Yves Richard
email: yves.richard@u-bourgogne.fr

Benjamin Pohl

Mario Rega

Julien Pergaud

Thomas Thevenin

Justin Emery

Julita Dudek

Thibaut Vairet

Sébastien Zito

Carmela Chateau-Smith

Is Urban Heat Island intensity higher during hot spells and heat waves (Dijon, France, 2014-2019)?

Keywords: Urban Heat Island intensity, hot spells & heat waves, hot day, medium-sized city, evapotranspiration, soil moisture

The Urban Heat Island (UHI) phenomenon is frequently associated with heat waves, both in scientific literature and in the media. Health problems and other issues often result from the co-occurrence of these two phenomena. Previous studies have not yet provided sufficient evidence to validate potential links between UHIs and heat waves. The MUSTARDijon network was set up in 2014, in Dijon, France. Its spatial density (60 sensors) and temporal depth (6 summers) provide information about several Hot Spells and Heat Waves (HS&HW), as well as the daily intensity of UHIs. For the period from June to August (the warmer months), no statistical relationship could be established between temperature and UHI intensity. The UHI phenomenon is strong when days are sunny and not very windy; these two conditions are frequently met during HS&HW, but not systematically. By contrast, these conditions can be fulfilled even without high temperatures. Strong UHIs can thus develop outside Hot Spell/Heat Wave (HS/HW) events. These HS&HW are not necessarily in phase with UHIs: maximum UHI intensity tends to occur before the onset or during the first few days of HS&HW. The intensity of the UHI decreases during HS&HW because nocturnal urban temperature generally remains stationary, whereas rural temperature tends to increase at night. The hypothesis proposed is that this increase in rural night temperature during HS&HW could be linked to the decrease in Actual Evapotranspiration (ETa) and soil wetness.

Introduction

In France and all over the world, heat waves are increasing in frequency, intensity, and duration [START_REF] Meehl | More Intense, More Frequent, and Longer Lasting Heat Waves in the 21st Century[END_REF][START_REF] Shindell | Estimating the potential for twenty-first century sudden climate change[END_REF][START_REF] Ouzeau | Heat waves analysis over France in present and future climate: Application of a new method on the EURO-CORDEX ensemble[END_REF][START_REF] Soubeyroux | Les vagues de chaleur en France : analyse de l'été 2015 et évolutions attendues en climat futur[END_REF]. Over the next few decades, this increase is likely to continue [START_REF] Schär | The role of increasing temperature variability in European summer heatwaves[END_REF][START_REF] Stott | Human contribution to the European heatwave of 2003[END_REF][START_REF] Barriopedro | The Hot Summer of 2010: Redrawing the Temperature Record Map of Europe[END_REF][START_REF] Suarez-Gutierrez | Dynamical and thermodynamical drivers of variability in European summer heat extremes[END_REF], raising the question of how communities will adapt to climate change (Adger et al., 2013). Heat waves are particularly deadly in cities [START_REF] Vandentorren | Mortality in 13 French Cities During the August 2003 Heat Wave[END_REF][START_REF] Robine | Death toll exceeded 70,000 in Europe during the summer of 2003[END_REF]2008;[START_REF] Barriopedro | The Hot Summer of 2010: Redrawing the Temperature Record Map of Europe[END_REF], even more so as they are generally associated with air quality degradation [START_REF] Shaposhnikov | Mortality Related to Air Pollution with the Moscow Heat Wave and Wildfire of[END_REF][START_REF] Churkina | Effect of VOC Emissions from Vegetation on Air Quality in Berlin during a Heatwave[END_REF]. The Urban Heat Island (UHI) phenomenon leads to even higher air temperature in cities, particularly at night [START_REF] Conti | Epidemiologic study of mortality during the Summer 2003 heat wave in Italy[END_REF][START_REF] Habeeb | Rising heat wave trends in large US cities[END_REF][START_REF] Mcgregor | Heatwaves and health: guidance on warning-system development[END_REF][START_REF] Heaviside | Attribution of mortality to the urban heat island during heatwaves in the West Midlands, UK[END_REF][START_REF] Paravantis | Mortality Associated with High Ambient Temperatures, Heatwaves, and the Urban Heat Island in Athens, Greece[END_REF][START_REF] Liao | Stronger Contributions of Urbanization to Heat Wave Trends in Wet Climates[END_REF]. In hot climates, where air-conditioning is used to cool buildings, UHIs also lead to greater energy consumption [START_REF] Hatvani-Kovacs | Assessment of Heatwave Impacts[END_REF]. During heat waves in France, UHIs are more likely to lead to health problems [START_REF] Pascal | Heat and cold related-mortality in 18 French cities[END_REF]). An index of vulnerability to thermal stress has already been developed for London [START_REF] Wolf | The development of a heat wave vulnerability index for London, United Kingdom[END_REF]. Further detailed analysis of the relationship between heat waves and UHIs is essential before proposing coherent solutions for these issues (Masson et [START_REF] He | Observational and modeling study of interactions between urban heat island and heatwave in Beijing[END_REF], and in Australia [START_REF] Rogers | Is the urban heat island exacerbated during heatwaves in southern Australian cities?[END_REF]. The results for one study in the USA showed an increase in UHI intensity during heat waves for larger cities, but observed no change for smaller cities [START_REF] Ramamurthy | Heatwaves and urban heat islands: A comparative analysis of multiple cities: Heatwaves and Urban Heat Islands[END_REF], while other studies found no change in UHI intensity during heat waves for Oklahoma City [START_REF] Basara | Diurnal cycle of the Oklahoma City urban heat island[END_REF]2010), or for Atlanta [START_REF] Zhou | Atlanta's urban heat island under extreme heat conditions and potential mitigation strategies[END_REF]. In Perth (Australia), in surprising contrast with results for Adelaide and Melbourne in the same study, observed UHI intensity was lower during heat waves [START_REF] Rogers | Is the urban heat island exacerbated during heatwaves in southern Australian cities?[END_REF]. A comparison of cities in the USA shows that daytime UHI intensity is related to differences in heat convection efficiency between urban and rural areas [START_REF] Zhao | Strong contributions of local background climate to urban heat islands[END_REF]. This convection effect depends on the local background climate (wet or dry). Several hypotheses have been proposed to explain the increase in UHI intensity during heat waves: atmospheric stability [START_REF] Tomlinson | Derivation of Birmingham's summer surface urban heat island from MODIS satellite images[END_REF], lower wind speed (Li and Bou-Zeid, 2013), anticyclonic summer conditions [START_REF] Heaviside | The effects of horizontal advection on the urban heat island in Birmingham and the West Midlands, United Kingdom during a heatwave: Effects of Horizontal Advection on the Birmingham Urban Heat Island[END_REF], and clearer skies [START_REF] Schatz | Urban climate effects on extreme temperatures in Madison, Wisconsin, USA[END_REF]. Factors such as evapotranspiration in rural areas [START_REF] Li | Synergistic Interactions between Urban Heat Islands and Heat Waves: The Impact in Cities Is Larger than the Sum of Its Parts*[END_REF], and impervious urban surfaces [START_REF] Ortiz | New York City Impacts on a Regional Heat Wave[END_REF] may also play a role in increasing UHI intensity. Higher UHI intensity can be observed in response to heat waves, even more noticeably at night in Beijing (e.g. [START_REF] He | Observational and modeling study of interactions between urban heat island and heatwave in Beijing[END_REF].

