data from the six previous days were used in order to train the ANN model. The next step was to define the number of the hidden layers. The number of hidden layers is increased until the MCA score begins to fall. This is the criterion for selecting the number of hidden units. Two ANN models were tested:

  • ANN model 3 (one hidden layer)

  • ANN model 5 (two hidden layers)

The results are depicted in Table 4. The ANN model 3 achieves higher MCA score. Therefore, one hidden layer was used for the appropriate structure of the ANN model. This option is in agreement το the literature. The ANNs with one hidden layer seem to be more reliable forecasting models than those with two or more hidden layers.

Then, using the structure of the ANN model 3 the number of epochs was defined. The following models were developed and tested:

  • ANN model 3 (1,000 epochs)

  • ANN model 6 (2,000 epochs)

  • ANN model 7 (3,000 epochs)

The results are depicted in Table 4. The ANN model 6 achieves the highest MCA score. However, ANN model 3 is very close to it. Therefore, further testing of these two models was necessary in order to define the more accurate.

In order to find the optimal number of PEs in the hidden layer, GA was used. These algorithms test all the possible scenarios and select the number of PEs that provides the best accuracy. Two models are tested:

  • ANN model 8. The same as ANN model 3 but uses GA to identify the number of PEs.

  • ANN model 9. The same as ANN model 6 but uses GA to identify the number of PEs.

The results are presented in Table 4. ANN model 8 outperforms ANN model 9 and also ANNs models 3, 6 and 7 (Table 4). It is therefore selected as the model that will further proceed. Finally, two more ANN models were created to find the best type of ANN model:

  • ANN model 10. It has exactly the same structure as ANN model 8 but the type of neural network selected was the GFFN.

  • ANN model 11. It has exactly the same structure as ANN model 8 but the type of neural networks selected was the TLRN. Moreover, the type of this network includes short-term memory structures which have the following characteristics:

    • Memory: Focused

    • Activation function: Lagguare Axon

    • Sample depth: 1

    • Trajectory length: 30

The results are presented in Table 4. The best performance was achieved by ANN model 10. This is the final model which was selected and was further analyzed. In order to summarize, the structure of the ANN model 10 that was finally selected is presented below:

  • Type of neural networks: Generalized feed forward neural networks.

  • Input parameters: All except the station number and the month number. Detailed description of the parameters is in Table 3.

  • Input data of the six previous days.

  • Cross-validation: 20 % of training data.

  • One hidden layer.

    • Number of PEs: 6 (As was defined by the use of genetic algorithms)

    • Activation function: Tanhaxon

    • Learning rule: Momentum

    • Step size: 0.1

    • Momentum: 0.7

  • Output layer

    • Number of PEs: 6

    • Activation function: Tanhaxon

    • Learning rule: Momentum

    • Step size: 0.1

    • Momentum: 0.7

  • Maximum epochs: 1,000.

  • Weight update: Batch

A detailed analysis of the developed ANN model is presented by using various statistical indices. The accuracy of the created ANN model as well as the ability to predict the exceedances was evaluated.

As concerns the daily DI values, an excess day is when the daily value of DI is greater or equal to 24 °C (over 50 % of the population feels discomfort due to hot). As concerns the consecutive hours with DI ≥ 24 °C, an excess day is when the number of consecutive hours is greater or equal to 12 (at least the half of the day). Tables 5, 6, and 7 present the performance of the developed ANN forecasting model for a 24, 48, and 72-h prediction ahead, respectively.

Table 5 Statistical analysis of ANN model 10; 24-h prediction ahead, year 2010
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Table 6 Statistical analysis of ANN model 10; 48-h prediction ahead, year 2010
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Table 7 Statistical analysis of ANN model 10; 72-h prediction ahead, year 2010
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According to Table 5, the predictive ability of the constructed ANN model 10 is very high. The values of the coefficient of determination, concerning the prediction of the next-day maximum daily value of DI, are ranging between 0.991 and 0.981. The same conclusion is clear based on the ΙΑ. The values of the IA are ranging between 0.993 and 0.997, showing a very high predictive ability. Similar conclusions are obtained for the predictive ability of the ANN model 10 in terms of the number of hours with strong thermal discomfort levels during the next 24 h.

Analogous results and conclusions obtained for the prediction of the exceedances, i.e., the days with DI ≥ 24 °C as well as the days with more than 12 consecutive hours with strong thermal discomfort levels, for the next day. The SI values are ranging between 98.0 and 99.4 % in terms of whether or not the next day is an exceedance day, showing a very good predictive ability.

According to Table 6, the prediction ability of ANN model 10, 2 days ahead, seems also to be very high. The values of the coefficient of determination, concerning the prediction of the maximum daily value of DI 2 days ahead, are ranging between 0.680 and 0.837. The same conclusion is clear based on the ΙΑ. The values of the IA are ranging between 0.902 and 0.948, showing a very high predictive ability. Similar conclusions are obtained for the predictive ability of the ANN model 10 in terms of the number of hours with strong thermal discomfort levels during the day and for 2 days ahead.

