Response of Near-Surface Meteorological Conditions to Advection under Impact of the Green Roof

: Due to rapid urbanization, the near-surface meteorological conditions over urban areas are greatly modulated. To capture such modulations, sophisticated urban parameterizations with enhanced hydrological processes have been developed. In this study, we use the single-layer urban canopy model (SLUCM) available within the Weather Research and Forecasting (WRF) model to assess the response of near-surface temperature, wind, and moisture to advection under the impact of the green roof. An ensemble of simulations with different planetary boundary layer (PBL) schemes is conducted in the presence (green roof (GR)) and absence (control (CTL)) of green roof systems. Our results indicate that the near-surface temperature is found to be driven primarily by the surface heat flux with a minor influence from the zonal advection of temperature. The momentum budget analysis shows that both zonal and meridional momentum advection during the evening and early nighttime plays an important role in modulating winds over urban areas. The near-surface humidity remains nearly unchanged in GR compared to CTL, although the physical processes that determine the changes in humidity were different, in particular during the evening when the GR tends to have less moisture advection due to the reduced temperature gradient between the urban areas and the surroundings. Implications of our results are discussed.


Introduction
The modern urbanization over the past several decades has significantly modified the types of land-use around the globe [1]. The changes in the surface thermal and hydrological processes due to urbanization have led to elevated temperature [2,3], changes in soil cover [4][5][6], variation in precipitation patterns [7], and modification of surface roughness [8,9]. The reduction of natural surfaces and vegetation due to urbanization causes the re-distribution of surface heat flux components: a greater loss of sensible heat but less loss of latent heat [4]. The higher surface and air temperature in urban areas when compared with rural areas, known as the urban heat island (UHI) effect [10,11], leads to a greater need for cooling energy by the urban population [12][13][14][15].
To respond to the potential threat of UHI, there are two major strategies that involve the construction of green infrastructure (e.g., urban lawn, tree, green roof) and the use of reflective materials (e.g., cool pavement, white roof) [16][17][18][19][20][21][22][23][24][25]. Roofs that constitute a high fraction of the exposed area can provide an excellent space to apply mitigation techniques in the urban area. Akbari and Rose [26] explored four cities in America and found that the roof areas range from 20% to 25%. The advantage of green roofs in the presence of plants on the top of a building is regarded as environmentally friendly and contributes positively to the building's energy efficiency. Green roofs have been shown to significantly mitigate the UHI effect by reducing near-surface temperature [27] and enhancing air quality [28] by increasing the evapotranspiration in urban areas and converting the available energy to latent heat. This mitigation mechanism over an urban area can be understood by looking at the surface heat flux components: G LH SH R net + + = (1) where Rnet represents the net radiation at the surface, SH is the surface sensible heat flux, LH is the surface latent heat flux, and G is the storage heat flux. The net radiation is expressed as where SWin and SWout are the incoming and outgoing shortwave radiation, and LWin and LWout are the incoming and outgoing longwave radiation. Unlike other strategies that change the albedo and thus reduce the net radiation, the nature of the green roof strategy is to enhance latent heat for given net radiation, thereby reducing the sensible heat flux and resulting in a reduction in atmospheric heating and heat storage over urban areas.
Many new urban parameterization developments and improvements have been made for the Advanced Research Weather Research and Forecasting (WRF-ARW) model [29], including the singlelayer urban canopy model (SLUCM) [30][31][32]. However, because of the poor representation of urban hydrological processes, the SLUCM has a larger bias in simulating the latent heat flux compared with other heat flux components [33][34][35]. Numerous efforts have been made to advance the performance of SLUCM in the WRF model by embedding five new urban hydrological processes [31,[35][36][37][38]: anthropogenic latent heat flux, the urban oasis effect, urban irrigation, evaporation from paved surfaces, and multi-layer roofs. A notable improvement of latent heat flux was found over cities after incorporating hydrological processes [37]. Li et al. [39] examined the effectiveness of green roofs with white roofs over the Princeton urban canopy model into WRF, although the impact of urban hydrological processes was not explored in their study.
The objective of this study is to explore the response of near-surface meteorological conditions to advection under the impact of green roof systems using high-resolution simulations of the WRF model with sophisticated urban parameterizations over Houston, Texas. Metropolitan Houston has developed tremendously over the past decades and has experienced a strong UHI effect [3,40,41]. Therefore, Houston seems to be an ideal place to quantify the impacts of green roofs on certain physical processes such as advection that may play an important role in modulating near-surface atmospheric conditions. We believe that our study and its approach have three major novelties: 1. The most significant novelty in this study is the estimation of the impact of green roofs in modulating the advection of heat, momentum, and moisture that influences the temperature, wind, and humidity over Houston. To the best of our knowledge, the impact of green roofs on advectionin particular, on momentum advection-has not been quantified before.
2. The impact of green roofs has typically been assessed using a single simulation (deterministic approach) in most studies [42][43][44][45][46]. To the best of our knowledge, physics-based ensemble simulations using green roofs have not been performed previously to study the role of advection in the urban environment, although Munck et al. [47] used three simulations which differ in the initialization of the drainage layer in the green roof setup. Ensemble members were obtained by the combination of two drainage layer parameter values with all the other substrate-drainage characteristic values (see Table 4 of [47]), which resulted in a total of 32 simulations per ensemble. Given that near-surface conditions over an urban area critically depend on the planetary boundary layer (PBL) schemes [48][49][50], we have used four different popular PBL schemes to construct our ensemble for the control (CTL) and green roof (GR) experiments which is a different approach than that of [47].
3. Previous studies on the impact of the green roof using the SLUCM have mostly ignored hydrological processes within an urban area. This has led to a poor simulation of surface latent heat flux [33][34][35]. The performance of SLUCM has been advanced by embedding five new urban hydrological processes [3,31,44,51] that were included in our simulations.
The rest of the sections are constructed as follows. Section 2 describes the model, data, and methods, followed by the discussion of the results in Section 3. A summary and conclusions are presented in Section 4.

