Modelled spatio-temporal variability of air temperature in an urban climate and its validation: a case study of Brno, Czech Republic 169Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.DOI: 10.15201/hungeobull.65.2.7 Hungarian Geographical Bulletin 65 2016 (2) 169–180. Introduction The spatial and temporal variability of the air temperature in urban environments has been studied frequently in recent decades in connection with the formation of Urban Heat Islands (UHIs) (Arnfield, A.J. 2003). With the development of new data sources and new methodological approaches in recent years, research in urban climatology has shift ed from identifying UHIs and estimates of UHI intensity to searching for the exact patt erns of the spatio-temporal variability of UHIs and temperature fi elds in urban environments. Given the diversity of urban structure (Bech- tel, B. and Daneke, C. 2012; Lelovics, E. et al. 2014; Lehnert, M. et al. 2015), qualities of relief (Saaroni, H. and Ziv, B. 2010; Bokwa, A. et al. 2015) and the variability of synoptic conditions (Gedzelman, S.D. et al. 2003; Przy- bylak, R. et al. 2015), it is a fairly complex and challenging task. Contemporary studies of the temperature fi elds of cities and their sur- roundings, therefore, impose high demands on the density and quality of the station net- work and the frequency and range of mobile measurements. At the same time, it appears that the current methods of remote sensing focusing on land surface temperature vari- ability may not provide relevant information about air temperature (Voogt, J.A. and Oke, T.R. 2003). Recently, numerical modelling has come to represent another opportunity leading to more detailed and more accurate Modelled spatio-temporal variability of air temperature in an urban climate and its validation: a case study of Brno, Czech Republic Jan GELETIČ1,2 Michal LEHNERT3 and Petr DOBROVOLNÝ1,2 Abstract This study compares the results of air temperature model simulations with real temperature measurements in an urban environment. The non-hydrostatic micro-scale model MUKLIMO_3 is used to predict air tem- perature fi elds in Brno (Czech Republic). The development of the air temperature fi elds on three diff erent days was modelled which characterising the radiation-driven weather conditions with high temperature that occurred during the summer of 2015. This analysis demonstrates that the model is able to reproduce the spatial distribution of the air temperature during the day. Statistical tests were applied to establish whether signifi cant diff erences exist between the modelled and measured air temperatures. Verifi cation of the model results against real temperature measurements was performed at fi ve meteorological stations. The mean ab- solute diff erences between the simulated and measured daily mean temperatures were 0.7 °C (4 July), 0.6 °C (18 July) and 0.5 °C (28 August), respectively. This demonstrates that the model overestimated the real values, however, not all the diff erences were statistically signifi cant. Moreover, there were no signifi cant diff erences in the variability of the temperatures that were compared. This study also shows that the proper defi nition of Local Climate Zones and their parameters is critical for more precise model performance. Keywords: MUKLIMO_3, urban air temperature, Local Climate Zones, GIS, spatial modelling 1 Department of Geography, Faculty of Science, Masaryk University Brno, Kotlářská 2, 611 37 Brno, Czech Republic. E-mails: geletic.jan@gmail.com, dobro@sci.muni.cz 2 Global Change Research Institute of the Czech Academy of Sciences, Bělidla 986/4a, 603 00 Brno, Czech Republic. 3 Department of Geography, Faculty of Science, Palacký University Olomouc. 17. Listopadu 12, 771 46 Olomouc, Czech Republic. E-mail: michal.lehnert@gmail.com Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.170 information about the spatio-temporal vari- ability of urban air temperatures and UHI parameters. Because of the progress in exploring the complexity of processes driving the climate system, models designed for application on scale of the city have gradually been devel- oped. The first models demonstrated the diff erences in the energy balance between the city and its surroundings (e.g. Mills, G. 2009). The current state of the art numerical models make it possible to solve the ther- modynamics of the atmosphere and com- plex relations between variables, such as the height of buildings and the structure of the buildings, materials used, height and the types of