The link between heat waves and UHI intensity remains difficult to assess, and no true consensus on this precise topic has so far emerged from the literature. To establish whether UHIs are stronger during heat waves, the dataset must be spatially coherent, and cover a long enough period for several heat waves to be recorded. These requirements are met in Dijon (northeastern France) by the Measuring Urban Systems Temperature of Air Round Dijon (MUSTARDijon) network [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF]. Almost half the urban European population (44%) lives in medium-sized cities [START_REF] Giffinger | City-ranking of European medium-sized cities[END_REF], of a similar size to Dijon. To investigate potential links between UHIs and heat waves, it is important to analyze the characteristics of both phenomena:

-time of day. The UHI phenomenon intensifies at sunset. How does it evolve during the night, and is the pattern different for heat-wave nights? -season. The UHI phenomenon is generally stronger in the warmer months. Does it vary during this period? In spring and early summer, Actual Evapotranspiration (ETa) is at a maximum in rural areas, whereas in mid-and late summer, ETa decreases. This decrease is particularly noticeable in cropland, where ETa is lower after the harvest.

-duration of heat waves. In cities, heat can accumulate during longer heat waves because of building thermal inertia, and the increased use of air-conditioning. In rural areas, ETa may decrease due to soil moisture depletion.

How does UHI intensity evolve during a heat wave? The meteorological conditions before the heat wave period may also affect UHI intensity. Rainfall in the previous days could increase ETa, particularly in rural areas, making soil wetness measurements essential [START_REF] Imran | Effectiveness of green and cool roofs in mitigating urban heat island effects during a heatwave event in the city of Melbourne in southeast Australia[END_REF].

In this paper, we use the term Hot Spells and Heat Waves (HS&HW) to cover all hot periods that might have a negative impact on human well-being. We focus on the relationship between UHI intensity and the Hot Spell and Heat Wave (HS/HW) events that have occurred in Dijon since the deployment of the MUSTARDijon network in 2014.

This study is structured as follows: in the material and methods section, the study area is presented, then the dataset, the time frame (seasonal and diurnal), the thresholds and criteria used to define HS&HW, and the UHI index. In the results and discussion section, UHI values will be assessed in relation to meteorological variables. The temporal relationship between UHI intensity and HS&HW will be analyzed in detail. Assessing the effects of ETa and soil moisture on UHI evolution during HS&HW will then bring to light potential explanations for the results observed.

Material and methods

Data

Since June 2014, hourly measurements of temperature (3 m above ground level) have been recorded by the MUSTARDijon network [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF], with a total of 60 sensors since 2016 (Fig. 1). This network was designed to capture meso-scale rather than micro-scale thermal conditions. Observations collected at Dijon-Longvic (DL), a synoptic weather station operated by Météo-France at an airport site (Fig. 1), include air temperature at 2 m above ground level (DLT), raingauge rainfall (RR1), wind speed at 10 m above ground level (FF), sunshine duration measured in minutes rather than hours (SH), and relative air humidity (RH). Other data for raingauge rainfall (RR2), potential evapotranspiration (ET), actual evapotranspiration (ETa), and Soil Wetness Index (SWI) are taken from Safran-Isba-Modcou (SIM) surface data (8 km * 8 km), a Météo-France product combining observations and model outputs [START_REF] Soubeyroux | Safran-Isba-Modcou (SIM) : Un outil pour le suivi hydrométéorologique opérationnel et les études[END_REF]. The period studied is from June 6, 2014 (deployment of MUSTARDijon) to July 29, 2019 (end of data collection for this study).

Key phases of the UHI day

Maximum UHI intensity is recorded during the warmer months, when heat waves also occur. The season analyzed in this study extends from April 1 to September 30, thus including 968 days and nights during the six warm seasons covered by MUSTARDijon (2014-2019). Data for a UHI day are not assessed from 0000 to 2300 UTC, but from 0700 UTC to 0600 UTC, to avoid a night period spanning two calendar dates. Each night is thus associated with the previous day. Three key moments within the UHI day are targeted: 1 / afternoon: maximum temperature (1300-1700 UTC): 2 / evening: when the temperature drops sharply, and UHI intensity increases (1900-2300 UTC); 3 / night: minimum temperature (0000-0400) UTC.

UHI Index: Urban Index minus Rural Index

The appropriate Local Climate Zone (LCZ; Stewart and Oke, 2012) was identified for each of the 60 sensors recording air temperature in the MUSTARDijon network [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF]; Fig. 1). An Urban Index and a Rural Index were built from representative sets of sensors, with almost no missing values. The UHI Index is the difference between the Urban Index and the Rural Index. The MUSTARDijon network contains a sufficient number of sensors for a robust UHI Index to be calculated, as was the case for Madison, Wisconsin, USA (Schatz and Kucharik, 2012).

