The Impact of Heat Waves on Diurnal Variability and Spatial Structure of Atmospheric and Surface Urban Heat Islands in Kraków, Poland

Abstract

The increasing number of heat wave (HW) days, combined with the urban heat island (UHI) phenomenon, poses a threat to the health and comfort of city residents. This study investigates the impact of HWs on the diurnal cycles of intensity and spatial structure of the atmospheric UHI (AUHI) and surface UHI (SUHI). A comparative analysis is conducted on the simultaneous night–day variability of AUHI and SUHI intensities in Kraków in two 24 h summer periods: one representing normal summer conditions (Period W) and the other HW conditions (Period H). Evaluating sub-daily UHI patterns based on integrated in situ and satellite data is a relatively novel approach. This study utilizes (1) air temperature from 21 measurement points located in different local climate zones and vertical (altitude) zones; and (2) land surface temperature from six NOAA/AVHRR satellite images. The findings indicate that AUHI and SUHI intensities in Kraków were generally up to 3 °C higher at night and up to 3 °C lower during the daytime in Period H compared to Period W, particularly in the valley floor. These results provide valuable insights into the increased heat load risk due to the co-occurrence of UHI and HW, with implications for sustainable urban planning strategies.

1. Introduction

The urban heat island (UHI) phenomenon is the most noticeable anthropogenic modification of the local climate in cities, and the key issue for urban climate research [1,2]. A particular aspect covered by this study is the interaction of UHI with heat waves [3], the frequency and intensity of which are increasing as a result of climate change [4].

The UHI phenomenon can be considered as multidimensional, and its intensity and dynamics are studied at different levels, including the near-surface layer of the atmosphere (i.e., the urban canopy layer, UCL) and the surface. Hence, the atmospheric UHI (AUHI) and the surface UHI (SUHI) are distinguished [5,6]. The AUHI is determined on the basis of air temperature (T_air), measured in situ and/or modeled [7,8], whereas the SUHI is assessed with the use of land surface temperature (LST), derived from remotely sensed thermal infrared (TIR) images [6,9].

The conditions of measuring T_air and retrieving LST through TIR image acquisition determine the assessment methods of AUHI and SUHI intensities. The representativeness of T_air measurement points for the local-scale environment [2] can be characterized by the so-called local climate zones (LCZs), which additionally take into account the influence of local relief (terrain), elevation, and/or water bodies on the measurement [10]. The LST pattern obtained from satellite data allows for monitoring the intensity and spatial structure of the SUHI exactly at the time of satellite image acquisition, with the spatial resolution of the thermal sensor, and only in cloudless weather. A pixel size of approx. 100 m enables the distinction between thermal structures inside a city district; however, such images are usually acquired every several days. TIR images with a lower spatial resolution, i.e., about 1 km, do not reflect the thermal heterogeneity of the city districts anymore, but they still detect LST patterns within the city and its surroundings [11] and are usually acquired twice a day by a polar-orbiting satellite.

The intensity and spatiotemporal structure of AUHI and SUHI are influenced by geographic location, topography (particularly relief), or distance from the open sea [9]. Significant factors are also the geometry and morphology of the urban area [12,13,14]. Both AUHI and SUHI differ in their dynamics throughout the day, and the time and location of their intensity peaks depend on properties of urban and rural surfaces [9,14]. The variability of AUHI and SUHI intensity may also be influenced by the emission of anthropogenic heat and the aerosol content in the atmosphere [1]. Another group of drivers includes synoptic situation and weather conditions [12,15].

The impact of relief on AUHI has been studied so far for some cities, e.g., Dublin [16], Beer Sheba [17], Stuttgart [18,19], and Lanzhou [20], while the influence of landforms on SUHI has been examined, e.g., for urban areas in South Tirol [21], Illinois [22], Chongqing [23], and Beirut [24]. The previous studies of AUHI and SUHI intensity and spatiotemporal structure in Kraków (Poland) have also revealed the important role of the relief in modifying the nocturnal AUHI by inducing katabatic flows and thermal inversions [25] and the impact of uneven surface exposure to sunlight on the SUHI in the daytime [26].

The simultaneous comparison of AUHI and SUHI intensities requires clear weather, occurring usually in an anticyclonic situation, due to the limitations of remote thermal measurements performed by satellite sensors. The remotely sensed LST data, corresponding with in situ T_air data, have been derived from either the high-resolution airborne TIR images (e.g., [27,28]), or the satellite TIR images at different spatial resolutions, i.e., of about 100 m, acquired by the instruments like ASTER onboard Terra (e.g., [29,30]), and TM, ETM+, or TIRS onboard Landsat series (e.g., [12]), and of about 1 km, acquired by such instruments as AATSR onboard Envisat (e.g., [31]), AVHRR onboard NOAA series (e.g., [32,33]), and MODIS onboard Terra and Aqua (e.g., [34,35,36,37,38]).

Many comparative analyses of AUHI and SUHI observed differences in the intensity of AUHI and SUHI in the daytime and/or the nighttime, mainly in the warm season (e.g., [5,28,30,31,36,39,40]), and less often in winter (e.g., [41]). The dependence of the AUHI and SUHI intensity on land use and/or advective processes has been also widely compared (e.g., [5,42]). Some other authors have focused their research on comparing the seasonal variability of AUHI and SUHI (e.g., [36,40,43]).

A crucial aspect of many studies has been the interaction between the UHI and heat waves (HWs), i.e., periods of extremely high air temperatures (e.g., [33,35,37,38,44,45,46,47,48,49,50,51]). Previous studies have included analyses of the nighttime and/or daytime monthly or seasonal averages of LST and T_air in urban and rural areas for the HW summers in comparison to the other (normal) summer months or seasons. A review of studies on the synergy between UHI and HWs conducted in the period 1951–2022 is presented by Cheval et al. [52]. In the aforementioned paper, the integration of data obtained from different sources was indicated as one of the priorities for further research. This approach would enable a better understanding of the interactions between the atmosphere and the urban surface. The results obtained in this way, with possibly reduced uncertainty, should help decision-makers to develop more effective solutions for sustainable urban planning.

Furthermore, urban climate studies have so far rarely compared the simultaneous time evolution of the AUHI and SUHI intensities. The daily cycle of AUHI intensity is quite well recognized, both theoretically [13] and empirically (e.g., [31,35,53,54]), whereas the daily cycle of SUHI intensity has been a rarely discussed topic up to date (e.g., [34,45]). Recently, Stewart et al. [50] have presented the theoretical (resulting from numerical simulations of climate models) day–night evolution of SUHI under summer HW conditions in various climates, defining the SUHI intensity (called magnitude by the authors) as LST difference for LCZ classes of urban built types (LCZ 2, LCZ 6, and LCZ 8) and rural land cover types (LCZ A, LCZ D, and LCZ C, respectively, for humid subtropical, humid continental, and hot desert climates). The authors concluded that the daily cycle of SUHI depends on the season, regional climate, urban morphology, rural land cover, soil moisture, and wind speed. Additionally, Stewart et al. [50] compared the daily cycles of SUHI and AUHI intensities. The differences between them were found to depend on the background climate, time of day, LCZ class, and soil moisture in rural areas.

Thus, the relationship between the daily cycle of AUHI and SUHI intensity and spatial structure during the HW has so far been addressed by few researchers. A detailed comparative analysis of the sub-daily AUHI and SUHI variability during and beyond HWs, based on integrated information from simultaneous in situ and satellite measurements, seems to be particularly useful for urban decision-makers and planners assessing the scale of the existing and potential threat and developing climate change adaptation and mitigation strategies.

In Poland, HWs are becoming more frequent and more intense [55,56]. In Kraków, Bokwa et al. [57] found that during HW events, a heat load is greater in the valley floor than in the higher areas during the daytime, and lower in the nighttime due to the effect of air temperature inversion. The results of previous investigations also conclude on the existence of the nighttime relief-modified AUHI in Kraków [25]. It was also found that daytime SUHI is characterized by the occurrence of stable cold and hot spots both in the city and its surroundings. Based on standardized LST values, approximately one third of the city’s area is thermally stable over time. Areas with continuous urban fabric as well as industrial and commercial areas were recognized as permanent hot spots in the daytime (i.e., at about 9:30 UTC), while forests and waters as stable cold spots [26]. Furthermore, previous studies revealed that the spatial distribution of LST, obtained from the Landsat thermal satellite images in the hours before noon, showed significant thermal contrasts over the area of Kraków and its vicinity caused by the mosaic of land use/cover types. The city center and the area of steelworks turned out to be the warmest [58]. On the basis of the LST values derived from the NOAA/AVHRR data, the surface UHI in Kraków was detected at the night, morning, noon, and evening hours. The greatest thermal contrasts occurred around noon in the summer season, and the smallest in the morning [59].

All previous research studies of UHI in Kraków provided a lot of insightful information about its characteristics, but this study attempts to integrate the data from different sources (in situ and satellite) for the purpose of the comprehensive analysis of the urban heat island at both levels: AUHI and SUHI. The specific research questions are as follows: (1) whether and how the daily variability of the intensity and spatial structure of both AUHI and SUHI in Kraków on a summer day with a HW differs from that observed on a normal summer day, i.e., warm, but not hot; (2) how these differences are influenced by the relief and land use/cover (LCZ). This paper presents two case studies selected according to specific criteria, thanks to which the influence of various factors of the spatiotemporal variability of AUHI and SUHI is minimized and the advective factor can be investigated. The night–day variability of the intensity and spatial distribution of AUHI and SUHI in Krakow during two mostly cloudless and windless 24 h summer periods is presented. The differences in AUHI and SUHI intensities between the periods with and without heat waves were analyzed on a sub-daily basis depending on the LCZ class and vertical (altitude) zone.

2. Study Area

Kraków (Cracow) is the second largest city of Poland with more than 800 thousand residents and an area of approx. 327 km² [60]. The city is situated in the southern part of the country (Figure 1a). The relief (terrain) map of the study area, based on SRTM 90 m Digital Elevation Database v4.1 [61], is shown in Figure 1b. The study area is located in a concave landform, i.e., in the Wisła (Vistula) river valley, stretching from west to east. The valley is narrow (about 1 km) in the western part of Kraków and much wider (about 10 km) in the eastern part. The city center is located at the bottom of the valley, at an altitude of approx. 200 m a.s.l. The study area includes smaller towns and villages located in the vicinity of Kraków, Kraków-Częstochowa Upland to the north of the Wisła river and the Carpathian Foothills to the south. At the edges of the study area, to the northwest and southeast of the city center, the hills exceed 400 m a.s.l., but on average the hilltops are about 100 m above the valley floor.

The local climate of Kraków is apparently modified by urbanization. The urban heat island in Kraków has expanded and intensified with the development of the city over the years [25,62]. In addition, the location of the city in a varied topography has a significant impact on meso-climatic conditions [63]. The natural ventilation is reduced. Atmospheric calms occur frequently, up to 27% throughout the year [64], and air temperature inversions are often observed, mainly at night, but also during the day, especially in winter [65,66]. For these reasons, the conditions of air pollution dispersion are poor [65,67]. Furthermore, the location of the city in a west–east-oriented valley results in a corresponding airflow pattern with an increased share of north-eastern and eastern winds as a result of the local circulation in the Wisła river valley [64]. The relief in the study area also influences the differences in the amount of solar radiation received by the surface at south- and north-facing slopes [68].

