Spatial neighborhood analysis linking urban morphology and green infrastructure to atmospheric conditions in Karlsruhe, Germany

Urban areas are affected by the urban heat island effect, resulting in increased heat strain compared to rural areas. In this article, we aimed to study how urban morphology (e


Introduction
Urban environments determined by climatic effects from the prevailing mesoscale down to the microscale influence the quality of life in cities.This refers mainly to the microscale's urban bioclimate, air quality, traffic, and noise in street canyons (Gehl, 2010;Matzarakis, 2020;Węziak-Białowolska, 2016).Therefore, bioclimate, and thus human thermal comfort, are severely threatened by the urban heat island effect (UHI), global climate change, increasing heatwaves, further sealing, and re-densification of urban areas (Masson et al., 2020a;Nowak and Greenfield, 2020;Revi et al., 2014;Santamouris, 2020).
A majority of studies focus on quantifying the UHI effect based on land surface temperature (LST) derived from satellite imageries.
However, these methods are currently insufficient for human-biometeorological purposes because the spatial resolution of freely available satellite imagery is insufficient for microscale analysis of urban areas (e.g., 30 m resolution of Landsat 7, and 8 and 20 m resolution of Sentinel-2 for the assessment of thermal infrared) (Ermida et al., 2020;Masson et al., 2020b;Sobrino et al., 2012).The temporal resolution is restricted to the overpass time of the space-borne platform, and the obstruction of the surface by clouds; i.e., a full assessment of diurnal cycles of the surface urban heat island (S-UHI) is currently not possible (Sobrino et al., 2012).Furthermore, in the complex urban environment, remote sensing instruments cannot entirely capture energy conversions on vertical surfaces or facades due to effective anisotropy (Voogt and Oke, 1998).It is not possible to measure air temperature or humidity directly by space-borne remote sensing, only land surface temperature which results in S-UHI in urban environments (Voogt and Oke, 2003).Nevertheless, the complexity of the human thermal bioclimate cannot be reduced to the assessment of surface temperature; it is necessary to assess all atmospheric conditions (air temperature, relative humidity or vapor pressure, wind speed, and long-and shortwave radiation fluxes in terms of Mean Radiant Temperature) in urban environments (Parsons, 2014;VDI, 2021).These conditions can be summarized by thermal indices in a comprehensive way (Höppe, 1999;Jendritzky et al., 2012;Matzarakis et al., 1999;Staiger et al., 2019).
In contrast to remotely-sensed measurements, in-situ observations, spatial surveys and traverses were used to determine the characteristics of the UHI, or rather the urban heat archipelago, based on measurements of the air temperature (Chandler, 1962;Kotharkar and Surawar, 2016;Liu et al., 2017;Romero Rodríguez et al., 2020a;Saaroni et al., 2000).Based on these measurements, spatial interpolation based on geostatistics (Inverse Distance weighting, b-spline, nearest neighbor, triangulated irregular network or kriging (Longley, 2005)) and statistical approaches of machine learning were used to determine the UHI with high spatial resolution over the entire area.
The combination of satellite data (LST by Sentinel-2) and in-situ measurements by statistical models has previously been applied (Shandas et al., 2019;Voelkel and Shandas, 2017).Air temperature observations from a citizen science-driven measurement campaign were used to predict the extremes of UHIs using machine-learning techniques (RandomForest).The selected algorithm was applied with descriptors for land use and land cover (LULC), derived from survey images.
In order to quantify and map the urban microclimate spatially, data on the urban morphology in terms of land use, building morphology, and vegetation are necessary (Masson et al., 2020b).These data can be supplemented by demographic and traffic data to assess anthropogenic heat release to capture the leading causes of the UHI effect (Romero Rodríguez et al., 2020a).These variables must be related to in-situ observations, spatial surveys, traverses, and remotely-sensed datasets.(Romero Rodríguez et al., 2020a) describe the traversed environment with a discrete grid.The above parameters characterize each grid cell.
The urban morphological surroundings are a subset of the urban morphology in the proximity of a point of interest.The urban morphology represents the size, shape, and physical structure of a city and can be viewed from different perspectives with different focus (D'Acci, 2019).