vegetation on the scale of the urban environment (Sievers, U. and Zdunkowski, W. 1985; Gross, G. 1989; Baklanov, A. et al. 2009). While numerical modelling off ers very important information on urban temperature fi elds, another quite important task is the validation of the model outputs. Hollosi, B. et al. (2014) indicate that these results could not be validated as a result of the lack of ob- servations. The MUKLIMO_3 thermodynamic model developed by Deutscher Wett erdienst (2014) in collaboration with Zentralanstalt für Meteorologie und Geodynamik was used to analyse the main features of air tempera- ture variability in Brno (Czech Republic). The primary aim of this contribution is to validate the MUKLIMO_3 outputs using air temperatures measured at several meteoro- logical stations located in the city of Brno. The comparison is performed for several days that represent typical air temperature (more detail in section Meteorological data) conditions in Brno during the heat waves in the summer of 2015. Study area The study area is situated in the south-eastern part of the Czech Republic (Figure 1). Brno (49.2N, 16.5E) is the second-largest city in the country (population 400,000, land registry area 230 km2) and is characterised by a ba- sin position with complex terrain. Altitudes range from 190 m to 479 m a.s.l. with the higher elevations lying largely in the western and northern parts of the region. Lower and fl att er terrain is typical of the southern and eastern parts of the study area. There is a wa- ter reservoir (area approx. 2.6 km2) located on the northwest border of the built-up part. The study area lies in one of the warmest and dri- est regions in the Czech Republic. The mean Fig. 1. Elevation in the study area of Brno, position of validation stations and boundary of compact city structure 171Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180. annual temperature stands at 9.4 °C, while the mean annual precipitation is around 500 mm (1961–2000 reference period). The highest density of built-up areas occurs in the historical city centre. These are largely residential (20% of the study area). There are several industrial zones and large shopping centres with high percentages of impervious surfaces (almost 14% of the total area). Several large parks are located rela- tively close to the city centre. Further from the centre, individual land-cover categories form a mosaic of diff erent surface types, such as blocks of fl ats, gardens, allotments and ag- ricultural fi elds. Arable land and grasslands cover 34% of the study region and are situ- ated mostly in the south, while forests take up 29% of the region and are to be found largely west and north of the built-up area, at higher elevations. Methods and data MUKLIMO_3 MUKLIMO_3 (3D Mikroskaliges Urbanes KLIma MOdel) is a non-hydrostatic micro- scale model with z-coordinates, which solves the Reynolds-averaged Navier-Stokes equa- tions to simulate atmospheric flow fields in the presence of buildings (Sievers, U. and Zdunkowski, W. 1985; Gross, G. 1989; Sievers, U. 1990, 1995). The thermo-dynam- ic version of the model includes prognostic equations for atmospheric temperature, rela- tive humidity, wind speed and wind direc- tion (Sievers, U. et al. 1983). The model uses high-resolution orography, land use distri- bution data and the vertical profi le of the at- mosphere (up to 1 km above ground level). Land use classes were defi ned on the basis of Local Climate Zones (see below). For each land use class a set of param- eters is defi ned which describes land use properties and urban structures: building fraction (γb), mean building height (hb), wall area index (wb), fraction of pavement of the non-built area (v), fraction of tree crown canopy (σt) and fraction of low vegetation of the remaining surface (σc), height of low vegetation (hc) (Table 1), as well as leaf area index (LAIc) of the canopy layer, the mean height (ht) and leaf area index (LAIt) of the trees, with separate values for the tree trunk and the tree crown area. The model does not include cloud processes, precipitation, hori- zontal run-off or anthropogenic heat. MUKLIMO_3 was used to generate the development of the air temperature fi eld in the study area during three selected days. The model simulation for each day was rep- resented with 23 temperature maps with a resolution of 100 m; the time step between two successive modelled fi elds was 60 min- utes. The corresponding modelled and meas- ured temperatures for fi ve localities (stations) were