3. Data and Methods

In order to assess the impact of heat waves on the daily variability of intensity and spatial structure of AUHI and SUHI in Kraków, daily data on meteorological and satellite measurements from the summer months of 2010–2019 were analyzed to find periods with heat waves and periods of normal summer (i.e., when the maximum T_air exceeds 25 °C, but no heat wave occurs), when all data were available. This paper presents two case studies selected according to specific criteria which have been specified to reduce the impact of the major factors of the spatiotemporal variability of AUHI and SUHI over the daily cycle, focusing on the advective factor.

3.1. Study Periods

The following criteria were used to select two 24 h periods for comparative analysis: (1) cloud cover up to 1 okta in each hour throughout the periods; (2) average wind speed below 4 m·s⁻¹; (3) anticyclonic synoptic pattern; (4) one summer period with a heat wave and one normal summer period (warm but not hot); (5) availability of satellite images with a spatial resolution of around 1 km (at least 6 images in 24 h at intervals of several hours); (6) no significant changes in land use/cover; (7) aerosol content in the atmosphere and air pollution at a similar level in both study periods; and (8) no significant differences between the compared periods in terms of air humidity and soil moisture.

The hourly observations of cloud cover in the summer months (June, July, and August) of 2010–2019 obtained from the Kraków Airport synoptic weather station were used as the first source data for the selection of study periods according to the predefined criteria. In the years and months considered, there were 26 periods lasting 24 h or longer, with nearly cloudless weather conditions.

According to the calendar of atmospheric circulation types for southern Poland [69], on the days of the pre-selected periods, 88% had anticyclonic types of air circulation accompanied by advection of either tropical continental (37%), polar continental (34%), or polar maritime (29%) air mass. The HW period was selected from among those with the tropical continental air advection, while the normal summer weather period from among those with the polar maritime air advection, which occurs most frequently in the summer season.

For the selection of the periods, T_air measurement data from the Kraków Airport synoptic weather station were also used. The HW period had to meet the criterion of a minimum of 3 consecutive days with the maximum T_air above 30 °C. This definition of HW was used in previous climatological studies for the area of Poland, e.g., by Wibig [55] and Tomczyk et al. [56]. The maximum T_air in the period of normal summer weather should have been higher than or equal to 25 °C and lower than 30 °C.

When selecting the study periods for the comparative analysis, the availability of AVHRR satellite images for the study area was taken into account as a source of LST data at a spatial resolution of approx. 1 km. The data from the AVHRR satellite sensor provide at least 6 thermal images of the study area within 24 h, with intervals of several hours due to the number of NOAA and MetOp satellites operating at the same time. In the years considered, the AVHRR sensor acquired images for the study area in the largest number within 24 h among all available satellite sensors providing images with a spatial resolution of about 1 km, such as MODIS, VIIRS, or SLSTR. Additionally, AVHRR images were acquired at different times of the day (i.e., at night, in the morning, at noon, and in the evening), so that the daily cycle of the SUHI intensity could be detected more accurately. The selected AVHRR satellite images were limited to those acquired by the satellite radiometer at a scanning angle not exceeding 30 degrees.

Finally, two 24 h periods were selected. Period W represents normal summer conditions (i.e., a warm summer day), and Period H represents HW conditions (i.e., a hot summer day). Period H includes the second consecutive day of a 4-day heatwave period, preceded by a 10-day period with maximum T_air exceeding 25 °C with negligible precipitation, which included a 3-day period of the previous heatwave. The study periods come from the same summer season (

Table 1. Dates and times for the start and end of the selected study periods with the corresponding sunset and sunrise times.

Period	Starting Date and Time	Ending Date and Time	Sunset Time	Sunrise Time
W	8 July 2013 18 UTC	9 July 2013 18 UTC	18:50 UTC	02:42 UTC
H	5 August 2013 18 UTC	6 August 2013 18 UTC	18:16 UTC	03:16 UTC

), which guarantees no significant changes in land use/cover.

The weather elements that may affect air temperature and land surface temperature patterns are primarily cloudiness, air humidity, and wind. The weather conditions in both selected periods can be considered similar, except for the air temperature (

Table 2. 24 h values of meteorological parameters at the Kraków Airport synoptic weather station during the study periods.

Period	Cloud Cover [%]	Air Temperature [°C]		Relative Humidity [%]		Wind Speed [m·s−1]		Wind Direction
		Avg	Min	Max		Avg	Max
W	2.5	20.3	12.3	26.3	64	1.7	4.0	NE
H	3.0	24.7	17.0	32.9	58	2.2	4.0	NE

).

Both spatial and temporal cloud cover patterns over the study area during the 24 h periods W and H were additionally examined with the use of the CM-SAF COMET Cloud Fractional Cover (CFC) dataset [70]. The COMET CFC data are provided in a 0.05° × 0.05° longitude/latitude grid. The hourly CFC values averaged for all pixels within the study area reached 1.9% in Period W and 10.6% in Period H, but were 0% in most hours in both periods. See Figure A1 for the CFC values.

The aerosol content in the atmosphere (including airborne particulate matter in the UCL), as well as soil moisture, are also important for the thermal conditions in the air and on the surface. Aerosol particles scatter or absorb solar radiation, while soil moisture determines evapotranspiration.

The aerosol content in the atmosphere during the study periods was assessed using the daily averaged values of Aerosol Optical Depth (AOD) at a wavelength of 500 nm on 9 July 2013 and 6 August 2013. The AOD values are based on the MOD04_L2 and MYD04_L2 satellite data products obtained from the MODIS instrument on board the Terra and Aqua satellites [71]. The mean AOD values over the study area were 0.24 in Period W, and 0.1 in Period H (see Figure A2). The AOD values do not exceed the multi-year average for summer in Poland [72].

Particulate matter (PM) pollution over the study area during the 24 h periods W and H was assessed using hourly concentrations of PM with a diameter up to 10 µm (PM10), measured at 4 stations (representing urban areas of background, traffic, and industrial type). The PM10 station network operates as a part of the air quality monitoring in Poland under the Chief Inspectorate of Environmental Protection. The maximum mean 24 h concentrations of PM10, noted at a traffic background station, in both study periods were similar, i.e., 38.3 µg·m⁻³ and 44.6 µg·m⁻³ in the 24 h periods W and H, respectively (see Figure A2).

The soil moisture conditions over the study area in the selected 24 h periods were assessed using the daily data from the reanalysis of surface soil moisture for Europe in 2000–2015 (ESSMRA v.1.1), with a spatial resolution of 3 km [73]. The mean value of volumetric soil water (VSM) at a 0–3 cm layer for the entire study area was 0.23 mm³·mm⁻³ in Period W, and 0.15 mm³·mm⁻³ in Period H; whereas, for the LCZ D class, the mean VSM values were slightly lower, i.e., 0.2 and 0.12 mm³·mm⁻³, respectively (see Figure A3).

Taking into consideration the above data, it was assumed that the influence of slight differences in cloud cover patterns, aerosol content, PM pollution, and soil moisture between periods on the observed daily variability of the AUHI and SUHI intensities in Kraków is negligible.

3.2. Vertical Zones and LCZ Classes

Three vertical zones are distinguished in the study area according to the concept of Relief-Modified Urban Heat Island (RMUHI) by Bokwa et al. [25]: (1) the valley floor in the western and eastern part of the city; (2) the slopes up to 50 m above the valley floor in the northern (N slopes) or southern (S slopes) part of the study area; and (3) the hilltops about 100 m (or more) above the valley floor in the northern or southern part of the study area (Figure 1b).

The LCZ map for the study area (Figure 1c) was prepared using the WUDAPT method [74] and then generalized by calculating, for each pixel, a focal majority frequency within a circular neighborhood around this pixel with a radius of 500 m, and then the boundaries between the obtained zones were smoothed. This method has been applied in relation to the definition of the LCZ as a region covering hundreds of meters to several kilometers on a horizontal scale [10]. The total and individual shares of LCZs for the vertical zones are presented in

Table A1. Share of LCZ classes in the vertical zones within the study area.

LCZ Class 1		All Vertical Zones	Valley Floor	N Slopes	S Slopes	Hilltops
		Share [%] of LCZ Class
LCZ 2 (compact mid-rise)		0.3	0.9	-	-	-
LCZ 5 (open mid-rise)		7.4	14.4	6.4	6.4	-
LCZ 6 (open low-rise)		3.2	3.8	1.5	8.9	0.1
LCZ 8 (large low-rise)		4.3	10.8	1.7	1.8	-
LCZ 9 (sparsely built)		24.7	20.1	17.4	40.4	27.0
LCZ 10 (heavy industry)		0.7	1.3	1.1	-	-
LCZ A (dense trees)		4.6	3.0	1.7	3.4	10.4
LCZ B (scattered trees)		5.2	6.6	0.9	7.7	5.8
LCZ D (low plants)		41.0	30.2	49.0	29.9	54.8
LCZ F (bare soil or sand)		8.3	7.9	20.2	1.4	1.9
LCZ G (water)		0.3	1.0	-	-	-

¹ LCZ class names and their graphic symbols according to Stewart and Oke [10].

. The built types, i.e., LCZ 2, LCZ 5, LCZ 6, LCZ 8, LCZ 9, and LCZ 10, all together are 40.6% in the whole study area. The largest share of LCZ built types, with the exception of LCZ 9, is in the valley floor (31.2%), while in the slopes zone it is much smaller. In the southern part, the share is higher (17.1%) than in the northern part (10.7%). The most common land cover LCZ class in the study area is LCZ D (41%).

3.3. Data Sources

3.3.1. Air Temperature Measurements

Air temperature data used in the study come from the network of 21 measurement points operated by the Department of Climatology, Institute of Geography and Spatial Management, Jagiellonian University in Kraków [25,63]. The measurement points were distributed all over the study area in different vertical zones and different urban and rural landscapes with a variety of land use/cover configurations (Figure 1;

Table 3. Characteristics of the air temperature (T_air) measurement points.