The Urban Index corresponds to LCZ2, in the city center (Fig. 1), as no area of Dijon corresponds to LCZ1 [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF]. The mean temperature was calculated for the only two sensors that fit the selection criteria (Place de la Libération and rue Chancelier de l'Hôpital, Fig. 1). Suitable candidate sensors for the Rural Index are located in sparsely built or unbuilt areas, at some distance from the city center, but at a comparable elevation. As sensors are attached to street lamps, few MUSTARDijon sensors are located in LCZA-G (Fig. 1). To the west, the plateaus and valley bottoms cause topographic effects (e.g. nocturnal inversions) that are not integrated into the LCZ typology, thus complicating any interpretation of the results (Suomi, 2014, Ketterer and Matzarakis, 2015, Leconte et al., 2017, Lee and Oh, 2018). The four sensors retained for the Rural Index are therefore Ahuy (LCZ9) to the north, Saint-Apollinaire (LCZD/104) and Magny-sur-Tille (LCZ9) to the east, and Perrigny-lès-Dijon (LCZD/104) to the south (Fig. 1). The mean temperature for these four sensors was then calculated. The UHI is defined as the difference between the Urban Index and the Rural Index (UHI = Urban -Rural). The DL station was not selected for the Rural Index, as Météo-France equipment is different from MUSTARDijon sensors.

Hot Spells and Heat Waves (HS&HW)

To identify HS&HW, two thresholds were applied to DLT. These thresholds, for maximum daily temperature (DLTx), and minimum daily temperature for the following night (DLTn), were set to select the largest possible sample, which unfortunately remains rather small for statistical analysis. Thresholds set for DLTx > 32 °C and DLTn > 16 °C identify clearly recognizable hot days. These values are, however, below the risk prevention thresholds (for Dijon, 34 °C and 19 °C) used to trigger regional health alerts in France. Another criterion used to define heat waves in France is temporal persistence, with a minimum of three consecutive days. The limit set in this study is two consecutive days, with a threshold of seven consecutive days for long Hot Spell/Heat Wave (HS/HW) events.

Results and discussion

The first results investigate the relationship between UHI intensity, temperature, and meteorological conditions, for the warmest six months (April-September), over a six-year period (2014-2019). All HS&HW occurring within the study period are thus identified. Further analysis of UHI intensity focuses on the comparison of long HS/HW events, and then on the first seven days of each long HS/HW.

UHI intensity, temperature, sunshine duration, and wind speed

Values for UHI intensity and DLT are plotted from June to August, for 2014 to 2019 (Fig. 2). Correlations between UHI intensity and DLT are -0.04 for afternoon, +0.32 for evening, and +0.09 for night. Although correlations for evening and night are significant (P = 0.01), the values are low, and no significant correlation is observed for afternoon. When the focus is on the 74 hot days (Fig. 2), correlations between UHI intensity and DLT are -0.11 for afternoon, -0.12 for evening, and -0.30 for night, but these slightly negative correlations are not significant. This result may seem counter-intuitive, because hot days and HS&HW are generally associated with sunshine and almost no wind, meteorological conditions that also result in increased UHI intensity.

Figure 3 presents data from April to September for 2015 and 2018, two years with long HS/HW events (see Fig. 4). The following observations can be made:

-during the warmer months, the seasonal temperature pattern is clear, with higher values in July and August (Fig. 3a,e), but no such pattern can be identified for UHI intensity (Fig. 3b,f); -in windy conditions (Fig. 3d,h), the temperature may be high, but UHI intensity is low (Fig. 3, black dotted outline); -when there is little or no sunshine (Fig. 3c,g), the temperature may still be high, but UHI intensity remains low (Fig. 3, black outline).

Although no statistical analysis is presented here, this visual comparison of data from April to September shows that strong UHIs can occur on days with sunshine when there is almost no wind. High temperature (Fig. 3a,e) is not always a key condition for higher UHI intensity (Fig. 3, red outline). Synchronicity between hot days and UHI intensity is not systematically observed during the warmer months.

UHI intensity and long HS&HW

All the HS&HW during the study period (2014-2019) occur between June 19 and August 31, with most occurring in July (Fig. 4). Three long HS/HW events (≥7 days) are identified in 2015, one in 2018, and two in 2019. Of the 53 days within these HS&HW, 14 are below the maximum daily temperature threshold, with only 3 days below the minimum daily temperature threshold (Tab. 1). The most affected event is HS/HW 3, with 6 days below the maximum daily temperature threshold, 2 days below the minimum daily temperature threshold, missing rainfall data for 3 of the days, low sunshine duration values, and a noticeable rainfall event (10.2 mm). In HS/HW 1 and in HS/HW 6, only one day is slightly below (31.9 °C) the maximum daily temperature threshold, while all values for HS/HW 5 are above the thresholds.

Direct comparison between DLT and UHI for each long HS/HW, aligned over a 30-day period, shows that the two phenomena are out of phase, both hourly and daily (Fig. 5). As expected, UHI intensity is highest in the evening and at night, whereas maximum DLT occurs in the afternoon. More surprisingly, maximum UHI intensity tends to occur slightly before the onset of long HS&HW, and is generally limited to the first few days of HS&HW.

No clear pattern is discernible in the DLT mean values for the six long HS&HW, aligned (as in Fig. 5) over a 30-day period (Fig. 6a). Mean daily DLT values show substantial variation for the first seven days and for the entire duration of the six long HS&HW,. The maximum daily values for UHI intensity for the six long HS&HW show a similar level of variability (Fig. 6b). There is, however, a general tendency for UHI intensity to diminish over time, more noticeably during HS/HW events 1, 2, and 4, and less clearly for HS/HW events 3, 5, and 6. The negative values suggest a daytime cool island, an interesting result for a compact mid-rise LCZ in a medium-sized city. Daytime cool islands have been observed in Hong-Kong, a compact high-rise high-density city [START_REF] Yang | The urban cool island phenomenon in a high-rise high-density city and its mechanisms: The UCI Phenomenon in Hong Kong and its mechanismes[END_REF], and in several other medium-sized cities: Taipei, Taïwan [START_REF] Chang | A preliminary study on the local cool-island intensity of Taipei city parks[END_REF]; Turku, Finland (Suomi and Käyhkö, 2012); Erbil, Iraqi Kurdistan [START_REF] Rasul | Spatial variation of the daytime Surface Urban Cool Island during the dry season in Erbil, Iraqi Kurdistan, from Landsat 8[END_REF]; Toulouse, France [START_REF] Martins | Impact of Urban Cool Island measures on outdoor climate and pedestrian comfort: Simulations for a new district of Toulouse, France[END_REF]; and Bragança, Portugal [START_REF] Gonçalves | Urban Cold and Heat Island in the City of Bragança (Portugal)[END_REF].

