Interfacing the Urban Land–Atmosphere System Through Coupled Urban Canopy and Atmospheric Models

Abstract

We couple a single column model (SCM) to a cutting-edge single-layer urban canopy model (SLUCM) with realistic representation of urban hydrological processes. The land-surface transport of energy and moisture parametrized by the SLUCM provides lower boundary conditions to the overlying atmosphere. The coupled SLUCM–SCM model is tested against field measurements of sensible and latent heat fluxes in the surface layer, as well as vertical profiles of temperature and humidity in the mixed layer under convective conditions. The model is then used to simulate urban land–atmosphere interactions by changing urban geometry, surface albedo, vegetation fraction and aerodynamic roughness. Results show that changes of landscape characteristics have a significant impact on the growth of the boundary layer as well as on the distributions of temperature and humidity in the mixed layer. Overall, the proposed numerical framework provides a useful stand-alone modelling tool, with which the impact of urban land-surface conditions on the local hydrometeorology can be assessed via land–atmosphere interactions.

Appendix 1: Calculation of Net Radiation in a Street Canyon

The net shortwave and longwave radiative fluxes for walls and ground inside a street canyon can be computed using a two-reflection model (Kusaka et al. 2001; Wang et al. 2013) as,

$$\begin{aligned} S_\mathrm{W}&= (1-a_\mathrm{W})\left[ {\begin{array}{l} S_\mathrm{D} \frac{l_\mathrm{shadow} }{2h}+S_\mathrm{Q} F_{\mathrm{W}\rightarrow \mathrm{S}} +S_\mathrm{D} \left( {\frac{w-l_\mathrm{shadow} }{w}} \right) a_\mathrm{G} F_{\mathrm{W}\rightarrow \mathrm{G}} \\ +S_\mathrm{Q} F_{\mathrm{W}\rightarrow \mathrm{G}} +S_\mathrm{D} \frac{l_\mathrm{shadow} }{2h}a_\mathrm{W} F_{\mathrm{W}\rightarrow \mathrm{W}} +S_\mathrm{Q} a_\mathrm{W} F_{\mathrm{W}\rightarrow \mathrm{S}} F_{\mathrm{W}\rightarrow \mathrm{W}} \\ \end{array}} \right] , \end{aligned}$$

(34)

$$\begin{aligned} S_\mathrm{G}&= \left( {1-a_\mathrm{G} } \right) \left[ S_\mathrm{D} \left( {\frac{w-l_\mathrm{shadow} }{w}} \right) +S_\mathrm{Q} F_{\mathrm{G}\rightarrow \mathrm{S}} +S_\mathrm{D} \frac{l_\mathrm{shadow} }{2h}a_\mathrm{W} F_{\mathrm{G}\rightarrow \mathrm{W}}\right. \nonumber \\&\left. +\,S_\mathrm{Q} a_\mathrm{W} F_{\mathrm{W}\rightarrow \mathrm{S}} F_{\mathrm{G}\rightarrow \mathrm{W}} \right] , \end{aligned}$$

(35)

$$\begin{aligned} L_\mathrm{W}&= \varepsilon _\mathrm{W} \left( {F_{\mathrm{W}\rightarrow \mathrm{S}} L^{\downarrow }+\varepsilon _\mathrm{G} F_{\mathrm{W}\rightarrow \mathrm{G}} \sigma T_\mathrm{G}^4 +\varepsilon _\mathrm{W} F_{\mathrm{W}\rightarrow \mathrm{W}} \sigma T_\mathrm{W}^4 -\sigma T_\mathrm{W}^4 } \right) \nonumber \\&+\,\varepsilon _\mathrm{W} \left( {1-\varepsilon _\mathrm{G} } \right) L^{\downarrow }F_{\mathrm{G}\rightarrow \mathrm{S}} F_{\mathrm{W}\rightarrow \mathrm{G}} \nonumber \\&+\,2\left( {1-\varepsilon _\mathrm{G} } \right) \varepsilon _\mathrm{W} \sigma T_\mathrm{W}^4 F_{\mathrm{G}\rightarrow \mathrm{W}} F_{\mathrm{W}\rightarrow \mathrm{G}} +\varepsilon _\mathrm{W} \left( {1-\varepsilon _\mathrm{W} } \right) L^{\downarrow }F_{\mathrm{W}\rightarrow \mathrm{S}} F_{\mathrm{W}\rightarrow \mathrm{W}} \nonumber \\&+\,\left( {1-\varepsilon _\mathrm{W} } \right) \varepsilon _\mathrm{G} \sigma T_\mathrm{G}^4 F_{\mathrm{W}\rightarrow \mathrm{G}} F_{\mathrm{W}\rightarrow \mathrm{W}} +\varepsilon _\mathrm{W} \varepsilon _\mathrm{W} \left( {1-\varepsilon _\mathrm{W} } \right) \sigma T_\mathrm{W}^4 F_{\mathrm{W}\rightarrow \mathrm{W}} F_{\mathrm{W}\rightarrow \mathrm{W}}, \end{aligned}$$

(36)

$$\begin{aligned} L_\mathrm{G}&= \varepsilon _\mathrm{G} \left( {F_{\mathrm{G}\rightarrow \mathrm{S}} L^{\downarrow }+2\varepsilon _\mathrm{W} F_{\mathrm{G}\rightarrow \mathrm{W}} \sigma T_\mathrm{W}^4 -\sigma T_\mathrm{G}^4 } \right) +2\varepsilon _\mathrm{G} \left( {1-\varepsilon _\mathrm{W} } \right) F_{\mathrm{W}\rightarrow \mathrm{S}} F_{\mathrm{G}\rightarrow \mathrm{W}} L^{\downarrow } \nonumber \\&+\left( {1-\varepsilon _\mathrm{W} } \right) \varepsilon _\mathrm{G} F_{\mathrm{G}\rightarrow \mathrm{W}} F_{\mathrm{W}\rightarrow \mathrm{G}} \sigma T_\mathrm{G}^4 +2\varepsilon _\mathrm{G} \varepsilon _\mathrm{W} \left( {1-\varepsilon _\mathrm{W} } \right) F_{\mathrm{W}\rightarrow \mathrm{W}} F_{\mathrm{G}\rightarrow \mathrm{W}} \sigma T_\mathrm{W}^4, \end{aligned}$$

(37)

where $S_\mathrm{W}$ and $S_\mathrm{G}$ are the net shortwave radiative fluxes for wall and ground respectively, $L_\mathrm{W}$ and $L_\mathrm{G}$ are the net longwave radiative fluxes for wall and ground respectively, $S_\mathrm{D}$ and $S_\mathrm{Q}$ are the direct and diffuse solar radiative fluxes, $a$ is the albedo (solar reflectivity), $F_{i\rightarrow j}$ are the view factors for radiation emitted from a generic surface $i$ and received by surface $j$, and $l_\mathrm{shadow}$ is the normalized shadow length. The shadow length is estimated by (Kusaka et al. 2001),

$$\begin{aligned} l_\mathrm{shadow} =\left\{ {\begin{array}{l@{\quad }l} h\tan \theta _z \sin \theta _\mathrm{n}, &{} l_\mathrm{shadow} < w \\ w,&{} l_\mathrm{shadow} \ge w \\ \end{array}} \right. , \end{aligned}$$

(38)

where $\theta _{z}$ is the solar zenith angle, $\theta _{n}$ is the difference between the solar azimuth angle and canyon orientation. All view factors for radiative exchange between canyon facets are directly related to the aspect ratio $h/w$ (Wang 2010).