# The Microscale Urban Surface Energy (MUSE) Model for Real Urban Application

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Microscale Urban Surface Energy (MUSE) Model

#### 2.1. Grid Representation and Urban Physical Processes

#### 2.1.1. Grid Representation of Urban Surfaces

#### 2.1.2. Urban Physical Processes

#### 2.2. Radiation Processes

#### 2.2.1. Shadow Model

#### 2.2.2. Patch View Factors

#### 2.2.3. Shortwave Radiation

^{−2}for the other shaded patches. On the other hand, the diffuse shortwave radiative flux at the patch $I$ (${S}_{I}^{dif}$) can be calculated by

^{−20}to further enhance computational efficiency, which leads to a negligible difference in surface temperature.

#### 2.2.4. Longwave Radiation

^{−8}W m

^{−2}K

^{−4}).

#### 2.3. Turbulent Sensible Heat Exchange

#### 2.3.1. Horizontal Roof and Road Patches

^{−3}), ${c}_{p}$ is the specific heat capacity at constant pressure (J kg

^{−1}K

^{−1}), ${u}_{*}$ is the friction velocity (m s

^{−1}), and ${T}_{*}$ is the temperature scale (K). $\mathsf{\kappa}$ is the von Kármán constant, ${z}_{0,I}$ and ${z}_{0T,I}$ are the surface roughness lengths for momentum and heat, respectively, $R{i}_{B}$ is the bulk Richardson number ($=\frac{gz\Delta T}{\overline{\theta}{U}_{a}{}^{2}}$), and F

_{h}is the atmospheric stability correction function. ${T}_{I}$ is the surface temperature of the patch $I$, and ${T}_{a}$ and ${U}_{a}$ are the temperature and wind speed at the adjacent atmospheric grid of the patch $I$, respectively.

#### 2.3.2. Vertical Wall Patches

#### 2.4. Subsurface Heat Conduction

## 3. Field Measurements and the MUSE Model Configuration for Validation

#### 3.1. Field Measurements

#### 3.2. Configuration of the Model

^{2}horizontally and 54 m vertically with the same grid resolution of 3 m (Figure 5b). The resultant total number of active patches is 24,323 in the simulation domain. The physical property parameters of each patch have been assigned according to the surface features of the real urban area. The aerodynamic roughness lengths for momentum are 0.05 m for roof and road patches, and the roughness lengths for heat are 0.0005 m for roof patches and 0.005 m for road patches. The radiative and thermal parameters of roof and wall patches are assigned for concrete and red brick, and those of road patches are for asphalt [64,70]. Table 3 summarizes the physical property parameters assigned for the real urban simulation. The roof, wall, and road patches are 0.5, 0.4, and 1.0 m in depth, configuring with ten sublayers at each patch. Each surface’s depth was determined based on the previous simulation studies that showed reasonable comparison against measurements (e.g., [64]).

^{−1}(Figure 6a). The low wind speed was found frequently in forming the surface layer on a hot summer day. The downward shortwave radiation reached approximately 825 W m

^{−2}around noon, but it was influenced by clouds observed during the measurement on the day (Figure 6b). The wind speed and air temperature profiles estimated from the measurements show characteristic diurnal variations within the surface layer on the day (Figure 6c,d). The wind speeds are quite low near the ground throughout the day, which gradually increases with height. The air temperature profiles are relatively homogeneous in the vertical direction during the night, which indicates that the atmosphere remained near neutral or weakly unstable.

## 4. Validation Results

#### 4.1. Shadow Model, View Factors, and Effective Albedos

#### 4.2. The Real Urban Simulation

^{−2}, while it overestimates the storage heat fluxes by MBE of −49.33 W m

^{−2}. The simulated turbulent heat fluxes are relatively well compared with the measurement with MBE of −1.69 W m

^{−2}. The statistical analysis shows that the model biases are systematic from the ratio of RMSE

_{s}to RMSE by 85% and 61% both in net radiation and storage heat flux, respectively. The temporal correlation coefficients are high—0.99 and 0.96 for net radiation and storage heat flux, respectively. These results imply that the model measurement discrepancies might be associated with static surface physical properties over the domain, such as surface albedo and thermal heat capacity. Despite the discrepancies, the MUSE model reproduces the surface energy balance over the area. The measured and simulated ratios of the storage heat flux to net radiation (G/R*) are about 0.72 and 0.69 during the daytime (0800-1600 LST) and 1.06 and 1.13 at night (2000-0200 LST), respectively. The relatively high G/R* is a characteristic feature of the heatwave period associated with weak winds in the urban area. Overall the MUSE model simulates diurnal variations of the surface fluxes and the relative energy balance measured in the urban area.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Comparison of the MUSE and TUF-3D Models

