Downscaling potential evapotranspiration to the urban canyon

The future increase in urban population will lead to progressing urbanization with urban sprawl and densification. Urbanized areas show distinct changes in their hydrological behaviour, water quality and climate. In the last decades, the ability of urban hydrological models to represent the dynamic hydrological behaviour of the different surface types has been improved continuously. Dissenting from the urban surface which is mostly represented in high spatial resolution, the climatic input to 10 these models, such as precipitation and potential evapo(transpi)ration, is usually observed at one or several reference climate stations that are representing a mesoscale urban foot print area or rural conditions. From urban climate studies it is known, that the meteorological variables that are governing potential evapotranspiration (Ep) can be highly variable even on a small spatial scale. Consequently, we expect Ep at the street level to be affected by this variability as well. We observed the urban microclimate with a mobile climate station and a rotational principle at 16 different locations in two 15 differently oriented street canyons with vegetated and non-vegetated sections, respectively, during three seasons (spring, summer, autumn) in Freiburg, in southwestern Germany. With these observations, we simulated Ep at the street level using FAO-56 Penman-Monteith reference evapotranspiration and compared it to reference Ep derived at a rooftop station. We found that Ep on street level is negatively influenced by changes in shortwave radiation and that it is barely sensitive to changes in the other input climate variables. Significant linear relationships between the relative differences in hourly and daily short20 wave radiation input and Ep at the street level have been established. The application of these relationships allows to simulate Ep at the street level for any location in a city based on simulated (or observed) short wave time series and observations at a reference climate station. Our findings can be transferred easily to existing urban hydrologic models to improve modelling results with a more precise estimate of potential evapotranspiration on street level.


