The WRF model is a limited area, nonhydrostatic, mesoscale modeling system with a terrain-following estimated time of arrival (eta) coordinate, which is coupled with land surface models and the urban canopy model (UCM) to provide a better representation of the physical processes related to the exchange of heat, momentum, and water vapor in an urban environment. The land surface model describes the physical soil hydrological processes explicitly, including infiltration, storage, redistribution, drainage, and evaporation. The UCM is a single-layer model with a simplified urban geometry, where its features include shadowing from buildings, reflection of short- and long-wave radiation, the wind profile in the canopy layer, and multilayer heat transfer equations for roof, wall, and road surfaces (Tewari et al., 2007). The impervious roads lack soil hydrological processes, but the evaporation of liquid water still occurs above the road, which can change the urban weather, climate, and environment.

A simple urban water usage scheme, including urban irrigation and road sprinkling, was incorporated into the WRF model, based on the scheme proposed by Zeng et al. (2017). Ecological and farmland irrigation were both treated as urban irrigation and implemented in the same manner in the model. The soil hydrological processes were changed, and the water balance between the land surface and atmosphere was disturbed, provided that the irrigation water was added to the first layer of the soil, and it was regarded as the available liquid water in the model. This process was conducted for farmland and urban land use types, and the water added from the surface soil was removed from the ground water table to maintain the water balance. According to the Requirements for Quality and Operation of City Road Sweeping and Cleaning (no. DB11/T 353-2014; Beijing M., 2014) the road sprinkling scheme was activated in the night, when water was applied to the impervious road layer to accelerate evaporation. A flowchart illustrating the urban water usage scheme, including irrigation and road sprinkling in the model, is shown in Fig. 1, and the specific scheme is represented by Eqs. (1)–(4). The advanced water usage scheme mentioned above was coupled into the WRF model. Water from urban irrigation with a specific spatial distribution was entered as an input for the model via a data interface with the WRF model. The program was initialized for the real-time case study, and the amount of water applied for road sprinkling was no more than the maximum water-holding capacity of the urban impervious layer, as follows: 1wi,j,t=wii,j,t,perviouslayera×pondmaxurban,imperviouslayer0,otherwise2Wi,j,t=Wi,j,t-1+wi,j,t3woi,j,t=wii,j,t,perviouslayer0,otherwise4zwti,j,t=zwti,j,t-1-woi,j,t, where the subscripts i, j, and t represent the latitude, longitude, and time, respectively, wii,j,t represents the amount of water from urban irrigation, a is a coefficient from 0 to 1, pondmaxurban is the maximum water-holding capacity of the urban impervious layer, which mainly refers to the impervious road in the present study, Wi,j,t is the surface liquid water entering the first soil layer or impervious layer, Wi,j,t-1 is the previous time step before Wi,j,t, woi,j,t is the amount of water that needs to be removed from the ground water table, zwti,j,t represents the water table at time t, and zwti,j,t-1 represents the previous time step at zwti,j,t.

Air temperatures obtained from reanalysis data and in situ data were used to validate the WRF model output. In situ data were obtained from 20 national meteorological stations in Beijing, and the regional reanalysis data came from the China Meteorological Administration Land Data Assimilation System (CLDAS) with hourly outputs with a resolution of 0.0625∘×0.0625∘. More detailed descriptions of the data are given in Table 1. In addition, these data were also collected to verify the effectiveness of the WRF physical schemes.

The grid water usage data were derived from the total water consumption in Beijing and distributed according to the grid population density, GDP, and water deficit efficiency. The downscaling method employed was reported in a previous study (Zeng et al., 2017). The spatial distributions of the water usage amounts for the summed irrigation and ecological water are shown in Fig. 2a, and the spatial distributions of the road area proportions related to road sprinkling are shown in Fig. 2b. Farmland irrigation was mainly located in the south of Beijing and ecological water consumption occurred mainly in the center of the city. A primeval forest with little human influence is located to the north of Beijing, and the water consumption was low in this area. The urban planning for Beijing can be separated into urban, suburban, and rural areas divided by the fifth and sixth ring roads. The area within the fifth ring road was treated as the urban area inhabited by the majority of the population. The population declined from the fifth to the sixth ring road in the so-called suburban transition area. The rural areas were located outside the sixth ring road, where they mainly comprised farmland with few buildings and factories.