Considering the urban morphology through remotely-sensed land-use classification (e.g.Local Climate Zones (LCZ, Stewart, 2011;Stewart and Oke, 2012), Urban Climate Zones (UCZ, Oke, 2004), CORINE Land Cover (CLC, Keil et al., 2005) or Urban Atlas 2018 (UA2018, European Union, 2018)) describes urban areas with varying degree of detail: LCZ has been widely applied to assess the UHI effects as the temperature difference between different LCZ classes (Leconte et al., 2015;Lehnert et al., 2021).LCZ provides 17 different classes to characterize urban areas at a local scale (1 × 10 2 m -1 × 10 4 m).LCZs are available for all of Europe at a spatial resolution of 100 m (Demuzere et al., 2019).However, the analysis based on LCZs is not suitable for the microscale due to insufficient detail in classes of urban areas, so the inner-zonal variation of the meteorological conditions cannot be resolved (Lehnert et al., 2015).
Vectorial Urban Atlas 2018 summarizes the distribution of urban, industrial, and green areas in a city and is especially suitable for European cities.Each type of land use is characterized by a different degree of building development, sealing, and greening, resulting in different thermal environments.Different resulting meteorological conditions characterize each environment in turn because it depends on the energy balance of the immediate surroundings, i.e., thermal properties (e.g., heat storage capacities), radiation-related properties (e.g., albedo and emissivity), and thus the sensible, latent, and radiative heat fluxes in the proximity (ASHRAE, 2017;Oke et al., 2017).Furthermore, intrinsic processes modify the thermal environment.These include anthropogenic processes (e.g., combustion), and natural processes such as the microclimate regulation by transpiration and shading of urban trees (Ferrini, 2017;Jones, 2013;Monteith and Unsworth, 2013).
In order to evaluate the thermal effects on the microscale of individual urban trees and buildings in an open system (such as the urban environment), it is not sufficient to consider only land use, since these classes cannot represent the diversity (of buildings and trees), and especially cannot resolve vertical structures.
Urban tree cover and species identity can significantly influence the urban microclimate at cityscape level.For instance, (Morakinyo et al., 2020) used ENVI-met simulators to use 54 generic tree forms and 10 urban morphology characteristics to prove that correct species selection is crucial to reduce the impact of UHIs.A study using Landsat imageries on 156 remotely-selected sample plots from 15 greenspaces in the city of Changzhou in China found that tree species diversity and tree canopy coverage can mitigate the heat stress created by UHIs (Wang et al., 2021).At single tree level, transpirational cooling can ameliorate urban microclimate at local level which can vary between species (Rahman et al., 2017(Rahman et al., , 2020)).
However, upscaling and modeling studies on the interrelationships between tree cover and urban microclimate by combining remotely-sensed data with field measurements from replicated sampling units covering diverse urban morphology are rare in the literature.
In this article, we quantified the microscale effects of urban morphological surroundings on the atmospheric conditions, and thus also on the bioclimate, based on remotely-sensed data, in-situ observations, and administrative data (e.g., managed tree cadaster and real estate cadaster) for the municipality of Karlsruhe in Germany.Mobile measurements were generalized to determine air temperature and humidity anomalies, along with a spatial survey without the influence of the absolute measured values.The measurement data were extensively processed to extinguish errors in the accuracy of the Global Navigation Satellite Systems (GNSS) in the city, and systematic errors (e.g., at traffic lights).The processed data were used to reveal relationships between observed meteorological conditions and urban structures near the route of mobile measurements.Vicinity to the route was characterized as a neighborhood by representative parameters: shares of Urban Atlas classes, Sealing and Normalized Difference Vegetation Index (NDVI).The size of the circular neighborhood was varied, and studied between 5 m to 500 m of the route, since the thermal range of individual urban structures (in terms of heat transfer) is unknown and dependent on the respective wind direction and -speed.
Based on the relation between normalized air temperature and characterized neighborhood the following research questions are addressed: 1. How can spatial measurement runs be used to quantify urban heat island effects? 2. What is the thermal influence of urban green and gray infrastructure on the ambient air temperature?3. How can local observation, remote sensing, and administrative data be combined and applied for short-and long-term climate adaptation and mitigation?
Urban planners and architects can actively modify all representative variables of a neighborhood to improve the quality of life for people in cities, but knowledge about the thermal effects of urban structures is crucial to do so, and enable reaction to the effects of a typified heat wave (Gehl, 2010).

