Impact of shading on evapotranspiration and water stress of urban trees

Evapotranspiration of urban street trees is essential in mitigating urban heat islands due to its cooling effect. However, current shifts in rainfall and temperature regimes towards drier and hotter periods in Central Europe have caused substantial water stress for street trees. Quantifying and subsequently managing these changing dynamics as well as estimating evapotranspiration and water availability is necessary but at the same time extremely challenging in urban environments. Both dynamics are influenced by soil sealing and complex shading patterns of the surrounding street canyon, which vary on a small spatial scale as a function of the canyon layout and orientation. In the present study, the diurnal patterns of six typical urban shading types for street trees were derived by considering a large set of street orientations, widths and tree positions within the street canyon. A shading model was integrated into a hydrological urban tree model to assess the impact of those shading types on diurnal patterns of radiation and evapotranspiration rates calculated using the Penman–Monteith approach and the resulting soil moisture conditions for several vegetation seasons and water‐supply scenarios. The modelling results showed that the six shading patterns significantly influenced the simulated hourly, daily and seasonal potential and actual evapotranspiration rates and water availability. Shaded trees have a substantially reduced, simulated water stress period, regardless of initial water supply, and are able to provide a longer‐lasting cooling function during dry periods due to higher evapotranspiration rates later in the summer season.


| INTRODUCTION
Urban ecohydrology remains of great interest due to the complex interactions of the heterogeneous built environment and the urban vegetation. Street trees in highly dense areas are of specific interest, as they are exposed to significantly different shading patterns (Gong et al., 2019) and high water stress during dry periods. In temperate zones, street trees are particularly vulnerable to summer heat waves and extended dry periods due to their limited adaption (Haase & Hellwig, 2022). The consequences of water stress are manifold, including limited tree growth (Rötzer et al., 2019), fitness and life expectancy (Bréda et al., 2006;Haase & Hellwig, 2022), reduced evapotranspiration (Rahman et al., 2017;Rötzer et al., 2021) and cooling potential (Adams et al., 2012;Bowler et al., 2010). Current measures, such as manual irrigation, are limited and only applied during extreme conditions in temperate zones in Central Europe (David et al., 2018;Dickhaut & Eschenbach, 2018;SenUVK, 2021). To improve irrigation management and avoid the risk of vitality losses and mortality of urban trees, it is necessary to clearly understand urban tree water demand, considering shading patterns and sitespecific effects (McDowell et al., 2008;Schütt et al., 2022;Wessolek & Kluge, 2021).
Microclimatic studies demonstrate that within a street canyon, short-wave radiation, both diffuse and direct components, is strongly influenced by shading (Mei & Yuan, 2022). To characterize shading within street canyons, the sky view factor (SVF) is used to describe the reduction in diffuse radiation by the ratio of built-up area to open sky (Johnson & Watson, 1984). A different binary approach additionally reduces the direct radiation to zero during shading periods (Gong et al., 2019;Ross, 1981). With the binary approach, it is possible to include the effects of shading based on street canyon orientation, sun elevation, building height and tree position.
Evapotranspiration (ET) is a key variable to quantify water flow and stress at the atmosphere-soil-plant interface (Allen et al., 2006;Olmedo et al., 2016). In many urban tree models, evapotranspiration is also used to evaluate the general cooling effect (Pace et al., 2021), including a reduction of global radiation (Grylls & van Reeuwijk, 2021;Hörnschemeyer et al., 2021;Wessolek & Kluge, 2021) or the occurrence of water stress (Revelli & Porporato, 2018;Rötzer et al., 2021;Vico et al., 2014). To our best knowledge up to date, no monitoring study has quantified the effects of shading on the water stress of street trees. For example, Vico et al. (2014) estimated the daily cooling capacity and irrigation needs of individual street trees, accounting for soil water storage, tree water requirements and different growing conditions. However, the effects of shading on evapotranspiration were not considered in calculating the water balance. Wessolek and Kluge (2021) developed hydro-pedotransfer functions (HPTFs) to calculate the annual water demand, potential ET (ETp), actual ET (ETa) and water stress of street trees. The function applies to different tree ages, species, soil sealings, soil types and global radiation is reduced with the SVF. The HPTFs provide a good approximation of the annual water balance of street trees. However, the critical water stress periods during the vegetation period cannot be identified. Finally, Hörnschemeyer et al. (2021) used the SWMM model to quantify the effect of shading on ETa for urban conifer areas by employing a shade factor that reduces ETa depending on monthly solar elevation.
In conclusion, existing water models for urban trees do not (Vico et al., 2014) or only partially include the effects of shading (Hörnschemeyer et al., 2021;Wessolek & Kluge, 2021). None of the studies considered varying shading patterns typically found within street canyons, which affect global radiation and potential evapotranspiration on a diurnal time scale. Therefore, we argue that different diurnal shading types need to be developed. Through this study, the effects of the shading patterns on the water balance of street trees were evaluated to identify the critical timeframes and site conditions for water stress in the urban environment.
We hypothesized that the daily and seasonal evapotranspiration rates are significantly influenced by shading and that street trees exposed to direct radiation experience considerably larger and longer lasting water stress than shaded trees. Therefore, by applying the contrario argument, shaded trees should be better adapted to heat and drought periods and may also provide their cooling function more efficiently than exposed trees. To test these hypotheses, the following objectives were formulated: We (i) conceptualized typical urban shading types for street trees, (ii) quantified the impact of the various shading types on diurnal patterns of global radiation and potential evapotranspiration as a function of different sky conditions, (iii) quantified the impact of the urban shading types on actual evapotranspiration and soil moisture rates comparing three cases, 'wellwater-supplied', a 'drought-induced' and a hypothetical 'legacy effect' throughout the vegetation period of four recent years, and (iv) assess the impact of typical urban soil sealing for the three cases.