Tair Measurement Point		Altitude [m a.s.l.]	Vertical Zone b	Land Use/Cover c	LCZ Class (% Shares) d
Symbol a	Name
1	Słowackiego Theatre	215	Valley floor	Compact built-up (with street canyons)	LCZ 2 (79%), LCZ 5 (16%), LCZ 8 (5%)
2	Krasińskiego St.	204	Valley floor	Compact built-up (with street canyons)	LCZ 5 (86%), LCZ 2 (14%)
3	Podwawelskie district	203	Valley floor	Blocks of flats	LCZ 5 (100%)
4	Szkolne district	205	Valley floor	Blocks of flats	LCZ 5 (94%), LCZ D (6%)
5	Bema St.	208	Valley floor	Residential built-up	LCZ 5 (54%), LCZ 6 (46%)
6	Błonia meadows	203	Valley floor	Urban green areas	LCZ 5 (93%), LCZ 2 (7%)
7	Botanical Garden	206	Valley floor	Urban green areas	LCZ 5 (97%), LCZ 6 (3%)
8	Malczewskiego St.	222	Valley floor	Urban green areas	LCZ 9 (90%), LCZ B (10%)
9	Wandy Bridge	197	Valley floor	Water bodies	LCZ 9 (91%), LCZ D (9%)
10	Przylasek Rusiecki	190	Valley floor	Water bodies	LCZ G (63%), LCZ D (37%)
11	Ojcowska St.	245	N slopes	Residential built-up	LCZ 9 (100%)
12	Czajna St.	258	S slopes	Residential built-up	LCZ 9 (100%)
13	Bojki St.	252	S slopes	Blocks of flats	LCZ 6 (64%), LCZ 5 (33%), LCZ 9 (3%)
14	Mała Góra St.	231	S slopes	Blocks of flats	LCZ 5 (94%), LCZ 6 (5%), LCZ 9 (1%)
A	Jeziorzany	211	Valley floor	Rural areas	LCZ D (100%)
B	Modlniczka	258	N slopes	Rural areas	LCZ D (93%), LCZ B (5%), LCZ A (3%)
C	Rzozów	251	S slopes	Rural areas	LCZ D (45%), LCZ B (23%), LCZ 9 (33%)
D	Garlica Murowana	270	N hilltops	Rural areas	LCZ D (100%)
E	Kocmyrzów	299	N hilltops	Rural areas	LCZ D (91%), LCZ F (9%)
F	Libertów	314	S hilltops	Rural areas	LCZ 9 (100%)
G	Chorągwica	436	S hilltops	Rural areas	LCZ 9 (94%), LCZ D (6%)

^a Numbers indicate the urban measurement points, letters indicate the rural measurement points; ^b vertical zones distinguished in the study area: (1) the valley floor; (2) the slopes about 50 m above the valley floor in the northern part of the study area (N slopes) and in the southern part of the study area (S slopes); and (3) the hilltops about 100 m (or more) above the valley floor in the northern part of the study area (N hilltops) and in the southern part of the study area (S hilltops); ^c land use/cover in the immediate vicinity of the measurement point; ^d LCZ (local climate zone) according to Stewart and Oke [10] based on LCZ map prepared using WUDAPT method (legend like in Figure 1c); % shares of LCZs are obtained for the areas of a 500 m radius around each T_air measurement point.

). Assuming that the LCZ class is representative of at least 1 km² of the area, the LCZ shares are calculated for the area of a 500 m radius around each measurement point. Additional topographic and land use/cover characteristics of the points and their nearest surroundings can be found in [25,63].

The measurement points were equipped with data loggers with embedded air temperature sensors (HOBO^® Pro series data loggers manufactured by Onset Computer Corporation, Bourne, MA, USA). The loggers were placed inside naturally ventilated solar radiation shields and mounted from 2 up to 4 m above the ground. More details about the technical specification of data loggers are described by Bokwa et al. [25]. Air temperature was recorded by the data loggers at 5 min intervals.

3.3.2. Satellite Images

NOAA/AVHRR data of about a 1 km spatial resolution were used to estimate land surface temperature. They were acquired by the satellite receiving station located in Kraków, operated by the Institute of Meteorology and Water Management—National Research Institute (IMGW-PIB). The NOAA/AVHRR data were used due to the availability of at least 6 images of the study area per day at intervals of several hours. A total of 12 NOAA/AVHRR images of the city of Kraków and its vicinities, i.e., 6 images in each period, were used (

Table 4. Acquisition times of the NOAA/AVHRR satellite images over the study area during the 24 h study periods.

Period W		Period H
AVHRR Image Time Over the Study Area	Satellite	AVHRR Image Time Over the Study Area	Satellite
8 July 2013 19:08 UTC	NOAA-16	5 August 2013 18:22 UTC	NOAA-16
9 July 2013 03:07 UTC	NOAA-18	6 August 2013 02:57 UTC	NOAA-18
9 July 2013 04:54 UTC	NOAA-15	6 August 2013 05:10 UTC	NOAA-15
9 July 2013 09:05 UTC	NOAA-16	6 August 2013 08:20 UTC	NOAA-16
9 July 2013 11:50 UTC	NOAA-19	6 August 2013 11:49 UTC	NOAA-19
9 July 2013 14:40 UTC	NOAA-15	6 August 2013 14:55 UTC	NOAA-15

).

3.3.3. Land Surface Temperature Retrieval

Land surface temperature was calculated on the basis of the brightness temperature ($T_{\lambda }$) values derived from the AVHRR TIR data using the split-window method, which includes atmospheric correction. The split-window algorithm used was proposed by Ulivieri et al. [75] and successfully tested by the other authors [76,77,78,79]:

$$LST=T_{\lambda i}+1.8\left(T_{\lambda i}-T_{\lambda j}\right)+48\left(1-\overline{\epsilon }\right)-75\Delta \epsilon$$

(1)

where i and j are the AVHRR TIR channels 4 and 5, $\overline{\epsilon }$ is an averaged land surface emissivity (LSE) calculated as an arithmetic mean of the LSE values estimated for both considered AVHRR TIR channels:

$$\overline{\epsilon }=\left({\epsilon }_{\lambda i}+{\epsilon }_{\lambda j}\right)/2$$

(2)

and Δε is the difference between the LSE values appropriate to the AVHRR TIR channels:

$$\Delta \epsilon ={\epsilon }_{\lambda i}-{\epsilon }_{\lambda j}$$

(3)

The radiance values from TIR channels 4 and 5 of AVHRR were used to calculate the $T_{\lambda }$ values on the basis of Planck’s law according to the following:

$$T_{\lambda }={\displaystyle \frac{c_2}{\lambda ln \left(\frac{c_1}{{\lambda }^5{L}_{\lambda }}+1\right) }}$$

(4)

where c₁ and c₂ are the Planck’s radiation constants (c₁ = 1.19104·10⁸ W·μm⁴·m⁻²·sr⁻¹ and c₂ = 1.43877·10⁴ μm·K), λ is the effective wavelength of TIR channel (4 or 5), and $L_{\lambda }$ is the spectral radiance from TIR channel (4 or 5).

The land surface emissivity estimation was made with the use of the narrowband albedo values in the visible (VIS) and the near-infrared (NIR) channels of AVHRR calculated from the reflectance values taken directly from the VIS channel 1 and the NIR channel 2 of AVHRR. The narrowband VIS and NIR albedo values (A_VIS and A_NIR, respectively) were used to calculate the Normalized Difference Vegetation Index (NDVI) according to the following equation:

$$NDVI={\displaystyle \frac{A_{NIR}-A_{VIS}}{A_{NIR}+A_{VIS}}}$$

(5)

Based on the relationship between thermal emissivity and NDVI, land surface emissivity (LSE; ${\epsilon }_{\lambda }$) for TIR channels of AVHRR was estimated by NDVI Thresholds Method (NDVI^THM) [80]. NDVI^THM uses certain NDVI values (i.e., thresholds) to distinguish between bare soil pixels (NDVI < NDVI_S), full vegetation pixels (NDVI > NDVI_V), and mixed (soil and vegetation) pixels (NDVI_S ≤ NDVI ≤ NDVI_V) [81]. In this study, the values of NDVI_S = 0.2 and NDVI_V = 0.5 were applied following Sobrino and Raissouni [82]. The LSE of bare soil pixels (NDVI < 0.2) was set as ${\epsilon }_{\lambda }$ = ${\epsilon }_{S\lambda }$, assuming bare soil emissivity (${\epsilon }_{S\lambda }$) 0.95 for AVHRR channel 4, and 0.96 for AVHRR channel 5. The LSE of full vegetation pixels (NDVI > 0.5) for both AVHRR TIR channels was set to 0.99 according to the following:

$${\epsilon }_{\lambda }={\epsilon }_{V\lambda }+C_{\lambda }$$

(6)

assuming typical full vegetation emissivity (${\epsilon }_{V\lambda }$) 0.985, and correcting by $C_{\lambda }$ (i.e., a term taking into account a cavity effect due to a surface roughness), which was set as 0.005. The LSE of mixed pixels was estimated according to the following:

$${\epsilon }_{\lambda }={\epsilon }_{V\lambda }{P}_V+{\epsilon }_{S\lambda }\left(1-P_V\right)+C_{\lambda }$$

(7)

where P_V is a proportion of vegetation (i.e., a fractional vegetation cover) derived from NDVI:

$$P_V={\left({\displaystyle \frac{NDVI-NDV{I}_S}{NDV{I}_V-NDV{I}_S}}\right)}^2$$

(8)

3.4. Methods for AUHI and SUHI Analysis

The processing and analysis steps in this study are graphically represented in a workflow diagram (Figure 2). The key analysis is the comparison of differences in the daily variability of the intensity of AUHI and SUHI between the study periods (Period H vs. Period W). For the purposes of the analysis, the consecutive hourly mean T_air values were calculated, and the LST data at a 1 km resolution were resampled to the 100 m pixels in order to increase the comparability of the T_air and LST measurement signals, taking into account the influence of the source area [6]. In the first step, resampling was performed using the nearest neighbor method. In the second step, for each 100 m pixel, a focal mean value within the circular neighborhood around the pixel with a radius of 500 m was calculated. The purpose of this “moving window” approach was to approximate the averaged measurement signal from the source area. The resampling method was additionally tested using 100 m LST data derived from Landsat. It was found that the average differences in SUHI intensity between individual summer days for most LCZ classes are comparable when using the original spatial resolution of 100 m and that obtained after upscaling to 1 km and resampling to 100 m (see

Table A2. Mean values (µ) and standard deviations (σ) of the SUHI intensity differences (Δ SUHII) between particular days for the LCZ classes (relative to LCZ D), for Landsat daytime LST of original spatial resolution 100 m and after upscaling to 1 km and resampling to 100 m.

LCZ Class Difference	Days Difference (7 August 2013–20 June 2013)				Days Difference (13 August 2015–12 July 2015)
	Landsat LST Original 100 m		Landsat LST Upscaled to 1 km and Resampled to 100 m		Landsat LST Original 100 m		Landsat LST Upscaled to 1 km and Resampled to 100 m
	ΔSUHII [°C]		ΔSUHII [°C]		ΔSUHII [°C]		ΔSUHII [°C]
	µ	Σ	µ	σ	µ	σ	µ	σ
LCZ 2–LCZ D	−3.3	1.5	−3.1	0.2	−1.9	0.6	−1.5	0.1
LCZ 5–LCZ D	−2.5	1.8	−2.3	0.6	−1.3	0.8	−1.1	0.5
LCZ 6–LCZ D	−2.0	1.6	−1.7	0.7	−1.6	0.9	−1.2	0.7
LCZ 8–LCZ D	−2.2	2.5	−1.8	1.0	−1.9	1.1	−1.4	0.7
LCZ 9–LCZ D	−1.5	1.7	−1.2	0.8	−1.2	1.2	−0.9	0.8
LCZ 10–LCZ D	−2.3	2.6	−2.1	0.7	−2.1	0.7	−1.7	0.4
LCZ A–LCZ D	−1.8	1.7	−1.4	0.9	−0.1	1.2	−0.3	0.8
LCZ B–LCZ D	−1.3	1.8	−1.0	0.8	−0.4	1.2	−0.4	0.8
LCZ F–LCZ D	−1.0	3.0	−0.9	1.5	−1.4	1.8	−1.1	1.0
LCZ G–LCZ D	−2.6	2.5	−1.6	0.6	0.2	1.0	−0.3	0.6

).

