**3. Results**

#### *3.1. Validation of Estimated LAI and ET*

The LAI estimated from the Sentinel-2-based NDVI was compared to the observed LAI for June 2018 in the Beijing Sponge City (Figure 2a). The observed LAI was measured within the region around 39.50–40.50◦ N, 115.40–116.10◦ E. The result shows that the Sentinel-2-based LAI has a high correlation with the observed values (R<sup>2</sup> = 0.74), indicating that the LAI at 10m resolution estimated from Sentinel-2 can be well applied to estimate ET for the Beijing Sponge City.

**Figure 2.** Validation of the Sentinel-2-retrieved LAI and the PML-V2-simulated ET. (**a**) The Sentinel-2-retrieved LAI compared to observed LAI for June 2018; (**b**–**d**) The PML-V2-simulated 8-day ET based on MODIS LAI compared to observed ET for the three flux tower sites at Daxing, Miyun and Guantao, respectively, in the Beijing area over 2008–2010.

We also validate the performance of PML-V2 in simulating ET in the Beijing region. Figure 2b–d shows the comparisons of PML-V2-estimated ET based on MODIS LAI with the observed ET over 2008–2010 from three field sites (i.e., Daxing, Miyun and Guantao)

which are located within the Beijing region. The result indicates that PML-V2 has satisfied performance in simulating ET for Beijing Sponge City with (R<sup>2</sup> = 0.64–0.90). Therefore, based on the above good performance in the Sentinel-2-estimated LAI and the PML-V2-estimated ET, we further evaluate NDVI, LAI, and ET and related variables at 10m resolution for Beijing Sponge City.

#### *3.2. Land Use and Vegetation Information in Beijing Sponge City*

By analyzing the Sentinel-2-derived 10m resolution LCC map in 2017, we find that the Beijing Sponge City project (Figure 3) covers ~1265 km<sup>2</sup> over the central Beijing city, China, including impervious surface buildings (59.27%), grasslands (26.08%), mixed forest (7.34%), croplands (5.10%), and wetlands and water bodies (~2%). Figure 3 presents fine spatial details of the urban ecosystem, such as clear patterns of lakes, rivers and streets. Most grasslands are parks, and fixed forests are mainly concentrated in northwestern Beijing Sponge City, while the eastern parts are croplands.

**Figure 3.** Land cover classification at 10m resolution for Beijing Sponge City. Land cover map for 2017 derived from the FROM-GLC10-based Sentinel-2.

We further analyze the NDVI and LAI for June 2018, which was composited from 10-day Sentinel-2 images in June 2018 in clear-sky conditions. We can see high spatial details in the NDVI from Figure 4a. The NDVI for lakes and rivers is ≤0.0, the impervious surfaces (e.g., large mansions and main streets) are 0.0–0.25, and grasslands and croplands are 0.1–0.5, while mixed forests and some parks with forest reserve have NDVI values of 0.5–0.7 (Figure 4a). A high NDVI indicates a high LAI in this study. Figure 4b shows the detailed pattern of LAI for different land cover classes for the sponge city area. As expected, the lakes and rivers have no LAI, and the impervious surfaces (e.g., large mansions and main streets) have only <1.0 m<sup>2</sup> m<sup>−</sup><sup>2</sup> of LAI, but 1~2 m<sup>2</sup> m<sup>−</sup><sup>2</sup> of LAI can be seen in many avenues with greenbelts. The mixed forests in northwestern Beijing Sponge City have LAI values ranging from 1 to 3 m<sup>2</sup> m<sup>−</sup>2. Most grasslands and croplands have 1~2 m<sup>2</sup> m<sup>−</sup><sup>2</sup> of LAI, but some parks with forest reserves show the highest values (3–8 m<sup>2</sup> m<sup>−</sup>2) of LAI (Figure 4b).

**Figure 4.** Vegetation index at 10m resolution for Beijing Sponge City. (**a**) NDVI and (**b**) LAI (m<sup>2</sup> m<sup>−</sup>2) for June 2018 derived from the Sentinel-2.

#### *3.3. ET and Related Variables in Beijing Sponge City*

Based on the Sentinel-2-derived LCC and LAI data, we conducted daily simulations for June 2018 at 10m resolution using the PML-V2 model with daily climate forcing data from CMFD v1.0. Figure 5 presents the spatial patterns of simulated monthly ET and GPP averaged over the daily output for June 2018. Lakes and rivers have the highest ET (≥8 mm <sup>d</sup>−1) due to the full water supply for evaporation in Summer. There is no GPP in lakes and rivers as simulated by PML-V2. The vegetation production activities are strongest in mixed forests and croplands, with the GPP ranging from 8 to 16 gC m<sup>−</sup><sup>2</sup> d−<sup>1</sup> (Figure 5b). In these mixed forests and croplands, the ET is also high (4–6 mm <sup>d</sup>−1), where the plant transpiration (Ec) plays a dominant role with ratios of Ec to ET larger than 0.8 (Figure 6a). In addition, the impervious surfaces have very small ET (<2 mm <sup>d</sup>−1) and GPP (<4 gC m<sup>−</sup><sup>2</sup> <sup>d</sup>−1), indicating both Ec and soil evaporation (Es) are very small in these areas. The grasslands have 2–4 mm d−<sup>1</sup> of ET and 4–8 gC m<sup>−</sup><sup>2</sup> d−<sup>1</sup> of GPP in the sponge city (Figure 5), where the ratio Ec/ET are 0.5–0.7 (Figure 6a).