Study area in Karlsruhe, Germany
Karlsruhe is located in the warm Upper Rhine Valley in Germany.The city center is located at 49.0 • N, and 8.4 • E at about 115 m above mean sea level (Fig. 1).In 2021, 308,436 inhabitants lived in an area of 173.4 km 2 (≈ 1778 inhabitants per km 2 ) in Karlsruhe (Stadt Karlsruhe, 2021).
In 2003, Germany's air temperature record of 40.2 • C, valid until 2015, was set at the meteorological station in Karlsruhe.The high heat stress in the Upper Rhine Valley reflects various climatic particularities, some of which are orographically caused.These result in warm, humid air, and high irradiation combined with low wind speeds (Hackenbruch, 2018), reflecting the Köppen-Geiger class Cfb for warm temperate; fully humid with warm summer (Rubel and Kottek, 2010).

Mobile measurements to determine the microscale influences of gray and green infrastructure
Spatial surveys were carried out with a mobile measurement vehicle in 2019 and 2020, each in June during the hot season in Karlsruhe (Fig. 2).The measurement vehicle drove through the most significant areas in Karlsruhe on a route with length of 19.6 km (which lasts 20 min on an average per run) (Fig. 1).The meteorological variables were measured with a temporal resolution of 1 observation ⋅ s − 1 .Therefore, the spatial resolution is variable due to the dynamic driving speed.Nevertheless, a constant speed of 30 km/h was maintained in urban areas as per the suggestion from (Ketterer and Matzarakis, 2015), and 50 km/h in rural areas, especially on highways in accordance with (Soltani and Sharifi, 2017).
The meteorological measurement system was installed at the front of the measurement vehicle and included measurements of actively ventilated air temperature (T a , • C) and relative humidity (RH, %) at 0.7 m and 2.0 m AGL, as well as surface temperature (T 0 , • C) and global radiation (G, W/m 2 ).Descriptive statistics of air temperature in the raw data are shown in Table 1 and Table 2.In total, the route was surveyed 26 times.In 2019 there were seven trips during the day and four during the night.In 2020 there were eight trips during the day and seven during the night.All measurement runs were carried out with a time interval of three hours.
The measurements were conducted during autochthonous weather conditions in order to determine the local and regional influences of urban structures, and vegetation.A barometric ridge gave the conditions for a successful measurement campaign over Central Europe in combination with a corresponding surface high.Large-scale subsidence prevented almost all cloud formation.The UHI condition was clearly pronounced during the measurement periods.

Preprocessing and preparation of observed data
The common challenges in mobile measurements are spatial and temporal accuracy (e.g., at traffic lights, traffic jams, GNSS inaccuracy) and human error (e.g., driving errors).Therefore, sequential preprocessing steps were implemented, and encompass the aggregation, relation, generalization, and transformation of the recorded data to counteract those errors (Fig. 3).
The preprocessing was conducted with R version 3.6.1,a free software environment for statistical computing suitable for human biometeorological analysis (Charalampopoulos, 2020; R Core Team, 2019).Further geoprocessing packages (rgdal-1.5-16,raster-3.3-13,exactextractr-0.4.0) and the Geographic Information Systems (GIS) Quantum GIS (QGIS-3.20.0RC) and SAGA GIS (2.3.2) (Conrad et al., 2015) were utilized.We have described the steps which were followed during the preprocessing of the data: 1. Raw data was first provided in comma separated values format (CSV) for each measurement run and then further processed in the GeoPackage format (Yutzler, 2021); 2. All outliers with a value greater than three times the standard deviation were removed from the data sets.Then, the data points with a wind speed of <0.5 m ⋅ s − 1 or >3.0 m ⋅ s − 1 were filtered out.Wind speed was obtained from the nearest meteorological station; 3.All measurement runs were sorted into four groups according to the time of day.The first group includes all runs during the night (between 22 and 4 UTC).The second group sorted the runs in the morning (between 4 and 10 UTC), and the third group sorted the runs during midday (between 10 and 16 UTC).Finally, the last group contains the runs in the evening (between 16 and 22 UTC);  (1) 5. The related observations (p rel ) are further differenced (Eq.2), normalized (Eq. 3) and standardized (Eq.4) to generalize from the absolute measured values: Table 1 Descriptive statistics for the observations of air temperature at 2.0 m AGL in Karlsruhe in June 2019.

Table 2
Descriptive statistics for the observations of air temperature at 2.0 m AGL in Karlsruhe in June 2020.The calculation of p Δ , p norm and p stand ideally allows a direct comparison of the measurements independent of the time of day and year in which the measurements were recorded.p norm was considered in the subsequent neighborhood analysis and applied to the relative, observed air temperature at 2.0 m AGL; 6. Due to the inaccuracy of GNSS, the measurement runs were several meters apart, although they were carried out on the same route (Fig. 5a).The mean error of all GNSS positions was 9.2 m, while 95% of all observations were within 14.1 m of the route (Fig. 4).An artificial data set with synthetic reference points with predefined positions, which was within exactly the driven route at a regular distance of 5 m, was created (Fig. 5b).The positions of these reference points were determined using the georeferenced roads from the OpenStreetMap dataset.This new artificial data set was used to correct the inaccuracies of GNSS positions and align the measurement runs spatially.Each measurement run was spatially aligned, based on the reference points, so that the normalized parameters were mapped to the reference points; 7. Finally, for each reference point, the max/min/mean/median normalized condition within a radius of 15 m of the overlapping and aligned observations was calculated (Fig. 5c).The radius of 15 m was selected due to the 95th percentile in the recorded locations during measurements (Fig. 4).This method ensures that all measurement runs and points are then located at the same georeferenced position.In these ways, the observations were also transferred from a temporal (1 observation per second) to a spatial observation series (1 observation per 5 m), and clustered measuring points (e.g., at traffic lights) were averaged (Fig. 5d).