The LST values for the 100 m pixels corresponding to the location of the T_air measurement points were then extracted. Zonal statistics such as mean and standard deviation values were calculated separately for each LCZ class and vertical zone. To estimate the intensity of AUHI (AUHII), the air temperature differences between urban and rural T_air measurement points were calculated (see

Table A3. Mean values (µ) and standard deviations (σ) of air temperature (T_air) in 3 h time intervals during the study periods for individual T_air measurement points located in different classes of local climate zone (LCZ) and different vertical zones.

Period	Vertical Zone	Tair Point	LCZ Class	Hour Interval [UTC]
				18–21		21–0		0–3		3–6		6–9		9–12		12–15		15–18
				Tair [°C]
				µ	σ	µ	σ	µ	σ	µ	σ	µ	σ	µ	σ	µ	σ	µ	σ
W	Valley floor	1	LCZ 2	22.3	1.2	18.7	0.8	16.2	0.6	16.8	1.7	22.8	1.1	25.0	0.5	26.3	0.2	26.1	0.4
		2	LCZ 5	21.3	1.6	17.1	0.7	15.1	0.4	15.7	1.4	23.6	2.8	28.0	0.9	28.7	0.4	26.3	0.6
		3	LCZ 5	20.6	1.6	16.7	0.9	14.3	0.5	16.3	2.7	25.9	1.5	28.9	0.6	29.5	0.6	26.4	0.8
		4	LCZ 5	20.5	1.5	17.0	0.8	15.0	0.4	15.9	1.5	21.7	1.6	24.8	0.5	26.7	0.6	26.0	1.0
		5	LCZ 5	20.8	1.5	17.4	0.8	15.1	0.6	17.5	2.7	25.2	1.2	28.4	0.6	29.4	0.1	27.7	1.1
		6	LCZ 5	19.7	2.1	15.3	0.7	13.5	0.4	14.6	1.8	22.3	1.9	25.4	0.5	27.1	0.3	26.3	0.6
		7	LCZ 5	20.5	1.4	16.9	0.8	14.7	0.5	14.8	0.9	20.3	1.9	25.4	0.8	27.1	0.3	26.2	1.0
		8	LCZ 9	18.0	1.4	14.3	0.9	12.1	0.4	13.3	1.8	21.3	2.3	26.9	1.1	28.1	0.1	25.6	1.7
		9	LCZ 9	20.1	1.9	15.9	0.6	14.0	0.4	15.5	1.6	21.8	1.8	25.1	0.5	26.3	0.1	25.5	0.7
		10	LCZ G	20.0	1.6	16.3	0.8	14.3	0.3	16.3	1.5	22.0	1.1	24.4	0.4	25.7	0.4	26.3	0.4
		A	LCZ D	17.6	2.1	13.5	1.0	11.0	0.6	16.0	3.5	24.5	1.3	26.7	0.5	27.9	0.2	26.9	1.2
	N Slopes	11	LCZ 9	19.5	1.7	15.9	0.7	13.9	0.6	15.9	2.7	24.2	1.5	27.6	0.6	29.6	0.2	27.0	1.1
		B	LCZ D	19.5	1.3	15.9	1.5	12.2	0.5	16.9	3.3	23.8	1.0	26.1	0.6	27.2	0.1	26.1	1.1
	S Slopes	12	LCZ 9	19.1	1.8	15.6	0.7	13.5	0.6	15.0	1.7	21.0	1.8	26.7	1.2	28.7	0.2	26.1	1.3
		13	LCZ 6	20.6	1.9	16.1	1.0	13.6	0.5	15.1	2.2	20.9	1.4	25.9	1.4	27.8	0.1	26.7	1.1
		14	LCZ 5	19.6	2.0	15.6	0.6	13.8	0.4	16.3	2.3	21.5	0.9	24.3	0.6	25.8	0.3	25.6	0.6
		C	LCZ D	18.6	2.4	14.1	0.7	11.8	0.3	15.2	2.7	23.7	1.4	26.2	0.5	27.1	0.3	25.9	1.0
	Hilltops	D	LCZ D	17.1	2.2	14.2	1.5	11.4	0.4	15.1	3.5	24.1	1.2	27.1	0.6	28.0	0.1	26.2	1.3
		E	LCZ D	20.7	0.9	18.9	0.4	16.1	0.8	17.6	2.0	23.5	0.6	25.4	0.6	26.7	0.2	26.0	0.9
		F	LCZ 9	20.6	0.7	17.8	0.7	15.2	0.4	15.8	0.7	20.4	1.5	25.5	1.7	27.9	0.4	25.2	1.3
		G	LCZ 9	19.6	0.4	18.5	0.4	16.6	0.6	18.8	0.8	21.6	1.0	23.7	0.4	24.6	0.2	23.8	0.7
H	Valley floor	1	LCZ 2	26.6	1.0	23.6	0.8	20.9	0.6	20.0	0.9	25.6	1.7	30.7	1.3	33.0	0.2	31.9	0.8
		2	LCZ 5	26.7	1.4	21.8	0.9	19.7	0.3	20.3	0.7	26.9	3.1	34.6	0.9	35.1	0.9	32.2	0.9
		3	LCZ 5	25.3	1.3	22.0	0.8	19.9	0.5	20.2	1.4	28.1	2.3	34.6	1.3	36.8	0.3	32.2	1.6
		4	LCZ 5	24.6	1.2	21.3	0.6	19.6	0.4	19.4	0.9	24.7	1.8	29.9	1.1	32.2	0.2	30.9	1.1
		5	LCZ 5	24.6	1.4	21.4	0.7	19.5	0.5	20.1	1.7	27.6	2.0	34.1	1.3	36.0	0.5	32.9	1.6
		6	LCZ 5	24.9	2.7	19.3	0.8	17.5	0.3	19.3	1.6	25.6	1.8	30.4	0.9	32.9	0.4	32.0	0.9
		7	LCZ 5	24.5	1.3	21.1	0.9	18.7	0.6	17.8	0.6	23.4	2.1	30.7	1.7	34.0	0.3	31.6	1.4
		8	LCZ 9	22.7	1.1	19.6	0.9	17.5	0.5	18.4	1.3	24.8	2.4	33.3	1.6	35.2	0.3	31.1	2.2
		9	LCZ 9	24.3	1.6	20.9	1.0	18.8	0.6	18.8	1.4	25.0	1.8	30.7	1.2	33.2	0.3	31.2	1.3
		10	LCZ G	23.1	1.3	19.9	0.7	17.9	0.6	18.3	1.6	24.8	1.7	30.2	0.9	32.0	0.3	30.6	1.5
		A	LCZ D	21.2	2.2	17.0	0.7	15.2	0.4	18.0	3.3	27.4	2.4	33.2	0.9	35.1	0.4	32.5	2.3
	N Slopes	11	LCZ 9	23.0	1.6	19.8	0.6	17.7	0.5	18.5	1.8	26.6	2.4	33.2	1.1	35.8	0.3	32.2	2.0
		B	LCZ D	23.6	0.9	21.3	0.7	19.4	0.5	19.8	1.3	25.9	1.9	31.8	1.3	33.8	0.3	30.9	1.6
	S Slopes	12	LCZ 9	22.8	1.3	19.5	0.7	17.2	0.5	17.2	1.1	23.7	2.4	31.9	1.7	34.9	0.5	31.2	2.7
		13	LCZ 6	25.5	0.7	22.3	1.2	19.4	0.7	18.7	0.8	23.7	1.9	31.4	2.1	34.1	0.9	31.4	1.3
		14	LCZ 5	23.8	1.5	20.5	0.7	18.3	0.5	18.1	1.0	23.9	2.1	30.2	1.1	32.5	0.3	31.1	1.4
		C	LCZ D	22.9	1.6	18.4	1.3	15.7	0.4	18.0	2.5	27.1	2.6	32.8	0.8	34.5	0.4	31.8	2.1
	Hilltops	D	LCZ D	20.4	1.7	16.8	0.6	15.7	0.2	18.4	2.1	26.2	2.0	31.9	1.4	34.2	0.1	30.5	2.3
		E	LCZ D	25.1	0.7	22.2	0.8	20.0	0.4	20.2	1.0	25.6	1.6	31.1	1.4	33.1	0.4	30.5	1.5
		F	LCZ 9	24.4	0.7	21.8	0.8	19.5	0.7	18.7	0.6	23.7	2.0	31.6	2.7	35.4	0.6	30.8	2.2
		G	LCZ 9	24.2	0.7	22.3	0.4	20.7	0.5	20.7	0.9	25.5	1.8	30.4	0.7	31.3	0.2	29.3	1.1

), separately for each vertical zone of the city, following the RMUHI concept, while to estimate the SUHI intensity (SUHII), the land surface temperature differences between particular LCZ classes and LCZ D class, i.e., the most common land cover type of LCZ in the rural areas, were computed (see

Table A4. Mean values (µ) and standard deviations (σ) of land surface temperature (LST) at the approximate acquisition times of the NOAA/AVHRR satellite images during the study periods for different LCZ classes in different vertical zones.

