Beijing is located at the northwestern section of the North China Plain (39°28ʹ-41°05ʹN, 115°25ʹ-117°30ʹE) (Fig. 1), with a total area of 16 410.5 km², of which 62% is mountainous area (Zhang et al., 2010). The climate of Beijing is a temperate semi-wet monsoonal continental climate, with a multi-annual mean temperature of 12.0 ℃ and multi-annual mean precipitation of 640 mm (He et al., 2016). The topography in Beijing is high in the northwest and low in the southeast, with the southeastern plain surrounded by mountains on three sides. The Beijing Municipal Major Functional Zoning Plan divides Beijing into CFCA, UFDA, UDNA and ECA (Fig. 1). The CFCA, including the Dongcheng District and Xicheng District, had a population of 2.162 million and an area of 92.4 km² in 2010. The UFDA, including the Chaoyang District, Haidian District, Fengtai District and Shijingshan District, had a population of 9.554 million and an area of 1275.9 km² in 2010. The UDNA, including the Tongzhou District, Shunyi District, Daxing District (Beijing Economy and Technology Development District) and the plain areas of Changping District and Fangshan District, had a population of 5.418 million and an area of 3782.9 km² in 2010. The ECA included the Mentougou District, Pinggu District, Huairou District, Miyun District, Yanqing District and the mountainous areas of Changping District and Fangshan District, with a population of 2.478 million and an area of 11259.3 km² in 2010. The ratio of the four functional areas (CFCA, UFDA, UDNA and ECA) was 23:47:26:4 for gross domestic product (GDP), 11:49:27:13 for resident population and 0.6:7.8:23.0:68.6 for land area in 2010, respectively.

The ECA is mainly located at the mountainous area. The land cover types have changed over time. Based on the average for 2005 and 2010, the forest area in Beijing was 8632.57 km², of which 94.4% was within the ECA and most of which was deciduous wide leaf forest and deciduous wide leaf shrubs. The grassland of ECA accounted for 80.9% of the total grassland area (692.94 km²), which was mainly thick grass. The wetland area was 259.35 km², of which 64.7% was located within the ECA. The cropland area was 2255.85 km², of which 54.7% was located in the UDNA and 39.6% was located in the ECA (mainly dry land). The artificial surface area was 2470.43 km², of which 41.0% was located in the UDNA and 31.15% was located in the UFDA (mainly residency area). Although the artificial surface in the CFCA only accounted for 3.43% of the total artificial surface in Beijing, it accounted for 91.63% of the CFCA. Other land cover types, including sparse grassland, bare rock and bare soil with an area of 68.47 km², were mainly located in the ECA (61.4%) and UDNA (35.8%).

Data about land cover, meteorology, soil, digital elevation, society and economy were needed. Land cover data (2005,2010) (spatial resolution 1 km) were derived from NationalEcosystem Survey and Assessment of China (2000-2010). Meteorological data were obtained from China Meteorological Data Sharing Service System (http://data.cma.cn/). To avoid the poor representativeness of data from a single year, daily meteorological data (including precipitation, wind speed, sunshine duration, average air pressure, monthly average temperature, daily maximum temperature, daily minimum temperature and average vapor pressure) of 28 meteorological stations in Beijing-Tianjin-Hebei Region for the periods of 2000-2007 and 2008-2015 were acquired. The digital elevation model (DEM) (spatial resolution 90 m) was obtained from the Data Center for Resources and Environmental Sciences of Chinese Academy of Sciences (http:// www.resdc.cn/). For the data of precipitation, potential evapotranspiration and actual evapotranspiration, a multi- year average was required first before obtaining the related spatial grid data (spatial resolution 90 m) for two stages by relying on Kriging spatial interpolation in ArcGIS 10 to calculate the water conservation amount.

This study used the following water balance equation to calculate the water conservation capacity, which was closely related to factors that include precipitation, evapotranspiration, surface runoff and land cover type:

$TQ=\underset{i=1}{\overset{j}{\mathop \sum }}\,({{P}_{i}}-{{R}_{i}}-E{{T}_{i}})\times {{A}_{i}}$(1)

where TQ is the total amount of water conservation (m³), P_i denotes precipitation on pixel i (mm), R_i represents surface runoff on pixel i (mm), ET_i is evapotranspiration on pixel i (mm), A_i is the area of pixel i, j is the total number of pixels.