Introduction 25
By 2050, 68% of the world's and 84% of Europe's population are expected to live in cities (UN, 2018), starting from 55% worldwide and 74% in Europe in 2018 (UN, 2018). This increase in urban population will lead to progressing urbanization with urban sprawl and densification. Cities and urban areas already have a great impact on the water balance and on the hydrology of the receiving waters (Bonneau et al., 2017;Fletcher et al., 2013;Lerner, 2002;Schirmer et al., 2013). In contrast to rural areas, fully or partly sealed surfaces in urban areas usually cause higher runoff, less groundwater recharge and lower 30 evapotranspiration.
In the last decades, the ability of hydrological models to simulate the dynamic hydrological behavior of urban areas has increased continuously (Bach et al., 2014;Salvadore et al., 2015;Zoppou, 2001). Dependent on the purpose of each model, surface and soil characteristics as well as drainage via the sewer system controlling the hydrologic processes on the soil surface and below ground are considered in detail in many urban hydrologic models. Even low impact development (LID) elements 35 can be implemented in some models (see Elliot and Trowsdale (2007) for an overview of urban drainage models which are able to represent LID tools). In contrast to the spatially highly resolved information on the urban surface, the meteorological input for these models is still derived from observations with a mesoscale footprint area. https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License.
Determining the actual evapotranspiration (ETa) of urban areas is demanding, in specific, in high spatial resolution for the area of a whole city (Nouri et al., 2013). Adequate observations of actual evapotranspiration for a city under interest in the desired 40 spatial and temporal resolution and extent are seldom available (Nouri et al., 2013). Even in cities with a high proportion of sealed surfaces evapotranspiration is a controlling component of the water balance, hence, it should not be neglected (Grimmond & Oke, 1999). To overcome the absence of ETa observations, many urban hydrological modells simulate ETa for the fraction of unsealed surfaces dependent on the potential evaporation (Ep) and the physical behavior of soils and plants (e.g. Grimmond & Oke, 1991;Mitchell et al., 2001;Berthier et al., 2006;Rodriguez et al. 2000;Rodriguez et al., 2008). Input 45 variables for Ep are usually derived from a reference climate station which is located e.g. in rural areas or typically for many cities at the airport close to the city or on a rooftop directly in the urban area under investigation. By using these mesoscale Ep rates, we neglect that climate variables can vary considerably within the city on a small spatial scale.
The urban microclimate has been investigated intensely in the last decades especially in terms of developing and implementing potential mitigation strategies against heat in cities (Bärring & Mattsson, 1985;Bourbia & Awbi, 2004;Norton et al., 2015;50 Oke, 1988;Salata et al., 2016;Shashua-Bar & Hoffman, 2000). From these studies it is known, that the climate variables thatwhich influence Ep -air temperature, relative humidity, wind speed, short-and longwave radiation -may be highly variable on small spatial scales, depending on surface characteristics as building height, orientation and width of the street canyon (Bourbia & Awbi, 2004;Oke, 1988), the presence of vegetation (Shashua-Bar & Hoffman, 2000) etc..
To our knowledge, no urban hydrologic model allows to adjust Ep to the specific microclimate conditions of an urban area. 55 The only related approach from the field of urban gardening, the landscape coefficient method (LCM) by Costello et al. (2000), includes a so-called microclimate coefficient (kmc) which adapts Ep (FAO-56 Penman-Monteith reference evapotranspiration (Allen et la., 1998)) to the specific microclimatic conditions of an urban green space. Daily Ep is calculated with meteorological data from a reference climate station and is then multiplied by kmc. This coefficient ranges between 0.5 and 1.4 and thereby decreases or increases Ep depending on whether the location is e.g. shaded or influenced by strong winds, respectively (Costello 60 et al., 2000). Generally, the estimation of kmc is very subjective because of the scarcity of urban ETa measurements (Costello et al., 2000) and so kmc is chosen individually for each green space based on visual examination. Litvak & Pataki (2016) established a significant relationship between kmc and the fractional tree canopy cover for several public lawns in Los Angeles, California. This study is restricted to lawns shaded by trees and excludes shade by buildings and the behavior of Ep in a more heterogenic urban environment. Consequently, this method is still not directly applicable to urban hydrological modelling. 65 Other procedures to downscale mesoscale Ep to the urban microscale could be to analyze the behavior of Ep for different urban microclimatic conditions, similar to a sensitivity analysis. Many sensitivity analyses have been performed on Ep in terms of adjustments in the water management that might be needed as consequences of climate change (Ambas & Baltas, 2012;Bormann, 2012;Gong et al., 2006;Sharifi & Dinpashoh, 2014;Tabari & Talaee, 2014) or in terms of estimation errors due to measurement uncertainties or missing input data (Beven, 1979;Bois & Pieri, 2005;Debnath et al., 2015). Of those, only Beven 70 (1979) analyzed variations below the diurnal resolution in an hourly time step. Since it is unknown whether the assumed changes in the input variables of formerly conducted sensitivity analyses are applicable in an urban setting, findings from these studies should not be used directly. The derivation of variation and cross-correlation of the micro-meteorolgical variables requires continuous observations of all input variables in high spatial and temporal resolution in an urban setting over a longer time period. However, observing these variables in cities is very difficult due to the risk of vandalism and the lack of space for 75 installing the sensors (Erell & Williamson, 2007;Oke, 2006). Further, it is very costly to establish a network of climate stations that represents the heterogeneity of a whole city (Erell & Williamson, 2007;Oke, 2006).
Mobile measurements are a novel way to gain highly resolved spatial information about the microclimatic conditions in cities without the disadvantages of a stationary observation network (Rajkovich & Larsen;. For example, several point and transect measurement campaigns examined the impact of different street and building designs on the urban heat/cool island 80 phenomena and on human thermal comfort (Voogt & Oke, 1998;Blankenstein & Kuttler, 2004;Conrads & van der Hage, https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License. 1971;Chen et al., 2012;Tsin et al., 2016;Heusinkveld et al., 2014;Unger et al., 2001;Rajkovich & Larsen;Brandsma & Wolters, 2011). The sensors were mounted on bicycles (Brandsma & Wolters, 2011;Heusinkveld et al., 2014;Rajkovich & Larsen, 2016) and cars (Blankenstein & Kuttler, 2004;Conrads & van der Hage, 1971;Unger et al, 2001;Voogt & Oke, 1998) or observations were carried out on foot (Chen et al., 2012;Tsin et al., 2016). It is also common to set up few portable stations 85 at specific locations for several hours (Dimoudi et al. 2013;Holst & Mayer, 2011;Lee et al., 2013;Salata et al., 2016). Since these microclimate studies aim typically on heat mitigation and human thermal comfort, such mobile measurements often represent only short time periods of a few hours during specific weather conditions and do not cover all meteorological variables needed to simulate Ep. In addition, mobile equipment has to be supervised for the whole observation period or at least has to be set up daily which leads to measurement campaigns with only a small number of replications. 90 In order to capture the spatial and temporal patterns of meteorological variables influencing the potential evapotranspiration in a complex urban environment, this paper presents the results of an intense monitoring study carried out in 2016 and 2017 with a mobile climate station mounted on a bicycle trailer, in Freiburg, Germany. The primary aim of this study was to develop an approach to downscale mesoscale or reference Ep observations to the urban microscale at the street level on a daily and diurnal time scale. 95 2 Methods