Period	Vertical Zone	LCZ Class	Timestamp [Hour UTC]
			19		3		5		9		12		15
			LST [°C]
			µ	σ	µ	σ	µ	σ	µ	σ	µ	σ	µ	Σ
W	Valley floor	LCZ 2	22.4	0.2	16.1	0.6	18.6	0.3	33.0	0.9	41.0	1.4	34.4	0.8
		LCZ 5	21.0	1.4	14.3	1.3	17.1	0.9	30.9	1.5	38.2	2.0	32.1	1.4
		LCZ 6	18.4	1.6	12.2	1.5	16.0	0.7	28.9	1.5	34.9	2.3	29.3	2.0
		LCZ 8	18.7	1.8	12.2	1.5	16.4	0.9	29.7	1.3	36.2	2.1	30.5	1.9
		LCZ 9	17.2	1.1	11.0	1.0	15.5	0.7	27.8	1.3	32.7	1.9	27.9	1.4
		LCZ 10	19.5	1.3	13.6	1.2	17.0	1.4	30.4	1.8	38.2	2.9	32.3	2.2
		LCZ A	16.9	0.8	10.7	0.5	15.1	0.6	27.0	1.3	31.2	1.5	26.5	1.0
		LCZ B	17.1	1.1	11.1	1.3	15.3	0.9	27.5	1.6	31.7	2.0	27.3	1.7
		LCZ D	16.5	0.8	10.6	1.1	15.4	0.7	27.2	1.1	31.6	1.7	27.0	1.3
		LCZ F	17.0	0.9	11.0	1.0	16.0	0.5	29.6	1.7	35.1	2.4	29.5	2.0
		LCZ G	17.3	1.4	11.2	1.3	15.9	0.5	27.7	1.5	32.0	2.2	27.2	2.0
	N Slopes	LCZ 5	21.2	1.0	13.9	0.9	16.8	0.6	30.6	1.2	38.0	1.8	31.8	1.2
		LCZ 6	18.5	1.5	12.3	1.2	15.9	0.7	28.4	1.3	33.7	2.4	29.3	1.6
		LCZ 8	19.5	1.8	12.6	1.3	16.4	0.9	30.1	1.4	36.5	2.4	31.0	1.7
		LCZ 9	18.1	1.3	11.8	1.0	15.7	0.6	27.7	1.4	33.1	2.5	28.2	1.6
		LCZ 10	20.7	1.3	14.0	1.1	17.9	0.6	30.8	1.3	40.8	2.6	33.5	1.4
		LCZ A	17.2	0.9	11.7	1.0	15.0	0.6	26.1	1.4	30.0	1.1	25.8	0.7
		LCZ B	17.3	0.8	11.8	0.4	14.8	0.6	26.1	1.3	30.4	0.9	25.9	0.8
		LCZ D	17.1	0.9	11.2	0.9	15.3	0.7	27.0	0.9	31.5	1.3	27.1	1.0
		LCZ F	18.3	0.8	12.6	0.8	16.3	0.6	29.4	1.7	35.2	1.9	30.0	1.5
	S Slopes	LCZ 5	18.7	1.2	12.0	1.1	15.7	0.7	29.9	0.9	35.7	1.5	30.1	1.2
		LCZ 6	17.8	1.2	11.4	1.1	15.4	0.6	28.5	0.8	34.1	1.5	28.8	1.3
		LCZ 8	17.8	1.8	11.5	1.1	15.2	0.9	28.4	1.1	34.6	2.5	29.3	1.3
		LCZ 9	16.6	0.9	10.8	0.9	15.0	0.7	27.4	1.1	31.8	1.6	27.2	1.2
		LCZ A	16.6	0.7	10.6	0.6	14.8	0.9	26.0	1.4	30.3	1.1	25.9	0.9
		LCZ B	16.2	0.8	10.5	1.0	14.6	0.8	26.6	1.0	30.7	1.6	26.1	1.0
		LCZ D	16.2	0.6	10.9	0.7	15.2	0.7	26.1	1.0	30.6	1.0	26.3	0.7
		LCZ F	16.4	0.3	10.9	0.6	15.5	0.7	26.5	1.0	31.1	0.6	26.7	0.5
	Hilltops	LCZ 6	16.4	0.2	11.8	0.1	15.6	0.3	26.7	0.9	30.8	1.9	25.8	0.7
		LCZ 9	16.2	0.8	11.2	0.7	15.3	0.5	26.2	0.8	30.8	1.0	26.1	0.9
		LCZ A	16.9	0.9	11.9	0.9	15.2	0.6	25.1	0.9	29.4	0.9	25.3	0.6
		LCZ B	16.1	0.6	10.8	0.6	14.8	0.6	25.8	0.8	29.8	0.7	25.4	0.6
		LCZ D	16.6	0.7	11.6	0.8	15.4	0.5	26.0	0.9	30.7	0.8	26.2	0.8
		LCZ F	17.7	0.8	12.4	0.8	16.0	0.7	27.5	1.1	32.5	1.7	28.1	1.3
H	Valley floor	LCZ 2	28.0	0.3	21.3	0.1	21.7	0.5	38.4	0.7	47.1	1.1	39.1	0.9
		LCZ 5	26.4	0.9	19.5	1.2	21.1	0.6	36.1	1.2	44.2	1.9	37.3	1.5
		LCZ 6	23.9	2.1	17.0	1.9	19.7	1.0	34.0	1.8	41.5	2.5	34.8	2.1
		LCZ 8	24.3	1.7	17.3	1.7	20.1	1.2	35.3	1.3	43.1	1.7	36.0	1.5
		LCZ 9	22.5	1.4	15.8	1.2	19.3	0.8	32.8	1.4	39.9	1.9	33.6	1.4
		LCZ 10	25.1	1.4	18.4	0.9	21.1	0.5	38.1	1.6	46.2	2.7	37.7	1.6
		LCZ A	21.8	0.7	14.8	0.9	18.4	0.6	31.4	1.5	38.4	1.4	32.7	1.1
		LCZ B	22.4	1.7	16.1	1.4	19.2	1.0	32.1	1.9	39.1	2.5	33.1	1.7
		LCZ D	21.6	1.1	14.8	1.3	19.0	0.9	32.5	1.4	39.2	2.0	33.1	1.3
		LCZ F	22.7	0.9	15.7	1.3	20.1	0.9	35.2	1.3	42.5	2.3	35.0	1.5
		LCZ G	22.6	1.5	16.2	1.7	19.9	0.7	32.5	1.3	39.3	1.9	33.5	1.5
	N Slopes	LCZ 5	25.5	0.8	18.9	0.8	21.0	0.3	35.6	1.0	44.1	1.0	37.2	1.0
		LCZ 6	23.0	1.0	16.9	0.7	20.0	0.4	33.4	1.2	40.9	2.7	34.2	2.1
		LCZ 8	24.0	1.3	17.9	1.2	20.7	0.5	35.4	1.1	43.0	1.4	36.6	1.5
		LCZ 9	22.8	1.0	16.7	1.1	19.9	0.7	33.0	1.5	40.4	2.1	34.2	1.8
		LCZ 10	25.1	0.9	18.4	0.7	20.9	0.3	38.0	1.2	46.0	1.5	38.3	1.8
		LCZ A	22.4	1.0	15.9	0.9	19.1	0.6	30.2	1.3	37.0	2.4	31.1	1.5
		LCZ B	22.5	1.2	15.7	0.6	19.0	0.4	29.4	1.5	36.9	2.0	31.6	1.5
		LCZ D	22.0	1.0	16.0	1.3	19.7	0.7	32.7	1.4	39.6	2.1	33.6	1.5
		LCZ F	23.0	0.5	17.4	0.8	20.6	0.6	35.0	1.0	43.2	1.4	35.8	0.9
	S Slopes	LCZ 5	25.3	1.1	17.9	0.9	20.4	0.6	35.4	1.0	42.6	1.2	35.8	1.3
		LCZ 6	24.1	1.5	17.0	1.2	19.6	0.5	34.5	1.1	41.2	1.5	34.6	1.5
		LCZ 8	24.6	1.8	17.4	1.4	19.7	0.9	35.0	1.4	42.2	1.9	35.5	1.9
		LCZ 9	22.0	1.3	15.3	1.1	18.7	0.9	32.8	1.2	39.0	1.6	32.8	1.4
		LCZ A	21.7	0.8	15.2	0.8	18.2	0.7	30.7	1.1	36.7	1.3	31.3	0.8
		LCZ B	21.4	1.2	14.8	0.9	18.1	1.0	31.8	1.2	37.8	1.8	31.8	1.4
		LCZ D	21.3	0.8	15.2	0.9	18.7	0.9	32.5	1.6	38.5	1.8	32.6	1.4
		LCZ F	20.9	0.5	14.7	0.6	17.8	0.9	31.8	1.2	38.1	1.5	32.0	1.3
	Hilltops	LCZ 6	22.5	0.6	16.7	0.7	19.0	0.7	33.0	0.4	38.3	0.2	32.2	0.5
		LCZ 9	21.1	0.9	15.7	0.9	18.5	0.7	31.4	1.0	37.2	1.5	31.4	1.1
		LCZ A	21.8	1.0	16.4	0.8	18.6	0.7	30.0	0.9	35.9	1.7	30.7	1.4
		LCZ B	20.9	0.7	15.2	0.6	18.4	0.6	30.4	0.7	36.1	1.1	30.7	0.8
		LCZ D	21.3	0.8	16.1	0.9	19.2	0.7	31.7	1.2	38.2	1.7	32.4	1.4
		LCZ F	22.6	0.7	17.0	1.0	20.0	0.6	33.6	1.0	40.8	1.4	34.4	0.9

). The AUHII values were calculated for all individual urban T_air points using the rural points located in the respective vertical zones as a reference, whereas the SUHII values for each satellite image acquisition time were calculated in two ways: firstly, using the extracted LST values for the pixels corresponding to the location of the T_air measurement points, performing a calculation similar to that of AUHII, and secondly, using the zonal mean LST values for the LCZ D class in the individual vertical zones by subtracting them from all LST pixels in the given vertical zone.

The comparative analysis included the differences in AUHII and SUHII (ΔAUHII and ΔSUHII, respectively) between the study periods for the following scenarios:

• AUHII and SUHII compatible in terms of location and time, i.e., at the T_air measurement points and the approximate acquisition times of satellite images;
• AUHII at individual T_air measurement points in a 3 h interval;
• SUHII at the approximate acquisition times of the NOAA/AVHRR satellite images for individual LCZ classes, separately for each vertical zone.

4. Results

4.1. Analysis of AUHII and SUHII Daily Variability and Spatial Structure

First, the night–day variability of AUHII and SUHII in both study periods have been analyzed, for the urban T_air measurement points located within different LCZ classes, in the valley floor and on the N and S slopes (Figure 3).

A roughly similar night–day variability of AUHII is observed in both study periods at individual T_air measurement points located in the built types of LCZs, especially in the valley floor. More specifically, a sharp rise in AUHII occurs around sunset, reaching a maximum after 2–3 h (at Point 1 up to 5.5 °C and 6.7 °C in Periods W and H, respectively) and persisting throughout the night until sunrise, after which AUHI gradually decays to form an atmospheric urban cold island (AUCI) during the day. Certain differences in the daily variability of AUHII in the study area occur between the vertical zones distinguished. At night, on the S slopes, a slower rise after sunset and lower AUHII values than in the valley floor are observed, while on the N slopes, the AUHI does not occur until the second part of the night in Period W or not at all in Period H. In the daytime, the AUCI, which is formed after the sharp disappearance of AUHI, persists at some measurement points in the valley floor throughout the day (Points 1, 4, 6, 7, 9, and 10), but at other points the AUHII values rise up to around 2 °C (Points 2, 3, 5, and 8). The same happens on the S slopes, but the rapid decrease in the AUHII value takes longer, by 2–3 h, than in the valley floor, while on the N slopes, the AUHII value increases around 6 UTC (following an earlier decrease in the value after sunrise in Period W), similar to some points in the valley floor. The variability of the AUHII is also noticeable for the same LCZ class in different vertical zones, e.g., for LCZ 5 at night in the valley floor, higher AUHII values are recorded than on the S slopes, while for LCZ 9 at night on the N slopes, lower AUHII values than in the valley floor appeared, and the opposite during the daytime. Differences in the AUHII daily cycle are also found between the T_air measurement points located within one LCZ class, e.g., LCZ 5, and in the same vertical zone.

The daily variability of SUHII is also approximately similar in both study periods at each T_air measurement point located in the built LCZ type, especially in the valley floor (Figure 3). At night (between 18 and 3 UTC), the SUHII values usually remain at a similar level, otherwise they slightly decrease or increase. In the valley floor, the nighttime values of SUHII differ between LCZ 2 and LCZ 9 classes by more than 4 °C (the highest SUHII values 6.5 °C and 8.4 °C are noted at Point 1, while the lowest values ~2 °C and ~4 °C are recorded at Points 8, 9, and 10, for both Periods W and H, respectively). Between 3 and 5 UTC in the morning (after sunrise) a decrease in SUHII value by a few degrees Celsius is observed in the valley floor (e.g., at Point 1 by a maximum of 3.1 °C and 5.5 °C in the Periods W and H, respectively), while on the N and S slopes, the changes in SUHII values are smaller. Then, at 9 UTC, there is usually a rapid increase in the SUHII value, especially in the valley floor, and around 12 UTC SUHII reaches its maximum (e.g., at Point 1: 12.7 °C in Period W and 10.9 °C in Period H). Until 15 UTC, the value of SUHII drops quite quickly to a similar level as at 9 UTC. At the points located within LCZ 2 and LCZ 5 in the valley floor, the highest values of daytime SUHII clearly exceed the values of nighttime SUHII. While, on the S slopes at the points representing LCZ 5 and LCZ 6, as well as at the points located within LCZ 9, both in the valley floor and on the N and S slopes, the level of exceedance is smaller.