MUSE (This Study) | TUF-3D (Krayenhoff et al. [40]) | |
---|---|---|

Shadow model | Geometric ray casting approach (this study) | Ray tracing algorithm (modified from Soux et al. [81]) |

View factor | Numerical method based on analytical formulation (Lee et al. [63]) | Exact plane parallel analytical equations (Siegel and Howell [57]) |

Turbulent sensible heat exchange for roof and road surfaces | Monin–Obukhov similarity (Lee and Park [64]) | Empirical formulation (Rowley et al. [66]; Cole and Sturrock [82]) |

Turbulent sensible heat exchange for wall surfaces | Empirical formulation (Rowley et al. [66]) | Empirical formulation (Rowley et al. [66]; Cole and Sturrock [82]) |

Subsurface heat conduction | 1-D heat conduction equation/explicit finite difference method on a staggered grid (Lee and Park [64]) | 1-D heat conduction equation/finite difference method on a regular grid (Masson [67]) |

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**Figure 1.**(

**a**) Three-dimensional representation of urban buildings and ground surfaces in the microscale urban surface energy (MUSE) model. (

**b**) Definition of the six patches (top, bottom, east, west, south, and north) and the active patches that interact with the surrounding atmospheric grid cells (blue). ${T}_{a}$ and ${U}_{a}$ are the air temperature and wind speed at the adjacent atmospheric grid cells, respectively.

**Figure 2.**Configuration of the subsurface layers at each patch and associated physical processes in the MUSE model. ${T}_{k,I}$ denotes the subsurface temperature at the layer $k$ of the patch $I$, and ${F}_{k,I}$ is the conductive heat flux at the vertical level $k$ of the patch $I$. ${S}^{dir\downarrow}$ and ${S}^{dif\downarrow}$ denote the downward direct and diffuse shortwave radiation, respectively, and ${L}^{dif\downarrow}$ is the downward longwave radiation. ${T}_{a}$ and ${U}_{a}$ are the air temperature and wind speed at the adjacent atmospheric grid cells, respectively.

**Figure 3.**Schematic of the shadow submodel of the MUSE model. It illustrates the shadow geometry formed by building A. Here, the shaded area denotes the actual shape of the building’s shadow calculated by the analytical computation, and the sol id line indicates the shaded patches estimated in the MUSE model. ${\theta}_{z}$ and ${\theta}_{a}$ are the solar zenith angle and the solar azimuth angle, respectively. ${l}_{hor}$ and ${l}_{vert}$ are the horizontal shadow length and the vertical shadow length, respectively.

**Figure 4.**Schematics of the patch–patch view factor computation for (

**a**) ground–wall patches and (

**b**) wall–wall patches (modified from Lee et al. [63]). $\Delta {A}_{I}$ and $\Delta {A}_{J}$ are the areas of the patches $I$ and $J$, respectively. $\Delta X$, $\Delta Y$, and $\Delta Z$ are the distances between the two patches in each directions, and $R$ is the distance between the two patches. ${n}_{I}$ and ${n}_{J}$ are the unit vectors perpendicular to the patches $I$ and $J$, respectively.

**Figure 5.**(

**a**) The aerial view of the study area for the real urban environment test of the MUSE model (Source: Google Earth). The study area (36.4717° N, 127.1426° E) is located in the Kongju National University, South Korea, and a micrometeorological flux tower has been installed at the rooftop of a campus building (~33 m a.g.l.) (red circle). The surface temperatures were measured at the roof and wall surfaces of the building (red circle) and the road site (white circle). (

**b**) The validation simulation domain and building height representation in the MUSE model. Each building height was represented using National Geographic Information System (NGIS) database from National Geographic Information Institute (NGII), Ministry of Land, Infrastructure and Transport (MLIT) of South Korea.

**Figure 6.**Diurnal variations of the (

**a**) air temperature and wind speed and the (

**b**) downward shortwave and longwave radiation measured from the flux tower at the Kongju National University campus on 19 August 2016. The measured global shortwave radiation is partitioned to the direct (${S}^{dir\downarrow}$) and diffuse (${S}^{dif\downarrow}$) shortwave radiation according to the diffuse radiation fraction (dashed line in (

**b**)) calculated following Overby et al. [43] and Monteith and Unsworth [71]. Time-height sections of the meteorological profiles of the (

**c**) wind speed and (

**d**) air temperature calculated from the meteorological and flux measurements at 33 m a.g.l. and the Monin–Obukhov similarity relation. The horizontal dashed line indicates the measurement height.

