Air Temperature Estimation by Using Artificial Neural Network Models in the Greater Athens Area, Greece

Air temperature (T) data were estimated in the regions of Nea Smirni, Penteli, and Peristeri, in the greater Athens area, Greece, using the T data of a reference station in Penteli. Two artificial neural network approaches were developed. The first approach, MLP1, used the T as input parameter and the second, MLP2, used additionally the time of the corresponding T. One site in Nea Smirni, three sites in Penteli, from which two are located in the Pentelikon mountain, and one site in Peristeri were selected based on different land use and altitude. T data were monitored in each site for the period between December 1, 2009, and November 30, 2010. In this work the two extreme seasons (winter and summer) are presented.The results showed that theMLP2model was better (higher R2 and lower MAE) than MLP1 for the T estimation in both winter and summer, independently of the examined region. In general, MLP1 and MLP2 models provided more accurate T estimations in regions located in greater distance (Nea Smirni and Peristeri) from the reference station in relation to the nearby Pentelikon mountain. The greater distance T estimations, in most cases, were better in winter compared to summer.


Introduction
Urban climate, in general, is characterized by higher air temperature () values compared to those at adjacent rural and mountainous regions.Increased urban  contributes to increased emissions of power plants pollutants and of smog production, higher energy consumption, particularly for air-conditioning [1], and unpleasant thermal conditions to people, mainly during the warmest period of the year [2,3], resulting, from a climatic point of view, in the degradation of human life quality.These conditions are associated in a high degree with urbanization of cities which is characterized as one of the most powerful anthropogenic forces all over the world [4].Mountainous regions are distinguishable from urban regions due to their special pattern based mainly on the impact of topography and composition of vegetation [5,6].It is well known that  decreases as height increases in the troposphere [7], and a direct relationship has been reported between  and the altitude of mountain regions [8].These regions present improved bioclimatic conditions in relation to urban regions, especially in the summer, for example, the case of mountainous Nafpaktia [9], and they are used extensively as tourist destinations [10].
It has been reported that the microclimatic conditions in urban regions, for example, Athens, are influenced mainly by the ground cover type, which relates to the land use [11].Since all ground cover types in urban regions are not covered by their meteorological stations (MSs), the estimation of microclimatic data is considered necessary for climatic and energy reasons.Also, in the case of mountainous regions, where the network of the meteorological stations at middle and high altitudes is sparse, there are many problems obtaining the precise meteorological data and their estimation at the aforementioned altitudes may be possible based on data collected from nearby lower-altitude areas [6].
Many researchers have examined the estimation of meteorological variables using various statistical techniques.Guler et al. [12] developed linear regression models to determine the mean distribution of , relative humidity and rainfall data.Other researchers [13] combined regression and kriging techniques for  interpolation.An artificial neural network (ANN) model is a robust computational technique [14]  which has been applied for the estimation of meteorological data as a function of the corresponding data of one or more reference stations.ANN models in many cases provide better estimations of  in comparison with linear regression techniques, for example, [15].Kisi and Shiri [16] reported that ANNs performed satisfactory estimations of  and precipitation within a wide range of altitudes of Iran.The use of ANNs provided very satisfactory predictions of the discomfort levels during the hot season of the year in various regions of the GAA [17], as reported in the case of  based on data in various agricultural regions in the United States of America [18].Furthermore, ANNs gave very good estimations of biometeorological conditions in high altitudes in mountainous regions of Greece [19,20].The existed MSs in GAA do not cover all recent ground cover types and this study contributes a first step to address this insufficiency, in terms of , a variable which is available in the majority of the MSs in Greece [6].Thus, this study focuses on the estimation of  data by using different ANNs approaches in urban and adjacent mountain regions of the GAA.

Study Regions and Measurement
Sites.The field experiment was performed in three regions.The first one, the municipality of Nea Smirni (NS), lies on the southern part of GAA, about 5 Km away from Athens, the capital of Greece.The region of NS possesses a central urban park which occupies an area of approximately 5 ha and contributes to a great degree to the recreation of visitors who come from many regions of Attica, Greece.
The second region, the municipality of Penteli, lies on the northeast part of GAA, about 12 Km away from Athens.The city of Penteli is characterized by many open vegetated spaces and detached houses with gardens.A great part of this city lies on the foothills of the Pentelikon mountain, which was used in a great degree for marble mining in the past decades.Nowadays, the ecosystem of the Pentelikon mountain has been degraded in a large scale, due to the marble mining, the pressure of the building development, and the repeated events of fires which resulted mainly in many burned pine forest areas.
The third region, the municipality of Peristeri, is the metropolitan municipality on the western part of GAA, about 6 Km away from Athens.The region of Peristeri is densely built with commercial and residential housing blocks and heavy traffic as in the case of NS.
One site in Nea Smirni, three sites in Penteli, and one site in Peristeri were selected based on different land use and altitude (Table 1 and Figures 1(a) and 1(b)).The altitude, the latitude, and the longitude of each site were evaluated using a mobile Global Positioning System (Garmin eTrex Vista) and cross-checked against 1 : 50000 topographic maps.The surrounding vegetation of the site S1 in Nea Smirni was irrigating in contrast with the natural vegetation of S2, S3, and S4 sites, in Penteli.There was no vegetation at S5 (Peristeri) but only asphalt and other structural materials.

