Impact of topography and land cover on air temperature space-time variability in an urban environment with contrasted topography (Dijon, France, 2014–2021)

The in�uence of topography and land cover on air temperature space-time variability is examined in an urban environment with contrasted topography through simple and multiple linear regression (SLR and MLR) models ran for each hour of the period 2014–202 to explain air temperature spatial patterns observed by a dense in-situ network. The SLR models reveal a complementary in�uence of topography and land cover, with largest in�uence during daytime and nighttime, respectively. The MLR signi�cantly improves upon the SLR models despite persistent intensity errors at night and spatial errors in the early morning. Topography in�uences air temperatures all year round, with an adiabatic gradient during the day and frequent thermal inversions at night (up to 30% of the time). Impervious surfaces are more in�uential in summer and early fall, especially during the late afternoon for the fraction covered by buildings, and during the early night for distance from the city centre. They contribute to warm air temperature close to the city centre and where the fraction covered by buildings increases. On the other hand, vegetation contributes to cool air temperature during the night, especially in spring and early summer for �eld crops, summer and early fall for forests and water, and late fall and winter for low vegetation. Our framework proves to be a low-cost and e�cient way to understand the static drivers of air temperature along the annual and diurnal cycles, and is easily transposable to other areas and study �elds, such as viticultural environments to further understand spring frost events.


Introduction
There is growing interest for understanding air temperature space-time variability in urban environments, because cities are highly vulnerable to climate change and are home for about 60% of the world's population -a percentage expected to reach 70% by 2050 according to the (United Nations 2019).The most popular phenomena under study are the so-called Urban Heat Islands (UHIs).UHIs correspond to a well-known mechanism inducing warmer surface and air temperature over urban than adjacent rural areas, due to sensible heat absorption and storage by mineral surfaces and buildings, and weak evapotranspiration of impervious surfaces (Oke 1973(Oke , 1982;;Oke et al. 2017).UHIs exacerbate human thermal stress in summer, especially during heat waves and hot spells (Fouillet et al. 2006 (Oke 1973) and under calm (wind speed < 2 m/s), clear-sky and dry-air conditions (Oke 1982; Morris et al. 2001;Mestayer et al. 2005; Hoffmann and Schlünzen 2013; Arnds et al. 2017).UHIs also tend also to intensify under thermal inversions even in relatively at cities (Oke and Maxwell 1975;Nkemdirim 1980;Goldreich 1984;Kuttler et al. 1996;Szymanowski 2005;Hidalgo et al. 2010;Bokwa et al. 2015).Elevation and landforms have been shown to modulate UHIs, with e.g.air temperature cooling with elevation during the day and colder conditions on northern than southern slopes (Zhao et al. 2016;Peng et al. 2020).In addition, landforms signi cantly affect air temperature spatial patterns (Geiger et al. 2003; Whiteman et al. 2004).At the end of the night, cold air tends to slide downslope and accumulate in the valley bottoms (katabatic wind) while the hilltops and upper slopes experience milder temperatures.Conversely, in the middle of the day, warm air is further heated by contact with the ground and tends to rise along hillslopes exposed to the sun (anabatic wind).These landform-induced thermal effects, also known as slope breezes, in uence air temperature well beyond the hillslopes where they are generated.Finally, land cover affects the surface energy and radiation balance (Oke 1982) and can lead to marked air temperature contrasts both within cities, but also between them and the surrounding rural environment.Mineral surfaces tend for instance to slow nighttime cooling (Eliasson 1996), unlike plant-covered surfaces that cool more rapidly (Sun et al. 2009;Sun 2011;Heusinkveld et al. 2014;Song et al. 2014).Green areas form Urban Cool Islands (UCIs), which can contribute to cool air temperature 300 to 1000 m beyond them (Petralli et al. 2014).City centres are not systematically the hottest parts of town due to local shading and canyon effect (Hart and Sailor 2009;Sun et al. 2009).
The assessment of topography and land cover effects on air temperature space-time variability has been facilitated thanks to the development of ne-scale digital terrain models and vectorial database describing land cover at high spatial resolution.These effects vary over both annual and diurnal cycles (e.g.Heusinkveld et al. 2014), thereby suggesting potential antagonist effects depending on the time of day and year.Furthermore, an accurate assessment of the drivers of urban air temperature variability requires to sample air temperature at high spatial resolution over a long time period (e.g., multiple years) to account for (i) the diversity of land cover and topographical properties within and around the city, (ii) huge air temperature amplitude along the annual and diurnal cycles and (iii) internal variability of the climate system.To date, very few networks ful l this requirement.In France, for instance, two cities only are equipped with a dense network recording air temperature for 10 years or so (Rennes and Dijon).This paper explores the individual and combined in uences of topography and land cover on air temperature space-time variability as measured in Dijon, France, by a dense station network (up to 67 sites) from 2014 to 2021.We build over previous studies by applying Simple and Multiple Linear Regression (SLR/MLR) analyses to examine the individual and combined effects of topography and land cover on air temperature spatial patterns along both the annual and diurnal cycles.The originality of the approach is twofold.First, the regression approach is not used in a predictive mode (e.g., one unique or few SLR/MLR models) but as a framework to objectively identify the individual factors and their combination explaining each air temperature spatial pattern.This implies one SLR/MLR model to be built for each hour for the period 2014-2021.Second, in addition to traditional metrics used to assess individual and combined in uences (e.g., root mean square error and coe cient of determination), we also examine the frequency of occurrence and mean regression coe cient associated with SLR and MLR predictors along the annual and diurnal cycles to pinpoint when and how they in uence air temperature spatial patterns.
The paper is organized as follows.Section 2 presents the site area, the data and the SLR and MLR frameworks.Section 3 presents both the individual and combined in uences of the predictors in the SLR and MLR frameworks, respectively.Section 4 gives the main conclusions and discusses the limitations of our work.

