Physics Overview¶

SOLWEIG (Solar and Longwave Environmental Irradiance Geometry) calculates the mean radiant temperature (Tmrt) by modeling the complete radiation budget at a point in an urban environment.

Radiation Budget¶

The total radiation received by a human body is:

\[ R_{total} = R_{short} + R_{long} \]

Where:

Shortwave (\(R_{short}\)): Direct and diffuse solar radiation
Longwave (\(R_{long}\)): Thermal radiation from sky, ground, and walls

Calculation Pipeline¶

graph LR
    DSM[DSM] --> SVF[Sky View Factor]
    DSM --> Shadows[Shadow Masks]
    SVF --> GVF[Ground View Factor]
    Shadows --> Radiation
    GVF --> Radiation
    Weather --> Radiation
    Radiation --> Tmrt[Mean Radiant Temp]
    Tmrt --> UTCI
    Tmrt --> PET

Component Models¶

Detailed specifications for each component are maintained in the specs/ directory.

1. Sky View Factor (SVF)¶

Fraction of sky visible from each point, accounting for buildings and vegetation.

SVF Specification

2. Shadow Calculation¶

Sun position and ray tracing to determine shadow patterns.

Shadow Specification

3. Ground View Factor (GVF)¶

View factor from point to ground surface, computing thermal emission from surrounding ground and walls.

GVF Specification

4. Radiation Model¶

Complete shortwave and longwave radiation budget.

Radiation Specification

5. Ground Temperature¶

Surface temperature model with thermal inertia.

Ground Temperature Specification

6. Mean Radiant Temperature¶

Integration of all radiation fluxes into Tmrt.

Tmrt Specification

Thermal Comfort Indices¶

UTCI (Universal Thermal Climate Index)¶

Fast polynomial approximation for outdoor thermal comfort.

UTCI Specification

PET (Physiological Equivalent Temperature)¶

Iterative solver based on human energy balance.

PET Specification

References¶

Lindberg F, Holmer B, Thorsson S (2008) SOLWEIG 1.0 – Modelling spatial variations of 3D radiant fluxes and mean radiant temperature in complex urban settings. Int J Biometeorol 52:697-713 doi:10.1007/s00484-008-0162-7
Lindberg F, Grimmond CSB (2011) The influence of vegetation and building morphology on shadow patterns and mean radiant temperatures in urban areas: model development and evaluation. Theor Appl Climatol 105:311-323
Lindberg F, Onomura S, Grimmond CSB (2016) Influence of ground surface characteristics on the mean radiant temperature in urban areas. Int J Biometeorol 60:1439-1452
Lindberg F, Grimmond CSB, Martilli A (2015) Sunlit fractions on urban facets – Impact of spatial resolution and approach. Urban Climate 12:65-84
Konarska J, Lindberg F, Larsson A, Thorsson S, Holmer B (2014) Transmissivity of solar radiation through crowns of single urban trees — application for outdoor thermal comfort modelling. Theor Appl Climatol 117:363-376
Lindberg F, Grimmond CSB, Gabey A, et al. (2018) Urban Multi-scale Environmental Predictor (UMEP) – An integrated tool for city-based climate services. Environ Model Softw 99:70-87 doi:10.1016/j.envsoft.2017.09.020