compared with several statistical tests. Basic statistical tests for testing true diff er- ence (t-test) and variance (f-test) were used. A null hypothesis for a two-sample paired t-test is that the true diff erence in the means is equal to 0. The critical value of the T-dis- tribution is 1.717144. For a two-sample f-test a null hypothesis that the true ratio of the variances is equal to 1 was used. The critical value of the F-distribution is 2.04777. Local Climate Zones (LCZ) The scheme of local climatic zones (LCZs) according to Stewart, I.D. and Oke, T.R. has become a standard for the description of the environment in the fi eld of urban climate research. LCZs are defi ned as regions with a characteristic surface cover, structure and material and human activity that span hun- dreds of metres to several kilometres on a horizontal scale (Stewart, I.D. and Oke, T.R. 2012). Bechtel, B. and Daneke, C. (2012), furthermore Lelovics, E. et al. (2014) subse- quently moved the LCZ concept toward a generally recognised regional typology. For this study an LCZ was delimited using a GIS- based method presented by Geletič, J. and Lehnert, M. (2016). The method was based on measurable physical properties of the en- Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.172 vironment derived from typical values of the geometric and surface cover properties of a particular LCZ as defi ned by Stewart, I.D. and Oke, T.R. (2012). The values of the physical properties of the environment were calculated for 100-m pixels on the basis of the ZABAGED vector geo-database and photogrammetric data (3D model of development). The pixels were sub- sequently classifi ed using a clearly defi ned decision-making algorithm that had been tested in the Central European environment. Finally, a two-stage majority fi lter was ap- plied to defi ne the local climate zones in the Brno (Figure 2). (For more details see Geletič, J. and Lehnert, M. 2016.) Meteorological data As MUKLIMO_3 provides the best results for radiation-driven weather conditions that are characterised by an almost clear sky, minimum cloud cover and weak advection (Hollosi, B. et al. 2014), three days in the high summer season of 2015 were used for model validation (4 July, 18 July and 28 August). The maximum daily temperatures exceeded 30 °C and each of these days was the third day of one of the heat waves which aff ected Brno in the summer season of 2015. A heat wave was defi ned as at least three consecutive days on which the air temperature reaches over 30 °C (Meteorologický slovník výkladový a terminologický 2016). Data from fi ve stations was used for the validation of the model outputs (Table 2, and see Figure 1). Four stations belong to the local meteorological monitoring network, which has been in operation since 2009. These sta- tions represent the specifi c features of urban weather, because they are located in urban areas among buildings and near the city centre with heavy traffi c. The fi ft h station is a professional station of the Czech Hydro- Meteorological Institute (CHMI), which is located at the airport in Brno-Tuřany (Dobrovolný, P. et al. 2012). Table 1. Parameters for Local Climate Zones in the MUKLIMO_3 model* Local Climate Zone γb % hb m wb v % σt % σc% ht m hc m 1 Compact high-rise 0.60 25.00 6.67 1.00 0.00 0.90 0.00 0.10 2 Compact midrise 0.45 16.50 3.42 0.70 0.00 0.90 0.00 0.10 3 Compact low-rise 0.45 9.20 2.40 0.40 0.00 0.80 0.00 0.10 4 Open high-rise 0.30 25.00 7.00 0.20 0.00 0.60 8.00 0.10 5 Open midrise 0.30 18.60 4.40 0.45 0.00 0.80 4.00 0.10 6 Open low-rise 0.30 6.50 2.10 0.40 0.00 0.70 0.00 0.10 7 Lightweight low-rise 0.75 3.00 1.80 0.20 0.00 0.30 0.00 0.10 8 Large low-rise 0.40 6.80 2.00 0.80 0.00 0.80 0.00 0.10 9 Sparsely built 0.15 8.50 2.10 0.45 0.00 0.80 8.00 0.10 10 Heavy industry 0.50 18.00 2.00 0.80 0.00 0.80 0.00 0.10 A Dense trees 0.00 0.00 0.00 0.00 0.80 0.90 21.00 0.50 B Scatt ered trees 0.00 0.00 0.00 0.00 0.40 0.90 14.00 0.50 C Bush, scrub 0.00 0.00 0.00 0.00 0.40 0.90 2.00 0.50 D Low plants 0.00 0.00 0.00 0.00 0.00 1.00 0.20 0.50 E Bare rock or paved 0.00 0.00 0.00 0.95 0.00 0.01 0.00 0.30 F Bare soil or sand 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.30 G Water 0.00 0.00 0.00 -1.00 0.00 0.01 0.00 0.30 *Parameters: building fraction (γb), mean building height (hb), wall area index (wb), fraction of pavement (v), fraction of tree crown canopy (σt), fraction of low vegetation (σc), tree height (ht) and height of the low vegetation (hc). The fractions γb and σt are relative to the total grid cell area (1 ha). The fraction v is relative to the area without buildings and trees and σc is relative to the remaining surface. 173Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180. Fig. 2. Local climate zones in Brno and its surroundings (Geletič, J. and Lehnert, M. 2016). The values 11 to 17 correspond with the classes A to G (Coordinate system: S-JTSK / Krovak East North; EPSG: 5514). Table 2. Validation stations and their characteristics* Station ID Altitude, m Longitude Latitude Exposure LCZ NDVI DENS BOTA FILO HROZ SCHO TURA 242 234 214 225 241 49.20417 49.20028 49.19361 49.20722 49.15306 16.59639 16.59806 16.57222 16.61389 16.68889 E E SW SW S 2 5 5 B D 0.18 0.21 0.34 0.31 0.24 27 39 14 17 5 *LCZ – LCZ class; NDVI – Normalised Diff erence Vegetation Index measuring amount of vegetation; DENS – density of buildings (%) in 200 m radius around station. All the station measurements were per- formed with a 10-minute frequency and hourly values of the air temperature were used for validation. The meteorological data (air temperature, relative humidity, wind speed and direction) necessary for the op- eration of the MUKLIMO_3 model were derived from the measurement of vertical profile of the atmosphere up a height of 1 km above surface at the Prostějov station located about 45 km north-east of Brno. In MUKLIMO_3 it is possible to use a minimum of one and a maximum of fi ve layers for the same meteorological elements (Deutscher Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.174 Wett erdienst 2014). We used three layers in our vertical profi le, at 350, 660 and 980 m. The height of the urban boundary layer can reach approximately 350 m above the ground (Menut, L. et al. 2015). Therefore it was sup- posed that the atmospheric conditions at these heights would probably be the same for Brno and for Prostějov. Meteorological data from the Brno-Tuřany station was used to represent the ground measurements of the study area. For each simulation diff erent ver- tical profi le was used. The water temperature in the reservoir during the summer season was measured by the Regional Hygienic Station of the South Moravian Region in Brno. Results It follows from the model simulations that the places with the lowest air temperatures in the early morning hours before sunrise were lo- cated in the deep river valleys in the north- ern part of Brno (Figure 3, a). Generally, lower air temperatures are typical of LCZ A. Aft er the sunrise the spatial distribution of the air temperature is predominantly infl uenced by altitude. At 7 a.m. (see Figure 3, a) the model forecasts 19 °C for areas with a lower location (particularly the south-eastern part of the area of interest and valleys) and 16 °C for areas with a higher location (particularly the north- ern and north-western parts of the area). As the air gets warmer the model gradu- ally generates areas with a higher propor- tion of LCZs 8, 10 or E that are warmer than their surroundings, including ar- eas located outside the compact urban development. However, the distinct UHI is not formed until 1 p.m. according to the results of the model simulations. At 2 p.m. the UHI is formed over most of the city centre, including areas of LCZs 1 and 2. Higher temperatures were also simulated for smaller sett lements with urban develop- ment. So-called hotspots were formed in ar- eas with a higher proportion of LCZs 8, 10 or E with air temperatures above 31 °C. On the contrary, relatively cooler spots within the city correspond to larger areas of LCZ B, where air temperatures reach about 29 °C. The lowest temperatures are predicted for forested areas (LCZ A) at higher elevations located in the northern and north-western parts of the area of interest (around 26 °C). Thus the model simulates temperature dif- ferences of up to 5 °C between the warm- est part of the city and the coolest forests at 2 p.m. (Figure 3, b). The city centre and areas with a higher proportion of LCZs 8, 10 or E are expected to remain slightly warmer than their surround- ings until the night hours. Higher tempera- tures occur around bodies of water (LCZ G). The model, however, forecasts a relatively low intensity of UHI during the evening and night hours. At 9 p.m. the warmest parts of Fig. 3. Modelled spatio-temporal variability of the air temperature (°C) in Brno on 28 August 2015 at 7.00 a.m. (a), at 2.00 p.m. (b) and at 9.00 p.m. (c) CET 175Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180. the city are only about 1 °C warmer than the agricultural