| Urban tree model
To determine the effect of shading on the water supply, a hydrological model (URbanTRee; Figure 1), including extensions and adaptions for individual street trees in typical urban settings, was further developed after preliminary work by Kirmaier (2020). URbanTRee calculates potential and actual water losses by evapotranspiration on an hourly time step based on the Penman-Monteith equation (Allen et al., 2006) using a subroutine of the R package 'Water' created by Olmedo et al. (2016) combined with a bucket model to calculate the soil moisture storage in the upper soil zone in R, version 4.1.2 (R Core Team, 2021). Moreover, it includes routines for interception derived after (Gash, 1979), infiltration calculation based on a constant runoff factor and percolation losses (all model equations of the URbanTRee model are given in Appendix A). The model domain of URbanTRee is given by the crown size and a model layer defined by the rooting depth of the street tree. URbanTRee considers the heterogeneous functioning of urban surfaces, such as open tree pits, pavement and asphalt surfaces, and calculates runoff, infiltration and changes to soil water storage separately for each surface and associated storage fraction.

| Urban shading submodel
The ShadingType submodel was integrated into the URbanTRee model by decreasing both parts of the global radiation rate R G ð Þ, direct radiation R D ð Þ and diffuse radiation R Diff ð Þ, to calculate ET during shading hours: Direct radiation R D is reduced to zero during shading hours, whereas diffuse radiation R Diff is reduced by the SVF, which can take values between zero and one and varies depending on the density of surrounding buildings (Johnson & Watson, 1984

| Identification of diurnal shading types
The geometric alignment of typical urban properties and sun elevation was used to identify typical urban shading types. Hourly shading patterns were derived for four different street orientations, a wide and narrow street, and for tree positions on either side of the street. The sun elevation α ð Þ and angle of the vector 'building-top to treereference-height' β ð Þ are being compared: where H is the building height (m), h is the tree reference height (m) and D is the distance from the building (m) (Figure 2). The temporal change in azimuth (γ) was included in the calculation of the two angles: To calculate the azimuth and solar elevation, the R-package 'solarPos' was used (Doninck, 2016). Here, the building height is defined by a typical Berlin eaves height of 22 m (Böhme et al., 2020), and the tree reference height refers to the midpoint of the tree crown, which was assumed to be 3 m. For simplification, we considered trees to be completely shaded or completely exposed to sunlight.

