## 3 Model Development
### Urban Parametrization  
A single-layer-type urban model is implemented within ECLand. A detailed description of the scheme, which includes a basic assumption of urban geometry, computes roughness lengths and considers fluxes from multiple surfaces (Figure 8), can be found in [69]. The Urban scheme is applied as a new sub-grid surface tile and uses mapped parameters and derived variables to compute surface energy and water fluxes. The urban environment is represented as both a canyon, consisting of walls and road, and a roof fraction. An infinite length canyon assumption is made to factor shadowing from buildings and is dependent on both urban parameters and the solar zenith angle. Building height and canyon characteristics are used to estimate surface roughness and any concept of canyon orientation is removed. Energy and moisture exchange between the surface and both the atmosphere and sub-surface is defined by urban parameters, including a simple representation of urban drainage. The scheme consists of both time varying (e.g., albedo based on solar zenith angle) and fixed variables (e.g., thermal heat capacity of a building). The variables required for the urban scheme are based on previous similar schemes [70; 71; 72] and listed in the Supplementary Materials.  
Currently, ECLand consists of eight sub-grid surface tiles and a lake tile. To represent the urban environment we have introduced a tenth tile and updated the high vegetation snow to include an urban representation. When considering tile fractions over land, the value summed across all tiles is equal to 1. For the land surface this was previously a combination of wet land, low vegetation, high vegetation and bare soil and, for the latter three with and without snow cover. Over urban areas the addition of an urban land cover map would increase the sum above one. To prevent this, existing tile fractions are re-weighted to account for the urban tile following an update of the ECLand tiles Equation (5) where high vegetation (\(C_{H}\)), low vegetation (\(C_{L}\)), bare soil (\(C_{B}\)) and snow under high-vegetation (\(C_{H_{mow}}\)) covered fractions are updated from the original values (\(C_{H_{orig}}\), \(C_{L_{orig}}\)) accounting for the urban fraction (\(C_{U}\)).  
\[\begin{split} C_{H}&=C_{H_{orig}}\times(1-C_{U}),\\ C_{L}&=C_{L_{orig}}\times(1-C_{U}),\\ C_{B}&=(1-C_{H}-C_{L}-C_{U}),\\ C_{H_{mow}}&=C_{sn}\times(C_{H}+C_{U}),\\ C_{U_{dry}}&=(1-C_{wet})\times(1-C_{sn})\times C_{U}, \end{split} \tag{5}\]  
where \(C_{sn}\), \(C_{U_{dry}}\) and \(C_{wet}\) represent the snow covered, dry urban and wet fraction, respectively.  
For land surface skin, future developments will merge the urban cover product with the remaining land cover so this re-weighting process is no longer required. For certain elements, for example, hydrology, this prevents a weighted average that neither fits an urban or non-urban regime. Currently, for sub-surface thermodynamic and hydrological properties, the urban tile re-weights the uppermost soil layer. The urban land cover used here is based on grid cell specific information provided by ECOCLIMAP-SG, at an initial 300 m horizontal resolution [73].  
Figure 8: Schematic of the single-layer urban model used in ECLand including key parameters (\(\alpha\): albedo, \(\varepsilon\): emissivity, \(\lambda\): thermal conductivity, \(C\): volumetric heat capacity), variables (\(T\): temperature, \(Q\): moisture content), and fluxes of heat and moisture (\(\Phi_{\text{H,W}}\)).