Mean temperature and UHI intensity during the first seven days of long HS&HW

As the six long HS&HW varied in duration from 7 to 14 days, mean temperature and UHI intensity for all long HS&HW were calculated for each of the first seven days (Fig. 7), for afternoon (Fig. 7a-b), evening (Fig. 7c-d), and night (Fig. 7e-f). Mean temperature for the Rural Index is systematically lower than for the Urban Index, whatever the time of day, for each day of the HS&HW (Fig. 7a, c, ande). Mean temperature is always high in the afternoon, with little difference between the Rural and Urban Indices (Fig. 7a). Mean temperatures are lower during evening and night, with much greater differences between the two indices (Fig. 7c ande). Mean UHI intensity is therefore higher during evening and night (Fig. 7d andf) than in the afternoon (Fig. 7b).

A more detailed analysis of temporal dynamics shows that the Urban Index rises on days 1 and 2, reaches a peak on days 3 to 5, and then falls on days 6 and 7, whatever the time of day (Fig. 7a,c, and e). The same pattern is observed for the Rural Index, but only in the afternoon. The resulting UHI intensity (0.5-1 °C) is stable (Fig. 7b). During the evening and at night (Fig. 7c ande), the Rural Index mean temperature does not fall on days 6 and 7. The resulting UHI intensity is highest on days 1 and 2, slightly lower on days 3 to 5, and lowest on days 6 and 7 (Fig. 7d andf). The standard deviation analysis seems to confirm the reliability of these results, revealing no discernible trend for the six long HS/HW events.

Relationship between mean values for UHI intensity, soil wetness, and Eta

Further and more detailed exploration is necessary for better understanding of these results. Two unresolved questions are therefore investigated together: the lack of synchronicity between HS&HW and UHI intensity, and the increase in temperature in rural areas together with the decrease in UHI intensity, in the evening and at night, during HS&HW. Maximum UHI intensity tends to occur before the onset of HS&HW, and is generally limited to the first few days, particularly for HS/HW events 1, 2, and 4, and less noticeably for HS/HW events 3, 5, and 6 (Fig. 6). During HS&HW, a gradual increase in evening and night temperatures is observed for the Rural Index, but not for the Urban Index, resulting in lower UHI intensity (Fig. 7).

In rural areas, fewer surfaces are impervious, so soil moisture is higher; greater plant density favors evapotranspiration, leading to lower nocturnal temperatures. Evapotranspiration is less likely to have an impact in cities, because of the greater area covered by impervious surfaces, thus contributing to the the limited temporal variation of higher nocturnal temperatures in the Urban Index during HS&HW. The gradual rural warming observed for mean evening and night temperatures during HS&HW could be explained by a decrease in soil wetness and ETa over time.

To test this hypothesis, daily mean and standard deviation (SD) values for soil and weather conditions were calculated for the first seven days of the six long HS&HW (Fig. 8). The data measured at DL include raingauge rainfall (RR1), sunshine duration (SH), wind speed (FF), and relative air humidity (RH). The data produced by SIM analysis include raingauge rainfall (RR2), potential evapotranspiration (ETP), actual evapotranspiration (ETa), and a Soil Wetness Index (SWI). No discernible pattern is observable in weather conditions, for both mean and SD, during the first seven days of the six long HS&HW (Fig. 8). Soil-atmosphere exchanges, however, tend to decrease (Fig. 8g: ETa), probably as a result of low soil moisture (Fig. 8h: SWI). The decrease is more clearly visible in SD than in mean values (Fig. 8g-h), as soil and weather conditions in the days before each of the six long HS&HW are unlikely to be identical.

Detailed analysis of each long HS/HW

As ET values are a synthesis of several meteorological variables (T, SH, FF, and RH), the discussion will now focus only on rainfall (RR1 & RR2) and ET, in relation to ETa, SWI, and UHI intensity for each long HS/HW (Fig. 9). Little or no rainfall (RR1) was recorded at DL during five of the six HS&HW (Fig. 9a). Among the uncertainties associated with SIM analysis, rainfall is often the most sensitive. As the results of SIM rainfall analysis (RR2; Fig. 9b) are very similar to the measured RR1 values, the remaining SIM variables may be considered fairly reliable. The SIM analysis covers a much larger area than the DL station, resulting in more frequent rainfall, but lower values. Rainfall data during HS&HW are also sensitive to local summer storms, which could explain the disparity between RR1 and RR2 for HS/HW 3 (Fig. 9a-b). With such low rainfall values, five of the six long HS&HW also show a related decrease in ETa (Fig. 9d) and SWI (Fig. 9e). The ETa values show greater daily variability than the SWI values, as ETa is the result of ET and SWI combined. The daily maximum intensity of UHI (Fig. 9f) over the same period decreases in a similar way to SWI and ETa, with daily variability similar to the ET pattern (Fig. 9c). Some differences in the pattern of UHI intensity are nevertheless observed for HS/HW 3, HS/HW 5, and HS/HW 6. The difference in UHI values between evening and afternoon (Fig. 9g) presents a very similar pattern to the daily maximum UHI intensity (Fig. 9f). The evening increase in UHI intensity is therefore almost equal to the daily maximum UHI intensity, a result coherent with the ETa hypothesis.