Representation of the urban morphology in the neighborhood of the route
In theory, the meteorological variables (T a,0 m , T a,0.7 m , T a,2.0 m , RH 0.7 m , RH 2.0 m , VP 0.7 m and VP 2.0 m ) depend on the energy balance of the immediate surroundings, and thus on sensible, latent, and radiative heat fluxes in the proximity to the route.These fluxes are influenced by different surface properties of the immediate surroundings (i.e., thermal properties (heat storage capacities and thermal conductivity), radiation-related properties (albedo and emissivity)) but also by intrinsic, anthropogenic, and natural processes in the city.These include, for example, combustion processes as well as tree-physiological processes (e.g., transpiration and photosynthesis).In addition, the outgoing and incoming radiation fluxes are determined by the Sky View Factor (SVF), which in turn is significantly influenced by the height of surrounding buildings and spacing between buildings.
The classification according to Urban Atlas 2018, was first used to quantify the spatial influence of immediate surroundings.This classification differentiates between five urban development classes based on the prevailing degree of sealing (section 2.4.1).
The immediate surroundings were additionally examined separately for the gray and green infrastructure.We undertook the following steps for that purpose: 1.The structure in a neighborhood was quantified by imperviousness (e.g., roads, buildings, and infrastructure) (European Union, 2018) (section 2.4.2); 2. The vegetation was taken into account by remotely-sensed Normalized Difference Vegetation Index (NDVI) (Ermida et al., 2020).In addition, data from the tree cadaster of the municipal garden and civil engineering departments were used (section 2.4.3).
The open-source GIS systems SAGA GIS (2.3.2) (Conrad et al., 2015) and QGIS (3.20.0RC) (Open Source Geospatial Foundation, 2018) were used to prepare the descriptors for subsequent neighborhood analysis.First, all descriptors were resampled to the spatial resolution of 1 m and transformed to the same metric projection (WGS 84 / UTM zone 32 N -SRID:32632), suitable for the study area.

Representation of the land use according to urban atlas 2018 land-use classification in the neighborhood (European Union, 2018)
Urban Atlas 2018 is a high-resolution (20 m) remotely-sensed dataset (European Union, 2018).A land-use classification based on 27 classes classifies urban areas based on urban fabrics, industrial areas, transportation infrastructure, artificial non-agricultural areas, and natural/semi-natural areas (Table 3).The Urban Atlas 2018 dataset is available in a vector data format compliant with standards of the Open Geospatial Consortium (OGC).
The measurement route is characterized according to the Urban Atlas classification in the neighborhood (Fig. 6a).For this purpose, the proportions of each land-use type within a radius of 5 m to 500 m from each preprocessed measuring point were recorded.The proportion of Urban Atlas classes UA2018:11100, UA2018:11210, UA2018:11220, among others, were calculated and assigned to each observation.The frequencies of the land-use types in different neighborhoods to the measurement route (5 m to 200 m) is shown in the histogram and corresponds essentially to that of the entire city (Fig. 6b).Densely built-up, urban-, industrial-, and wooded areas represent the central part of land use in the city.Thus, it is assumed that the survey route represented the entire city.

Representation of the gray infrastructure in the neighborhood
(European Union, 2018) also provides a high-resolution layer (HRL) for the degree of sealing.The layer for imperviousness is a remotely-sensed dataset in 20 m spatial resolution, which depicts the dimensionless degree of sealing from 0 to 1. Areas with a sealing degree of 0 (e.g., urban forests) are undeveloped, unsealed areas.These surfaces are characterized by a reduced heat storage capacity and increased evapotranspiration.
In contrast, wholly sealed areas have a sealing degree of 1 (e.g.inner-city areas).These areas are characterized by an increased heat storage capacity and reduced evapotranspiration.The imperviousness within a radius of 5 m to 500 m from each measuring point was recorded and is exemplarily shown in Fig. 7.

Representation of green infrastructure in the neighborhood
Vegetation in the proximity to the route was parameterized by the Normalized Difference Vegetation Index (NDVI), because this dataset is available for the entire urban area, especially for the urban forest in the north (Hardtwald) (Fig. 8).NDVI was calculated from remote satellite imagery of Landsat-8.Landsat-8 provides thermal infrared spectral bands (TIR) through its sensors TM, ETM+, and TIRS, to calculate NDVI in a resampled resolution of 30 m. NDVI was calculated by the script of (Ermida et al., 2020), utilizing Google Earth Engine and the spectral bands for near-infrared (NIR) and red (R) of Landsat-8.The index is defined as: NDVI is 0 if the respective surface is fully sealed and not covered with vegetation, and 1 in fully vegetated and unsealed areas.NDVI is available throughout the whole city but does not provide further information about the obstruction of the upper hemisphere.This means that shading effects due to the tree canopy cannot directly described by NDVI.Depending on the density of the tree Fig. 6.Characteristics of the neighborhood in terms of land-use types.For detailed description of the LULC classes see Table 3.

M. Gangwisch et al.
canopy, longwave radiation emitted by surfaces below the tree canopy could also be limited and not assessed by NDVI.

Spatial neighborhood analysis
All descriptors mentioned above were used to characterize the immediate vicinity of the measurement route.In addition, for each measuring point, descriptors values within a radius of 5 m to 500 m were used.The preprocessed meteorological data (Fig. 3) were  related to the characteristic descriptors of the neighborhood to show the effects of urban structures and vegetation on the urban atmospheric conditions.