landscape around the city (pre- dominantly LCZ D) and up to 3 °C warmer than the forested areas (Figure 3, c). In general, the MUKLIMO_3 simulations overestimate the real air temperatures on all three of the days that were analysed (Figure 4). The simulated mean daily temperatures were, on average, higher by 1.2 °C (4 July), 0.6 °C (18 July), and 0.9 °C (28 August) than the measured temperatures. The tempera- tures were especially overestimated at the BOTA (LCZ 2) and HROZ (LCZ 5) stations. The minimum absolute diff erence occurred at the TURA station (0.9 °C) and maximum at the BOTA station (1.2 °C). Clearly higher model temperatures compared to measured ones occurred only on 4 July (in the starting phase of the model) and on 28 August (the model simulation assumes a sharp peak in the daily air temperature curve, whereas the real daily temperature curve showed lower maximum temperatures and simultaneously temperatures remained at relatively higher values for longer intervals). Minimum daily average diff erence occurred at the TURA sta- tion on 4 July (0.8 °C) and maximum at the FILO station on 4 July (1.7 °C). A comparison of measured and simulated air temperatures for the three selected days demonstrates that the model successfully approximates the temperature variability through day and night at the locations of the individual stations (Figure 5). The smallest absolute diff erence between real and simu- lated air temperature was found for TURA. Station is located outside the compact urban structure at the international airport (LCZ D). The maximum mean diff erence is typical of the BOTA station, which is located within a compact city structure (LCZ 2) in a botanical garden inside the built-up area. The diff erences between the modelled and measured air temperatures were further eval- uated with several statistical tests (Figure 6). It allows evaluate the statistical signifi cance of the diff erences that had been found between measurements and model outputs. The re- sults of the t-test confi rm that most model Fig. 4. Diff erences between real measurements and model outputs Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.176 Fig. 5. Comparison between real measurements (left ) and model outputs (right) outputs are overestimated for all stations. While the mean daily modelled temperatures were signifi cantly higher than the measured ones at all fi ve stations on two of the days that were analysed (4 July, 28 August), there were no signifi cant diff erences on 18 July (p > 177Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180. 0.05 for all stations except HROZ). Moreover, there were no signifi cant diff erences in the temperature variability according to the F- test (p >> 0.05) at any of the stations on all three days that were analysed. Discussion The comparison of the real station measure- ments and MUKLIMO_3 simulations in Brno and its surroundings shows that the model is able accurately to simulate the daily cycles of the air temperature at the fi ve selected loca- tions and to take into account some of the specifi c local features. The model corresponds best with the situation on 28 August 2015 (see Figure 4); this may be related to more stable atmospheric conditions very close to clima- tological autumn. Individual problems with the accuracy of the model simulation were primarily related to the starting phase of the modelling (esp. on 4 July 2015; see Figure 4). This problem may be related to the interac- tion of the 1D and 3D models. The 1D model starts before the 3D model and prepares the atmospheric conditions for the 3D model (Deutscher Wett erdienst 2014). In our case it starts 24 hours before the 3D model. This may be too far in advance. The correct set- tings of the Land Use Table parameter may also be responsible (see below). At times when the surface displays a nega- tive energy balance MUKLIMO_3 frequently assumes a sharp drop in the temperature ear- lier than the measurements (for example at the TURA station on 4 July) or steady decline rather than a sharp drop aft er sunset (at all stations on 18 July). This could largely be due to the complexity of the relief in Brno and its surroundings and the related local circula- tion systems. The spatial patt erns of the simulated tem- perature fi eld correspond to the theoretical expectations in those periods when there is a positive energy balance. The fi rst hotspots were formed in the morn- ing in LCZs 8, 10 and E, which indicates the beginning of UHI formation. In the early aft er- noon hours (1–3 