Site area
The study area is Dijon located in Burgundy, eastern France.Dijon is a mid-sized European city of about 260 000 inhabitants that covers 240 km 2 (Fig. 1).The city is bordered to the west by a ~ 500 m plateau (Fig. 2a-c) that is largely forested (Fig. 2g).This plateau is incised by a steep-sided valley (Fig. 2a-c) that is mostly grassland (Fig. 2i).The ~ 220 m plain lying east of the city (Fig. 2a-c) is covered by eld crops (Fig. 2h), forests and ponds further east (Fig. 2i).The city is characterized by three main built-type categories forming a concentric pattern: compact mid-rise in the city centre and compact low-and highrise further from the city centre (Emery et al. 2021).Forests and low vegetation are sparse within the city, except for in a 33 ha urban park some 3 km south-east of the city centre, around a 37 ha lake in the western part of the city, and beside the River Ouche (Fig. 2g, i) that ows through the city from northwest to southeast (Fig. 1).
Dijon is characterized by a Köppen temperate oceanic climate (Cfb) on the European scale and by a continental-like climate on the French scale (Joly et al. 2010).The climatological conditions, derived from the Météo-France weather station located south-east of the city (blue dot in Fig. 1), are characterized by wide variability in diurnal temperatures and insolation over the annual cycle, with relatively hot summers and cold winters (Fig. 3a-b).This contrasts with rainfall amounts, which vary barely over the mean diurnal and annual cycles (Fig. 3c).Rainfall amounts seem to be slightly higher in the late afternoon when convective precipitation dominates (April to July: see Marteau et al. 2015), and at night when stratiform precipitation prevails (November to February: ibid.).Wind speeds display a somewhat insubstantial annual cycle, but a prominent diurnal cycle showing higher speeds during the day (Fig. 3d).
At night, south-westerlies dominate during winter and north-westerlies dominate during the remaining seasons (Fig. 3e-f).Wind direction varies a lot during the day, hence weak climatological values (Fig. 3ef.)