The overall pattern for HS/HW 3 is different from that of the other five long HS&HW. It is the only HS/HW with a noticeably high level of rainfall (RR1, Fig. 9a), and even higher values for RR2 (Fig. 9b). In fact, HS/HW 3 includes rainy days that would completely change all physical processes (Table 1). This is not the case with the other HS&HW, with warm anomalies being favored by atmospheric stability and enhanced by soil dryness [START_REF] Zampieri | Hot European Summers and the Role of Soil Moisture in the Propagation of Mediterranean Drought[END_REF][START_REF] Stéfanon | Soil moisture-temperature feedbacks at meso-scale during summer heat waves over Western Europe[END_REF][START_REF] Whan | Impact of soil moisture on extreme maximum temperatures in Europe[END_REF]. The SIM values for ETa (Fig. 9d) and SWI (Fig. 9e), which are partly based on RR2 values, show a similar rising pattern, different from the decreasing trend observed for the other long HS/HW events. The high UHI intensity that persists during HS/HW 5 (Fig. 9f) could perhaps be explained by the Rural Index for this period (not shown), where evening and night temperatures show no increase. The ETa (Fig. 9d) and SWI (Fig. 9e) values are high at the onset of HS/HW 5 and remain higher than for the other five HS&HW. In fact, HS/HW 5 is the only long HS/HW to occur entirely in June (Fig. 4), before the end of the harvest, which could contribute to the relatively low nocturnal temperatures observed in the Rural Index. Maximum UHI intensity occurs before maximum DLT (Fig. 6) during HS/HW 6, the hottest event (Fig. 6a), which also has remarkably high ET values (Fig. 9c). The UHI intensity (Fig. 9f) remains high throughout HS/HW 6, despite low values for ETa (Fig. 9d) and SWI (Fig. 9e).

Spatial analysis of soil wetness and Eta during the first seven days of long HS&HW

Although the SIM data are low resolution (8 km) at the scale of the Dijon administrative area (Dijon Métropole), they provide some spatial information about ETa and SWI (Fig. 10). The daily mean values were calculated for the first seven days of the six long HS&HW. Precise identification of built and unbuilt surfaces within the urban area is not possible at this resolution, but the heterogeneous nature of surfaces in the surrounding areas can be identified, with a marked difference between the wooded areas in the northwest, and the croplands on the plains in the southeast. The ETa values are highest in the northwest, lower in the southeast when the soil is bare, after harvest (which is generally the case during the long HS&HW), and lowest of all in the urban built areas, as expected (Fig. 10a). During the first seven days of the six long HS&HW, mean values decrease for ETa (Fig. 10a) and for SWI (Fig. 10b), throughout the study area. It is not possible to provide a robust quantification of the difference between urban and rural values at this low spatial resolution (8 km), with the limited size of the sample (6 long HS/HW events).

Perspectives for further studies

These preliminary results, from the dense MUSTARDijon network, over a six-year period, provide sufficient basis for further experiments using high-resolution climate models with an urban canopy model (e.g. Meso-NH / TEB; [START_REF] Masson | A Physically-Based Scheme For The Urban Energy Budget In Atmospheric Models[END_REF]. Sensitivity experiments on soil moisture could provide information about sensible and latent heat fluxes at the interface between land surface and atmosphere. Such experiments could help quantify to what extent these fluxes differ (i) between urban and rural areas, (ii) between the early and later stages of HS&HW, and (iii) in the long term, how they could be perturbed by ongoing climate change. The relative weight of these fluxes, synthesized for instance through the Bowen ratio, and its variability in space and time, could have considerable impact on the intensity of local temperature gradients and on UHI intensity. Combining high-resolution climate models with dense local networks, extended to cover additional parameters (wind speed & direction, and global radiation), will provide the perennial tools required for long-term investigation of urban climate change.

Conclusion

In temperate zones, UHI intensity causes societal problems in summer, during HS/HW events. In general, HS&HW develop in sunny conditions, with little or no wind, which are also the ideal conditions for an increase in UHI intensity. In Dijon, a medium-sized European city, during the three warmer months (June to August), there is little correlation between UHI and air temperature, whether for the entire period, or for those days identified as hot days. There is no synchronicity between UHI and temperature: UHI intensity is highest before HS&HW onset, or during the first few HS&HW days. During the six long HS&HW identified in this study, the nocturnal gradient between urban and rural temperatures (used to calculate UHI intensity) decreases, as rural temperatures rise at night. The decrease in SWI and ETa in rural areas during HS&HW leads to a decrease in surface latent heat fluxes, closer to urban conditions. The long-term evolution of climate change is a complex problem, with many parameters: summer temperatures will almost certainly increase, while soil moisture and rainfall will probably decrease. As dry conditions become more prevalent, UHI intensity, measured as the gradient between nocturnal urban and rural temperatures, will tend to decrease. Conditions in urban areas will also evolve (with changes in size, building materials, spatial extent, and surface impermeability). Such changes are negligible within the six-year period analyzed in this study, but will be more difficult to take into account at a longer time-scale. A systemic approach with climate models can integrate changes in both climate and urbanization.

Adapting to climate change would not seek to limit UHI intensity, but more generally to reduce nocturnal temperatures in urban areas and their rural surroundings. Vegetation, soil moisture and ETa can all contribute to lower temperatures at night. In urban areas, soil moisture and ETa can be raised by increasing vegetation, but irrigation requirements must be taken into account. In temperate zones, many cities are surrounded by fields of crops that will generally have been harvested before the main HS&HW period, leaving the soil bare. Forest belts (e.g. the woods northwest of Dijon) and market gardening could contribute to ecosystemic resilience, with beneficial effects on nocturnal temperatures within and around the city. (a) to (f ) Hot Spell/Heat Wave 1 to 6 (see Fig. 2). DLT air temperature at 2 m at Dijon-Longvic in °C (above). UHI intensity in K (below). Hot Spell/Heat Wave onset: day 11.

Black outline: total Hot Spell/Heat Wave duration. NB: White patches indicate missing data.

2Fig. 1 .Fig. 2 .

 12 Fig. 1. Map of the study area, showing LCZ, MUSTARDijon sensors, and Dijon-Longvic Météo-France station.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Meteorological conditions (hourly values) April to September: 2015 (a-d) and 2018 (e-h). (a) & (e) Dijon-Longvic air temperature at 2 m (DLT) in °C. (b) & (f ) UHI intensity in K. (c) & (g) Sunshine hours (SH) at DL in minute/hour. (d) & (h) Wind speed (FF) at DL in m.s-1. Red outline: lower T °C, sunny & not very windy, with strong UHI. Black outline: higher T °C, not very sunny, without strong UHI. Black dotted outline: higher T °C, sunny & windy, without strong UHI. N.B. White patches indicate missing data.