Results
In the following, we first show the results of the preprocessing of the measurement data from steps 1 to 7 (Fig. 3).Subsequently, the results of the actual spatial neighborhood analysis are presented for imperviousness and NDVI along the route.
The night condition (22-4 UTC) depicted the UHI in its most dominant form.The spread of the air temperature as expressed as the difference between absolute minimum and maximum was the largest value with 5.6 K compared to other time intervals (Table 4).This spread represented the classic UHI intensity in Karlsruhe, assessed by measured air temperature.
This was particularly evident from the relative and normalized air temperature difference between the core of the city, south of Karlsruhe Palace (LCZ 6) and Karlsruhe Hardtwald (LCZ B) in the north (Fig. 9).In addition, a decreasing gradient of relative and normalized air temperature between Karlsruhe city center (LCZ 2) and Karlsruhe Durlach (LCZ 5) in the east was pronounced.Overall, the relative and normalized air temperature during the nighttime condition was relatively homogeneously distributed throughout the study area and thus characterized by large spatial auto-correlation.The normalized air temperature was not changing in an abrupt manner.The most significant changes took place in areas of land use change (e.g., at forest boundaries).
Spatial auto-correlation was analyzed separately in a variogram for the four time intervals (Fig. 10).In the variogram it can be clearly seen that the variance of relative and normalized air temperature at 2.0 m AGL with increasing distance between the measuring points was lower in the night condition (in blue) than during the day (in red).This means that the small-scale influence of different urban structures within the city was minimal during the night.
The condition in the morning (4-10 UTC) showed the weakening of the UHI effect -the spread was reduced to 3.3 K.At the same time, the cooling by urban trees intensified with increasing solar irradiance and Photosynthetically Active Radiation (PAR) in the Hardtwald area (LCZ B), but especially in the Zoologischer Stadtgarten (LCZ 6 and B) (Fig. 11).The observed values of air temperature at 2.0 m AGL were spatially heterogeneous and exhibit more significant variance than at night (Fig. 10).
The conditions at noon (10-16 UTC) showed a further intensification of the cooling effect of urban parks.Especially Zoologischer Stadtgarten (LCZ 6 and B) in the south unfolded its cooling potential (Fig. 12).At the same time, measurement results showed a greater variation.This also decreased spatial autocorrelation, which was reflected in an increase in the variance of relative and normalized air temperature (Fig. 10).The warmest area along the measured section was on the busy main road (Reinhold-Frank-Straße).
The evening conditions (16-22 UTC) showed the spatial development of the UHI (Fig. 13).The spread was increasing again to 5.2 K.The same pattern as in the night but with a lower magnitude was recognizable, meaning that the UHI was not yet fully developed (compare Fig. 9 and Fig. 13).

Influence from different neighborhoods
For each observation, each descriptor in the 5 m to 500 m orbit to the route was calculated.Descriptors for gray infrastructure (imperviousness (Fig. 7)) and green infrastructure (NDVI (Fig. 8)) were applied and related to the derived relative and normalized air temperature at 2.0 m AGL.The complete result set for all time intervals and buffer sizes is given in Appendix A and B. In the following, only selected buffer sizes and time intervals are presented for simplicity.It is important to note that the number of observations per descriptor class did not vary between different time intervals, but between the analyzed buffers by design of the analysis.

Impact of gray infrastructure
High degree of sealing in urban areas (bars in dark-red) resulted in high values of relative and normalized air temperature at 2.0 m

Table 4
Descriptive statistics (min, max, standard deviation) of the processed air temperature at 2.0 m AGL.The data of each interval was related to the nearest meteorological station.Local Climate Zones of minima and maxima locations are given to classify and compare the results to other studies.The spread (difference between min and max) corresponds to the urban heat island intensity.AGL, especially during the nighttime intervals 22-4 UTC and 16-22 UTC, independently of the buffer size (Appendix A).The median values were increasing from left to right for each of these time intervals.The nocturnal intervals were, independently of the buffer size, above the levels of diurnal intervals and thus represent the nocturnal intensity of UHI on the normalized scale between 0 and 1.We present the results for sealing within 100 m range in the morning hours (22-4 UTC) in detail (Fig. 14).Areas with low degree of sealing (white) were cooler in terms of relative and normalized air temperature at 2.0 m AGL (median ( T a,2.0,norm ) ≈ 0.6) compared to areas with high degree of sealing (dark-red) (median ( T a,2.0,norm ) ≈ 0.8).Unsealed areas (gray) were the coldest of the study areas (median ( T a,2.0,norm ) ≈ 0.1), but showed the greatest interquartile range   (IQR).This increase of relative and normalized air temperature from low-to high degree of sealing was also observable in the morning (4-10 UTC) and evening (16-22 UTC) hours throughout all buffer sizes.The conditions after noon (10-16 UTC) showed an indifferent pattern without a clear structure.The relative and normalized air temperature remained rather constant (T a,2.0,norm ≈ 0.5) (Appendix A).
The size of the buffer, and therefore the size of the unsealed area in range, was most important for cooling.The cooling effect was increased with an increased size of the unsealed area.Large-scale unsealed areas in a 500 m range to the route had therefore the most significant impact on cooling.In the morning condition (22-4 UTC), the median value for normalized and relative air temperature at 2.0 m AGL dropped from ≈ 0.5 to 0.1 for buffer sizes from 5 m to 500 m (Fig. 15).
It was found that cooling by small unsealed (and possibly vegetated) surfaces was more effective during the day in comparison to the night.With the increasing size of the unsealed area (radius larger than 50 m) the relative and normalized air temperature decreased faster at night, so that large and unsealed areas were also coolest at night and the aforementioned observation was inverted.