Hourly air temperature measurements
Hourly air temperatures come from the MUSTARDijon network (Richard et al. 2018; Fig. 1).The network has been designed to capture mesoscale rather than local or microscale thermal conditions (Oke 1984(Oke , 2006) ) over the various land cover categories found in Dijon.The network is equipped with sensors measuring near instantaneous temperatures every hour at 3 m above ground level since 6 June 2014.The network has been progressively densi ed from 50 sensors in 2014 to 67 in 2021 (Fig. 1).Until 2019, air temperatures were measured with HOBO Pro v2 U23-001A sensors, which were accurate to ± 0.25°C from − 40 to 0°C and ± 0.2°C from 0 to 70°C, and measurements were collected manually, once a year.These sensors were replaced by automatic HOBO MicroRX stations equipped with HOBO S-THC-M002 sensors between 2020 and 2021 (Fig. 1).The new sensors have a similar accuracy but their response time is shorter (~ 4 minutes compared to ~ 10 minutes for the previous sensors).This induces slightly more pronounced air temperature variability when measured by the newer sensors, but these changes do not signi cantly impact our results.The period studied runs from 6 June 2014 to 31 December 2021, with ~ 3.5% missing values due to sensor failure/maintenance.

Topography and land cover descriptors
Three categories are used as potential predictors to explain observed air temperature space-time variability at the hourly timescale: (i) topography, (ii) distance from the city centre and (iii) land cover (Fig. 2).
Topography descriptors are derived using the 50 m resolution Digital Terrain Model (DTM) from the Institut Géographique National (IGN).We consider the elevation of the closest 50 m pixel for each sensor (Fig. 2a and Table 1) since elevation drives a west-east gradient in air temperature across Dijon (Richard et al. 2018).Landform effects are accounted for by considering the magnitude of humps and of valleys (Fig. 2b-c), which characterize the height or depth of a positive or a negative relief relative to a topographic reference point.Following Joly et al. (2012), the magnitude of humps and valleys has been computed in three stages.First, ridgelines and thalwegs have been identi ed using the Peucker and Douglas (1975) algorithm applied to the DTM elevation spatially averaged considering 7 50 m pixels.The spatial averaging of 7 pixels allows to focus on the most prominent ridgelines and thalwegs, which would have been too noisy using 5 pixels and too smoothed using 9 pixels (Supplementary Fig. S1).Second, we have constructed two ctitious topographic surfaces: (1) the "ceiling" passing through all the ridgelines to encompass all of the emerging relief and (2) the " oor" joining up all the thalwegs.Between these two surfaces, the distance varies locally with the altitudinal position of the ridgelines relative to the thalwegs.The ridgelines and thalwegs, often separated by great distances, depict surfaces with a long radius of action.Finally, the hump magnitude is obtained by the difference between the altitude of the oor vertically below pixel p and the elevation of the same pixel p provided by the DTM.The valley magnitude is the difference between the altitude of the ceiling vertically above pixel p and the altitude of pixel p.
The distance from the city centre is an isotropic tendency term which implicitly describes the decrease in urban density (resulting therefore in a similar decrease in impervious surfaces) with distance from the city centre (Fig. 2d).This tendency term is known to affect air temperature spatial patterns in urban environments (Edmondson et al. 2016) and is computed as the Euclidean distance between each station and the city centre (Libération square: black cross in Fig. 1).
Land cover descriptors have been derived using a hybrid product mixing the French BD TOPO database (version 2, 2020) developed by IGN and one satellite image from Pléaides acquired in August 2015 at 2 m resolution.The BD TOPO2 is preferred to other products (e.g.MAPuCE; Bocher et al. 2018) for consistency with other projects in which our team is currently involved.Vegetation in BD TOPO2 is obtained by automatic classi cation using supervised learning followed by a series of processing operations during which the unwooded vegetation-covered surfaces are removed (e.g., meadows and grasslands) for polygons of less than 50 ares (i.e., 5000 m 2 ).The Pléiades image is used to make up for this missing information by calculating the modi ed soil-adjusted vegetation index (MSAVI version 2: Qi et al., 1994) based on the red (590 to 710 nm) and near infrared (740 to 940 nm) spectral bands (Eq.1).