In summary, on average, for the whole sponge city, we find that the LAI in June 2018 is 0.83 m<sup>2</sup> m<sup>−</sup>2; the ET is about 1.6 mm d−1; the GPP is 2.8 gC m<sup>−</sup><sup>2</sup> d−1. Table 2 further gives the evaluation for different districts in the sponge city. It shows that the central areas (i.e., Xicheng and Dongcheng districts) have the smallest LAI (0.66–0.7 m<sup>2</sup> m<sup>−</sup>2), ET (~1.61 mm <sup>d</sup>−1) and GPP (2.36–2.44 gC m<sup>−</sup><sup>2</sup> <sup>d</sup>−1), while the western areas (i.e., Shijingshan and Haidian districts) have the highest LAI (0.93–1.05 m<sup>2</sup> m<sup>−</sup>2), ET (~1.65 mm <sup>d</sup>−1) and GPP (3.10–3.53 gC m<sup>−</sup><sup>2</sup> <sup>d</sup>−1).

**Figure 5.** ET and GPP at 10m resolution for Beijing Sponge City estimated using the PML-V2 model and Sentinel-2 data. (**a**) Monthly ET (mm <sup>d</sup>−1) in June 2018; (**b**) Monthly GPP (gC m<sup>−</sup><sup>2</sup> <sup>d</sup>−1) in June 2018.

**Figure 6.** Spatial sensitivity of ET to LAI for the Beijing Sponge City. (**a**) Spatial pattern of the fraction of Ec to ET in June 2018; (**b**) Change in the fraction of Ec to ET with LAI; (**c**) Spatial pattern of the ratio of ET to LAI in June 2018; (**d**) Change in ratio of ET to LAI with LAI.


**Table 2.** The ecohydrological environment in different districts in Beijing Sponge City.

We further investigate how ET changes spatially with increasing LAI for June 2018. It is shown that the fraction Ec/ET increases with LAI for the three vegetation types (grassland, mixed forest and cropland) in the sponge city (Figure 6b). The Ec/ET for mixed forests increase from 0.4 (LAI = 0.5) to 0.8 (LAI > 3), while Ec/ET for grasslands and croplands show higher values, increasing from 0.6 (LAI = 0.5) to 0.9 (LAI > 3). The ratio ET/LAI represents the amount of water loss per unit LAI. In Figure 6c, we can find that ET/LAI for mixed forests and some grassland parks show the lowest ET/LAI (0.8–1.2), while impervious surfaces have the highest ET/LAI, with about 2-3 times larger values (2.4–3.6). The ET/LAI for the major vegetation types (grassland, mixed forest and cropland) decrease with LAI increase (Figure 6d); with LAI increasing from 0.5 to 5.0, the ET/LAI for mixed forests decrease from 2.0 to 0.6, and ET/LAI for grasslands and croplands from 3.0 to 1.0. This result indicates that grasslands and croplands have much higher water consumption per unit LAI than mixed forests.

Fractional contributions of other ET components to ET have been estimated (Figure 7). Soil evaporation (Es) contributes a relatively small fraction (≤0.2) due to a very small fraction of bare lands and large vegetation coverage in mixed forests, grasslands and

croplands in June 2018 in the Beijing Sponge City. The fraction of Ei/ET is small (≤0.1) in most LCC types but in grasslands is 0.1–0.2 (Figure 7b). According to a previous study, the city impervious surface could contribute less than 20% of ET [4]. Surprisingly, the impervious surface evaporation (Eu) for the Beijing Sponge City contributes 0.2–0.3 fractions to the ET in June 2018 in most impervious areas (Figure 7c). Finally, all ET from lakes and rivers are contributed by water body evaporation Ew (Figure 7d).

**Figure 7.** The fraction of Es, Ei, Eu and Ew to ET in June 2018 for the Beijing Sponge City. (**a**) Spatial pattern of fraction Es/ET; (**b**) Spatial pattern of fraction Ei/ET; (**c**) Spatial pattern of fraction Eu/ET; (**d**) Spatial pattern of fraction Ew/ET.

ET can be converted to latent heat flux (LE, in W m<sup>−</sup>2) and plays an important role in regulating surface energy balance (Figure 8). For June 2018 in Beijing, the surface receives about 260–270 W m<sup>−</sup><sup>2</sup> of shortwave radiation, but about half is reflected in the atmosphere with the net radiation (Rn) for impervious surface less than 130 W m<sup>−</sup>2. For mixed forests and grasslands, the Rn is about 140–150 W m<sup>−</sup>2, and the croplands and water bodies have a higher Rn of 170–180 W m<sup>−</sup><sup>2</sup> (Figure 8b). Lakes and rivers have the highest LE (>250 W m<sup>−</sup>2) but the smallest sensible heat flux (SH, <−60 W m<sup>−</sup>2). The SH for mixed forests, forest parks and croplands are relatively small (−20 to 20 W m<sup>−</sup>2), while both impervious surfaces and grasslands are high (40–60 W m<sup>−</sup>2) (Figure 8d). This result indicates that the high surface air temperature (reflected by SH) in the summer of Beijing's central city is mostly contributed by impervious surfaces and grasslands.

**Figure 8.** Energy fluxes in June 2018 for the Beijing Sponge City. (**a**) Downward shortwave radiation; (**b**) Surface net radiation; (**c**) Latent heat flux; (**d**) Sensible heat flux. Units are in W m<sup>−</sup>2.