The surface runoff (R_i) is the product of precipitation and surface runoff coefficient, the formula is as follows:

${{R}_{i}}={{P}_{i}}\times {{\alpha }_{i}}$(2)

where α_i is the average surface runoff coefficient on pixel i (%). Based on the regional conditions of Beijing in combination with data from the literature, we obtained the average runoff coefficient for various land covers in Beijing (Table 1).

Actual evapotranspiration (ET_i) was calculated using the Technical Guidelines for the Redline Delimitation of the Ecological Protection:

$E{{T}_{i}}=\frac{{{P}_{i}}(1+{{\omega }_{i}}\times E{{T}_{0i}}/{{P}_{i}})}{1+{{\omega }_{i}}\times E{{T}_{0i}}/{{P}_{i}}+{{P}_{i}}/E{{T}_{0i}}}$(3)

where ET_0i is multi-annual mean latent evapotranspiration on pixel i, and ω_i is the underlying surface (land cover) impact coefficient from the Technical Guidelines for the Redline Delimitation of the Ecological Protection (Table 2) on pixel i.

The latent evapotranspiration was calibrated with the FAO56 Penman-Monteith formula (Allen, 1998) based on daily meteorological data of each weather station:

$E{{T}_{0}}=\frac{0.408\Delta \times ({{R}_{n}}-G)+\frac{900}{T+273}\times {{U}_{2}}\times ({{e}_{s}}-{{e}_{a}})}{\Delta +\gamma \times (1+0.34{{U}_{2}})}$ (4)

where R_n is surface net radiation (MJ m^-2 d^-1) from the crops, G is the soil heat flux density (MJ m^-2 d^-1), T is monthly mean temperature (℃), U₂ is 2-m wind velocity(m s^-1), e_s is saturated water vapour pressure (kPa), e_a is the actual water vapour pressure (kPa), ${\Delta}$ is the slope of the saturated water vapour-temperature curve (kPa ℃^-1) and ${\gamma}$; is the psychrometric constant (kPa ℃^-1).

In 2005, the average water conservation amount was -8.96 mm in Beijing and the actual evapotranspiration and surface runoff were generally higher than precipitation. Compared to 2005, water conservation amount in Beijing in 2010 showed an overall increasing trend, with an average of 12.21 mm and a total amount of 2.00×10⁸ m³. Precipitation, actual evapotranspiration and runoff are the three key factors determining the WCS when considering the water balance. Precipitation is an important variable of climate change, and the actual evapotranspiration and runoff are affected by both climate (solar radiation, temperature, humidity, wind speed) and land cover. Precipitation, actual evapotranspiration and runoff in 2010 in Beijing all increased relative to 2005. The annual mean precipitation in 2010 was 109.33 mm, more than that in 2005. The average actual evapotranspiration increased 65.40 mm in 2010 and the average runoff increased from 75.28 mm in 2005 to 98.04 mm in 2010.

Among the previous studies on the water conservation amount in Beijing, Zhang (2012) calculated that the annual mean evapotranspiration was 494 mm, and river runoff was 46 mm and precipitation was 485.4 mm in Beijing between 2001 and 2009 based on the precipitation-runoff-evapotranspiration equilibrium model. Because the river runoff was more than the average runoff, the annual mean water conservation amount of Beijing between 2001 and 2009 was approximately -54.6 - -8.6 mm for each soil cover type based on the water balance equation. Zhou (2015) determined that the average water conservation amount for Beijing in 2003-2012 was less than 6 mm based on the water balance method, with an average evapotranspiration of 517 mm and an average precipitation of 523 mm. Li et al. (2017) calculated the Beijing-Tianjin-Hebei water production in 2000, 2005 and 2010 based on the InVEST model, indicating that the water production in 2010 in Beijing was higher than that in 2005. The above water conservation estimations from the literature are comparable to those calculated in this study.

The spatial patterns of the WCS in Beijing in 2005 and 2010 were similar (Fig. 3), which increased from the central city to its vicinities. The northern and western areas were the high-value zones of Beijing’s WCS, which belonged to the ECA of the Beijing Municipal Major Functional Zoning Plan. Within the ECA, the water conservation amount was the highest in the northeastern Miyun Reservoir and its sur-ounding area, with an average of 170-243.91 mm. With dense urban construction land use, the central city was a negative area of water conservation amount, indicating that this area generally did not have water conservation capacity. In addition, the demand for WCS was becoming increasingly urgent due to population growth and socioeconomic development. According to the water balance equation, the water conservation amount is positively correlated with precipitation and negatively correlated with the actual evapotranspiration and surface runoff (Xu et al., 2016). Therefore, the spatial distribution pattern of the water conservation is closely linked to the spatial difference for each meteorological factor. The spatial distribution of precipitation interpolation showed that precipitation was high in the northeastern area and low in the southwestern and northwestern areas of Beijing (Fig. 4). The latent evapotranspiration and actual transpiration both decreased gradually from the northeast to the southwest. The surface runoff decreased from the centre of the city to its vicinities mainly because the urban construction land was mostly impermeable surface without conservation capacity (Yao et al., 2018).