Eq. (1)
The MSAVI2 is an index designed to substitute the normalized difference vegetation index (NDVI) where it fails to provide accurate data due to low vegetation or a lake of chlorophyll in the plants (Qi et al. 1994).It improves on the NDVI by incorporating a soil adjustment factor into the denominator of the NDVI equation.The incorporation of soil-adjusted indices greatly improves vegetation models (Bannari et al. 2000).This factor varies inversely with the amount of vegetation present, which increases the dynamic range of the vegetation signal while further minimizing the soil background in uences (Qi et al. 1994).
The BD TOPO2 -Pléiades hybrid product is used to derive the area fraction covered by (i) buildings (Fig. 2e), (ii) arti cial surfaces (buildings and transport infrastructures; Fig. 2f), (iii) forests and water (Fig. 2g), (iv) eld crops (Fig. 2h) and (v) low vegetation (Fig. 2i).Following Foissard et al. (2019), these descriptors have been computed within a circular buffer of 50m to 600m radius, every 50m, and around each sensor, to assess the impact of the buffer size on air temperature spatial variability.The impact of the buffer size is weak for the fraction covered by buildings and eld crops but is non-negligible for the fraction covered by forests and water and by low vegetation (Supplementary Fig. S2).Among the buffer size tested, a 300m radius leads to satisfactory results for all land cover descriptors, and is thus retained in this study.Thus, the total area fraction covered by arti cial surfaces and the three vegetation categories equals 100%, a necessary step guaranteeing there is no loss of information and no overlapping information in our BD TOPO2 -Pléiades hybrid product.Importantly, this product gives an instantaneous view of land cover, which is by no means perfect since we use it to assess its impacts on air temperature spatial patterns for the period 2014-2021.However, land cover properties did not drastically change around the sensors during this period, allowing us to use static land cover descriptors with con dence.
To limit information redundancies, the collinearity between the above-described descriptors has been examined (Supplementary Fig. S3).Four couples of descriptors depict strong collinearities: (i) elevation and hump magnitude (r = 0.87), (ii) distance from the city centre and fraction of buildings (r=-0.71),(iii) fraction of buildings and arti cial surfaces (r = 0.66), and (iv) fraction of arti cial surfaces and eld crops (r=-0.62).Based on these results, we decided to exclude arti cial surfaces from the analyses since this descriptor is signi cantly correlated with many others (Supplementary Fig. S3).On the other hand, we opted to keep the best predictor (based on p values) between elevation and hump magnitude and between the distance from the city centre and the fraction covered by buildings when assessing the combined effects of the predictors.The exact list of predictors mobilized in this study and the way they are computed are summarized in Table 1.

Assessing individual and combined in uences of topography and land cover on air temperature space-time variability
Individual and combined in uences of the above-described descriptors on air temperature space-time variability are assessed using simple and multiple linear regression (SLR and MLR) frameworks, respectively.In both cases, the aim is not to build a predictive model for air temperature, but to assess the individual and combined in uences of the predictors in terms of frequency of occurrence and thermal effect (i.e., regression coe cient) without imposing subjectively the nature and number of predictors for MLR models.
To do so, we have constructed one SLR/MLR model for each hour of the period 2014-2021 when at least 40 sensors have no missing values.Each SLR model is built with each of the eight predictors listed in Table 1, regardless of the statistical signi cance of its in uence.This leads to 66 347 SLR models for each predictor out of the 66 386 hourly timesteps of the period.
Slightly less MLR models are built (66 289) because, unlike the SLR models, they account for the statistical signi cance of the predictors.Each MLR model is built as a combination of 1 to 5 out of 6 potential predictors (Table 1: distance from the city centre or fraction of buildings, fraction of forests and water, eld crops and low vegetation, elevation or hump magnitude and valley magnitude).Retaining 5 predictors at most is the best compromise between MLR skill and MLR complexity (Supplementary Fig. S4).The number and ranking of predictors used to build each MLR model are chosen objectively based on p value at the 95% con dence level, implying that the number and nature of predictors feeding the MLR models are not xed in time (even between two successive hours).Out of the 66 289 MLR models built for the period 2014-2021, 16% use 5 predictors, 23% 4 predictors, 35% 3 predictors, 22% 2 predictors and 4% only are based on SLR (with 1 predictor).In all cases, the predictors used to build the MLR models weakly co-vary when two or more predictors are used as inputs.The variance in ation factor remains below 2 more than 90% of the time and is almost always below 5 (