Model
We use the SLUCM [31,32,37,52] available within the WRF model (version 3.7) with terrainfollowing coordinates [52]. The WRF model uses a fully compressible, non-hydrostatic modeling system that can be used at different spatial resolutions. The model domains are shown in Figure 1a with grid-spacings of 9 km (104 × 106), 3 km (190 × 196) and 1 km (280 × 262). The outermost domain is designed to be large enough to simulate any synoptic activity within the domain boundaries for the duration of the simulations. The innermost domain, DO3 (Figure 1b), includes the urban part of Houston and the observational stations. The model has 35 vertical levels from the surface to 50 hPa. The time step was 30 s for the outermost domain. The model output was taken every 10 min to capture the diurnal evolution of the urban atmosphere. All the simulations were integrated from 0000 UTC 24 August to 1800 UTC 26 August 2000. This period was chosen because August 25 was a day described by a stable air mass with weak convection [52,53]. This helps to avoid complexities associated with moist convection since our primary goal here is to evaluate the role of green roof systems on advection and how advection may influence near-surface meteorological conditions.

Simulations
We use four different PBL schemes available in the WRF model to construct an ensemble (Tables  2 and 3) since the simulations are arguably dependent on the PBL schemes used over the near-surface urban areas [48][49][50]63]. Further details about these PBL schemes can be found in [50] and [64], among others. To explore the mitigation effects of green roofs, we use multi-layer green roofs with 50% of the roof as green roof in the urban grid cell. The choice of 50% coverage is arguably more realistic than 100% coverage, which is too optimistic. Unless otherwise mentioned, the control (CTL) and green roof (GR) simulations are referred to as the ensemble mean of simulations without and with green roofs, respectively (Table 2). A comparison of CTL and GR is expected to provide a quantitative idea of the response of near-surface meteorological conditions to advection due to the use of green roofs. Same as control (CTL), but with multi-layer green roof systems To explore the extent to which the multilayer green roof can influence the advective processes

Data and Method
The 2 m temperature (T2) and 10 m wind (W10) observations were taken from the 12 Texas Commission on Environmental Quality (TCEQ) stations ( Table 4). The model output was hourly averaged to match the frequency of TCEQ observations. The urban land use data was taken from the 2001 National Land Cover Database (NLCD, 30 m resolution). The initial and boundary conditions were taken from the National Centers for Environmental Prediction (NCEP) final analysis (NCEP_fnl). Figure 2 exhibits the schematic urban grid cell with both impervious and pervious fractions. The impervious fraction over the urban area has buildings, tar roads, and pavements. The conventional roofs can transfer most of the incoming energy to sensible heat flux, thereby enhancing the air temperature near the surface and above. On the other hand, green roofs can mitigate the surface temperature through evapotranspiration. Net cooling will occur when the sensible heat is reduced, with an increase in latent heat if the net radiation remains unchanged. The green roofs in WRF for this study have four layers with a total depth of 50 cm, which consists of 15 cm soil layer of vegetation, 15 cm of growing layer, and 20 cm of concrete roof layer. For the pervious surface, the green surface is also part of an urban grid cell. The surface temperature over an urban cell can be calculated by area-averaged temperature, which is based on the surface temperature over the impervious and the vegetated area:

Green Roof Modeling
The impervious surface temperature is calculated as the area-averaged temperature from the roof and street canyon: The sensible heat flux over the urban grid cell is calculated in a similar way to surface temperature. The T2 is determined by the urban surface temperature and the total sensible heat flux (Htotal) from the impervious surface and the vegetated surface: where ρ is the air density, U2 is the 2-m wind speed, and Ch2 is the turbulent transfer coefficient. The calculation of T2 can be used as a representative temperature that human beings can feel [65]. In the WRF, the grid cells where the major land use category is one of the three urban categories (lowintensity residential, LIR; high-intensity residential, HIR; and commercial/industrial, COI) are considered as the urban grid cells. level of an atmospheric model, at the street canyon, and at the vegetated fraction, respectively. Out of the total roof area, 50% of the roof was considered as GR, and the other 50% was the conventional roof.

Near-Surface Temperature and Winds
The model performance is assessed for the model ensemble mean against observations from TCEQ urban stations for T2 and W10 (Figure 3). In the LIR (Figure 3a), the observed T2 is higher than the CTL during the daytime, but the CTL follows the observation well at night. In the COI/HIR area (Figure 3b), the T2 in the CTL shows a larger discrepancy during the night compared with the LIR area (Figure 3a). The performance of the simulations concerning mean error and the root mean squared error (RMSE) for different PBL schemes along with their ensemble mean is given in Table 3. The CTL winds, in general, are lower than that in the observation during the morning hours ( Figure  3c,d). However, for the early evening and overnight periods, they remain higher than the observations. The peak W10 in CTL appears later than the observations, leading to a phase lag between the model and the observation. This phase lag is likely due to the use of SLUCM, with hydrological options that lead to the over-moistening of the urban surfaces. As a result, during the morning hours, solar radiation is used to evaporate the moisture (i.e., increased latent heat flux), leading to a smaller sensible heat flux. As the surface moisture reduces, sensible heat flux increases, leading to an increase in near-surface temperature which lags behind that from the observation. The lag in near-surface temperature causes a lag in mixing in the planetary boundary layer and nearsurface winds in the simulations. A previous study by Brownlee et al. [38] also found this lag in temperature and winds using the MYJ PBL scheme when they used SLUCM with hydrological options; however, without the hydrological options, they found the lag to be smaller. Thus, there may be a systematic bias in surface wind speed in the WRF model [66], which may have been enhanced in our simulations due to the use of hydrological options. Over the 24 h period, all four PBL schemes produced stronger winds in LIR and weaker winds in COI/HIR than the observation, except for MYJ, which has little to no bias in W10 over LIR, and YSU, which has a positive bias in W10 (Table 3).  Figure 4 shows the difference between the GR and CTL simulations concerning the surface skin temperature (TSK, Figure 4, left) and T2 (Figure 4, right) over urban areas. The mitigation of heat stress by the green roofs is clear, with the maximum amplitude of TSK decreasing by 1.1 °C in LIR to 1.9 °C in COI/HIR. The decrease in TSK in GR compared to CTL is due to a larger loss in surface latent heat flux (Figure 5c). The change in the T2 (Figure 4, right) is much smaller due to green roofs compared to that in the TSK (Figure 4, left). The reduction in T2 (see Equation (5)) due to GR ( Figure  4b) is due to the smaller sensible heat loss (Figure 5f). With green roof systems, there is an increase in the soil layer on the top of each building (see Figure 2) which can retain more energy than traditional roofs [44,67]. It is well known that, compared with the nighttime average (Figure 4, bottom), the green roof can have a larger effect over urban areas during daytime (Figure 4, middle). To explain the changes in temperature in GR compared to CTL, we present an analysis of the surface heat flux components that are a dominant factor in controlling the near-surface conditions.   Figure 5 shows the surface latent heat flux (LH), sensible heat flux (SH), net shortwave radiation (Net_SW), net longwave radiation (Net_LW) and storage heat flux (SHF) from the CTL and GR and their differences. The LH is much smaller in the COI/HIR (green in Figure 5a) than LIR (yellow in Figure 5a) due to there being less surface moisture over the COI/HIR area. The addition of green roofs in urban areas increases surface moisture and hence the LH, particularly during the daytime ( Figure  5c). This leads to a much cooler TSK in the GR simulation (Figure 4a). The opposite happens for SH (Figure 5f), where SH is larger over COI/HIR than LIR. As expected, the change in the SH from CTL to GR is the opposite of the change in LH; i.e., as the SH decreases, the LH increases. Overall, the net turbulent flux (LH + SH) in GR is lower than that in CTL over urban areas ( Table 5). The range of values of LH, SH, and TSK shows the sensitivity of the results due to the use of different PBL schemes. The reduction in TSK in GR is much larger over HIR than over LIR. The implementation of a green roof leads to increased net shortwave radiation (Figure 5i). For net surface longwave radiation, there is also a moderate increase in GR compared to CTL (Figure 5l). The difference in storage heat flux (Figure 5m-o, [68]) between the CTL and GR varies (−20 to 20 W m −2 ) over the day and nighttime, with larger storage heat flux in GR during the daytime. Apart from the analysis of surface heat flux components, the extent to which the temperature advection modulates the near-surface temperature is examined in the next section.