Fig. 5 .

 5 Fig. 5. Comparison of DLT and UHI intensity (hourly values), aligned over a 30-day period.(a) to (f ) Hot Spell/Heat Wave 1 to 6 (see Fig.2). DLT air temperature at 2 m at Dijon-Longvic in °C (above). UHI intensity in K (below). Hot Spell/Heat Wave onset: day 11.Black outline: total Hot Spell/Heat Wave duration. NB: White patches indicate missing data.

Fig. 6 .

 6 Fig. 6. Evolution of DLT and UHI for each long HS/HW, aligned over a 30-day period. Each Hot Spell/Heat Wave (HS/HW) is aligned to begin on Day 11. Red line: values during the HS/HW. Black line: values before and after the HS/HW. Black dotted outline: rst seven days of the HS/HW. (a) DLT: Mean daily air temperature at 2 m for Dijon-Longvic in °C. (b) Maximum daily UHI intensity in K.

Fig. 7 .

 7 Fig. 7. Mean rural temperature, urban temperature, and UHI intensity for the rst seven days during long HS&HW. (a) & (b): Afternoon (1300-1700 UTC). (c) & (d) Evening (1900-2300 UTC). (e) & (f ) Night (0000-0400 UTC). (a), (c), & (e): T °C (rural in blue, urban in red). (b), (d), & (f ) UHI intensity in K (mean +/-SD indicated by black error bars).

Fig. 8 .Fig. 9 .

 89 Fig. 8. Mean meteorological and soil conditions for the rst seven days during long HS&HW. (a) RR1: daily rainfall, observed at DL. (b) RR2: daily rainfall, mean of 4 grid-points analyzed in SIM. (c) SH: sunshine duration (DL). (d) FF: wind speed (DL). (e) RH: relative air humidity (DL). (f ) ET: potential evapotranspiration (SIM). (g) ETa: actual evapotranspiration (SIM).(h) SWI: soil wetness index (SIM). Mean +/-SD indicated by red error bars.

Fig. 10 .

 10 Fig. 10. Mean for ETa and SWI during the rst seven days of the six long HS&HW. Light blue outline: Dijon administrative area (Dijon Métropole). Red outlines: built areas. Black dots: grid-points used in Figs. 8 & 9. (a) ETa in mm. (b) SWI.

  al., 2013; Lemonsu et al., 2015; Hendel et al., 2016; Rajkovich and Larsen, 2016; Lehoczky et al., 2017; Daniel et al., 2018). Studies investigating possible correlations between heat waves and UHI intensity are often based on observations (e.g. Schatz and Kucharik, 2015; Ramamurthy et al., 2017; Rogers et al., 2019), but some studies also include climate modeling with WRF (Weather Research and Forecasting; e.g. Li and Bou-Zeid, 2013; Heaviside et al., 2015; Ramamurthy and Bou-Zeid, 2017; Ortiz et al., 2018; He et al., 2020). Several studies have shown that UHI intensity increases during heat waves, in the UK (Tomlinson et al., 2012; Heaviside et al., 2015), in the USA (Li and Bou-Zeid, 2013; Schatz and Kucharik, 2015; Ramamurthy and Bou-Zeid, 2017; Ramamurthy et al., 2017; Ortiz et al., 2018), in China

Table 1 :

 1 Values for below-threshold days within long Hot Spell HS/HW: Hot Spell/Heat Wave event.Orange cells: DLTn ≤ 16 °C. Red cells: DLTx ≤ 32 °C. RR1: Raingauge rainfall at Dijon-Longvic in mm. SH: Sunshine duration (measured in minutes).

	Year Month Day HS/HW	DLTn DLTx RR1 SH
	2015	6	1	18,8	31,9	0	875
	2015	18		19,1	32	0,2 314
	2015	19	2	16,7	30,9	0	499
	2015	20		17,6	31,9	0	556
	2015	4		13,7	26,7 10,2 341
	2015	5		15,1	31,1	0	720
	2015 2015	8 9	3	18,6 18,2	24,9 22,5	NA 132 NA 7
	2015	10		16,6	21,7	NA	1
	2015	11		19,1	29,5	0	572
	2018	28		15,8	25,9	0,4 253
	2018	29	4	19,2	30,9	0	854
	2018	1		19,1	29	0	639
	2019	21	6	19	31,9	0	641

DLT: Dijon-Longvic air temperature at 2 m in °C.

Acknowledgments

The Agence de l'Environnement et de la Maîtrise de l'Énergie (ADEME) Bourgogne-Franche-Comté (Franck Dumaitre and Patricia Dubois), Dijon Métropole (Oanez Codet-Hache, Marie-Françoise Dodet and Sophie Bientz), Météo-France (Denis Thévenin and Agnès Tamburini), and the Centre de Calcul de l'université de Bourgogne (CCuB) are thanked for financial and technical support.


Anthony Pamart
email: anthony.pamart@gamsau.map.archi.fr

David Lo Buglio
email: david.lobuglio@gamsau.map.archi.fr

Livio De Luca
email: livio.deluca@gamsau.map.archi.fr

Morphological Analysis of Shape Semantics from Curvature-based Signatures The Case Study of the Columns of Saint-Michel de Cuxa

Keywords: Architectural representation, morphological analysis, semantic characterization, discrete curvatures

Over the past few years, advancements in the field of 3D digitizing has increased the fidelity of geometric models. So far and despite of this acuity enhancement, a gap remains between the growth of collected data and its uses as vehicle of knowledge. New challenges have emerged to handle massive content of a 3D footprint. Considering those un-interpreted data as starting point for further investigations, the hypothesis is to rely on a "low-level" analysis of geometric features aiming to enrich informative and scientific value of "high-level" semantic studies. This article describes an approach using discrete curvature assets to link morphological identification and semantic characterization. The mean curvature has been parametrized to highlight it use as an eloquent shape description. At this point, a comparative analysis within an architectural collection composed of similar entities would be led according to the remoteness degree compared to an average geometric reference model. The introduced principle explores the construction of curvature-based signatures so as to reassess the conceptual articulations of 31 Romanesque columns from the cloister of the abbey of Saint-Michel de Cuxa.