Comparing the spatial structure of AUHI and SUHI in Kraków (Figure 4), it has been found that, in both study periods, they are approximately similar at night, as they refer to the structure of buildings in the city, i.e., the distribution of the built types of LCZs.

4.2. Analysis of ΔAUHII and ΔSUHII Daily Variability

By comparing the values of ΔAUHII and ΔSUHII at the T_air measurement points locations and at the NOAA/AVHRR images acquisition times (

Table 5. ΔAUHII and ΔSUHII at the approximate acquisition times of the NOAA/AVHRR satellite images for the T_air measurement points (relative to the rural ones) located in different LCZ classes and vertical zones.

Vertical Zone	Difference of Tair Measurement Points (Urban–Rural)	LCZ Class Difference	Period H–Period W
			Timestamp [Hour UTC]						Timestamp [Hour UTC]
			19	3	5	9	12	15	19	3	5	9	12	15
			ΔAUHII [°C]						ΔSUHII [°C]
Valley floor	Point 1–Point A	LCZ 2–LCZ D	−1.6	0.6	0.4	−0.8	−0.3	−0.7	0.6	1.9	−1.0	−0.8	−1.9	−1.3
	Point 2–Point A	LCZ 5–LCZ D	−0.3	1.1	1.9	−0.7	−0.4	−1.5	1.1	2.2	0.0	−1.0	−1.0	−2.5
	Point 3–Point A	LCZ 5–LCZ D	−0.6	1.6	1.4	−1.8	−0.4	0.3	0.1	2.8	0.4	0.3	−2.9	−1.6
	Point 4–Point A	LCZ 5–LCZ D	−1.3	0.5	0.5	−1.6	−1.2	−2.3	2.7	3.0	0.6	−1.3	−0.5	−1.2
	Point 5–Point A	LCZ 5–LCZ D	−1.0	0.3	−0.5	−1.8	−0.6	−1.1	−0.1	1.7	−0.5	−1.2	−0.9	−0.9
	Point 6–Point A	LCZ 5–LCZ D	1.5	0.2	2.6	−1.1	−1.5	−1.0	0.9	2.2	−0.1	−1.9	−1.2	−2.8
	Point 7–Point A	LCZ 5–LCZ D	−1.2	−0.2	−0.1	−2.3	−0.6	−0.6	−0.2	1.6	−1.2	−1.2	−1.4	−0.6
	Point 8–Point A	LCZ 9–LCZ D	−0.3	1.3	2.7	−1.9	−0.1	−0.6	0.7	1.8	−0.4	−0.6	−3.4	−2.1
	Point 9–Point A	LCZ 9–LCZ D	−0.9	0.1	0.6	−1.4	−0.6	−0.3	−0.2	1.2	−0.8	−1.9	−2.4	−0.8
	Point 10–Point A	LCZ G–LCZ D	−2.1	−1.3	−0.5	−1.1	−0.8	−1.0	−0.2	2.6	−0.3	−2.1	−0.2	−1.2
N Slopes	Point 11–Point B	LCZ 9–LCZ D	0.0	−2.6	0.9	−0.2	−0.4	−0.3	−1.4	0.1	−0.9	−1.4	1.0	−3.1
S Slopes	Point 12–Point C	LCZ 9–LCZ D	−0.6	0.3	−1.8	−2.7	−1.4	−0.5	0.0	0.6	−0.7	−1.6	−0.8	−2.6
	Point 13–Point C	LCZ 6–LCZ D	−0.7	2.2	−0.6	−2.2	−0.9	−2.1	0.8	2.9	0.7	−0.6	−1.5	0.2
	Point 14–Point C	LCZ 5–LCZ D	0.1	1.0	−2.8	−1.8	−0.7	−0.5	0.6	1.9	0.2	−1.0	−1.4	−2.1

), the information obtained from in situ measurements and satellite data is significantly reduced. Continuous T_air time series has been limited to 6 timestamps for each study period, while the spatial continuity of the LST data has been reduced to pixel values corresponding to the T_air measurement points. The values of ΔAUHII and ΔSUHII indicate an enhancement of both AUHII and SUHII during Period H by approximately 3 °C, mainly around 3 UTC. The ΔAUHII values for most of the points located in the built types of LCZs are also positive at 5 UTC, whereas positive values of ΔSUHII are noted additionally at around 19 UTC. For the remaining timestamps, negative values prevail. For Point 10 (located near the water bodies), and Point 7 (located in the immediate vicinity of a wooded urban green area), the ΔAUHII values are negative for all timestamps. The highest values of ΔAUHII are noted at Points 6 and 8 which are directly adjacent to open urban green areas. At Point 11 on the N slopes, the ΔSUHII values are negative at almost all timestamps, except for 12 UTC, while at the points on the S slopes, the daily variability of ΔSUHII is similar to that for the points located in the valley floor. In particular, a similar variability in the value of ΔSUHII in the following timestamps is observed at Points 13 and 14 as well as Points 3 and 4 (all located in close proximity to the blocks of flats).

Table 6. Mean values (µ) and standard deviations (σ) of ΔAUHII in 3 h time intervals for the urban T_air measurement points (relative to the rural ones) located in different LCZ classes and vertical zones.

Vertical Zone	Difference of Tair Measurement Points (Urban–Rural)	LCZ Class Difference	Period H–Period W
			Hour Interval [UTC]
			18–21	21–0	0–3	3–6	6–9	9–12	12–15	15–18
			ΔAUHII 1 [°C]
			µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)
Valley floor	Point 1–Point A	LCZ 2–LCZ D	0.8 (0.4)	1.4 (0.4)	0.5 (0.2)	1.1 (0.9)	−0.1 (0.4)	−0.8 (0.5)	−0.4 (0.2)	0.2 (0.8)
	Point 2–Point A	LCZ 5–LCZ D	1.8 (0.4)	1.2 (0.6)	0.5 (0.2)	2.6 (0.9)	0.4 (0.8)	0.1 (0.5)	−0.7 (0.6)	0.4 (0.8)
	Point 3–Point A	LCZ 5–LCZ D	1.1 (0.4)	1.9 (0.3)	1.5 (0.2)	2.0 (1.3)	−0.8 (0.3)	−0.8 (0.4)	0.2 (0.4)	0.3 (0.6)
	Point 4–Point A	LCZ 5–LCZ D	0.5 (0.4)	0.8 (0.3)	0.4 (0.2)	1.4 (0.7)	0.0 (0.9)	−1.4 (0.3)	−1.6 (0.5)	−0.7 (1.0)
	Point 5–Point A	LCZ 5–LCZ D	0.3 (0.2)	0.5 (0.4)	0.2 (0.1)	0.6 (1.1)	−0.5 (0.3)	−0.8 (0.4)	−0.5 (0.5)	−0.3 (0.7)
	Point 6–Point A	LCZ 5–LCZ D	1.6 (1.0)	0.6 (0.6)	−0.2 (0.2)	2.8 (1.1)	0.4 (1.1)	−1.5 (0.2)	−1.2 (0.2)	0.2 (0.8)
	Point 7–Point A	LCZ 5–LCZ D	0.5 (0.3)	0.7 (0.5)	−0.2 (0.3)	1.0 (0.6)	0.1 (1.0)	−1.2 (0.5)	−0.3 (0.2)	−0.1 (0.7)
	Point 8–Point A	LCZ 9–LCZ D	1.2 (0.4)	1.9 (0.4)	1.2 (0.3)	3.1 (1.0)	0.5 (1.0)	−0.2 (0.2)	0.0 (0.4)	−0.1 (0.7)
	Point 9–Point A	LCZ 9–LCZ D	0.6 (0.5)	1.6 (0.8)	0.6 (0.5)	1.3 (0.6)	0.2 (1.0)	−1.0 (0.3)	−0.3 (0.1)	0.1 (0.6)
	Point 10–Point A	LCZ G–LCZ D	−0.5 (0.5)	0.1 (0.3)	−0.5 (0.4)	0.0 (0.5)	−0.2 (0.5)	−0.7 (0.2)	−0.8 (0.2)	−1.2 (0.1)
N Slopes	Point 11–Point B	LCZ 9–LCZ D	−0.6 (0.4)	−1.6 (0.8)	−3.3 (0.2)	−0.4 (1.3)	0.3 (0.2)	−0.2 (0.4)	−0.4 (0.2)	0.4 (0.5)
S Slopes	Point 12–Point C	LCZ 9–LCZ D	−0.6 (0.4)	−0.5 (0.6)	−0.1 (0.3)	−0.5 (0.7)	−0.7 (0.6)	−1.4 (0.3)	−1.1 (0.4)	−0.8 (0.3)
	Point 13–Point C	LCZ 6–LCZ D	0.6 (0.6)	1.8 (0.4)	2.0 (0.1)	0.8 (1.3)	−0.6 (0.7)	−1.1 (0.5)	−1.0 (0.8)	−1.2 (0.9)
	Point 14–Point C	LCZ 5–LCZ D	0.0 (0.4)	0.6 (0.5)	0.6 (0.3)	−1.0 (1.3)	−1.0 (0.2)	−0.8 (0.4)	−0.6 (0.2)	−0.4 (0.4)

¹ Bold and underlined numbers mean that 95.5% of the values are in the range µ ± 2σ, keeping the sign of the number (positive or negative); bold numbers without underlining mean that 68% of the values are in the range of µ ± σ, keeping the sign of the numbers (positive or negative).

shows the mean ΔAUHII values at the 3 h intervals. In the valley floor, the greatest positive ΔAUHII occurs between 3–6 UTC (reaching 3.1 °C), whereas in the daytime hours, at most points, the mean values of ΔAUHII are negative (reaching −1.6 °C) or close to zero. Point 10 (LCZ G) located in the valley floor, where both at night and day the mean ΔAUHII values are negative or close to zero, is an exception from this rule. On the N slopes (Point 11), negative mean values of ΔAUHII (exceeding −3 °C) are observed at night and at most 3 h intervals in the daytime. While on the S slopes, at Point 12, all the mean values of ΔAUHII are negative, but at Points 13 and 14, positive values prevail during the night till 3 UTC, and the values in the daytime are positive.

The daily variability of the mean ΔSUHII values for LCZ classes, including those not represented by the T_air measurement points, is presented in

Table 7. Mean values (µ) and standard deviations (σ) of ΔSUHII for the LCZ classes (relative to LCZ D) in different vertical zones, at the approximate acquisition times of the NOAA/AVHRR satellite images.