We used the WRF model (Skamarock, 2008) with the Advanced Research WRF Dynamic Core version 3.9.1, coupled with a single-layer UCM, in the experiments. Three types of experiments were conducted to consider no water usage, urban irrigation, and road sprinkling in the city center, suburbs, and rural areas. The urban irrigation experiments comprised 21 individual model simulations, where the grid water usage data ranged from 0.1 to 1.9 times the estimated urban irrigation in the city center, suburbs, and rural areas. In each case, the data were regarded as new input variables and added to the initial model input files with the same spatial resolution as the model when the WRF model was running. The road sprinkling experiments comprised 27 individual model simulations, where the amount of water sprinkled on roads ranged from 0.2 to 1 times the maximum water-holding capacity of the impervious layer in three parts of the city with different urban sprinkling frequencies and strengths. Detailed descriptions of the experimental designs are shown in Table 2.

Three-layer nested domains with horizontal resolutions of 15 km (d01; mesh size 95×121; most of northern China), 5 km (d02; mesh size 135×185; almost all of the Jing-Jin-Ji metropolitan area), and 1 km (d03; mesh size 205×270; Beijing as the area of interest) were designed for the experiments (Fig. 3). The National Centers for Environmental Prediction Global Final Analysis 6 h data (soil water, moisture, and temperature) were used for the first guess in the initial field and lateral boundary conditions. The MODIS-based land use classifications data provided in the WRF model described the real terrestrial and land cover characteristics of the regions of interest, and the default static data were used in the experiments. Climate summertime periods from 2000 to 2017 were averaged to 4 d to represent climatic May, June, July, and August. First, we obtained all of the data for May from 2000 to 2017, before averaging all these data to 1 d to represent climatic May. Finally, climatic June, July, and August were obtained by repeating these two steps. The first day (climatic May) was considered as the spin-up period. The schemes are shown in terms of the physical options in Table 3.

Considering that random processes in the atmosphere may lead to uncertainty regarding the cooling effect, offline comparative experiments were conducted to understand the cooling effects of urban irrigation and road sprinkling. These experiments comprised raw simulations without urban water usage and with urban irrigation and road sprinkling, using the community land model (CLM 4.5). The simulations were driven by atmosphere forcing data (June to August in the year 2012) obtained from the Data Assimilation and Modeling Center for Tibetan Multi-spheres, Institute of Tibetan Plateau Research, Chinese Academy of Science (Yang et al., 2010a). The simulation results showed that urban irrigation decreased the groundwater table due to groundwater extraction, as also shown by Yang et al. (2010b), and the surface soil moisture increased (Fig. 4). There were no changes in the water table and surface soil moisture from road sprinkling due to the lack of underground water processes below the impervious layer. Evapotranspiration was strengthened when more water was applied to irrigate soil or farmland, and heat from the ground and air was taken away. Similar results were obtained from road sprinkling, but the physical process was slightly different. As a result, both schemes decreased the sensible heat flux, ground temperature, air temperature, and wind speed, and increased the latent heat flux (Fig. 5). In addition, the impacts of land surface variables were limited to the areas where water was applied because the offline simulations did not consider climate effects between the atmosphere and land surface. Thus, the cooling effects were fairly obvious following urban irrigation and road sprinkling, as also shown in previous studies (Wang et al., 2019; Hendel and Royon, 2015). Moreover, road sprinkling has been conducted in Beijing and Tokyo. In addition, the sensible heat flux and latent heat flux results obtained from the urban water usage simulations (including both urban irrigation and road sprinkling) were better than the raw model results (Fig. 6). Flux station observations from July to August in 2012 and the station simulation results were interpolated from the regional simulation results in 2012. Comparisons of these data showed that the correlation coefficient increased slightly, and the root mean squared errors for sensible heat flux and latent heat flux decreased by 4.69 and 6.94 W/m2, respectively, while the absolute errors for sensible heat flux and latent heat flux decreased by 7.3 and 9.62 W/m2. Therefore, urban water usage, including urban irrigation and road sprinkling, should be considered when conducting weather and climate simulations.

In addition to the comparisons of station observations and offline model simulations, we conducted comparisons of the 7 year average summer temperatures in the CLDAS and WRF simulations, to evaluate the simulation capacity of the raw WRF model, where the temperatures were higher in the city center than the suburbs. The similar spatial distributions showed that the WRF physical scheme was reasonable. The correlation coefficients between the CLDAS temperatures and WRF simulation results were generally close to one, and the average root mean square error (RMSE) for the two data sets was 0.8 ∘C. The grid model results were interpolated to the sites according to the coordinates of the stations in urban and suburban areas, and comparisons of the site observations and WRF simulation results also showed that the temperature simulation results were in good agreement with the observations (see Fig. 7). The WRF model simulation results were reasonable, where the simulated temperatures were slightly higher than the observations, and RMSE was mostly less than 2.5 ∘C. Thus, the WRF model may be a suitable tool for this type of research.