| Input data and model parametrization
Hourly climate input data used originated from the secular station Berlin-Potsdam (DWD Climate Data Center, 2022). In Berlin, the climate is described as warm temperate and humid continental (Köppen and Geiger: Cfb after Kottek et al., 2006), with an average precipitation sum of 570 mm/year. In this study, the period 2017-2020 was  (Table A2).

| Model scenarios for the analysis of shading impact
Different modelling approaches were applied to investigate the influence of urban shading types on global radiation, ETp and ETa rates and soil moisture.  F I G U R E 2 Schematic illustration of sun path (α) and street geometry (vector building-top to tree-reference-height, β) effecting shading patterns: shading occurs when α < β.

| Identification of urban shading types
The simulation to identify typical urban shading types was performed for different months during the vegetation period, but no substantial differences were observed. In the 16 scenarios, the sun position resulted in different shading patterns (Figure 3), which were clustered into six groups: sun all day (≥9 h), no sun (≤2 h), afternoon sun (3-5 h, after 13:00), morning sun (3-5 h, before 13:00), midday sun (3-5 h, after 10:00 and before 15:00) and morning and evening sun (>2 h, before 10:00 and after 15:00).
By applying the urban shading model, the global radiation was reduced during the shaded hours. Figure 4 shows that the diurnal pat- 3.2 | Impact of shading on global radiation and potential evapotranspiration rates Considering the daily cumulative global radiation and daily sum of ETp during the entire vegetation period (Figure 7), the global radiation of shading type A on clear sky days was seven times higher than that of type B and two to three times higher than that of types C-F. On cloudy days, type A was up to three times higher than types B-F, and on grey sky days up to two times.
The difference in ETp was less evident; however, the mean ETp was still two times higher for type A compared to type B and 1.3-1.6 times higher compared to types C-F. On cloudy and grey sky days, the difference between all shading types compared to A was negligible.
F I G U R E 3 Shading patterns for 16 different urban settings in April and June. True indicates exposure to sunlight, and false the shaded hours.
3.3 | Impact of shading on actual evapotranspiration rates and soil moisture dynamics

| Comparisons within the open soil 'well water supplied' case
Modelling results showed that actual evapotranspiration (ETa) was highest for type A (up to 10 mm/day) and lowest for type B (up to 7 mm/day) at the beginning of the growing season (April) (Figure 8).
Throughout the vegetation period, the dynamic changes, as the water content for type A decreased more rapidly than for type B. ETa year differed from one another considerably (Figure 11).

| Comparisons within the open soil 'droughtinduced' case
In the water-stressed case, the modelling results showed significantly reduced ETa rates for all shading types, with a maximum ETa of approximately 5 mm/day. The highest ETa values were mainly found in shading type A, and only when the permanent PWP was reached (mid-May), ETa was higher for shading type B (Figure 9).
In all years, the FDD was reached between the 135th-150th DOY in shading type A and up to 2 months later in type B (2020) ( Figure 11). On average, shading types B-F reached the FDD 1-12 days later than type A.
The SDD in shading type A ranged between 25 (2017)  shorter. The highest deviation in SDD occurred, with 1 month less, in type B (2020) and the lowest, with 5 days less, in type D (2020).
Again, the ETa sum showed no significant difference between shading types, although the temporal occurrences were rather different ( Figure 11).  The FDD in shading type A occurred around the 150th-170th DOY, and in shading types B-F around 2-6.5 weeks later ( Figure 11).