Impact of green infrastructure
Green infrastructure, expressed by the Normalized Difference Vegetation Index, showed an inverse impact on the urban thermal Fig. 13.The evening conditions (16-22 UTC) showed the spatial development of the urban heat island.The same structure as in the night (Fig. 9) but with a lower magnitude was recognizable.environment.High degree of greening led to low values of relative and normalized air temperature at 2.0 m AGL independently of the buffer size under consideration (Appendix B).This holds for each time interval except for the daytime interval (10-16 UTC), when the relative and normalized air temperature remained rather constant.We present the results for NDVI within 100 m range in the morning hours (22-4 UTC) in detail (Fig. 16a).Areas with low degree of NDVI (light-green) were warmer (median ( T a,2.0,norm ) ≈ 0.8) compared to areas with high degree of NDVI (median ( T a,2.0,norm ) ≈ 0.1).A more detailed analysis revealed that the warmest areas were located in densely built-up urban (dark-red) and industrial areas (pink), according to the Urban Atlas classification.The coldest zones were clearly located in the urban forests (green) (Fig. 16b).
The dependency on the size of the area under consideration is also evident for NDVI, just as it is for sealing (Fig. 17).With an increase in the greened area from 5 m to 500 m, the mean relative and normalized air temperature decreases from ≈ 0.6 to 0.1 for NDVI-levels between 60% to 100%.
When we look at Fig. 6, Fig. 15 and Fig. 17, we notice that the change in land use and the change in relative air temperature by unsealed and vegetated areas show a similar pattern as the buffer size increases.

Discussion
The observed intensity of the urban heat island in Karlsruhe is comparable to results of over 100 cities in Australia and Asia.The average UHI intensity as observed by studies in Australia and Asia using mobile traverses was 4.1 K (Santamouris, 2015).The average observed spread in Karlsruhe was 4.3 K with fluctuations between 3.1 K and 5.6 K, and therefore comparable to mentioned UHI intensities (Table 4).The greatest intensity of the UHI (the largest spread) was also observed in the nighttime period between 22 and 4 UTC (Table 4), as also shown by other studies (Arnfield, 2003;Dobrovolný and Krahula, 2015).

Relative and normalized air temperature
In this study, measurements were referenced to the nearest meteorological station and then min-max-normalized to the unit-less range between 0 and 1 (Eq.1-3).The proposed method is in principle independent of the geographic location and of the prevailing weather conditions due to the abstraction of absolute values.We decided on a specific, representative weather condition that represents the conditions during a heat wave, while all measurements were related to the nearest two meteorological stations.
For comparability of different cities of mid-latitude, we propose a meteorological framework.Wind speed should be above 0.5 m ⋅ s − 1 , below 3.0 m ⋅ s − 1 , and the daily maximum air temperature should be above 30 • C with clear sky conditions.Standardization of these meteorological boundary conditions lead to a transferable method, which can be applied to other cities in such a way that the results, which describe the UHI, are also comparable.
The distribution of the data is not altered by min-max normalization but it is not directly possible to revert the dimensionless values to the original UHI intensities unless the minimum and maximum values of the respective cold and hot spots are explicitly measured.If this is the case, it would be possible to assess all UHI intensities in absolute values.This is the reason, why the normalization procedure is most suitable to assess the spatial pattern of the UHI.
Besides the relative and normalized air temperature, one could also think about other relative and normalized meteorological variables (e.g., vapor pressure, wind speed, global radiation).However, it is necessary to find out how large the spatial variability of the individual variables is.If the variables have a large spatial variability, or if the range of values of the variable is very large (e.g., shaded vs. unshaded, calm vs. strong wind), then the mentioned method is not suitable, since small differences of the values are not recognizable.NDVI is divided into groups with intervals of 20%, increasing from left to right.NDVI was calculated after (Ermida et al., 2020) within 100 m range of the route.
In order to assess generalized effects on humans, the calculation of relative and normalized thermal indices like perceived or physiologically equivalent temperature, could also be considered.But these indices require spatially-resolved wind speed along the measurement route which was not available, but could potentially be provided by numerical process-based models.
Other studies set the surveys in relation to the start-and end points of each measurement run (Romero Rodríguez et al., 2020b).Normalization was also applied for other cities (Szeged and Debrecen) to calculate correctly-weighted average values of the UHI, showing the concentric shape of the UHI effect observed by different measurements (Unger et al., 2010).In that case, the measurement runs were distributed throughout the year to obtain a comprehensive result.The individual measurement runs were mapped onto a discrete grid by averaging several measurement points within a 0.5 km × 0.5 km grid point.All grid points were then referenced to the rural reference cell according to the following equation: It is not necessarily given that the rural cell also represents the minimum value, since the selection of rural and urban sites is not standardized.
In our study, each individual measurement run was normalized separately, so that the minimum and maximum values refer to the individual measurement run (Eq.3), while (Unger et al., 2010) applied the normalization procedure on the discrete grid according to: In addition to determining the outdoor conditions of human thermal comfort, indoor conditions are of great importance because people in the city spend much of their time at work indoors (Sulzer et al., 2022).