Study area
Data were collected in two adjacent urban street canyons in Freiburg, southwestern Germany. Freiburg is located close to the Black Forest, 278 m above sea level, in a warm and humid temperate climate zone with mean annual air temperature and precipitation of 11.4°C and 837 mm, respectively. The two streets selected as study sites are located in the residential district 100 "Wiehre" -the street "Hildastraße" (HS), is north-south, the other street, "Erwinstraße" (ES), is east-west oriented, both intersecting each other. Four-storey buildings from the late nineteenth and early twentieth century line the streets generating the typical characteristics of an urban canyon. Both streets consist of sections with and without vegetation. In the vegetated sections, trees line the sidewalk and lawns, bushes and hedges grow in the front yards. The non-vegetated sections show no vegetation at all, with sidewalks right in front of the buildings and parking lanes along both sides of the roads. Sidewalks and 105 roads are fully paved in the vegetated and non-vegetated sections in both streets. Both streets offer distinctive boundary conditions due to their homogeneous building structure and their straight orientation. We selected in both streets one vegetated (v) and one non-vegetated (n) section for data collection. In HS the vegetated section is south, in ES it is east to the non- In each street, eight measurement locations were selected (Fig. 2). The locations were situated on the sidewalks approximately 50 cm away from the curb. In HS, four locations were selected in each section, two on each side of the road respectively. In ES, two locations were selected in the vegetation free section, one on each side of the road, and six in the vegetated section, three on each side of the road, respectively. 120 https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License.

Observations
We performed microclimatic measurements with a mobile climate station, mounted on a bicycle trailer. We pulled the trailer by bike to the streets and moved it around by hand to the measurement locations within the streets. We observed air temperature (Ta), relative humidity (rh), wind speed (u), incoming shortwave radiation (K↓) as well as the infrared surface temperature of the ground (Ts,ground), the four cardinal directions (Ts,NESW) and from above (Ts,up) ( Table 1 was also fixed to the vertical pole. When the vertical pole is oriented correctly, the extension bar is pointing south to avoid shadow from the vertical pole. The sensors at the extension bar are fixed 160 cm away from the vertical pole so the trailer 135 platform does not appear in the FOV of the Ts,ground sensor. The measurement interval was set to 7.5 seconds and data were logged every 15 seconds as the arithmetic mean of two observations. The measurement locations in each street were visited consecutively in the same order in a rotational principle. Within one 140 hour, we ensured a 4-minute measurement at all measurement locations in one street including the time to move the trailer between the locations and the rearrangement of the mobile climate station. After each 4-minute interval, i.e. while moving to the next location and rearranging the station, the logger was switched off. Observations were carried out throughout the day for several days in three different seasons (spring, summer and autumn) in the years 2016 and 2017 in each street (Table 2).
Since we only had one mobile climate station available, both streets were observed one after the other in each season. The 145 daily observation period in each season started approx. two hours after sunrise and ended two hours before sunset.
Since the conditions at each measurement location might change within one hour (heating/cooling, sunny/shaded), we varied the starting point of the rotation from day to day, meaning, one measurement location might be visited early in each hour on one day but late on the other, thus we can catch as much of the variety as possible.
We did not account for changing weather conditions within the season, meaning that we observed sunny and dry conditions as 150 well as wet and cold conditions. However, we had to interrupt the observations under harsh weather conditions such as heavy rain or strong wind to avoid damage on the electronic parts or if technical issues resulted in measurement problems. Hence, the samples for calculating hourly averages per season and measurement location might originate from different days and vary in size (Fig. 4). At the end of each observation day, the data was read out and edited manually, e.g. to delete data of periods during which the logger was only switched on to check the device or by accident. We created one metafile for each street and 155 season containing the dates of the observation days, the number of rotations and the starting point of the day as well as if locations had to be skipped in a specific hour which happened mainly because the observations had to be interrupted, started late or ended early.    We used two reference climate stations for permanent climate observation. One is located on a flat roof approximately 15 m above street level and 2.5 km distance south-west from the study area in a similar urban area. It observes Ta, rh, K↓ and u continuously with a time step of one minute. The second reference station observes K↓ with a 10-minute time step and is 170 located on a high-rise, 52 m above ground, 2 km distance north from the study area. We used the K↓ data from the high-rise station because we had foggy conditions in winter and spring in the morning hours at the other station while in the streets, we observed clear sky conditions. The continuous reference observations allow to correct for the changes in the system over time when comparing the microclimatic conditions between the single measurement locations. By choosing reference stations which are also located in the city, we avoid observing an urban-rural difference of the atmospheric condition (Nunez et al., 2000;175 Blankenstein & Kuttler, 2004) which is not subject of this study.
In addition to the meteorological observations we derived the sky view factors Ψsky for each measurement location in each season by taking pictures pointing vertically towards the sky using a NIKON D5100 camera with a SIGMA 4.5 mm F2.8 EX DC fish-eye lens with 180° opening angle. The pictures were taken at 115 cm height which is the same as for the upward pointing sensors. We used ImageJ (https://imagej.nih.gov/ij/index.html, last visited 13 July 2020) software to derive binary 180 images with white pixels representing sky and black pixels representing obstacles (example in Fig. 5). We achieved this by setting thresholds in the brightness of the pictures and/or by rendering the obstacles manually. Ψsky was then calculated using the RayMan model (Matzarakis et al., 2007;Matzarakis et al., 2010) which relates the number of sky-pixels to the total number of pixels in the image, considering the image is representing a hemisphere.