Also, WRF simulations with and without urban water usage schemes were conducted from July to August 2012. The comparisons of the reanalysis data (CLDAS) and station observations showed that the simulations with urban water usage were better than the raw WRF simulations in terms of the heat flux and temperature (Fig. 8). The mean absolute error of the air temperature decreased from 2.9 to 1.7 ∘C, compared with the CLDAS reanalysis data. Compared with the station observations, the correlation coefficients for sensible heat flux from simulations with and without water usage schemes changed little, and correlation coefficients for latent heat flux increased by 0.07, and the root mean square errors decreased from 57.6 to 52.6 W/m2 after applying urban water usage schemes.

Figure 9 shows that road sprinkling and urban irrigation both decreased the air temperature. Road sprinkling was mainly conducted at night to avoid disturbing traffic. The simulation results in Fig. 9 show that the temperature decreased by a maximum of around 0.5–1 ∘C in the city center where most roads were found, whereas there were no significant decrease in the temperature in rural areas where the lowest amount of road sprinkling occurred due to the low quantity of road surfaces in these areas. However, urban irrigation during the daytime decreased the temperatures in the day and night. Figure 10 shows that urban irrigation in the city center decreased the temperature by more than 1 ∘C when large volumes of water were applied. In the rural areas, the water applied for farmland irrigation had a reasonable cooling effect in the daytime, and the cooling effect continued, but it was smaller in the nighttime due to the evaporation from farmland crops and urban plants after irrigating in the daytime. This effect was much more significant in the rural areas than in the city center and suburbs. In addition, localized water usage could influence all of the areas, whereas road sprinkling or urban irrigation in the city center could decrease the temperatures in the suburbs or rural areas, and this effect may also occur in other locations. In general, the cooling effect of urban irrigation was stronger than that of road sprinkling because the amount of water applied for urban irrigation was greater than that for road sprinkling.

The application of water in urban areas could change the energy cycles and dynamic processes. Figure 11 shows that the changes in these variables were most significant in the areas where road sprinkling or urban irrigation were conducted, and they could weaken the dynamic atmospheric processes. The application of water by road sprinkling or urban irrigation increased the latent heat flux, decreased the sensible heat flux, and lowered the boundary layer heights locally. However, changes could be more general throughout the whole region. For example, urban irrigation in the city center lowered the boundary layer height in the city center but also affected the suburbs and rural areas. Similar results were found for the latent heat flux and sensible heat flux, but they were not as significant.

The quadratic functions fitted to the relationships between the amounts of water applied and the cooling effects in the simulations are shown in Fig. 12 and Table 4. The normalized amounts of water applied in the city center, suburbs, and rural areas for road sprinkling and urban irrigation were 0.528×108, 0.2868×108, and 0.039×108, and 0.81×108, 1.72×108, and 4.45×108 m3/month, respectively. The actual amounts of water applied can be determined by multiplying the values on the x axis and those given above. The results showed that the cooling effects of road sprinkling were similar in three parts of the city, where the temperature decreased by a maximum of about 0.55 ∘C, and the cooling effects remained stable when more water was sprinkled on the roads in the suburbs and rural areas. Sprinkling the roads in the city center changed the regional temperature more rapidly compared with sprinkling water in the suburbs and rural areas. However, the cooling efficiency did not increase according to the amount of water applied (for each normalized amount of water applied, the effect of water sprinkling in the city center was twice that in the suburbs and 10 times than that in the rural areas, but the cooling effect was similar where the cooling efficiency was lower in the city center than suburb and rural areas), possibly because the water sprinkled in the city center was concentrated in a smaller area where the wind was reduced, and this decreased the cooling efficiency. The cooling effect of urban irrigation was generally greater than that of road sprinkling, and it was most significant in rural areas. However, the cooling efficiency of urban irrigation was lower in rural areas than the city center and suburbs because, in order to apply the same normalized amount of water for irrigation, the actual amount of water applied in rural areas was almost five times that in the city center and two times that in the suburbs, but the temperature decrease in the rural areas was only 1.5 times higher than that of the city center and suburbs. Thus, the effect of urban irrigation was most efficient in the city center. The cooling effects in the city center and suburbs increased as the amount of water applied increased, which differed slightly from the effect of road sprinkling. We also found that some points deviated greatly compared with others in the city center, following road sprinkling, according to regression analysis (Fig. 12a), possibly because road sprinkling was limited to a small area in the city center with a low amount, and the overall effect could not be determined based on the cooling of the city center due to the occurrence of random processes in the atmosphere. Also, other researchers showed that the cooling effect varied with different water amounts, regions, and weather conditions (Broadbent et al., 2018; Wang et al., 2019; Gao et al., 2020).