**Figure 7.**Three-dimensional distributions of sunlit/shaded patches over the real urban area calculated by the shadow model at (

**a**) 09 LST, (

**b**) 12 LST, (

**c**) 15 LST, and (

**d**) 18 LST on 19 August 2016.

**Figure 8.**Comparison of the patch–sky view factor (${\psi}_{I\to sky}$) at horizontal patches estimated by the MUSE model and the analytical method (Johnson and Watson [59]) for (

**a**) symmetrical finite length street canyon and (

**b**) nonsymmetrical finite length street canyon. The computation by Equation (12) in Lee et al. [63] is also compared.

**Figure 9.**Three-dimensional distribution of patch–sky view factors at each horizontal and vertical patch over the real urban area.

**Figure 10.**Comparison of the observed and simulated effective albedos for the (

**a**,

**b**) flat surface, (

**c**,

**d**) north-south canyon model, (

**e**,

**f**) east-west canyon model, and (

**g**,

**h**) cube array canyon in the summer (left panels) and winter (right panels) experiment days. R is the correlation coefficient. The dotted line (

**c**–

**h**) denotes the effective albedo computed without time-varying roof and road surface albedos.

**Figure 11.**Three-dimensional distributions of the simulated surface temperatures at the horizontal and vertical patches over the real urban area at (

**a**) 09 LST, (

**b**) 12 LST, (

**c**) 15 LST, and (

**d**) 18 LST on 19 August 2016.

**Figure 12.**Comparison of the measured and simulated surface temperatures of the (

**a**) east wall, (

**b**) west wall, (

**c**) south wall, (

**d**) north wall, (

**e**) roof, and (

**f**) road surface on 19 August 2016.

**Figure 13.**Comparison of the measured and simulated net radiation (R*), turbulent heat fluxes (H), and storage heat fluxes (G) on 19 August 2016. The measured turbulent heat fluxes were calculated by the sum of sensible heat fluxes (H) and latent heat fluxes (L). The storage heat fluxes were estimated as a residual term between net radiation and turbulent heat fluxes.

Variable | Symbol | Unit | |
---|---|---|---|

Meteorological forcing variables | Wind velocity components | ${U}_{a}\left(U,V,W\right)$ | m s^{−1} |

Air temperature | ${T}_{a}$ | K | |

Downward direct shortwave radiation | ${S}^{dir\downarrow}$ | W m^{−2} | |

Downward diffuse shortwave radiation | ${S}^{dif\downarrow}$ | W m^{−2} | |

Downward longwave radiation | ${L}^{dif\downarrow}$ | W m^{−2} | |

Predicted variables | Friction velocity | ${u}_{*}$ | m s^{−1} |

Incident direct shortwave radiation | ${S}_{I}^{dir}$ | W m^{−2} | |

Incident diffuse shortwave radiation | ${S}_{I}^{dif}$ | W m^{−2} | |

Reflected shortwave radiation | ${S}_{I}^{R}$ | W m^{−2} | |

Net shortwave radiation | ${S}_{I}^{*}$ | W m^{−2} | |

Emitted longwave radiation | ${L}_{I}$ | W m^{−2} | |

Incident diffuse longwave radiation | ${L}_{I}^{dif}$ | W m^{−2} | |

Reflected longwave radiation | ${L}_{I}^{R}$ | W m^{−2} | |

Net longwave radiatio${L}_{I}^{R}$ | ${L}_{I}^{*}$ | W m^{−2} | |

Sensible heat flux | ${H}_{I}$ | W m^{−2} | |

Heat flux at subsurface layer $k$ | ${F}_{k,I}$ | W m^{−2} | |

Temperature at layer $k$ | ${T}_{k,I}$ | K |

**Table 2.**Physical property parameters of the MUSE model used to represent the physical properties of urban surfaces.

Parameter | Symbol | Unit |
---|---|---|

Roughness length for momentum | ${z}_{0}$ | m |

Roughness length for heat | ${z}_{0T}$ | m |

Surface albedo | $\alpha $ | - |

Surface emissivity | $\epsilon $ | - |

Thermal conductivity | $k$ | W m^{−1} K^{−1} |

Volumetric heat capacity | $C$ | J m^{−3} K^{−1} |

Thickness of each subsurface layer | $\Delta z$ | m |

**Table 3.**Physical property parameters used for validation simulation of the Kongju National University campus site.

Parameter | Unit | Roof | Wall | Road |
---|---|---|---|---|

Roughness length for momentum (${z}_{0}$) | m | 0.05 | - | 0.05 |

Roughness length for heat (${z}_{0T}$) | m | 0.00005 | - | 0.00005 |

Surface albedo ($\alpha $) | - | 0.28 | 0.20 | 0.18 |

Surface emissivity ($\epsilon $) | - | 0.90 | 0.90 | 0.94 |

Thermal conductivity ($k$) | W m^{−1} K^{−1} | 0.90 | 0.70 | 0.79 |

Volumetric heat capacity ($C$) | J m^{−3} K^{−1} | 1.40 × 10^{6} | 1.60 × 10^{6} | 1.83 × 10^{6} |

Thickness ($\Delta z$) | m | 0.5 | 0.4 | 1.0 |

**Table 4.**Comparison of the average patch–sky view factors (${\psi}_{I\to sky}$) estimated from the analytical formulation (Johnson and Watson [59]: JW84), the numerical method (Equation (12) in Lee et al. [63]: Lee18), and the MUSE model. Two different canyon geometries of the symmetrical and nonsymmetrical canyons are considered, and the patch–sky view factors calculated from each method are averaged across the street canyon (east-west direction), along the street canyon (north-south direction), and over the entire canyon surface. The value in parenthesis denotes the relative error (%) defined by $\frac{\psi -{\psi}_{JW84}}{{\psi}_{JW84}}\times 100$.