Statistical analyses
The individual and combined in uences of topography and land cover on air temperature space-time variability is assessed by examining SLR/MLR skill metrics, as well as the frequency of occurrence of the predictors and their regression coe cients.
Two skill metrics are considered.First, the root mean square error (RMSE), computed for each sensor using a leave-one-out cross validation (LOOCV) then area-averaged, gives insights on the SLR/MLR capability in capturing the observed air temperature magnitude across the city.Second, the coe cient of determination (R2) for SLR models and adjusted R2 (R2-Adj) for MLR models, computed for all sensors at a time, assess the SLR/MLR capability in capturing the observed air temperature spatial patterns.These two metrics give complementary information (magnitude and spatial errors, respectively) and are used to hierarchy the individual (SLR models) effects of topography and land cover on air temperature spacetime variability and discuss the extent to which MLR models improves on SLR models.
The frequency of occurrence of the predictors is examined in three different ways.First, we analyse the frequency of occurrence of SLR-derived positive/negative regression coe cients over the annual and diurnal cycles, to discuss the stationarity in the thermal effects of these predictors.Second, we compute the frequency of occurrence of each MLR-derived predictor as the ratio between the number of times it is selected in the MLR models at a given hour of a given month for the period 2014-2021 (nominator), and the total number of predictors used for the same hour, month and period (denominator).Third, we compute the frequency of occurrence of each predictor as the ratio between the number of times it enters the MLR models for each hour and month for the period 2014-2021 (nominator), and its total occurrence all months and days combined for the same period (denominator).This ratio is then compared to equiprobable occurrence along the annual and diurnal cycles (1/288, with 288 = 12 months x 24 hours) to pinpoint when the predictors are more (positive values) or less (negative values) frequent than expected.The difference between real and equiprobable distributions is tested using a Chi-2 test.This way to compute the frequency of occurrence allows assessing when each MLR-derived predictor preferentially occurs over both the annual and diurnal cycles.
The SLR-and MLR-derived regression coe cients describe the thermal effect of each predictor, i.e. whether a given predictor contributes to warm or to cool air temperature in the SLR/MLR frameworks.We examine both the probability density function of SLR-derived regression coe cients and the mean MLRderived values along the annual and diurnal cycles to qualitatively assess the thermal effect of topography and land cover.

Individual effects
Individual effects are assessed by analysing the results from the SLR models built for each hour of the period 2014-2021 and fed by each predictor listed in Table 1.

Hierarchizing the predictor's in uence
Figures 4 and 5 show, for each predictor, the SLR-derived RMSE and R2 along both the diurnal and annual cycles, respectively.The mean RMSE are relatively similar for all predictors (Fig. 4).They are the lowest in the early morning (0.3°C to 0.5°C), increase during the day and reach their largest values during the night (0.7°C to 1°C).Such a diurnal cycle in the RMSE is less marked in fall and winter than in spring and summer, i.e. when air temperature and insolation are the lowest (Fig. 3a-b).
Spatial errors depend on the predictor feeding the SLR models.Four out of the eight predictors contribute to explain a signi cant fraction of air temperature spatial patterns: (1) elevation and (2) hump magnitude during daytime, especially in the late afternoon (R2 up to 0.9 and 0.6, respectively); (3) distance from the city centre and (4) fraction covered by buildings during nighttime (R2 up to 0.5).The remaining predictors have a much lower in uence, with R2 values never exceeding 0.2 during nighttime and rarely exceeding 0.1 during daytime.These results suggest complementary in uences of topography and land cover throughout the diurnal cycle, hence the need to account for both of them to capture observed air temperature space-time variability.