Data Analysis
With the data set created with our observations we were able to calculate hourly potential evaporation rates for the measurement locations (Ep,s) and corresponding hourly potential evaporation rates for the reference station (Ep,r). We treated the mean of 190 each 4-minute measurement as a representative sample of the hourly mean. We selected the corresponding reference observation at the same time and treated it as an hourly mean instead of working with the "real" hourly mean at the reference station. Giving each observation at each measurement location its "own" reference value avoids mixing temporal and spatial signals. For the 1-minute reference observations we took exactly the same minutes in which the mobile observation took place  For all measurement locations and the observations at the reference stations, FAO-56 Penman-Monteith reference evapotranspiration (Allen et al., 1998) was calculated with Eq. (1). Assuming that most urban green spaces consist mainly of well-maintained turf grass, the FAO-56 Penman-Monteith reference evapotranspiration (evapotranspiration "from an extensive 205 surface of green grass of uniform height, actively growing and adequately watered" (Allen et al., 1998)) seems to be a suitable estimator for the potential evapotranspiration from these surfaces under the given atmospheric conditions. For simplifying the denotation later, we refer to it as Ep:  Parameters characterizing the surface of the measurement locations were kept constant representing a reference grass surface independent of the real surface at each location to allow comparison at all locations independent of the mix of real surfaces.
Consequently, differences in Ep among measurement locations originate from differences in meteorological conditions. 220 Additionally, we adapted Eq. 1 to not only observe the impact of the climate variables but also the longwave radiation influence of each location from buildings and trees. In Allen et al. (1998) the net outgoing longwave radiation L* is modelled on the basis of Ta, rh and K↓ without differentiating between incoming and outgoing longwave radiation (L↓ and L↑ respectively): * = * ( + 273.15) 4 * (0.34 − 0.14 * √ ) * (1.35 The clearness index is defined as cc = K↓r/K↓0 where K↓r is solar global radiation observed at the reference station and K↓0 is the exoatmospheric shortwave radiation at a horizontal surface (Offerle et al., 2007). With rearranging Eq. (2), L↓ and L↑ could be modelled separately resulting in L↓ being the atmospheric counter radiation for an unobstructed hemisphere: εgrass is the emissivity of a grass surface according to FAO-56 Penman-Monteith reference evapotranspiration (Allen et al. 235 1998) and was set to εgrass = 0.98 (Matsui & Osawa, 2015). Input for L* and L↓ was taken from the reference stations as the measurements are not influenced by surrounding objects and we assume that the atmospheric conditions are the same for the whole city area (Blankenstein & Kuttler, 2004).
In a next step, we included the longwave input from the urban surroundings in the calculation of incoming longwave radiation by using the observed infrared radiation surface temperatures. The infrared sensors measured the integrated infrared radiation 240 surface temperature for all "seen" surfaces (Ts). At some measurement locations, the lateral infrared sensors also "saw" the ground, which in relation to the radiation balance represents an outgoing term of radiation, while we were interested in the incoming longwave radiation. Therefore, we had to subtract the part of the infrared radiation surface temperature originating from the ground. We took additional fish eye photos from each cardinal direction and corrected them for a 90° opening angle to represent the FOV of the infrared sensors (Fig. 7). We calculated the fraction of the ground in the FOV and refer to it here 245 as the ground view factor of the infrared sensors (Ψground). We calculated Ψground by simply relating the number of pixels showing the ground to the total number of pixels of the "flat" circle.