East-West Direction | North-South Direction | Whole Area | ||
---|---|---|---|---|

Symmetric canyon | JW84 | 0.646 | 0.777 | 0.681 |

Lee18 | 0.647 (0.15) | 0.778 (0.12) | 0.682 (0.14) | |

MUSE | 0.645 (−0.07) | 0.777 (−0.01) | 0.681 (−0.06) | |

Asymmetric canyon | JW84 | 0.545 | 0.663 | 0.589 |

Lee18 | 0.546 (0.14) | 0.664 (0.09) | 0.590 (0.14) | |

MUSE | 0.545 (−0.08) | 0.663 (−0.01) | 0.589 (−0.07) |

**Table 5.**Comparison of mean absolute errors ($\left|{\alpha}_{MOD}-{\alpha}_{OBS}\right|$) of the effective albedos (${\alpha}_{MOD}$) from Sievers and Zdunkowski [77] (SZ95), TUF-3D, and the MUSE model against Aida’s experiment (Aida [76]) for two typical days of 15 June 1978 and 3 December 1977. The three different canyon geometries are model 1 (north-south canyon model), model 2 (west-east canyon model), and model 3 (2 × 2 cube array model). The value in parenthesis denotes the fractional error defined as $\left|\frac{{\alpha}_{MOD}-{\alpha}_{OBS}}{{\alpha}_{OBS}}\right|\times 100$.

15 June 1978 | 3 December 1977 | |||||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |

SZ85 | 0.015 | - | 0.020 | - | ||

TUF-3D | 0.009 | 0.007 | 0.022 | 0.014 | ||

MUSE | 0.002 (0.1%) | 0.006 (0.2%) | 0.016 (1.0%) | 0.009 (0.5%) | 0.014 (0.9%) | 0.013 (0.6%) |

**Table 6.**Performance statistics (°C) of the surface temperatures simulated at the roof, road, and walls surfaces at the urban area for 19 August 2016. MBE is the mean bias error, RMSE is the root mean square error, and R is the correlation coefficient. RMSE

_{s}and RMSE

_{u}are the systematic and unsystematic components of RMSE, respectively.

West | East | South | North | Roof | Road | |
---|---|---|---|---|---|---|

MBE | −0.97 | −1.95 | −2.72 | −1.17 | −0.64 | 1.34 |

RMSE | 2.09 | 2.80 | 3.49 | 1.90 | 2.97 | 4.11 |

(RMSE_{s}/RMSE_{u}) | (1.66/1.27) | (2.13/1.82) | (3.01/1.78) | (1.72/0.81) | (1.40/2.62) | (2.81/3.01) |

R | 0.97 | 0.94 | 0.96 | 0.98 | 0.97 | 0.97 |

**Table 7.**Performance statistics (W m

^{−2}) of the simulated net radiation, sensible heat fluxes, and storage heat fluxes at the real urban area for 19 August 2016.

Net Radiation | Sensible Heat Flux | Storage Heat Flux | |
---|---|---|---|

MBE | −50.52 | −1.69 | −49.33 |

RMSE | 64.21 | 37.43 | 69.01 |

(RMSE_{s}/RMSE_{u}) | (59.34/24.51) | (20.55/31.29) | (53.67/43.39) |

R | 0.99 | 0.78 | 0.96 |

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## Share and Cite

**MDPI and ACS Style**

Lee, D.-I.; Lee, S.-H.
The Microscale Urban Surface Energy (MUSE) Model for Real Urban Application. *Atmosphere* **2020**, *11*, 1347.
https://doi.org/10.3390/atmos11121347

**AMA Style**

Lee D-I, Lee S-H.
The Microscale Urban Surface Energy (MUSE) Model for Real Urban Application. *Atmosphere*. 2020; 11(12):1347.
https://doi.org/10.3390/atmos11121347

**Chicago/Turabian Style**

Lee, Doo-Il, and Sang-Hyun Lee.
2020. "The Microscale Urban Surface Energy (MUSE) Model for Real Urban Application" *Atmosphere* 11, no. 12: 1347.
https://doi.org/10.3390/atmos11121347