The problem of distributing water to plants and roads in different parts of a city in order to obtain the optimal cooling effect can be solved using an optimization scheme. In this study, we divided the city into three parts according to the population density and urban type, i.e., the city center, suburbs, and rural areas. If the relationships between the amounts of water applied and the cooling effects were known for the three parts of city, then an optimal water usage scheme could be developed, where the optimization objective could be defined as the comprehensive temperature decrease attributable to both road sprinkling and urban irrigation in the city center, suburbs, and rural areas. The optimal water usage scheme could be described as follows: 5Max:∑j=13∑i=12fi,j(wi,j), where i represents road sprinkling and urban irrigation, with i equal to 1 or 2, respectively. j represents the city center, suburbs, and rural areas, with j equal to 1, 2, and 3, respectively. fi,j(wi,j) is a function of the normalized amount of water applied and the cooling effect, which can be fitted based on the model simulation results presented in Sect. 3.2.

Considering that the total amount of urban water supplied for road sprinkling and urban irrigation is a fixed value, the water demand for each part of city should satisfy the minimal needs for the municipal services and plants in terms of ecology, farmland, and roads. Thus, the constraint conditions for optimizing the usage of water are as follows: 6s.t.∑j=13∑i=12wi,j=A,7bj≪w1,j≪Bj,j=1,2,3,8cj≪w2,j≪Cj,j=1,2,3, where A represents the total water supplied for road sprinkling and urban irrigation. j represents the city center, suburbs, and rural areas, with j equal to 1, 2, and 3, respectively. bj represents the minimal water demand for road sprinkling, Bj represents the maximum water supply for road sprinkling, cj represents the minimal water demand for urban irrigation, and Cj represents the maximum water supply for urban irrigation. In addition, other water restrictions applied in each part of the city can be expressed as other equalities or inequalities in this optimal water usage scheme.

Based on the historical water demand and supply for municipal services described in the Water Resources Bulletin of Beijing, the Requirements for Quality and Operation of City Road Sweeping and Cleaning, and the textbook entitled Water Supply Engineering, we set the constraint conditions given in Table 5. In addition, according to Beijing's 13th 5 Year Plan, the water supply for the whole city was set as 43×108m3/year and the total amount of water for road sprinkling and urban irrigation as about 17×108 m3/year, which was mainly consumed in summer periods, excluding the water usage by industry and residents. Solving this optimization problem started by artificially assigning initial values to the solution and then solving the initial objective function value in Eq. (5) before assigning new values to the solution according to the search algorithms and the constraint conditions in Eqs. (6)–(8). A new objective function value was solved during this step. These two steps were repeated until the objective function value changed little. We used the Optimization Toolbox in MATLAB to solve the problem. After 24 loop iterations, the results showed that the normalized amounts of water applied for road sprinkling in the city center, suburbs, and rural areas were 0.4, 0.2, and 0.1 (the actual amounts of water applied were 0.21×108, 0.06×108, and 0.04×107 m3/month, and road sprinkling in the whole city accounted for almost 10 % of the total water supply), respectively. The normalized amounts of water applied for urban irrigation in the city center, suburbs, and rural areas were 0.43, 0.36, and 0.40 (the actual amounts of water applied were 0.35×108, 0.62×108, and 1.78×108 m3/month, respectively and urban irrigation in the whole city accounted for almost 90 % of the total water supply) to obtain the greatest cooling effect, with a temperature decrease of 1.9 ∘C. These results were reasonable because the enhanced cooling effect of road sprinkling decreased as the amount of water applied increased, so the lowest water demand was similar when more water was applied by road sprinkling. Urban irrigation in rural areas accounted for a large proportion of the total water supply in order to satisfy the needs for crop growth and environmental cooling.

The optimized results may be slightly higher than the actual requirements because the water usage in one part of a city will affect the cooling effects in other parts. The uncertainties related to the constraint conditions will also affect the results. The total amount of water applied for road sprinkling and urban irrigation (A in Eq. 6) must be considered among these uncertainties. Thus, we conducted sensitivity based on proportions ranging from 0.7 to 1.5 relative to 17×108m3/year for the total amount of water applied. The results showed that the relationship between the total amount of water applied (A) and the cooling effect was nonlinear, where the temperature decreased sharply as the total amount of water applied (A) increased (see Fig. 13).