250
Using Ψground and Ts,ground observed by the downward pointing infrared sensor, it was then possible to subtract the infrared radiation surface temperature of objects and sky (Ts↓). This was done for each sensor at all locations for each time step with as a transformation of The mean "incoming" infrared radiation temperature for the whole hemisphere at each measurement location ( ↓ ̅̅̅̅ ) can then be derived as the arithmetic mean from the four cardinal directions and the upward pointing sensor: Since the ground surface cannot be seen by the upward pointing sensor, the observed Ts is equivalent to Ts↓ for this sensor. We finally calculated incoming longwave radiation at the measurement locations (L↓s) by: 260 with εobj being the emissivity of the surrounding objects. We selected εobj = 0.97 on the basis of a study conducted by Verthegy & Munro (1989) who measured the longwave emissivity of a variety of surface materials.
Modelling Ep,s with a separate term for L↓s instead of the net radiation given in Eq.
(2) is necessary because otherwise K↓s, which is highly influenced by the shading of buildings and trees, would lead to a wrong calculation of the clearness index and 265 consequently to wrong estimations of net longwave radiation at the measurement locations (see Eq. (39) in Allen et al. (1998) and its description). As recommended by Allen et al. (1998) the minimal wind speed was set to 0.5 m/s. All calculations were done for hourly time steps assuming the 4-minute-measurement being representative for the hour the measurement was taken in. If not mentioned otherwise, parameters were taken from Allen et al. (1998)  To investigate the behavior of Ep in the street (Ep,s) in relation to the reference (Ep,r) we decided to display the results as the difference between Ep,s and Ep,r relative to the absolute Ep,r value and call it the relative difference of Ep with: If , < 0 or , < 0 there are condensation conditions at the reference station or in the street, respectively. 275 To derive average daily sums of K↓ and Ep (for street and rooftop), we first calculated for each measurement location in each season the average hourly values and summed these up to a daily (daytime) sum. With these, we calculated daily δK↓ and δEp according to Eq. (8).
When substituting Ep,s by Ep,OAAT in Eq. (8) we receive δEp,OAAT showing the relative difference between Ep,OAAT and Ep,r. 280

Mean diurnal variations of Ep rates derived from continuous reference observations during each observation period show
expected values for our region (Fig. 8). It is noticeable that Ep rates in spring during the ES observation period were relatively high due to consistently sunny and warm weather conditions (Table 3). The days (or half days) chosen for mobile data collection were overall representative for each observation period. During the observation periods in HS, we slightly 285 overestimated Ep (Table 3). For observations in ES in summer, we unintentionally selected days that were sunny in the morning but became cooler and cloudier in the afternoon which led to an underestimation of afternoon Ep rates. Daily observation durations in spring were short compared to summer and autumn or rather started and ended too early since observations were not distributed symmetrically around the midday maximum.

±0.1
The comparison between street and reference observations of the different input variables showed no significant difference for Ta and rh (displayed and tested as vapor-pressure deficit), with values distributed evenly close around the 1:1-line for all three 300 seasons (Fig. 9). We used a one-sided t-test to test if the street observations of each variable (both streets, all three seasons) are different to its observed mean at the roof top stations. Wind speed in the streets was generally lower but sometimes higher and L↓ in the streets was nearly always higher than at the reference station. The largest influence of the urban surroundings can be seen for K↓, where most of the street observations are below the reference values. The differences between reference and street observations are significant at the 5% level for u, L↓ and K↓.  The strongest correlation between meteorological variable and derived Ep can be observed for K↓ with a Spearman's rho of rK↓,s = 0.93 for the street observations and rK↓,r = 0.96 for the reference observations (Fig. 10). For all other variables, we 310 calculated positive, but weaker correlations. In the streets, the correlation between L↓,s and Ep,s with rL↓,s = 0.62 is very similar to that for vapor pressure deficit (r(es-ea)s = 0.69) and air temperature (rTa,s = 0.67). We found the weakest correlation between us and Ep,s with ru,s = 0.33. For the reference observations we found very weak correlations between Ep,r and L↓,r with rL↓,r = 0.41 and wind speed with ru,r = 0.43. Correlations are quite strong between Ep,r and vapor pressure deficit (r(es-ea)r = 0.84) and air temperature (rTa,r = 0.81). Between street and reference observations, the correlation coefficients for L↓ differ the most. All 315 correlation coefficients are lower for the street than for the reference observations, except rL↓, which is higher for the street observations. https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License.