I. INTRODUCTION

Nowadays, digital 3D scanning techniques provide great tools for conservation, documentation and promotion of cultural heritage. However, in the field of architectural surveying, these technologies enable new practices that need to contribute for cognitive and analytic plus-values all along theirs uses. Indeed, the ease of use made possible by both automated acquisition and data processing, obtaining an accurate "footprint" is no longer an end in itself [START_REF] Gattet | A versatile and low-cost 3D acquisition and processing pipeline for collecting mass of archaeological findings on the field[END_REF] [START_REF] Toschi | On the evaluation of photogrammetric methods for dense 3D surface reconstruction in a metrological context[END_REF]. This gain of efficiency in terms of completeness, accuracy and quickness -now accessible and affordable to a broader audience -allows to collect an (over)load of metrical and colorimetric characteristics on an increasing numbers of object. Simultaneously, arise methodological issues for archiving, structuring and extracting from real-based model its meaningful information for analysis [3] [4].

This work focuses on surface curvature, which seems to be an appropriate descriptor to lead a morphological analysis. It continues and completes a first research which had revealed geometric discontinuities profiles within the same collection [START_REF] Lo Buglio | What do thirtyone columns tell about a 'theoretical' thirty-second?[END_REF]. The aim of this study is to determine if and how the construction of curvature-based signatures enables and can help a shapes analysis. Thus the morphological description provided might be deepened in order to define and asset the link between geometric and semantic layout.

II. FROM MULTIPLICITY OF LOW-LEVEL DATA TOWARD INTELLIGIBILITY OF HIGH-LEVEL KNOWLEDGDE

According to recent researches, it does'nt seems that the overgrowth of data intrinsically expands its level of intelligibility [START_REF] Biasotti | 3D artifacts similarity based on the concurrent evaluation of heterogeneous properties[END_REF]. Moreover, morphological analysis of an architectural object is historically based onwards a possible interpretation of presupposed knowledges that were established and codified by the architectural treatises or dictionaries [6] [7]. This so-called "top-down" approach is no longer operating to manage large and complex dataset ones need to be manually mined. In this context, it seems more appropriate to rely on data accumulation for bringing out of itself main characteristics contained in the digital instance. This "bottom-up" approach minimizes the interpretation degree of human analysis. Thus, the latter seems like more relevant for cumulative studies, i.e. to deal with the complexity of an object's geometric properties multiplied by the amount of artifacts composing a collection.

Gauss introduced in 1928 surface curvature on non-Euclidian geometries, the principle is to define how much bends a given curve for each point of a surface. The curvature has already been implemented and used for shapes analysis of heritage artifacts [START_REF] Leymarie | The SHAPE Lab: New technology and software for archaeologists[END_REF] [START_REF] Gatzke | Curvature Maps For Local Shape Comparison[END_REF]. Such researches still request an intervention of an operator or have used the curvature map but to detect local similarities within a single object. And so, they can't be applied nor to comparison of multiple artifacts neither on analogies between several collections. For these reasons, a preliminary study was necessary in order to define an ad-hoc parameterization of the discrete curvatures for enhancing the readability of a surface [START_REF] Adrian | Evaluating the curvature analysis as a key feature for the semantic description of architectural elements[END_REF]. It provides a framework using curvature as a suitable descriptor to link massive low-level morphological features and relevant h semantics.

III. METHODOLOGICAL DATA DISCRIM

This section describes methodological s starting from millions of three-dimension morphological signature that can be comp points. All of the 31 columns of this coll collected during a photogrammetric survey c Raw photographs and so on have been repr common and updated protocol benefiting image matching and advanced meshing [START_REF] Ign/Matis | [END_REF] A. Pre-processing : from point set to surface

The aim of those preliminary steps is homogeneous dataset for all artifacts. For clean and consistent (both metric and visu obtained including normals. A first triangula from optimized parameterization of the Surface Reconstruction so as to fit close point-set [START_REF] Kazhdan | Screened poisson surface reconstruction[END_REF]. Then, the meshes are s oriented in a same world space and their u bounding-box.

B. An helpful mesh reparameterization proce

A reparameterization process is aimed to mesh into a regular and quadrangular mesh. project on the mesh a uniform wireframe g was the geometric primitive chosen in order possible at the column "Fig. 1". The batch pr done using MEL (Maya Embedded Languag step is highly recommended as the goal identical given point onto different surfaces set of digitized columns). Indeed, thanks to be transcribed in tabular form and each coordinates, normal, curvatures…) is compa the reparameterization is needed to:

• Enable extraction of point value into • Guarantee the data comparison i model.

• Decimate the model to get faster

preserving a correct detail level.

C. Construction of geometrical reference mo

According to an identical M-by-N grid mesh is composed of a same number of inde it's possible to transform this reorganized M*N-by-X table where X corresponds to a po y, z, Nx, Ny, Nz …). Hence a 32 nd geometrica computed from the arithmetic mean of the 2" shows, a reference model that could be c wing of the cloister: rocessed through a g fully automatic [START_REF] Kazhdan | Screened poisson surface reconstruction[END_REF].

e

D. Extracting curvature matrix

The discrete curvatures a describe morphological variat term of concavities and convex of the minimal surfaces, the m with the discrimination aim of could be applied (e.g. Gau maximal) depending of ob performed. Extracted as a digi could be manipulated and co tools, pattern recognition computing. Once again, the co table is based on a "homemad used for batching the whole col

E. Curvature-based signatures

A curvature matrix can b map, i.e. a three-dimensional dimensional format. In this respectively rows and column located point and Z is associa cell. One can proceed to an ari dimension to obtain a signal profile section. A so-called "si dimensional array describin variations related to the seman As the collection's dataset has reparameterization step, it allo signatures with no kind of bias IV. SHAPE SIGNATURES AND At this point, a short revi some asset of this approach provides a first global glimpse appear to be a key feature to tion of an object's surface, in xities. As a possible expression mean curvature was chosen to fit f this study, but any other types ussian, absolute, minimal or bservations that need to be ital matrix, the curvature values ompared using shapes analysis methods or the numerical omputation of curvatures and its de" MATLAB GUI and scripts llection [START_REF] Peyre | Toolbox Graph [MATLAB toolbox[END_REF]. computation e seen as a 2.5D cartographic characteristic is stored in a bicase the couple X and Yns of the matrix -represents a ated to its curvature value in a ithmetic mean along a pertinent corresponding to a real-world gnature" is defined by this oneng the main morphological ntic articulations of the object. been processing with the same ows direct comparison of shape (interpolation, extrapolation...).