| Comparisons within the open soil
The SDD in type A varied from 16 (2017)

| DISCUSSION
A modelling approach was used to evaluate cascading effects of shading on global radiation rates, modelled ETp, ETa and soil moisture availability for urban street trees under different climatic conditions.
The model output clearly indicated the impact of different shading types on simulated water availability of street trees in all three case studies (well water supplied, drought-induced and legacy effect).
Comparing the beginning of the water stress period of shading types B-F to shading type A, the response was least pronounced in the well water supplied case study with a delay of 1-12 days and most pronounced in the drought-induced case study with a of 2-8 weeks.
Although there were minor differences in the yearly ETa sums, the seasonal distribution of ETa was significantly influenced by shading: shading type A showed higher ETa than shading types B-F at the beginning of the growing and summer season, whereas shading types B-F frequently had higher values towards the end of the growing season, when they still had water available for transpiration. These ETa patterns were found in all three cases studies (well water supplied, drought-induced and legacy effect).
We intended to use our modelling approach for hypothesis build-

| Uncertainties
In our model, we used a soil hydrological modelling approach, which takes a completely different perspective on ETa calculation than micro-meteorological models (Robineau et al., 2022). The majority of micro-meteorological models for urban water and surface energy balances yield good temperature estimates within the urban canopy but have a poor representation in terms of hydrological processes (Järvi et al., 2011). The evapotranspiration flux is widely assumed to be proportional to the air-specific humidity gradient between the surface and a reference level (Masson, 2000), but the latter is provided by the meteorological model itself (Berthier et al., 2006). On the other hand, the effect of shading is presented in a better fashion, as they consider its effects not only on radiation but also on surface temperature, wind patterns and resulting air temperature within a street canyon (Mei & Yuan, 2022) as a function of aspect ratios, orientation and building materials (Athamena et al., 2018;Chen et al., 2020). It remains a challenge to couple hydrological and micro-meteorological models. One of the first attempts were made by Robineau et al. (2022) who described the effect of water stress of a street tree on the surrounding climatic conditions, but not the effect vice versa.
To adequately represent the impact of trees on the urban environment, the canopy reference area is a conversely discussed parameter (Wang et al., 2021). It can be represented by the leaf area index, single-layer or multi-layer approaches (Gkatsopoulos, 2017;Grylls & van Reeuwijk, 2021;Wessolek & Kluge, 2021). In our model, we used the horizontal canopy area (single-layer approach) as the reference for ET calculations. The single-layer reference indicates that, at a given hour, only part of the tree actively participates in transpiration. As a result, no further partial-shading scenarios were included in this evaluation-an assumption that might need further evaluation beyond this study.

| Future research
The results suggest that shading can be an advantage as it results in delayed and lower water stress and thus helps to provide a longer lasting cooling effect throughout the vegetation period. In evaluating the influence of shade in this study, we focused primarily on soil moisture and the resulting actual evapotranspiration of trees. Nevertheless, in future research, all benefits and detriments of shading need to be discussed in terms of CO 2 storage and biomass production (Rötzer et al., 2019), cooling capacity (Rahman et al., 2017) and life expectancy (Horváthová et al., 2021) of a street tree.

| CONCLUSIONS
After developing six typical urban shading types, we showed in our modelling study that daily and seasonal evapotranspiration rates of street trees were significantly influenced by those shading patterns.
We demonstrated that shading types B-F had a significantly reduced water stress period in comparison to shading type A, regardless of initial soil moisture contents at the beginning of the vegetation period in the three case studies. Thus, trees in shading types B-F provided a longer lasting cooling function during dry periods later in the summer season due to higher evapotranspiration rates and a more effective shading function because of improved tree health. Based on these results the next steps are the upscaling of shading types and water stress quantification to district and city scale by identifying the proportions of street trees that exhibit the six shading types and by estimating water supply or stress and ecosystem services of multiple street trees.
Several uncertainties remain regarding urban site conditions. A field campaign, which was guided by the modelling result, is on the way to substantiate the cascading effect of shading, direct and diffuse radiation, sap flow and soil moisture on diurnal to seasonal scales. In a long run, studies on water stress of street trees will aid to develop strategies for an effective irrigation management under a warming climate. A hypothesis for a future study might entail that with limited resources, shaded rather than exposed trees should be irrigated as they later retain their cooling function more efficiently in contrast to the former who transpire water and dry out rapidly.

CONFLICT OF INTEREST STATEMENT
The authors have declared no conflict of interest for this article.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.