Thermal effects
Individual thermal effects are examined by analysing both the frequency of occurrence of SLR-derived regression coe cients (i.e., slopes of the SLR models) according to their sign (Table 3 and Fig. 6) and the probability density function of regression coe cients (Fig. 7).Topography and landform predictors are associated with regression coe cients that signi cantly vary in sign with time (Table 3).The regression coe cients are negative 80% of the time and positive 20% of the time for both elevation and hump magnitude, indicative of much more frequent adiabatic gradient than thermal inversion conditions.Adiabatic gradients are almost systematic during daytime (Fig. 6a-b) with a modal value of -0.9°C/100m for elevation (Fig. 7a) and − 0.3°C/10m for hump magnitude.They are also frequent during nighttime (70% of the time: Fig. 6a-b), albeit their slightly weaker magnitude (Fig. 7a-b).Symmetrically, thermal inversions are rare during daytime while occur up to 30% of the time during nighttime (Fig. 6a-b).They can reach up to 2°C/100m for elevation and 0.7°C/10m for hump magnitude, against maximal values of -1.5°C/100m and − 0.5°C/10m in the case of adiabatic gradients (Fig. 7a-b).Valley magnitude is associated with regression coe cients that are positive 35% of the time (and thus negative 65% of the time: Table 3).For this predictor, negative regression coe cients denote colder air temperature in than out of the valleys, which can result from different mechanisms including e.g.thermal inversions during nighttime or lower insolation in incised valleys than plateaus and plains during daytime.Such a con guration is more frequent during nighttime than daytime and reaches up to -0.5°C/10m (Figs.6c and   7c).
The remaining predictors (distance from the city centre and fraction covered by buildings and by the three vegetation categories) have almost constant qualitative thermal effects, since the sign of their regression coe cient is the same at least 90% of the time (Table 3, Fig. 6d-h).Air temperature increases towards the city centre, together with the fraction of buildings (Fig. 7d-e).By contrast, air temperature decreases as the fraction covered by vegetation increases (Fig. 7f-h).The thermal effects of the distance from the city centre and land cover tend to be stronger during the night (Fig. 7d-h), i.e. when the UHI is the strongest (Richard et al. 2021) and wind speed the lowest (Fig. 3d).The remaining 10% (reversal in the sign of the regression coe cient) mostly occur just after sunrise (Fig. 6d-h) and denote weak drop shadows in the study area more than land cover effects, hence positive (negative) regression coe cients for distance from the city centre and the fraction covered by the three vegetation categories (fraction covered by buildings).

Combined effects
Combined effects are assessed by analysing the results from the MLR models built for each hour of the period 2014-2021, and using a maximum of ve predictors among those listed in Table 1.

Mean model skill
Figure 8 shows the RMSE and R2-Adj of the MLR models averaged for the period 2014-2021 over both the diurnal and annual cycles.The RMSE metric depicts the same pattern as for SLR models, but errors are much lower (Fig. 8a compared to Fig. 4).They reach up to ~ 0.6°C at night and ~ 0.4°C during the day, with the largest errors occurring from March to September (Fig. 8a).The mean spatial errors are also signi cantly lower in the MLR than SLR models (Fig. 8b compared to Fig. 5).They depict a strong diurnal cycle, with the lowest skill (mean R2-Adj = 0.65) found in the early morning immediately after sunrise, and the best one (mean R2-Adj = 0.8) in the evening and in the early night (Fig. 8b).
The worst RMSE and R2-Adj reach as much as 1°C at night and 0.3 in the early morning, respectively (Supplementary Fig. S5a-b).Symmetrically, the best RMSE and R2-Adj reach 0.1°C and 0.87 (Supplementary Fig. S5c-d).This indicates a large spread in MLR skill, probably linked to meteorological conditions that are not accounted for.
The better performance of MLR models to explain the space-time variability of air temperature around the agglomeration of Dijon demonstrates that it is signi cantly in uenced by more than one factor, like elevation, landform and land cover.The following section examines when and how each predictor in uences air temperature in the MLR framework.