Analogous results and conclusions obtained for the prediction of the exceedances, i.e., the days with DI ≥ 24 °C as well as the days with more than 12 consecutive hours with strong thermal discomfort levels, 2 days ahead. The SI values are ranging between 86.9 and 90.9 % in terms of whether or not the next day is an exceedance day, showing a very good predictive ability.

According to Table 7, the prediction ability of ANN model 10, 3 days ahead, seems also to be enough satisfactory. The values of the coefficient of determination, concerning the prediction of the maximum daily value of DI 2 days ahead, are ranging between 0.423 and 0.687. The same conclusion is clear based on the ΙΑ. The values of the IA are ranging between 0.785 and 0.879, showing a very high predictive ability. Similar conclusions are obtained for the predictive ability of the ANN model 10 in terms of the number of hours with strong thermal discomfort levels during the day and for 2 days ahead.

Analogous results and conclusions obtained for the prediction of the exceedances, i.e., the days with DI ≥ 24 °C as well as the days with more than 12 consecutive hours with strong thermal discomfort levels, 2 days ahead. The SI values are ranging between 75.2and 83.2 % in terms of whether or not the next day is an exceedance day, showing a very good predictive ability.

The observed vs. the predicted values of the DI are depicted in Figs. 2, 3, and 4 for the 24, 48, and 72-h prediction ahead correspondingly. In each figure, the eight regions of the GAA are displayed separately. Figure 5 presents the differences between the predicted and observed values of DI for the best and the worst prediction respectively. In order to provide quantitative relations, the differences between the predicted and observed values of DI were calculated, for the best and the worst prediction respectively, by means of the coefficient of determination and the index of agreement for the forecasting cases of 24, 48, and 72 h ahead

Fig. 2
figure 2

Observed (blue line) vs. predicted (red line) maximum daily DI values using the ANN forecasting model 10 during the warm period of the year; 24 h prediction ahead, year 2010

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Fig. 3
figure 3

Observed (blue line) vs. predicted (red line) maximum daily DI values using the ANN forecasting model 10 during the warm period of the year; 48 h prediction ahead, year 2010

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Fig. 4
figure 4

Observed (blue line) vs. predicted (red line) daily DI values using the ANN forecasting model 10 during the warm period of the year; 72 h prediction ahead, year 2010

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Fig. 5
figure 5

Differences between predicted and observed values of DI for the best (left panel) and the worst (right panel) prediction; 24 h ahead prediction (a), 48 h ahead prediction (b) and 72 h ahead prediction (c), year 2010

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In the case of 24-h prediction ahead (Fig. 5a), the best prediction concerns the station Ano Liosia. The differences (predicted–observed values) range from −1.7 to +2.0 °C. The worst prediction concerns the station Menidi. The differences (predicted–observed values) range from −1.4 to +5.2 °C. In both cases, it seems that the highest differences between the predicted and the observed values are presented during the last 10 days of September. This may be due to the fact that during the last 10 days of September, the weather is, in general, changeable since autumn season begins.

In the case of 48-h prediction ahead (Fig. 5b), the best prediction concerns the station Ilioupoli. The differences (predicted–observed values) range from −2.5 to +5.6 °C. The worst prediction concerns the station Penteli. The differences (predicted–observed values) range from −3.4 to +5.2 °C.

Finally, in the case of 72-h prediction ahead (Fig. 5c), the best prediction concerns the station Ilioupoli. The differences (predicted–observed values) range from −3.1 to +6.4 °C. The worst prediction concerns the station Penteli. The differences (predicted–observed values) range from −3.7 to +5.6 °C.

4 Conclusions

The aim of this work was the prediction of the discomfort levels due to the combination of high temperature and air humidity during the hot period of the year for eight different regions within the greater Athens area. For this purpose, numerous artificial neural networks were developed and applied as forecasting models. For the choice of the best ANN model architecture, the technique of multiple criteria analysis was applied.

The analysis showed that the best type of ANN models for the discomfort levels prediction was the generalized feed forward neural networks. The prediction of the discomfort levels was done using an appropriate and simplistic index known as the Thom’s discomfort index.

The developed artificial neural network that was used for the prediction of Thom’s discomfort index daily value, performed very well for 3-day predictions ahead. More specifically, the accuracy of the created forecasting model for the first (0.98 < R 2 < 0.99, IA > 0.99), second (0.68 < R 2 < 0.84, IA > 0.90), and the third day (0.42 < R 2 < 0.69, IA > 0.79) was quite satisfactory. The predictions of the exceedances, in other words the days where at least 50 % of the population feel discomfort due to hot according to DI value, for the first (TPR > 95 %, SI > 97 %), second (TPR > 75 %, SI > 86 %), and the third day (TPR > 51 %, SI > 75 %) are very satisfactory.

It appears that the ANN models have the ability to predict the DI levels within an urban environment as well as the days exceeding hazardous levels of discomfort. The results of this study may be useful in many human activities such as the better distribution and savings of the electric energy in the GΑΑ according to the public needs, the protection of public health, knowing in advance the hazardous levels of the discomfort in different regions of the GΑΑ, and a better and more efficient operation of the government, the hospitals, the transportations, etc. A future work of the authors will be the application of ANN models to predict more complex thermal indices such as PET or UTCI.