Therefore, the precipitation infiltration was limited, and the runoff due to the large runoff coefficient was substantially higher than the surrounding area that was covered by vegetation. Compared to 2005, the water conservation amount in 2010 in Beijing increased to some degree citywide. The increase in the average water conservation amount in the northeastern area of the city was large, with an average increase of 23-50 mm. In contrast, the average water conservation amount in the central city showed a decreasing trend, with a magnitude of 0-27.64 mm, indicating that the central city did not have water conservation capacity and that its water conservation loss increased gradually.

Compared to 2005, the average water conservation amount for each land cover type in 2010 in Beijing generally increased to some degree (Fig. 5, Fig. 6), consistent with the temporal changes in the average water conservation amount for the entire city of Beijing. The only exception was that the average water conservation amount for the artificial surface indicated a decreasing trend, which was mainly due to the fact that the climate-induced increase in the actual evapotranspiration and surface runoff was more even though precipitation increased. Among land cover types, the average water conservation capacity decreased in the following order: wetland, forest, grassland, cropland, bare land and artificial surface. The total amount of water conservation was related to the average water conservation capacity and area of each land cover type. The total amount of water conservation decreased in the following order: forest, grassland, wetland, bare land, cropland and artificial surface, among which the contribution of forest water conservation was the largest, with a total of 2.91×10⁸-5.20×10⁸ m³. Overall, wetlands, forests and grasslands can provide WCS, whereas the other land cover types indicate mostly negative quantities of water conservation. There are few studies on the overall average water conservation amount for the land cover types in Beijing. Zhang’s estimation of the water conservation amount in the northern water conservation area of Beijing showed that the annual mean water conservation amount decreased in the following order: shrub land, forest land, sparse forest land and grassland, which was consistent with the order of the water conservation amount for the relevant land cover types in this study (Zhang, 2012).

The average water conservation amount for each main functional area of Beijing varied considerably (Fig. 7). Among the four main functional areas, only the ECA showed a positive average water conservation amount of 18.23-41.96 mm, and the total amount of water conservation was up to 2.06×10⁸-4.74×10⁸ m³. The average water conservation quantities for the other main functional areas were all negative, and larger absolute values for the negative values suggested more loss of the water conservation per unit area. This was due to the differences in precipitation, actual evapotranspiration and surface runoff in each functional area. The average precipitation and actual evapotranspiration for each functional area varied slightly between 2005 and 2010. They were slightly higher in the ECA and the UDNA than in the CFCA and UFDA. However, the average surface runoff varied substantially among the four main functional areas, indicating a trend of CFCA > UFDA > UDNA > ECA. The average surface runoff was up to 236.56-336.45 mm in the CFCA, which was over six times that in the ECA (41.33-51.12 mm). The reason for the large difference was that the runoff generation in each land cover type was different and decreased in the following order: construction land, shrub, grassland, forest and cropland (Zhu and Li, 2005; Zhu, 2007; Wang et al., 2014; Guo et al., 2014; Farley et al., 2005). Based on the average for 2005 and 2010, the ratio of the artificial surface with high runoff generation capacity in each functional area was 91.63%, 60.31%, 27.00%, and 5.34% in the CFCA, UFDA, UDNA and ECA, respectively (Fig. 8, Fig. 9). The ratio of forest and cropland of low runoff generation capacity was 4.87%, 32.87%, 67.91% and 86.66% in the CFCA, UFDA, UDNA and ECA, respectively. Therefore, the water conservation function of the ECA was critical to the water resource conservation of the entire city of Beijing. It was suggested that protection of the wetlands and forests for water conservation should be enhanced within the ECA of Beijing and that the occupation of ecological land should be avoided due to the chaotic expansion of urban construction land use.