top left corner show Spearman's rho correlation coefficient.
Overall, Ep,s is lower than Ep,r for nearly all measurement locations in all seasons throughout the day which is indicated by negative values for δE p ̅̅̅̅̅ (Fig. 11). The lowest δE p ̅̅̅̅̅ (mean hourly) values from each season and each street range from -1.01 (ES,summer,v_S3,7:00h)  In addition to the observed distinct diurnal variation of δEp, also δK↓ and ΔTa showed diurnal variations that were dependent on the position of the measurement location. The diurnal variation of shortwave radiation at the different measurement locations represents the shading by buildings and trees. For example, in HS on a sunny day in summer, δK↓ at v_W1 rises after 12:00h when the sun emerges from the trees and drops after 13:00h, when the sun disappears behind the building (Fig. 12). At 340 n_W2, where no trees are shading the sun, the sun emerges already at around 09:00h which causes an earlier rise in δK↓ compared to v_W1. Consequently, the measurement locations show different diurnal patterns of ΔTa due to different inputs of shortwave radiation: On a hot and sunny summer day, we observed the largest difference in ΔTa at 12:30h, when ΔTa at v_E1 (which was shaded by trees and by a building in the morning) was 2.1°C below ΔTa at n_W2 (Fig. 12). Three hours later at the same day, we found a similar large difference in ΔTa with v_W1 being the cooler site with ΔTa being 1.8°C below ΔTa at 345 n_E1. Since the two locations with the biggest differences between ΔTa are in different street sections and additionally, on opposite sides of the road, we can assume that this maximum "cooling effect" is caused by both, shade by vegetation and shade by building.  In order to quantify the high sensitivity of Ep to changes in K↓, we applied a linear regression between δK↓ and δEp (Fig. 14).
We excluded all cases when δK↓ > 0 from the regression analysis because we assumed these cases are mainly affected by the measurement design (shading by clouds at the reference station but not in the street canyon). We established the linear 360 regression with normalized Ep,r rates (scaling between 0 and 1) to give more/less impact to observations in seasons, where potential evapotranspiration is actually higher/lower and therefore plays a bigger/smaller role in the annual water balance.
Additionally, the relationship of average daily δK↓ and δEp for each measurement location in each season was determined (Fig.   14). δK↓ ranges between -0.96 and -0.00 for hourly, and between -0.85 and -0.40 for average daily values. For both linear regressions with hourly and daily data we achieve very good fits (R²=0.94/0.96, respectively) with slopes close to 1 365 (b=1.07/1.01; p<0.01) and similar intercept (a=0.08/0.05; p<0.01).
This procedure allows to calculate Ep,s at any location in a city based on simulated (derived from the simulated sky view factor (e.g. Middle et al., 2018) or observed short wave time series and observations at a reference climate station to derive Ep,r.

Short wave radiation
The observed shading (δK↓) at each measurement location represents the sun path plotted in the binary fish eye images very well (Fig. 15). However, the mean diurnal variation of δK↓ at one measurement location may not represent the sun path exactly. This might be due to the position adjustments of the trailer when parking cars were blocking the target location. In special cases, when the sky was partly clouded, we observed cloudy conditions in the street but clear sky conditions at the roof top 380 station during the 4-minute-measurment interval. In such a case we got a low δK↓ even if there was no shade created by trees or a wall. Vice versa, we got positive δK↓ when we had cloudy conditions at the roof top station, but sunny conditions in the streets.

Long wave radiation/ infrared surface temperatures
The longwave radiation observations and evaluation method presented in this study is a rough approximation to direct longwave radiation measurements and inhibits several uncertainties. Errors in estimating incoming longwave radiation as described in Eq. (3)-(6) might be induced by taking ground surface infrared radiation temperature observed at one small spot 390 at one measurement location as representative for the entire ground seen by all four lateral sensors: In Eq. (4) and (5), we used Ts,ground to correct the bulk surface temperature observed by the lateral pointing sensors for the fraction contributed by the ground appearing in their FOVs. But the fractions of ground seen by the lateral sensors might have completely different infrared radiation surface temperatures due to vegetation or deviating antecedent expositions to shortwave radiation. When the ground screened by the lateral sensors is overall warmer than the observed Ts,ground, L↓s is overestimated and vice versa. 395 When calculating the mean incoming infrared radiation surface temperature ↓ ̅̅̅̅ (Eq. 6), the upper parts of walls and trees and the lower parts of the sky are overrepresented since they appear in one or multiple lateral sensors and in addition in the upward pointing sensor. This overlapping of surfaces is caused by the technical issue of the upward pointing sensor being fixed lower on the trailer than the lateral pointing sensors. We expect this error to be small compared to the error induced by the ground infrared radiation temperature correction. 400 We derived ↓ ̅̅̅̅ from the four lateral and the upward pointing sensor because we wanted to represent the hemisphere and the sky view factor at the measurement locations. But the so derived ↓ ̅̅̅̅ leads to an underestimation of L↓s in Eq. (7) because the sky "seen" by the upward pointing sensor overall decreases ↓ ̅̅̅̅ compared to ↓ from the lateral sensors, where the proportion of walls is higher. Underestimation of L↓s is larger for measurement locations with higher SVFs. However, despite these uncertainties in our observation and evaluation method, the L↓s estimates seem to be plausible. Comparing L↓s with L↓r, a clear 405 influence of the urban surroundings on incoming longwave radiation with L↓s being nearly always above L↓r becomes visible ( Fig. 9). This positive contribution of horizon obstructions to incoming longwave radiation in general is also described in other studies (Blankenstein & Kuttler, 2004;Nunez et al., 2000;and Verseghy & Munro,1989). Therefore, the scatter in the L↓s observations for each season (in addition to changes in atmospheric counter radiation) is mainly related with the different sky view factors at the measurement locations. We found overall negative correlations between Ψsky and ΔL↓ within each street in 410 each season, comparable to those described by Blankenstein & Kuttler (2004), Nunez et al. (2000) and Verseghy and Munro (1989). Since we observed only daytime incoming longwave radiation, we identified an influence of the exposition of the measurement locations and their adjacent walls to K↓. Such an influence was also mentioned by Verseghy and Munro (1989).
For example, for sunny conditions in summer in ES, the direct solar radiation to the northern wall in the non-vegetated section caused higher ΔL↓ at n_N1 and n_S1 compared to v_N3 and v_S2 which had very similar sky view factors but were shaded 415 by the vegetation (results not shown). In contrast, when the sky is very cloudy, the atmosphere has a higher emissivity compared to clear sky conditions in the same season while the surface temperature of the walls stays relatively cool due to reduced short wave radiation input. Consequently, ΔL↓ for cloudy conditions (cc < 0.5) was close to or little below zero at all measurement locations in all seasons and was hardly dependent on Ψsky.
Further validation and investigation of our longwave radiation observation and estimation method would be interesting but is 420 beyond the scope of this study. Since Ep was second most sensitive to changes in δL↓, we recommend to further investigate the effect of longwave radiation emission from the surroundings when investigating Ep in an urban environment.