Measurements and Neural Network Modeling.
In each study site,  data were monitored simultaneously every 10 min by sensors with data loggers (Hobo Pro v2, U23-001, Onset Computer Corporation, USA, accuracy ± 0.2 ∘ C for  over 0 ∘ C to 50 ∘ C) for the period between December 1, 2009 and November 30, 2010.This period can be considered as representative for our study, because the mean  values of the S4 site (reference site) during winter of 2009-2010 (9.9 ∘ C) and summer 2010 (26.0 ∘ C) were similar to the respective values (10.1 ∘ C in winter and 26.0 ∘ C in summer) calculated from the MS of the National Observatory of Athens at Thissio for the base period from 1961 to 1990 [21], about 14 Km away from S4 site.The instruments, before their installation in the measurement locations, were calibrated in the laboratory against reference sensors and tested for a period of five days.Additionally, every month, the instruments were tested in situ against reference sensors.These tests revealed no shift errors for any of the sensors.The instruments were enclosed in appropriate shelters screened from precipitation and direct solar radiation and mounded on selected plant species and pillars 1.5 m above ground surface.The aforementioned measuring height was selected for comparison reasons, taking into account that the meteorological shelter is located at the height of 1.5 m approximately above the ground surface [22].Air temperature mean values were calculated on an hourly basis for every study site and separately for each month and season.In this paper, we present  processing data for the extreme seasons of the year, winter and summer.
One of the most commonly used ANN architectures, the multilayer perceptron (MLP) with one hidden layer, was used for  estimation in the present study.The site S4, was used as a reference station; that is to say,  of S4 was used to estimate  for the other sites (S1, S2, S3, and S5).The maximum and minimum distances among S4 and the other measurement sites were 16.3 and 3.4 Km, respectively.For the training, the backpropagation algorithm was used [23][24][25].A major consideration in the use of MLPs for model building is the determination of the optimal architecture of the network (number of inputs, number of layers, and number of nodes per layer).Usually, a trial and error method is applied to test various alternative models.
The MLPs developed and used in the present study are of two architectures (MLP1 1-6-1 and MLP2 2-6-1).The first (MLP1) had one input variable ( at the reference site); one hidden layer with 6 nodes, since it was found that this is the number of nodes that gave the best results; and one output (the temperature at the test sites).The only difference of the second architecture (MLP2) is that the input had two variables ( at the reference site and the time of the corresponding ).The activation function for the hidden layer was the hyperbolic tangent function, while for the output layer it was the logistic sigmoid function.The training set consisted of 1/2 of the data, the selection set of 1/4 of the data, and the test set of the remaining 1/4 of the data, randomly assigned.All the results refer to the test set of the data.After applying the sensitivity test for the input variables, we found that all variables used (time of the corresponding  and/or ) are significant to our model at  < 0.05.

Results and Discussion
The results of the development and application of the MLP method at the examined sites of GAA are presented in Figures 2 and 3.In winter,  estimations for the S1 site were very satisfactory in MLP1 and MLP2 models (Figure 2  In summer, the effectiveness in estimating  at Nea Smirni site using MLP1 model (Figure 3  compared to Nea Smirni (S1) in both applied models (MLP1 and MLP2).In Peristeri, the use of MLP1 showed less accurate  estimations ( 2 and MAE values higher and lower, resp.)compared to Nea Smirni and middle alt. of Pentelikon Mt. (S3).In the case of the higher examined alt. of Pentelikon Mt. (Figure 3(b)),  2 and MAE took the lowest and highest values, respectively, regardless of the applied MLP model.In general, the applied MLP models were more accurate to estimate  data at greater distances from the reference site.Both MLP1 and MLP2 models presented, in most cases, better  estimations, in terms of higher  2 and lower MAE values, in regions located relatively far away (Nea Smirni and Peristeri) from the reference site (S4) in winter compared to summer.Regarding the studied sites of Pentelikon Mt., located in relatively small distances from S4, better  estimations were found clearly in the case of the top (S2), using the MLP2 model, in summer in relation to winter.The comparison of MLP1 and MLP2 for each examined site showed clearly that MLP2 was always better (higher  2 and lower MAE values) than MLP1 in estimating  in both seasons (winter and summer).It has been reported that the input of the actual time of measurement in MLP models attributed to more accurate estimations of the thermohygrometric index in mountainous regions, Greece, in summer [6].

Conclusions
This study estimated  in the regions of Nea Smirni, Penteli, and Peristeri using one of the most commonly used artificial neural network models, MLP [6].This estimation was based on  data of a reference station in Penteli.Two MLP approaches were followed: the first (MLP1) used  as input parameter and the second (MLP2) used additionally the time of the corresponding , in accordance with other studies [6,20].We showed that the MLP2 model was better (higher  2 and lower MAE) than MLP1 in estimating  in both seasons (winter and summer), independently of the examined region.In general, MLP1 and MLP2 models showed better  estimations in regions located at greater distances (Nea Smirni and Peristeri) from the reference site in relation to the nearby mountainous region in Penteli and in most cases, the greater distance  estimations were more accurate in winter than in summer.
(a)) according to the higher values of the determination coefficient ( 2 > 0.90) compared to the other examined cases (Figures 2(b), 2(c), and 2(d)).Furthermore, the efficiency of both MLP1 and MLP2 models to estimate  in Nea Smirni based on  of the reference site (S4) was strengthened by the lower MAE values in relation to the respective values of the other examined regions.The  estimation in the case of S5 (Peristeri) may be considered as more accurate in comparison with S3 (Pentelikon Mt. alt.796 m) because MAE values were lower in S5 compared to S3 for both MLP1 and MLP2 (Figures 2(c) and 2(d)), although  2 values were almost equal.These models provided less accurate estimations in the higher examined alt. of Pentelikon Mt. (1086 m) as both of them showed lower and higher values of  2 and MAE, respectively, (Figure 2(b)) in comparison to the other studied regions.MLP1 and MLP2 models showed better  estimations in regions located at greater distances from the reference site in relation to the nearby mountainous region.