p.m.) the central part of the Brno area was about 1-2 °C warmer compared to suburban areas and up to 4 °C warmer than the surrounding forests, according to the model outputs. The air temperature of a large part of the urban areas was not higher than in the areas where there was an agricultural landscape with a predominance of fi elds (LCZ D). This is in agreement with the fi ndings of several other studies which indicated that the daily measurements of air temperatures in LCZ D may be higher than the temperatures measured in some types of compact built-up areas (e.g. LCZs 5 or 9; Houet, T. and Pigeon, G. 2011; Lehnert, M. et al. 2015). At night during the period of negative energy balance MUKLIMO_3 assumed a temperature that was just 1 °C higher in the centre of the city than in the suburbs and temperature that was 3 °C higher in the city centre than in the coldest forests. This may be compared to the results of mobile measure- ments in the Brno area (Dobrovolný, P. and Krahula, L. 2015). These authors claim that during the fi rst half of the night in summer the city centre is almost 2 °C warmer com- pared to the suburbs and almost 5 °C warmer than the surrounding rural areas. The actual comparison of the model results and station measurements does not refer to an underes- timation of the intensity of the UHI eff ect. The diff erences in the average daily mini- mum temperatures between the stations that were analysed here, because of the absence of a reference station located in a cool area, smaller than measured Dobrovolný, P. et al. (2012). The surroundings of the city may ac- tually be cooler than the model expects. The analysis of the spatial patt erns of the simulated temperature fi eld shows that the MUKLIMO_3 model primarily refl ects the ef- fect of altitude. This is especially evident in the late aft ernoon and evening hours and during the night. The model predicts globally higher temperatures at lower altitudes. It can be con- sidered as a simplifi cation (Bokwa, A. et al. 2015). On the other hand, the model does not refl ect the extent of the variability of building density (i.e. the amount and eff ect of accumu- Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180.178 Fi g. 6 . B ox pl ot s of a ir te m pe ra tu re m ea su re m en ts a t t he s ta tio ns , m od el o ut pu ts a nd re su lts o f s ta tis tic al te st s (p ai re d t-t es t a nd f- te st ) 179Geletič, J. et al. Hungarian Geographical Bulletin 65 (2016) (2) 169–180. lated heat). It is anticipated that for more ac- curate simulation of the spatio-temporal tem- perature fi eld it is necessary to focus att ention on a Land Use Table. Moreover, it is possible that the concept of local climate zones (LCZ) is too general for modelling on a detailed level. It may cause incorrect sett ings of the thermal capacity of individual surfaces. Conclusion Using numerical models for the prediction of air temperature on a local scale represents progress in urban climatology. Although the MUKLIMO_3 simulations showed a number of uncertainties and customisation which must be improved (e.g. the classifi cation of local climate zones seems to be too general as input for the Land Use Table), the model showed good performance in its approxima- tion of the daily courses of air temperature in diff erent urban environments. The degree of imprecision is highly dependent on the quality (e.g. representatives of meteorologi- cal measurement) and degree of generalisa- tion (e.g. spatial resolution) of the input data. The model outputs may be used to study the development of the air temperature fi eld in high temporal resolution (e.g. 60 minutes) but also for quantifi cation of the eff ect of re- lief, land cover/use and weather conditions on local (urban) climate. The model is also useful to analyse UHIs. To reach a bett er performance the model must be validated in various cities with diff erent landscape struc- tures throughout the moderate climate zone. Therefore, it is necessary to continue to study the model sett ings and try to prepare optimal inputs for bett er results. Acknowledgments: This contribution was prepared within the project “Urban climate in Central European cities and global climate change” of the International Visegrad Fund’s Standard Grant No. 21410222 and the project “UrbanAdapt – Development of urban adaptation strategies using ecosystem-based ap- proaches to adaptation”, supported by grant EHP- CZ02-OV-1-036-2015 from Iceland, Liechtenstein and Norway. 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