Frequency of occurrence
Elevation, valley magnitude and the fraction covered by buildings are the main drivers of air temperature spatial patterns, especially from March to October.At this time, the frequency of occurrence reaches up to 35% in the late morning and early afternoon for elevation, 25% during the night for valley magnitude, and 30% during the day for the fraction covered by buildings (Fig. 9).By contrast, hump magnitude is the least frequent predictor, occurring 10% of the time at most from November to February, and 15% of the time during the morning from March to October.Since the MLR models cannot use elevation and hump magnitude as predictors at the same time to limit multicollinearity issues, we conclude that the former has an overall larger in uence on air temperature patterns.The remaining predictors occur up to 20% of the time during the night, especially from October to March for the fraction covered by low vegetation and from March to October for distance from the city centre and the two remaining vegetation predictors (Fig. 9).
We now better highlight when, over the annual and diurnal cycles, each predictor in uences air temperature spatial patterns, as well as the relationship between these predictors.Elevation in uences air temperature all year long (Fig. 10a).Hump magnitude in uences early morning air temperature from March to October (Fig. 10b), and valley magnitude in uences nighttime air temperature from July to October (Fig. 10c).The largest in uence of city mineral properties is found in summer and early fall ( rst hours of the night for distance from the city centre: Fig. 10d; late afternoon for the fraction of buildings: Fig. 10e).Vegetation categories have different in uences over the year: the forests and water category mainly in uences air temperature during the night in summer and early fall for (Fig. 10f), low vegetation predominates in late fall and winter (Fig. 10h) and eld crops in spring and early summer (Fig. 10g).Interestingly, the in uence of eld crops on air temperature spatial patterns starts ~ 1 month earlier in spring and nishes ~ 1 month earlier in summer than that of forests and water.The main eld crops around Dijon are wheat, rapeseed and barley (Colbach et al. 2014).They are harvested in July, leaving bare soils from August to October.Even though vegetative cycles are not explicitly accounted for, the seasonality in the occurrence of these two vegetation predictors is consistent with the observed vegetative cycle in Burgundy.

Thermal effects
Mean MLR-derived regression coe cients are very consistent with those derived from the SLR models in terms of sign.Elevation, valley magnitude and, to a lesser extent, hump magnitude are associated with regression coe cients with reversed signs between night and day (Fig. 11a-c).Adiabatic gradients prevail during daytime, while thermal inversions dominate at night.For instance, the mean in uence of elevation reaches as much as ~ -1°C/100 m during daytime almost all year long and ~ + 0.5°C/100 m at night from spring to autumn.The apparent weaker intensity of nocturnal thermal inversions compared to daytime adiabatic gradients conceals a "mean effect", due to the fact that both adiabatic gradients and thermal inversions can occur at night, while adiabatic gradients are nearly systematic during the day.
For the remaining predictors, air temperatures increase systematically towards the city centre and where the fraction covered by buildings increases, especially at night (Fig. 11d-e).The largest in uence of these two predictors is found from spring to autumn, also corresponding to their most frequent occurrence (Fig. 10d-e).While the fraction of buildings is more rarely selected as a predictor during nighttime (Fig. 10e), it promotes much more intense warming than in daytime (Fig. 11e).In contrast with urban predictors, vegetation predictors mostly contribute to cool air temperatures at night (Fig. 11f-h).The only exception concerns low vegetation in the early morning in late summer, which tends to promote warmer conditions.Such a warming effect of low vegetation (and, to a lesser extent, of eld crops) during the early morning may relate to the fact that low vegetation is generally located over at and open land with no cast shadows, which therefore warms quickly after sunrise.