Wind
Wind speed in the streets was usually below roof top wind speed. This was expected considering the additional roughness in the streets compared to the roughness at the roof top station (Nakamura & Oke, 1988). Sometimes, wind speed in the streets 425 exceeded rooftop wind speed (Fig. 9). Due to the spatial distance between the rooftop station and the two streets and the short measurement intervals of four minutes, wind gusts may only have been observed in the streets but not at the roof top station (but also vice versa). Another reason for positive Δu might be traffic at calm days. It is also possible, that roof top station and https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License. streets in Freiburg might be situated in two different mountain-plain wind systems leading to different wind dynamics, especially in the morning and in the evening. Another reason could simply be an error in correction of observation height of 430 reference wind speed observations. Nakamura and Oke (1988) observed wind speed in Kyoto, Japan, in August 1983 andAugust 1984 in an E-W oriented canyon and compared it to observations from a reference station on top of a building directly adjacent to the canyon. For their overall measurements they found us = 2/3*ur. But they also observed positive Δu values especially for low velocities of ur < 1 m -1 even though their reference data was taken right above the canyon, was not corrected for measurement height and their data was analyzed as 10-minute means from 1-minute measurements or 10-second 435 measurements.

Air temperature
The cooling effect caused by shading that we observed in HS in summer, is similar to that reported by Shashua- Bar & Hoffman (2000). They investigated the cooling effect of trees in Tel Aviv during a sunny and hot period. They compared air temperature within several streets with trees against air temperature observations at relatively open spaces at the entrance of each street. 440 For two N-S-oriented streets characterized as urban canyons with trees along the sidewalks, they observed the largest difference in air temperature for both streets at 15:00h (solar noon was at 14:20h) when ΔTa was -1.3 K for one and -2.3 K for the other street. This is very similar to our findings. Shashua- Bar & Hoffman (2000) also found that the cooling effect of green spaces and vegetated streets is perceivable up to 100 m from the site boundary. They observed an exponential decay of the cooling effect from the border of the green area into the surrounding area which for example was an intersecting road without trees. 445 This means that air temperature in the non-vegetated section in HS might be affected by the cooler air in the vegetated section and that the cooling effect of the trees in HS might be more intense when compared to a non-vegetated section further away from the vegetated section.