Vertical Zone	LCZ Class Difference	Period H–Period W
		Timestamp [hour UTC]
		19	3	5	9	12	15
		ΔSUHII 1 [°C]
		µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)	µ (σ)
Valley floor	LCZ 2–LCZ D	0.5 (0.3)	1.1 (0.6)	−0.6 (0.5)	0.1 (0.4)	−1.5 (0.4)	−1.3 (0.7)
	LCZ 5–LCZ D	0.3 (1.2)	0.9 (0.8)	0.3 (0.7)	−0.1 (1.2)	−1.6 (1.3)	−0.9 (1.0)
	LCZ 6–LCZ D	0.4 (1.1)	0.6 (0.9)	0.1 (0.9)	−0.2 (1.2)	−1.1 (0.7)	−0.6 (1.0)
	LCZ 8–LCZ D	0.5 (1.0)	0.9 (0.9)	0.1 (1.0)	0.3 (1.1)	−0.8 (1.5)	−0.6 (1.3)
	LCZ 9–LCZ D	0.3 (1.1)	0.6 (0.8)	0.1 (0.9)	−0.2 (1.1)	−0.5 (1.5)	−0.3 (1.1)
	LCZ 10–LCZ D	0.5 (1.2)	0.6 (0.7)	0.5 (1.1)	2.5 (1.7)	0.4 (1.6)	−0.6 (2.0)
	LCZ A–LCZ D	−0.2 (0.8)	−0.2 (0.9)	−0.4 (0.9)	−0.9 (1.2)	−0.4 (1.2)	0.1 (1.0)
	LCZ B–LCZ D	0.2 (1.3)	0.8 (0.7)	0.3 (0.8)	−0.7 (1.2)	−0.2 (1.2)	−0.2 (1.3)
	LCZ F–LCZ D	0.7 (0.8)	0.6 (0.9)	0.5 (0.8)	0.3 (1.1)	−0.2 (1.4)	−0.6 (1.2)
	LCZ G–LCZ D	0.2 (1.0)	0.7 (1.0)	0.4 (0.5)	−0.5 (1.1)	−0.3 (0.8)	0.2 (1.1)
N Slopes	LCZ 5–LCZ D	−0.7 (1.2)	0.2 (0.7)	−0.2 (0.5)	−0.8 (1.0)	−2.0 (1.2)	−1.0 (0.8)
	LCZ 6–LCZ D	−0.4 (1.0)	−0.3 (1.0)	−0.3 (0.5)	−0.7 (1.0)	−0.8 (1.2)	−1.5 (1.1)
	LCZ 8–LCZ D	−0.4 (1.3)	0.5 (0.9)	0.0 (0.7)	−0.4 (1.3)	−1.5 (1.3)	−0.9 (1.0)
	LCZ 9–LCZ D	−0.2 (1.2)	0.1 (1.1)	−0.2 (0.7)	−0.4 (1.4)	−0.8 (1.4)	−0.4 (1.1)
	LCZ 10–LCZ D	−0.5 (1.8)	−0.3 (0.8)	−1.3 (0.5)	1.4 (1.0)	−2.9 (1.6)	−1.7 (1.3)
	LCZ A–LCZ D	0.3 (1.2)	−0.5 (1.1)	−0.2 (0.9)	−1.7 (1.4)	−1.1 (1.9)	−1.1 (1.3)
	LCZ B–LCZ D	0.3 (1.2)	−0.9 (0.7)	−0.2 (0.7)	−2.5 (1.6)	−1.5 (1.4)	−0.8 (0.8)
	LCZ F–LCZ D	−0.2 (0.9)	0.0 (1.0)	−0.1 (0.8)	−0.1 (1.4)	−0.1 (1.4)	−0.7 (1.2)
S Slopes	LCZ 5–LCZ D	1.5 (0.8)	1.6 (0.7)	1.1 (0.6)	−0.9 (0.8)	−1.0 (0.9)	−0.6 (1.1)
	LCZ 6–LCZ D	1.3 (0.8)	1.3 (1.0)	0.8 (0.9)	−0.4 (0.8)	−0.8 (0.7)	−0.6 (0.8)
	LCZ 8–LCZ D	1.7 (1.0)	1.6 (1.0)	1.0 (1.3)	0.2 (1.4)	−0.3 (1.5)	−0.1 (0.9)
	LCZ 9–LCZ D	0.4 (1.1)	0.2 (1.0)	0.3 (1.1)	−0.9 (1.1)	−0.7 (1.1)	−0.7 (1.0)
	LCZ A–LCZ D	−0.1 (1.0)	0.3 (1.1)	−0.1 (0.9)	−1.7 (1.0)	−1.5 (0.9)	−0.9 (0.7)
	LCZ B–LCZ D	0.1 (1.1)	0.1 (1.0)	0.0 (1.3)	−1.2 (1.0)	−0.8 (1.5)	−0.6 (0.9)
	LCZ F–LCZ D	−0.7 (0.6)	−0.5 (0.8)	−1.1 (1.4)	−1.1 (1.2)	−0.9 (1.3)	−1.1 (1.2)
Hilltops	LCZ 6–LCZ D	1.4 (0.5)	0.4 (0.7)	−0.4 (1.0)	0.6 (0.5)	0.0 (1.7)	0.2 (1.2)
	LCZ 9–LCZ D	0.3 (0.9)	0.0 (0.8)	−0.6 (0.8)	−0.5 (0.8)	−1.1 (1.1)	−0.8 (0.8)
	LCZ A–LCZ D	0.2 (0.9)	0.0 (0.8)	−0.3 (1.0)	−0.8 (0.8)	−1.0 (1.3)	−0.8 (1.2)
	LCZ B–LCZ D	0.2 (0.6)	−0.1 (0.7)	−0.2 (0.8)	−1.1 (1.0)	−1.2 (1.0)	−0.9 (0.6)
	LCZ F–LCZ D	0.3 (0.6)	0.1 (0.8)	0.2 (0.4)	0.4 (1.3)	0.8 (1.1)	0.2 (0.8)

¹ Bold and underlined numbers mean that 95.5% of the values are in the range µ ± 2σ, keeping the sign of the number (positive or negative); bold numbers without underlining mean that 68% of the values are in the range of µ ± σ, keeping the sign of the numbers (positive or negative).

. In the valley floor, the LCZ class with positive mean values of ΔSUHII (up to 2.5 °C) at almost all the timestamps is LCZ 10. For other LCZ built types (i.e., LCZ 2, LCZ 5, LCZ 6, LCZ 8, and LCZ 9) as well as for such LCZ land cover types like LCZ B, LCZ G, and LCZ F, located in the valley floor, positive mean values of ΔSUHII are noted at night (up to 1.1 °C), while in the daytime hours, the values are negative (down to −1.6 °C) or close to zero. For LCZ A in the valley floor, negative (down to −0.9 °C) or close to zero mean ΔSUHII values are observed in all the timestamps. On the N slopes, for most LCZ classes, the mean values of the ΔSUHII at individual timestamps are negative, close to zero, or weakly positive. In the LCZ built types within this vertical zone, the greatest negative mean ΔSUHII values (reaching −2.9 °C) occur at 12 UTC, especially for LCZ 5, LCZ 8, and LCZ 10, while for the LCZ land cover types, the highest negative mean values of ΔSUHII (down to −2.5 °C) are observed at 9 UTC. On the S slopes, for the LCZ built types, positive mean ΔSUHII values (up to 1.6 °C), higher than in the valley floor, are noted in the nighttime and morning timestamps, while in the remaining daytime timestamps, the mean ΔSUHII values are mostly negative (down to −1 °C). For the LCZ land cover types on the S slopes, the mean values of ΔSUHII are close to zero or negative (down to −1.7 °C) in the nighttime and daytime timestamps. On the hilltops, for LCZ 6 and LCZ F, positive or close to zero mean ΔSUHII values are noted at most of the timestamps, whereas for LCZ 9, LCZ A, and LCZ B there is a similar night–day variability of the mean ΔSUHII, i.e., values close to zero at night and negative values (down to −1.2 °C) in the daytime hours.

5. Discussion

The average night–day cycle of AUHII observed in Kraków is consistent with the theoretical temporal evolution of AUHII during the day in anticyclonic, cloudless, and poorly windy conditions, presented by Oke [13], and also empirically confirmed for other European cities, namely Bucharest [35], Szeged [54], and Madrid [53]. The observed differences in the daily variability of AUHII between the vertical zones are consistent with the previous findings regarding RMUHI in Kraków [25]. However, the effect of relief on AUHI may be superimposed by the effect of air mass inflow, which manifests itself most clearly on the slopes in the northern part of the study area. Moreover, there is a greater variation in AUHII values between LCZ classes at night than in the daytime, which corresponds to the results presented by Núñez-Peiró et al. [53].

The differences in the AUHII daily cycle between the T_air measurement points located within one LCZ class may have been influenced by terrain-related katabatic flows and the subsequent formation of a deep air temperature inversion manifested mainly at night, with T_air differences between rural areas located in different vertical zones, representing mostly LCZ D (see Table A3).

The observed differences in the AUHII diurnal cycle between T_air measurement points located within one LCZ class and in the same vertical zone are probably caused by the influence of the immediate surroundings (e.g., proximity of open or forested green areas) on the air temperature. It is also possible that some inaccuracy of the LCZ classification method may have an influence on the obtained results, as a result of which individual T_air measurement points may not fully represent the LCZ class obtained from the prepared map (Figure 1c). The area generalization used in the LCZ classification may sometimes be too large and ignore smaller areas with characteristics of a different LCZ class than those of a nearby larger area. The ambiguous representation of the LCZ class by some points is visible in the percentage shares of the LCZ classes in the area around the point with a radius of 500 m (Table 3).

The SUHII values are generally positive for 24 h in all LCZ classes and vertical zones, which is consistent with the findings of Annibale et al. [34] and Stewart et al. [50]. The observed mean time course of SUHII in Kraków is roughly consistent with the results presented by Stewart et al. [50] for a humid continental climate. At night, the intensity of SUHI in Kraków is the highest in the city center, and during the daytime in the center and in the industrial areas, which is in line with the observations for Paris [45].

A comparison of the simultaneous time evolution of the intensity of AUHI and SUHI in Kraków can be referred to the results presented by Stewart et al. [50]. For a humid continental climate, these authors noticed that the highest SUHII is observed in the early afternoon when the AUHII is close to the minimum. The maximum value of SUHII in Kraków is recorded around 12 UTC, but the AUHII is not necessarily the lowest during the day. Also, similarly to the study by Stewart et al. [50], the maximum AUHII in Kraków occurs between midnight and sunrise, but the SUHII is not at minimum at that time, as shown by the findings of Stewart et al. [50]. The minimum value of SUHII in Kraków appears more than 2 h after sunrise. As in the study by Stewart et al. [50], in Kraków, the most intense AUHI and SUHI at night are found for LCZ 2 class, which occurs only in the valley floor. Furthermore, the discrepancies between AUHII and SUHII during both study periods have been generally lower at night than during the daytime, which corresponds to the findings of Sobrino et al. [28]. Additionally, the observation of positive SUHII values over 24 h as well as positive AUHII values at night and negative AUHII values during the daytime are consistent with previous observations in other European cities [28,83].

Similar results regarding the spatial structure of SUHI and SUHI at night were presented by Annibale et al. [34]. The correspondence of the SUHI pattern and the building structure in the daytime is even more pronounced. The highest SUHII values, both in the W and H periods, are found in the city center (LCZ 2) and in the steelworks area (LCZ 10). Furthermore, the surface agricultural heat island is visible in the areas of LCZ F as the heat accumulation by urban surfaces is so large that at the end of the night cooling the LST does not equalize between urban and rural areas. The presence of AUCI during the day in most of the city area is probably the result of more intense convective mixing than in the rural areas and/or the proximity of larger clusters of trees or water bodies that have a cooling effect on the air temperature. Their absence may be the reason for the positive AUHII values in the daytime and the formation of atmospheric urban heat micro-islands.