Accuracy of GNSS in cities
The positioning accuracy is limited due to shading and reflections of the GNSS signals in street canyons.(Merry and Bettinger, 2019) demonstrated that GPS accuracy of smartphones is in the range of 7 m to 13 m on average.(Abdi et al., 2014) showed that GPS accuracy in urban green space is within the range of 9 m to 12 m, and depends on the time of day and the season.Our observations fit to this range with a mean error of 9.2 m (Fig. 4).
The preparation of the specific positions posed a particular challenge, as the inaccuracies with respect to the road were nevertheless very large.In the future, an improved position determination in the city could be achieved by a Differential Global Positioning System (DGPS), by correction method Real Time Kinetics (RTK), or by the advanced Post Processed Kinematic (PPK) in combination with an Inertial Measurement Unit (IMU) on the measurement vehicle (Puente et al., 2013).
The inaccuracy is not only in the location of the measurement points, but also in the location of the administrative geodata (e.g., positions of street trees in urban tree cadasters, if provided by GPS and not georeferenced orthophotos).
We improved accuracy by error reduction in the preprocessing, using the background knowledge from really driving on the road and introducing standardized measuring points.To our knowledge, such a procedure has not yet been applied for mobile measurement runs to determine the UHI.In addition to the positional inaccuracies of the measurement runs and the data of the administrative geodata, there are also inaccuracies in the space-borne, remotely-sensed datasets (e.g., NDVI has a spatial resolution of 20 m).

Spatial autocorrelation
Tobler's first law of geography is also valid in Karlsruhe: "everything is related to everything else, but near things are more related than distant things".However, the spatial continuity of meteorological conditions depends on the time of day, as they are modified by different processes in the city.This is particularly evident from the variogram (Fig. 10), but also from the direct comparison between the individual time intervals of the measurement runs (Fig. 9 -Fig.13).Fig. 6, Fig. 15, and Fig. 17 also make it clear that it is not only the closer neighborhood that is important in modifying the meteorological conditions, but also the urban structures that are located some distance away.
The large spatial auto-correlation at night can perhaps be attributed to limited mixing by convection and advection.The absence of shortwave radiation at night, especially Photosynthetically Active Radiation, suspends the tree-physiological processes controlled by radiation (e.g., transpiration and photosynthesis) (Jones, 2013;Monteith and Unsworth, 2013).Energy conversion at building surfaces is also limited, except for the emission of longwave radiation (Oke et al., 2017).
In contrast, thermal and radiation-based processes are intensified in the morning with increase in global radiation.Due to a large Sky View Factor, these processes start especially in open spaces in the city, because the upper hemisphere is only slightly obscured by buildings (Gangwisch et al., 2021).During the day, the coldest spots in the city are found in the Hardtwald (LCZ B) area as well as in the Zoologischer Stadtgarten (LCZ 6 and B), which could be related to intensified cooling by transpiration and shading.Unfortunately, we could not determine the tree-physiological processes (e.g., sap-flow, transpiration rates, stomatal conductance) during our measurements.
Furthermore, the spatial auto-correlation is lowest during the day.The variogram shows a large variance, which is possibly caused by the mixing of the atmosphere by convection and advection.Concurrently, this makes it very difficult to determine the thermal effects of microscale structures, since it can no longer be traced back to individual structures.

Spatial neighborhood analysis -links between atmospheric conditions, urban descriptors and buffer sizes
We use circular buffers to spatially quantify neighborhoods' influence.By doing so, we made the assumption that all urban structures in the neighborhood contribute equally to meteorological conditions.However, this assumption is not valid under conditions with higher wind speeds.According to the wind direction, the influence of urban structures would have to be weighted more heavily upwind, and weaker to none at all downwind.This could possibly be realized by eccentric buffers.In addition, the influence of nearby structures should be weighted more heavily than the influence of structures that are distant.However, during our measurements there was only very weak wind.Furthermore, observations with wind speeds > 3.0 m ⋅ s − 1 and < 0.5 m ⋅ s − 1 were filtered out.In principle, spatial neighborhood analysis can be applied to different spatial descriptors to describe the neighborhood.We focus on parameters describing vegetation and sealing; but other descriptors (e.g.building height, building density, etc.) are quite conceivable.(Aksoy et al., 2022) demonstrated that Urban Atlas provides higher spatial resolution and improved accuracy compared to CORINE land cover.In contrast to CORINE land cover (one class for urban areas), Urban Atlas provides four distinguished classes for urban areas, and is therefore more suitable for urban microscale analyses of outdoor human thermal comfort.It was shown that urban structures have the greatest impact to increase relative and normalized air temperature at 2.0 m AGL (Fig. 16b).In particular, denselypopulated areas, industrial areas (with flat roofs) and streets were the warmest.In contrast, natural areas (urban forests and parks) were the coldest among the study area.But Urban Atlas classes also show inner zonal variation of meteorological conditions in each class.In general, no statements can be made about land uses that do not occur along the route.For example, water areas hardly occur, and the city center of Karlsruhe is not topographically characterized, so that these results cannot be transferred to other cities with larger water areas or elevations.