Potential evapotranspiration
Sensitivity analyses have already been applied to Eq. (1) in several other studies. In most of these studies, the focus is on long 450 term changes in Ep as a reaction to climate change (Ambas & Baltas, 2012;Bormann, 2012;Gong et al., 2006;Sharifi & Dinpashoh, 2014;Tabari & Talaee, 2014) or on potential errors of Ep estimations due to inaccurate observations of input variables (Beven, 1979;Bois & Pieri, 2005;Debnath et al., 2015). The OAAT approach is a common method to perform a sensitivity analysis. One input variable may be changed within a range of ± 20 % with an interval of ±5 % while the other variables are kept constant (Gong et al., 2006;Sharifi & Dinpashoh, 2014;Tabari & Talaee, 2014). In contrast, after exchanging 455 reference against street observations during our OAAT approach, we observed changes in wind speed and incoming shortwave radiation that were mostly below -20% and rarely positive. Changes in incoming longwave radiation were mostly positive with a maximum change of + 23 % (Fig. 9). This shows, that the assumed changes of the input variables with a range of ± 20 % are not suitable for a sensitivity analyses of Ep in an urban context. To our knowledge, the sensitivity to L↓ has not yet been investigated directly in other studies. 460 Beven (1979) studied the sensitivity of Penman-Monteith actual evapotranspiration (Ea) estimates of a grass surface on changes in the input variables on a sub daily time scale. For his analysis, Beven (1979) took the changes in input variables and in Ea that appeared from time step to time step with an hourly time interval. For daytime data, Beven (1979) found that Ea was most sensitive to changes in net radiation and that the seasonal variation in the sensitivity coefficients was small relative to changes in predicted Ea. The mean monthly mid-day sensitivity coefficient for hourly net radiation found by Beven was around 0.7 for 465 the whole observation period from May to November 1976. Since the observations took place at an unobstructed site, net radiation may have been mainly influenced by changes in the incoming shortwave radiation flux due to changes in cloud cover.
We did not analyze the sensitivity of Ep,r to the reference input variables or to net radiation comparable to Beven's (1979) approach but the very high correlation coefficient between Ep,r and K↓,r (rK↓,r = 0.96) provides an indication to the sensitivity https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License.
of Ep to variations in K↓. When considering the street observations, short wave radiation becomes even more important since 470 the correlation coefficients for all other variables except incoming longwave radiation are lower compared to correlation coefficients between Ep,r and its input variables.
Our findings reflect the results of the study conducted by Litvak & Pataki (2016) who found high sensitivity of ET0 to shade provided by trees. They calculated daily kmc values from ET0(in situ) = kmcET0 based on the LCM method (Costello et al., 2000), where daily ET0(in situ) was derived from in situ meteorological measurements on eight urban lawns and daily ET0 was derived 475 from a reference weather station. According to the regression approach by Litvak & Pataki (2016), they derived a δK↓ = -0.44 for 83.7 % tree cover. This lies at the upper end of the range of our observed daily δK↓ values and means that daily K↓ on a greenspace 83.7 % tree cover would be expected to be 56 % of K↓r. This seems quite plausible since shade by trees is less "intense" than shade by building walls and in addition, when the sun is low, short wave radiation may pass below the treetop.
For unshaded lawns, Litvak & Pataki (2016) did not find a significant difference between ET0(in situ) and ET0. We did not have 480 measurement locations that were unshaded during the whole day but for hours in spring and summer with δK↓ > -0.05, δEp ranged between -0.16 and 0.17 and the difference between Ep,s and Ep,r was not significant as well (results not shown).
We did not investigate the sensitivity of δEp during nighttime hours, when shortwave radiation cannot play a role in governing Ep rates. But the contribution of nighttime Ep to total daily (24h) Ep is very low (Fig. 8 and Table 3) and the error when using Eq. (10) to simulate daily (24h) Ep,s rates is expected to be very small. When estimating Ep,s with an hourly time step, we 485 suggest to use reference Ep for nighttime hours.
The influence of changes in the other variables on Ep was only small. Their mixed effect on δEp is represented by the intercept of our hourly and daily regression curve, respectively. This mixed effect might be changed for areas with a different street design (wider streets, more/less vegetation, heterogenic arrangement of buildings) or in a different climate zone. Especially in cities that are very densely built and where streets are shaded most of the day, Ep might become more sensitive to changes in 490 other variables than K↓. On the other hand, we can assume that areas between buildings in those cities do not contribute very much to evapotranspiration. The sensitivity of Ep to changes in the input variables also changes with different climate. Since changes in K↓ will be the most intense within an urban area compared to changes in the other variables, we assume that the overall relationship between K↓ and Ep will not be changed, but that the mixed effect of the other variables may be altered.
More observations are needed to investigate a wider range of urban conditions. Especially sites that are shaded/never shaded 495 for the whole day should be included in future studies to complete the range of daily δK↓.

Conclusion
We collected a unique and comprehensive data set of urban micro-meteorological variables that are needed to calculate FAO-56 Penman-Monteith reference evapotranspiration at a high spatio-temporal resolution in an urban environment. This data set allowed for analyzing the influence of urban microclimatic conditions in an urban canyon on potential evapotranspiration. 500 According to our results, potential evapotranspiration is most sensitive to changes in incoming shortwave radiation. Changes in incoming shortwave radiation on street level are induced by shading of trees and buildings which lead to an overall decrease in potential evapotranspiration in the streets compared to potential evapotranspiration at a reference station on a rooftop. The strong sensitivity to changes in incoming shortwave radiation enabled to estimate the change in potential evapotranspiration in dependence of the change in incoming shortwave radiation as the only input variable. Incoming shortwave radiation on 505 street level can easily be simulated with a digital elevation model of the city of interest and a common GIS software (e.g. with the solar radiation tool by ArcGIS). The dependence of potential evapotranspiration on street level on changes in incoming shortwave radiation causes a strong variability in the diurnal variation of potential evapotranspiration at the different measurement locations in the street which is consequently affected by their exposition to incoming shortwave radiation. This should be taken into account when considering green or blue infrastructure as tools for heat mitigation in cities. In summary, 510 https://doi.org/10.5194/hess-2021-24 Preprint. Discussion started: 4 February 2021 c Author(s) 2021. CC BY 4.0 License.