Temperature Advection
Previous studies have demonstrated the importance of the surface heat fluxes on the nearsurface temperature and winds, but they have not presented any quantitative estimates of heat advection over an urban area. The higher temperature in the urban areas compared to rural areas leads to a temperature and pressure gradient [69] which can initiate the advection of heat and momentum. Nevertheless, it is not well known how this advection alters temperature evolution over the city. Ignoring the material derivative and vertical advection of temperature, the local tendency in temperature is given by where −u(∂T/∂x) is zonal temperature advection and −v(∂T/∂y) represents meridional temperature advection. The horizontal temperature advection is the sum of zonal and meridional temperature advection. Figure 6 shows the influence of each term in CTL and GR and their difference. In the LIR area, the horizontal temperature advection reaches peaks before 00Z August 26 in both CTL ( Figure  6a) and GR (Figure 6c) simulations. The GR has higher temperature advection (Figure 6e) which is mostly from meridional temperature advection due to onshore winds. Over the COI/HIR area, temperature advection becomes negative and appears after 00Z August 26 indicating that temperature advection plays a cooling role in GR compared with CTL in COI/HIR (Figure 6f). Overall, the meridional advection of temperature dominates over zonal advection, and the total horizontal advection plays some role between 1700 and 2200. For the rest of the time, it seems that the near-surface temperature is driven primarily by the surface heat flux.

Momentum Advection
The momentum budget analysis has been extensively used [70][71][72][73][74] to understand the evolution of winds in a variety of meteorological conditions. However, such an analysis, to the best of our knowledge, has not been performed to understand the role of green roof systems on advection. The zonal and meridional momentum budgets are given by where (u, v, ω) are three-dimensional wind vectors, φ is the geopotential height, f is the Coriolis parameter, and R stands for residual, which includes friction and errors in the calculation. The term on the left-hand side represents the local tendency, whereas the first three terms on the right-hand side represent zonal, meridional and vertical advection (VADV), respectively. The combined zonal and meridional advection is referred to as horizontal advection (HADV, red in Figures 7 and 8). The last three terms represent the pressure gradient, the Coriolis, and the residual. We merge the vertical advection and the residual into one term (green in Figures 7 and 8), and the pressure gradient and Coriolis into another term (blue in Figures 7 and 8) to focus on any possible influence from HADV. For the zonal momentum budget (Figure 7), the local tendency peaks are similar in both urban areas and experiments (~02 August 26, Figure 7, top two panels). The increase in HADV from 2100 August 25 to 0300 August 26 is also similar to the increase in local tendency indicating that the winds were influenced by the HADV. Over LIR areas, the combined VADV and residual is positive during 1900-2200 August 25 and then becomes negative, whereas over COI/HIR areas, the VADV + R remains mostly negative. The difference between CTL and GR is most prominent from 1800 August 25 to 0000 August 26 (Figure 7, bottom). The meridional momentum budget analysis.  (6)), horizontal advection or HADV (sum of the first two terms on the RHS in Equation (6)). The VADV + Residual (vertical advection plus residual; i.e., the sum of the third and sixth terms on the RHS in Equation (6)) and the pressure gradient and Coriolis (PGF + Cori; i.e., the sum of the fourth and fifth terms on RHS in Equation (6)). Unit m s −1 day −1 . Figure 8 shows a similar relationship between local tendency and HADV, but stronger association over COI/HIR area in CTL (Figure 8b). Compared with LIR areas in CTL (Figure 8a), the local tendency and HADV in GR have a higher correlation (Figure 8c). The peak of local tendency is different in GR over LIR (~0000 August 26, Figure 8c) and COI/HIR (~2000 August 25, Figure 8d). Notice that the magnitude of several terms during the period from 1800 August 25 to 0000 August 26 is larger than other times, and hence is further illustrated in Figure 9. Although the local tendency of zonal (Figure 9, top) and meridional (Figure 9, bottom) momentum advection is similar, the HADV terms are quite different in CTL and GR over LIR areas.