The links between atmospheric conditions and urban vegetation was considered by the NDVI
We used NDVI because this vegetation index is available area-wide for all of Karlsruhe.However, NDVI has the disadvantage that it is not possible to distinguish between low-and high vegetation cover.Here, in the middle latitudes, there might be the possibility to calculate a summer and a winter NDVI to at least distinguish between deciduous and coniferous trees.In addition, there are now also approaches from the field of machine learning that allow the vegetation types to be determined from LiDAR-generated point clouds.
The most important variable that has an influence on transpirational cooling of urban trees is water availability in the root zone.Unfortunately, spatially-resolved data on water availability were not available to us.Thus, we also do not have information on the irrigation of urban vegetation.
The results showed that the size of the green cover has great influence on the cooling potential of the green space.Larger green areas should therefore be preferred.
However, these statements are only valid for the meteorological conditions under which the measurements were carried out, since the day of the year or seasonality also has a great influence due to different adaptation of the vegetation.
Our analysis also revealed that sealing in Karlsruhe is inversely related to the NDVI.

Fig. 1 .
Fig. 1.Study area and mobile measurement route in Karlsruhe, Germany.Additional points and areas of interest are shown for discussion: Hardtwald is an urban forest in the north of the city center, Reinhold-Frank-Straße is a busy main road, Zoologischer Stadtgarten is an urban park, with green spaces and water bodies, Durlach is an urban district with a distinctive old town.The palace is the main landmark of Karlsruhe.Main basemap: TopPlusOpen © Federal Agency for Cartography and Geodesy (2023), Aside basemap: Made with Natural Earth.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .
Fig. 2. Measurement vehicle of the German Meteorological Service to measure air temperature, relative humidity (at 0.7 m and 2.0 m height above ground level (AGL)), surface temperature and global radiation.

4.
The data were set to the closest measuring station (10-min data) (Eq.1).All observed variables (p obs ∈ {T a , RH, VP, T s , G}) of each measurement run were related to the closest official meteorological station in Karlsruhe in order to account for the diurnal cycle of the corresponding variable: p rel = p obs − p station [unit(p obs ) ]

Fig. 3 .
Fig. 3.The steps for preprocessing and preparation of recorded data for the Spatial Neighborhood Analysis.

Fig. 4 .
Fig. 4. Distribution of the distances between registered GNSS positions and standardized reference points.

Fig. 7 .
Fig. 7. Representation of the gray infrastructure in the 200 m neighborhood to the route by remotely-sensed imperviousness (European Union, 2018).This layer contains the sealing in the entire urban area in 20 m spatial resolution.(Basemap by OpenStreetMap).

Fig. 8 .Fig. 9 .
Fig. 8. Representation of green infrastructure in the neighborhood in 200 m range to the route.Remotely-sensed Normalized Difference Vegetation Index based on the script by (Ermida et al., 2020) with 30 m spatial resolution.(Basemap by OpenStreetMap).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10 .
Fig. 10.Variogram showing the spatial autocorrelation of relative and normalized air temperature at 2.0 m AGL.

Fig. 11 .
Fig. 11.The conditions in the morning (4-10 UTC) showed the weakening of the UHI due to morning insolation.The transpirational cooling effect of urban parks and the heating of open squares and streets started.

Fig. 12 .
Fig. 12.The conditions at noon (10-16 UTC) showed further intensification of the cooling effect of urban parks.Especially the Zoologischer Stadtgarten (LCZ 6 and B) in the south unfolded its cooling potential.At the same time, measurement results showed a greater variation due to thermally induced mixing by convection and advection.

Fig. 14 .
Fig. 14.Modification of relative and normalized air temperature at 2.0 m AGL in morning hours (22-4 UTC) by sealing within 100 m range by its magnitude.The degree of sealing is divided into groups with intervals of 20%, increasing from left to right.Remotely-sensed imperviousness was provided by (European Union, 2018).

Fig. 15 .
Fig. 15.Modification of relative and normalized air temperature at 2.0 m AGL in morning hours (22-4 UTC) by the area size under consideration with sealing between 0% -20%.Remotely-sensed imperviousness was provided by (European Union, 2018).

Fig. 16 .
Fig. 16.Modification of relative and normalized air temperature at 2.0 m AGL by NDVI in the morning hours (22-4 UTC).NDVI is divided into groups with intervals of 20%, increasing from left to right.NDVI was calculated after(Ermida et al., 2020) within 100 m range of the route.

M.
Gangwisch et al.Appendix B. Impact of NDVI and spatial range on relative and normalized air temperature AT 2.0 M AGL M. Gangwisch et al.

Table 3
Urban Atlas 2018 land-use classification dividing the land into 17 urban classes and 10 rural classes for land use and land cover (European Union, 2018).Each class evokes a specific thermal environment.