Some discrepancies in the results of analyses ΔAUHII and ΔSUHII daily variability, conducted in different ways, are caused by the variable representativeness of the values from the instantaneous measurement for the time interval in the case of AUHII and the variable representativeness of the values from the point location for the area of a given LCZ class in the case of SUHII. For example, mostly positive ΔAUHII values for around 3 UTC (Table 5) are consistent with the mean values for the 0–3 UTC interval (Table 6), but negative ΔAUHII values observed around 19 UTC are recorded in the 18–21 UTC interval only for Points 10 (the valley floor), 11 (the N slopes), and 12 (the S slopes). The reason for the discrepancy in this case is, firstly, the different acquisition time of satellite images from which the T_air consecutive hourly averages used to calculate AUHII are derived, and secondly, the times of sunset and sunrise are different in the compared periods. In Period W, the satellite image acquisition time around 19 UTC is 10 min later compared to sunset than in Period H, which undoubtedly affects the compared AUHII values, because, after sunset, the dynamics of AUHI formation is high. In addition, there are significant differences in cooling rates between urban and rural areas that begin to become apparent even before sunset. Whereas the satellite image acquisition at around 3 UTC takes place 25 min after sunrise in Period W, and around 20 min before sunrise in Period H. However, in this case, it does not seem to have such a significant impact, as there are large differences in the rate of air heating between urban and rural areas, which are visible with a delay after sunrise. Furthermore, the sunset is slightly more than 30 min earlier, and the sunrise is slightly more than 30 min later, i.e., the night is about 1 h longer in Period H than in Period W. This may have an impact on the time evolution of ΔAUHII during the night as well as in the morning. Larger differences in AUHII between the study periods are observed in the first part of the night, i.e., at the intervals 18–21 and 21–0 UTC. The ΔAUHII values decrease in the second part of the night (0–3 UTC), while in the morning (3–5 UTC), they increase (Table 6), which is probably caused by the difference in sunrise time.

The daily variability of the ΔSUHII values at the T_air measurement point locations (Table 5) is mostly comparable with that found on the basis of the mean ΔSUHII values for LCZ 2, LCZ 5, LCZ 6, LCZ 9, and LCZ G classes in particular vertical zones (Table 7). However, not all LCZ classes are represented by the T_air measurement points, while on the basis of LST data it is possible to estimate SUHII for all LCZ classes occurring in the study area. In addition, the SUHII values for individual LCZ classes (in different vertical zones) are calculated in relation to the mean LST value for LCZ D, and not in relation to the pixel value corresponding to the location of the T_air measurement point representing LCZ D. Hence, for some LCZ classes within a given vertical zone, depending on the satellite image acquisition time, there is a greater or lesser variation in the SUHII values (e.g., partially positive and partially negative values). This may be the result of different surface conditions (e.g., abundance of vegetation, soil moisture) within one LCZ class or a different inflow of solar radiation to these surfaces. Furthermore, one should not forget about the uncertainty of LST estimation on the basis of the NOAA/AVHRR satellite images, related to inaccurate geographic correction (an error equal to 1 pixel is assumed).

The analysis of the daily variability of the differences in the AUHII and SUHII between the two study periods, representing summer days in Kraków without HW and with HW, has provided the results that contribute to the contemporary research on the influence of HW on the atmospheric and surface UHI. The outcomes of this study indicate that a significant influence of the advective factor on the intensity of AUHI and SUHI in Kraków is causing generally higher AUHII and SUHII values during HW at night and lower ones during the day. The results support the findings of Cheval et al. [35] that HW could affect the AUHI and SUHI in Bucharest. Kabisch et al. [47] found that the nighttime AUHI in Hannover intensifies significantly in years with extremely warm summers, whereas Kong et al. [48] noticed that the AUHI in greater Sydney at night is more intense during HW than before HW, while it is even more intense during post-HW period. In the same study, these authors found the nighttime SUHI intensity to be 4 °C higher, i.e., 1 °C more than observed in Kraków in the present study. Schwarz et al. [49] observed that the SUHI intensity in Leipzig at night is greater in July with an extreme HW than in normal July, and the opposite is true during the daytime. Higher intensity of the nighttime SUHI in Valencia on the HW days was also detected [51]. Dezső et al. [44] found that the SUHI intensity in Budapest weakens in summer months, especially in the HW conditions, because of less moisture available in the rural area. In contrast, García [46] showed that in Andalusian cities (Spain) the daytime SUHI intensifies during HWs. According to Azevedo et al. [42] advection processes play an important role in forming the AUHI in Birmingham. Considering the results of this study, hot air advection in Kraków likely affects not only the AUHI but also the SUHI. Furthermore, the impact of heat waves reaching the city located in a diversified relief on the intensity of AUHI and SUHI depends on both the LCZ class and the vertical (altitude) zone, resulting in the greatest strengthening at night and the greatest weakening during the day in the valley floor zone. On the valley slopes, the influence of hot air advection is additionally conditioned by the slope direction.

6. Summary and Conclusions

This study presents a comparative analysis of the simultaneous night–day variability of the AUHI and SUHI intensities in Kraków in two 24 h summer periods, mostly cloudless and windless. The study periods differ mainly in the advection of air mass, which influences the thermal conditions in the near-surface layer of the atmosphere, i.e., a warm day with maximum T_air < 30 °C occurs during polar maritime air advection, and a hot day with maximum T_air > 30 °C occurs during tropical continental air advection. Assuming that the effect of other factors, such as cloud cover, wind conditions, the content of aerosol, PM pollution, or soil moisture, on the nighttime and daytime AUHII and SUHII values is comparable in both study periods, it is possible to investigate the influence of the advective factor, specifically the impact of HW, on the daily cycle of AUHI and SUHI intensities.

Based on the comparative analysis of the selected two 24 h periods, it has been found that in addition to land use/cover (given by LCZ classes) and relief, the daily variability and spatial structure of the atmospheric and surface UHI in Kraków are further affected by the HW, i.e., the advection of hot tropical continental air mass. Despite the significant differences between the daily cycles of AUHI and SUHI intensities, the circulation factor similarly affects both AUHII and SUHII, i.e., mostly higher values have been recorded in the nighttime and mostly lower values in the daytime in the study period with the HW (Period H) than in the study period with normal summer weather conditions (Period W). During nighttime hours, the AUHII and SUHII values higher by up to 3 °C in Period H than in Period W have been mainly found for LCZ 2, LCZ 5, LCZ 6, and LCZ 8, in the valley floor and on the slopes in the southern part of the study area. The above LCZ classes belong to the built types, with different building densities and heights (see Table A1). In LCZ 2 and LCZ 8, occurring in the study area, there is usually a greater heating of the surface and air, while in LCZ 5, warmer surfaces and air can be expected than in LCZ 6. The location of LCZs in individual vertical zones can modify the above relationships, e.g., in the valley floor zone, generally weaker ventilation causes faster surface and air heating during the day and greater heat accumulation at night, while on the valley slopes, stronger surface and air heating will occur in the southern part of the study area, because in the northern part, greater shading can be expected. The additional heat input associated with the advection of tropical air (i.e., heat wave) increases heat accumulation in built types of LCZ at night (by limiting urban radiative cooling), which results in higher AUHI and SUHI intensities. The degree of heat accumulation in the urban area during Period H is probably also a result of weather conditions in the preceding days (a 10-day warm and partly hot period without precipitation). In the daytime, rural areas are more heated than in normal summer conditions, presumably due to the altered convective air movement during heat waves, hence, weaker AUHI and SUHI intensities are recorded. During daytime hours, the AUHII and SUHII values are therefore lower by down to 3 °C in Period H than in Period W, observed for all classes of LCZs, and in the case of SUHII, the greatest reduction in values is recorded on the slopes in the northern part of the study area. A prolonged advection of hot air over a city area located in a concave landform (i.e., varied relief) may therefore enhance AUHI and SUHI effect in the nighttime, and reduce it during the daytime, especially in the vertical zone located at the lowest point (i.e., the valley floor). The occurring increase or decrease in the AUHII and SUHII on the valley slopes during the HW appears to be dependent on both LCZ class (including the density of buildings and trees) and the direction of slope.

The influence of the circulation factor on the atmospheric and surface UHI can be clearly stated from the comparison of selected cases, but more precise investigation (for general confirmation) is needed using a larger number of cases (with and without HW). Long-term statistical analysis can be performed if a sufficiently large sample is possible. A variable such as LST can be observed only under cloudless conditions, which may be less frequent in urban areas as well as in certain climatic zones. Furthermore, factors such as the satellite viewing angle, overpass time or land cover change should be taken into account in the long-term studies of LST trends.

In future studies, among the factors affecting AUHI and SUHI, the effect of the total aerosol content and the rural soil moisture should be particularly considered. The role of topography in shaping UHI patterns also requires further analysis, conducted under different wind conditions, to determine in particular whether a wind corridor effect is noticeable. For this purpose, proper model simulations would be helpful.

The stronger relative warming of the urban area (i.e., UHI effect) in Kraków, especially in the valley floor, during the HW undoubtedly increases the heat load at night and thus the demand for energy and water. The increase in the number of days with the HW, combined with the UHI phenomenon, should be treated as a priority threat to the health and comfort of the city residents, as well as the urban infrastructure. Therefore, comprehensive analyses similar to those presented in this study are needed. They should be conducted with the integrated use of in situ air temperature data, especially from automatic measurement networks, and satellite data on LST, especially those with a spatial resolution of about 1 km, available several times a day. For a more complete assessment of the UHI effect, it is important to recognize the sub-daily dynamics of intensity and variability of spatial structure, both AUHI and SUHI, taking into account variations in LCZ classes, as well as different vertical (altitude) zones if the city is located in diversified relief.

This research indicates that with the rising frequency of heat waves over Kraków due to global warming, the UHI effect will particularly pose an increasing health risk to city inhabitants. The results of the study provide insights into the threat of increasing the heat load posed by the co-occurrence of urban heat islands and heat waves, which may have implications for sustainable urban planning strategies. The results of studies like these have a practical dimension primarily for local governments responsible for developing and implementing measures and actions to adapt and mitigate the effects of climate change.

This study uses quite a pioneering approach to investigate the influence of HW on the sub-daily spatial and temporal variability of AUHI and SUHI intensities based on integrated in situ and satellite data. The methodology is reusable for other cities, subject to data availability, which in the case of in situ data, depends on the density of the urban air temperature measurement network, and in the case of satellite data, on the latitude of the city, since the number of available daily observations acquired by several simultaneously operating polar-orbiting satellites increases towards the poles. The usability of AVHRR data to estimate the LST pattern is also influenced by the frequency of cloud cover or fog, which is locally determined. Furthermore, in many cities around the world, T_air data are widely and freely available, e.g., from a network of low-cost crowdsourced sensors. Whereas, AVHRR satellite images are collected by many national weather services and should be made available free of charge upon request. It is also possible to use the available LST satellite products from various sensors with a spatial resolution of about 1 km, provided that their usually lower temporal resolution (e.g., night and day) is considered sufficient. Additional data used in this study can also be easily and cost-free obtained, and the tools for generating LCZ maps are publicly available. Due to the above-mentioned availability of data sources, the research method used in this study can therefore be considered as applicable to other cities, especially those located in diversified relief.