Conclusion And Discussion
This paper examines the individual and combined in uences of topography (elevation and landform: hump and valley magnitude), land cover (fraction covered by buildings, low vegetation, eld crops and forests and water) and urban morphology (distance from the city centre) on air temperature space-time variability measured by a dense in-situ network, in a middle-size city (Dijon, North-Est France) surrounded by contrasted topography.These descriptors are used as predictors in simple and multiple linear regression (SLR and MLR) models ran for each hour of the period 2014-2021.Their individual in uences are assessed through the SLR models and their combined in uences through the MLR models.Both are examined along the annual and diurnal cycles by analysing to extent to which these linear models capture the area-averaged intensity (RMSE) and spatial patterns (R2 or R2-Adj) of observed air temperature, as well as the frequency of occurrence and thermal effects of the predictors objectively selected to build them.
The analysis of individual in uence reveals a complementary in uence of topography and land cover on air temperature space-time variability.Thus, accounting for the combined in uence of topography and land cover in the MLR models signi cantly improves air temperature area-averaged magnitude and spatial patterns compared to observations, especially during the day and early night.
Topography in uences air temperature all year long for elevation, in the early morning from March to October for hump magnitude and during nighttime from July to October for valley magnitude.French cities.The predictors themselves remain the most critical levers for improvement.The fact that the predictors used are constant in time does not seem to be a major source of error, as suggested, for example, by realistic annual cycle in the frequency of occurrence of the three vegetation categories (low vegetation, eld crops and forests and water) compared to the observed vegetative cycle in Burgundy.
The main source of improvement would be the inclusion of physically-based descriptors, such as sensible and latent heat uxes, insolation or cloudiness, atmospheric stability and circulation and soil moisture.Including such physical processes would require observations or reanalyses for the entire 2014-2021 period at a su ciently high resolution to account for spatial heterogeneity within the study area.The state of available data is not yet quite there, making it di cult to account for physical processes at this time.Similarly, we did not include the sky view factor at this stage to focus on mesoscale drivers of temperature patterns.Yet, the sky view factor may help improve the SLR/MLR skill in capturing air temperature spatial variability associated with UHI (Dirksen et al. 2019) and during the early morning, even though its physical meaning is questionable at mesoscale.
Our SLR/MLR framework proves to be a low-cost, e cient and replicable way to understand the individual and combined in uences of topography and land cover on air temperature space-time variability.While applied here to an urban environment, it can easily be transposed to other environments, such as viticultural environment to understand the high space-time variability in air temperature during spring frost events.
; Matzarakis et al. 2009; Gabriel and Endlicher 2011; Steeneveld et al. 2011; Pascal et al. 2018), but may also be an opportunity to reduce energy consumption (Li et al. 2019) and cold-related mortality during winter compared to adjacent rural areas (Macintyre et al. 2021).Many previous studies dedicated to assess the drivers of urban air temperature variability have focused on UHIs and compared individual effects through correlation and regression analyses.This has been done considering individual factors (Oke 1973; Jusuf et al. 2007; Imhoff et al. 2010; Tan and Li 2015) and more rarely multiple factors (Peng et al. 2012; Coseo and Larsen 2014; Wang et al. 2021).The UHI intensity increases proportionally to the size and population of the urban area

Figure 1 Location
Figure 1

Figure 9 Frequency
Figure 9

Table 2
Key statistics of the Variance In ation Factor (VIF) computed for each MLR model set with 5 predictors at most for the period 2014-2021.

Table 3
Frequency of occurrence (%) of SLM-derived regression coe cients (i.e., slopes) associated with positive and negative values for the period 2014-2021.
Eliasson 199680;Goldreich 1984;Bokwa et al. 2015)with contrasted topography(Nkemdirim 1980;Goldreich 1984;Bokwa et al. 2015).Impervious surfaces are more in uential in summer and early fall, especially in late afternoon for the fraction covered by buildings and in early night for distance from the city centre.They contribute to warm air temperature towards the city centre or where the fraction covered by buildings increases.Vegetation contributes to cool air temperature at night with complementary in uences of the three vegetation categories over the annual cycle (low vegetation: late fall and winter; elds crops: spring and early summer; forests and water: summer and early fall).The only exception concerns low vegetation at sunrise during summer, which contributes to increase air temperatures in our MLR models.However, we have limited con dence in this warming effect, since observations associated with a large fraction of low vegetation are essentially located at the foot of hill slopes oriented from north-east to south-west, and are thus well exposed to insolation at sunrise.The thermal effects of land cover found in Dijon are in line with previous works and consistent with the wellknown drivers of UHI (e.g.,Eliasson 1996; Sun et al. 2009; Sun 2011; Heusinkveld et al. 2014; Song et al. 2014; Stewart 2019).These SLR and MLR models are not perfect by any means.They struggle in capturing air temperature patterns at night and early in the morning when observed air temperature tends to be noisy spatially.
Topography is associated with almost systematic adiabatic gradients during daytime and frequent (up to 30% of the time) thermal inversions during nighttime.Such a diurnal reversal in the thermal effect of topography is Such di culties are also found in other cities using different statistical models (e.g., Nikoloudakis et al. 2020).More sophisticated approaches may slightly improve upon our MLR approach (e.g., Szymanowski and Kryza 2009; Ho et al. 2014; Schneider Dos Santos 2020).For instance, Gardes et al. (2020) found very slight improvements with the Random Forest algorithm compared to MLR in predicting UHI over 42