Moisture Advection
The atmospheric moisture budget is given by (e.g., [75,76]) (9) where q is the specific humidity, vh is the horizontal wind vector, is the vertical velocity, E means the evaporation, P represents the precipitation, and R is the residual. The symbols < > stand for the mass-weighted vertical integral from 1000 hPa to 100 hPa. The term on the left-hand side is the moisture tendency. The first two terms on the right-hand side are the horizontal (HADV) and vertical (VADV) moisture advection. This equation is used extensively to understand the variability of atmospheric moisture and precipitation [77] that is important for water-climate-society research [78]. Figure 10 presents the terms in the moisture budget with a small residual that provides confidence regarding the estimates of the terms and their interpretations. Since there was no precipitation, we have not shown this in Figure 10. Over the LIR, the evaporation is compensated mostly by VADV in both experiments. In the COI/HIR area, the increase in evaporation in the presence of GR (see Figure  6) is compensated by an increase in HADV and VADV.

Discussion
The response of near-surface meteorological conditions (temperature, winds, and moisture) to advection under the impact of green roofs is evaluated over Houston using the WRF model. An ensemble mean of four simulations based on four widely used planetary boundary layer schemes was used for the control simulation (CTL) and the simulation with green roofs (GR). The main results are the following.
Models (CTL) T2 and W10 were found to be in good agreement when evaluated against available observations, although with a lag in time. With the inclusion of green roof systems (GR), the nearsurface temperature and winds decrease. During the daytime, the LH (SH) increases (decreases) in GR compared to CTL leading to a cooling effect when the temperature decreased by 1-2 °C. Yang et al. [3] found that by using a 50% fraction of green roof, there is a reduction in surface temperature ranging from 2-4 °K at four different locations (Beijing, Vancouver, Phoenix, and Montreal). Our results also indicate that the green roofs can also cause cooling over the night, which is in contrast to Yang et al. [44] who found that the temperature was 1 °C higher during the nighttime. This discrepancy may be due to our short simulation period, the seasonal dependence of the impact of green roofs, and the differences in model horizontal resolutions, among other reasons.
Our results indicate that, in the CTL over LIR areas, a stronger temperature gradient leads to a stronger advection of temperature in the presence of onshore winds. Over COI/HIR, the temperature advection in GR plays a cooling role compared with CTL in COI/HIR. The temperature advection shows that it does not play a significant role, suggesting that the near-surface temperature is driven by the surface heat flux. The timing of peak temperature advection, however, should be treated with caution, given that there was a lag in model peak temperature and wind compared with the observations (Figure 3).
The analysis of the momentum budget shows that the differences between CTL and GR occur from 1800 August 25 to 0000 August 26 (Figures 7-9). The variation of local tendency follows the variation of HADV over both LIR and COI/HIR in both zonal and meridional momentum budget analysis. Similar to temperature advection, the timing of peak momentum advection (Figures 7, 8) in the model may be different from observations since the timing of peak T2 and W10 was different in model and observations. However, when the momentum advection is averaged over time, the lag in temperature and winds has expected to have less influence on our estimations of different advection quantities.
The moisture budget analysis suggests that, over the LIR area, the evaporation is mostly compensated by VADV in both CTL and GR experiments ( Figure 10). In the COI/HIR area, the increase in evaporation in the presence of GR (see Figure 6) is compensated by an increase in HADV and VADV.
Our results imply that, even with a small change in temperature over cities due to green roofs, advective processes that influence near-surface temperature, winds, and humidity can have a large difference compared to control. The differences were most prominent during the evening when the temperature gradient between the urban areas and surroundings was small due to the cooling of the urban areas because of green roofs.

Conclusion
In summary, we have estimated the impact of green roofs in modulating the advection of heat, momentum, and moisture that influences the temperature, wind, and humidity using urban-aware simulations. Such an impact of the green roof, especially on momentum advection, has not been quantified before. We have accomplished this by employing physics-based simulations using different PBL schemes, whereas earlier studies were based on a single simulation (i.e., a deterministic approach). Unfortunately, because of the lack of observational data of heat flux components at the surface and other meteorological parameters in the PBL, our study lacks rigorous validation. However, since the model was able to capture the near-surface temperature and winds, the model simulations were likely realistic. A logical extension of our work would be to quantify the impact of the green roofs on advective processes under different green roof fractions and determine how this impact may change in a future climate.