D SEMANTICS COMPARISON iew has to be done to express h. A template as "Figure 5" whereof a few columns emerge rence models (S0, W0 and C0)

regarding their similarities and/or disparities. Therefore the following morphological analysis among statistical, geometrical and semantical point of views focuses on 4 columns from each wing (S3, W24, N27 and E28). Notice that these observations were facilitated thanks to the average geometry revealed from the C0 model; on which one can deduce some interesting findings "Fig. 2".

A. Statistic assessment

Both curvature matrix and signature as a digital signal provide capacity for quantitative approaches that can be transposed into a metric system afterwards. A reliable method has been chosen to quickly quantify variations and so to sort the four columns of this restricted case-study according to a certain degree of remoteness. First the difference to C0 was computed to obtain a delta signal for each signature on which the standard deviation has been used to quantify with a single index their closeness to the reference model "Fig. 3". Obviously, other difference operators (e.g. cross-correlation, Dynamic Time Warping, Euclidean distance…) could be additionally used to get a finer analysis at a lower reading scale.

B. Geometric description

The sharp transition between the echinus and the historiated capital (b) on C0 verifies a regular position of this upper part. Contrarily to the dimension of the abacus (a) on S3, fitting with the average, other columns present a smaller instances of this element. One can also read signature amplitude (X axis) as an indication about the state of conservation. As an example, the signal of the upper part of W24 is smoother than the sleeked one of C0. But, there are no common measures with the fuzzy result of the lower partand its un-readable signature on W0 and so C0 -that clearly indicates a sensitive variation of this element. One shall notice the downscaled base of the column N27 and the difference with S3 closest to majority proportion of these elements.

C. Semantic characterization

Semantic layer is defined as each architectural concept that could be identified according to recognizable signal, frequency or pattern on the shape signature. Moreover, most of the interesting observations enabled on the curvature matrix are still perceivable on the curvature profile; degradation on the shaft of W24, such as the particular echinus (ab) of E28. The most surprising variation of the shape-semantics concerns the astragal position (c); lower on S3, upper on W24 and N27, hydrid on E28. Despite of the lack of intelligibility of the current reference models they are complementary to previous "theoretical" models [START_REF] Ign/Matis | [END_REF]. Indeed the geometric C0 revelation is the highlighting of a doubled astragal -clearly identifiable on the signature -resulting from the different location of this entity. This revelation could have lead to recover of the original disposal of columns. Indeed, eight of the ten columns that belong to this upper position of the astragal actually correspond to the historiated capitals that were moved from the tribune to the cloister during the 1955 reconstitution.

V. CONCLUSIONS AND PERSPECTIVES

The curvature-based signatures resulting from this process appeared to be a pertinent response to summarize a shape to its essential representation. Beyond a curvature signal that proves more eloquent than the original data (e.g. picture, pointcloud, mesh), this approach exposes an efficient data discrimination aiming to identify and classify both "theoritical" and "specifical" column's geometric features according to shape semantics. As a lightweight and synthetic description, it provides interesting abilities to treat and study a wide dataset. The latter needs to be extended over possibilities of cross-analysis with other artifacts or collections. For already having performed some tests, one shall notice that the current methodological process may be transposed to any other kind of UV mapping (e.g. colored texture, depth, normal, ambient-occlusion…) depending the aim of the observation "Fig. 4". This lead makes possible to enrich both description and analysis for a complementary shape reading using multiple descriptors [START_REF] Biasotti | 3D artifacts similarity based on the concurrent evaluation of heterogeneous properties[END_REF]. Moreover, this extended method has already been applied on different dataset (architectural and archaeological fragments) with minor adjustments and if a planar or a cylindrical projection can be used. Thus it was shown that signatures are more morphologically significative if the artifact presents symmetries.

But, to reach this goal the next step is to move forward a generic framework to get rid of the reparameterization limits. For example, one can think of an exploration of the spherical geometry and parameterization. One another may be thinking Fig. 3 Sorting the collection using the standard deviation Fig. 4 Different UV maps and their respective signatures to proceed directly on the raw data (i.e. the point cloud) to avoid bias and decimation. Even if for accurate architectural and archaeological analysis purposes, this method still remain relevant, the current geometric primitive based re-meshing and its accordance to object's shape imply few limitations:

• The inadequacy of this method to compare different morphology of large and heterogeneous collections. • The difficulty encountered to unwrap complex geometry into table format. • The shape approximation resulting from the wireframe projection. The main finding of this research is the great analysis support provided and offering a valuable help for an easy and fast graphical comparison. Even though its enlightening about tendencies and remoteness of semantic variations within the collection -over and above theirs hypotheses of interpretation -we had to come back to a manual analysis. Visual analytics will have to be promoted to overpass the skill and the need of human operator to manipulate high-level knowledge. In this case, signal processing would be explored so as to reproduce the automatic detection of formal discontinuities already done before [START_REF] Lo Buglio | What do thirtyone columns tell about a 'theoretical' thirty-second?[END_REF]. Moreover, aware of what is needed to look at, machine learning can be a way to reach the so-called "big data" processing.

In light of all of these elements, it would be interesting for a further investigation to assess and link morphological signatures compared to a shape thesaurus [START_REF] De Montclos | Architecture: description et vocabulaire méthodiques[END_REF].

Fig. 1

 1 Fig. 1 Reparameterization process with regula high-level shape

ar wireframe [ 10 ]Fig. 2

 102 Fig. 2 Geometrical refer erage morphology of the 13 uth wing. verage morphology of the 12 est wing. verage morphology of the 31 ole cloister; including the 6 orth (2) and East (4) wing.