The water conservation capacity within the ECA varied substantially between each district and county (Fig. 3). The contribution of each district and county to the overall water conservation of the ECA is the key in determining the protection focus. In 2005 and 2010, the overall water conservation function of Miyun District was the largest, accounting for 55.23% and 34.13%, respectively, followed by Huairou District (28.97%, 21.97%), Pinggu District (14.14%, 11.44%), Mentougou District (5.58%, 10.69%) and Yanqing District (2.65%, 10.37%), whereas the contributions from the mountainous Fangshan District and the Changping District were small. The average water conservation quantities for the districts and counties within the ECA in 2005 and 2010 were 15.93 mm and 40.45 mm, respectively. Only Miyun District, Pinggu District and Huairou District exceeded the average (Fig. 10). The average water conservation amount was the largest in Miyun District, which was 51.09-72.66 mm, followed by the Pinggu District (30.71- 57.17 mm), Huairou District (28.13-49.08 mm), Mentougou District (7.94-34.97 mm), Yanqing District (2.73-24.55 mm), the mountainous Changping District (-1.70- 26.67 mm) and Fangshan District (-7.38-18.08 mm).

The contribution of each district and county to the total amount of water conservation was determined by the average water conservation amount and land cover composition, especially the average water conservation amount and area of the wetlands, grasslands and forests in each district and county. The average water conservation amount of the wetlands was the highest in each district and county in 2005 and 2010, whereas the magnitude varied with district and county, which generally decreased in the following order: Miyun District, Pinggu District, Huairou District, Changping District (mountainous area), Fangshan District (mountainous area), Mentougou District and Yanqing District (Fig. 10). The average water conservation amount for forests was lower than that of wetlands in each district and county and generally higher than grasslands. The magnitude of the average water conservation amount for forests in descending order was Pinggu District > Miyun District > Huairou District > Yanqing District, Changping District (mountainous area) > Fangshan District (mountainous area) > Mentougou District. The magnitude of the average water conservation amount for grasslands in descending order was Pinggu District > Miyun District > Huairou District > Fangshan District (mountainous area) > Mentougou District > Yanqing District > Changping District (mountainous area). Although the average water conservation amount for wetlands was the largest, its contribution to the total amount of water conservation in each district and county was not large due to its small area and generally comparable to that of grasslands. The contribution of forest from each district and county to the total amount of water conservation was the largest, and the changes in forests and the total amount of water conservation of each district and county were consistent with the highest correlation. This suggested that forests played a key role in regional water conservation. In summary, water conservation for forests in Miyun District, Huairou District and Pinggu District played an indispensable role in the water conservation function for the entire city of Beijing, and the forests in these three functional areas were the main forest body of Beijing that was important for WCS. Therefore, the resource construction and management of forests in these three areas should be enhanced. In addition, the enhancement of forest resource protection and water conservation capacity for the other functional areas should also be emphasized.

The estimation using the water balance equation is intended for the entire study area, which is helpful in evaluating the overall condition of the regionally conserved water resources and is a suitable method for calculating the water conservation amount of Beijing. However, this method is difficult to use in evaluating the differences in the water conservation function within the assessed area and ignores the spatial heterogeneity. The method assumes a homogeneous distribution of precipitation, evapotranspiration and surface runoff in the assessed area. In fact, precipitation, evapotranspiration and runoff indicate considerable spatial heterogeneity for an individual land cover type. 1) In addition to atmospheric circulation, precipitation is also affected by local elevation, topography and vegetation. For example, the annual mean precipitation isoline for Beijing is generally consistent with the orientation of the mountains. The southeastern warm and humid airflow is forced upwards along the southeastern slopes of the mountains to generate precipitation during the summer, forming multiple rain centres in an arc direction along the southeastern slopes of the western and northern mountains (Huang, 2012). This characteristic of precipitation is difficult to evaluate in a large-scale precipitation calculation. 2) Evapotranspiration includes vegetation transpiration, canopy interception and soil evaporation. The actual evapotranspiration is subject to not only the growth status and physiological characteristics of vegetation but also the environmental factors, including meteorology, topography and soil, which show distinct temporal and spatial heterogeneity (Lu et al., 2015). 3) The surface runoff is impacted by many factors, including soil moisture, litter layer thickness and soil porosity, which also has considerable spatial heterogeneity. Therefore, the water conservation amount calculated by the water balance method ignores the spatial heterogeneity of topography, elevation, vegetation, litter and soil, resulting in uncertainty. The water conservation amount is subject to the combined effect of land surface conditions and meteorological parameters, which have complex driving mechanisms. It exhibits an important influence on regional water use. Currently, it is difficult to monitor the actual evapotranspiration at a regional scale, and the measurement of surface runoff requires designated baselines. The future research should focus on how to monitor the areas with little data to estimate water conservation amount more accurately, which is important to the rational allocation and management of regional water.