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Ground View Factor (GVF)

Computes ground- and wall-emitted radiation integrated across all visible surfaces from a point at person height. Despite the name, the primary outputs are thermal emission (Lup in W/m²) and albedo-weighted view factors, not a simple dimensionless view factor.

Reference: Lindberg et al. (2008) Section 2.3

Algorithm

GVF is computed by integrating visible ground and wall surfaces across 18 azimuth directions (5° start, 20° step, covering 360°). For each azimuth, rays march outward from each pixel to detect buildings and walls, accumulating their thermal and reflective contributions.

Integration Distances

Two distance scales are used, based on person height:

first  = round(height × pixel_scale), min 1   (near-field, ~person height in pixels)
second = round(height × 20 × pixel_scale)      (far-field, ~20× person height in pixels)

Near/Far Weighting

The final GVF is a weighted blend of near-field and far-field results:

gvf      = (gvf1 × 0.5 + gvf2 × 0.4) / 0.9
gvf_lup  = (gvfLup1 × 0.5 + gvfLup2 × 0.4) / 0.9 + lup_local × (1 - buildings)
gvf_alb  = (gvfalb1 × 0.5 + gvfalb2 × 0.4) / 0.9 + alb_grid × (1 - buildings) × shadow

The near-field captures local wall effects; the far-field captures distant ground/wall contributions. The (1 - buildings) term adds the local ground contribution for non-building pixels.

Longwave Emission (Differential Formula)

The Lup contribution per azimuth uses a differential formula — computing excess emission above ambient:

lup_diff = SBC × emis × (Tg × shadow + Ta + 273.15)⁴ - SBC × emis × (Ta + 273.15)⁴

The final gvf_lup adds the ambient baseline back:

gvf_lup = weighted_sum(lup_diff) + SBC × emis × (Tg_local × shadow + Ta + 273.15)⁴
          - SBC × emis × (Ta + 273.15)⁴ + that last term for non-building pixels

For walls, a similar differential:

lwall = SBC × ewall × (tgwall + Ta + 273.15)⁴ - SBC × ewall × (Ta + 273.15)⁴

Where tgwall is the wall temperature deviation from air temperature (K), only applied to sunlit walls.

Water Temperature Override

When land cover data is active (landcover=true), water pixels (lc_grid == 3) have their ground temperature overridden:

Tg_water = Twater - Ta    (Twater from weather file)

This bypasses the land cover parameter table (TgK/TmaxLST) for water surfaces.

Sunwall Mask

A sunwall mask identifies building pixels adjacent to sunlit walls:

sunwall = 1.0 if wallsun > tolerance AND walls > 0

This determines whether wall-temperature terms (heated walls) or ambient-temperature terms are used for nearby building faces.

Geometry Caching

The ray-tracing geometry (building blocking distances, wall influence masks) can be precomputed once and reused across timesteps. The cached path (sun_on_surface_cached) skips the expensive ray-marching and only recomputes the thermal-dependent outputs (gvf_lup, gvfalb). The purely geometric output (gvfalbnosh) is taken directly from the cache.

Inputs

Input Type Description
wallsun 2D array (f32) Sunlit wall height from shadow calculation
walls 2D array (f32) Wall height grid
buildings 2D array (f32) Building mask (1.0 = building, 0.0 = ground)
shadow 2D array (f32) Combined shadow mask (0.0-1.0)
dirwalls 2D array (f32) Wall aspect (orientation) in degrees
tg 2D array (f32) Ground temperature deviation from air temp (°C)
emis_grid 2D array (f32) Ground surface emissivity per pixel
alb_grid 2D array (f32) Ground surface albedo per pixel
lc_grid 2D array (f32) Land cover classification grid (optional)
scale float Pixel size in meters
first float Person height parameter (m), typically 1.1
second float Far-field height parameter (m), typically 22.0
tgwall float Wall temperature deviation from air temp (K)
ta float Air temperature (°C)
ewall float Wall emissivity
sbc float Stefan-Boltzmann constant (5.67051e-8)
albedo_b float Building wall albedo
twater float Water temperature from weather file (°C)
landcover bool Whether to use land cover classification

Outputs

Output Type Description
gvf_lup 2D array (W/m²) Longwave upwelling from ground/walls (center)
gvfalb 2D array Albedo-weighted ground view (shadow-dependent, center)
gvfalbnosh 2D array Albedo-weighted ground view (no shadow, geometric only, center)
gvf_lup_e 2D array (W/m²) Longwave upwelling, east-facing contribution
gvfalb_e 2D array Albedo-weighted view, east
gvfalbnosh_e 2D array Albedo view (no shadow), east
gvf_lup_s 2D array (W/m²) Longwave upwelling, south-facing contribution
gvfalb_s 2D array Albedo-weighted view, south
gvfalbnosh_s 2D array Albedo view (no shadow), south
gvf_lup_w 2D array (W/m²) Longwave upwelling, west-facing contribution
gvfalb_w 2D array Albedo-weighted view, west
gvfalbnosh_w 2D array Albedo view (no shadow), west
gvf_lup_n 2D array (W/m²) Longwave upwelling, north-facing contribution
gvfalb_n 2D array Albedo-weighted view, north
gvfalbnosh_n 2D array Albedo view (no shadow), north
gvf_sum 2D array Geometry normalization sum (used internally)
gvf_norm 2D array Geometry normalization factor (used internally)

Note: gvf_lup has units of W/m² (contains emission calculation), not dimensionless. gvfalb already contains albedo weighting and is used directly by the radiation budget — it is not a pure view factor.

Properties

Output Properties

  1. gvf_lup contains thermal emission
  2. Not a dimensionless factor — units are W/m²
  3. Includes both ground and wall longwave contributions

  4. Higher in urban canyons (more wall emission)

  5. gvfalb includes albedo

  6. Already albedo-weighted; no further multiplication by albedo needed

  7. Shadow-dependent: higher in sunlit areas (more reflected shortwave)

  8. gvfalbnosh is purely geometric

  9. Independent of shadow state and weather
  10. Can be cached across timesteps (used by geometry cache)

Geometric Properties

  1. Flat open terrain
  2. gvf_lup ≈ local ground emission only

  3. No wall contributions

  4. Urban canyon has high wall contribution

  5. Walls on both sides increase gvf_lup

  6. More reflected and emitted radiation in canyons

  7. Directional asymmetry

  8. East-facing wall contributes to western GVF (seen from west)
  9. Asymmetric building layout → asymmetric directional outputs

Role in Radiation Budget

GVF outputs feed directly into the radiation computation:

Reflected Shortwave (Kup): Uses gvfalb and gvfalbnosh directly (albedo already baked in):

kup = gvfalb × rad_i × sin(altitude) + ct × gvfalbnosh

Longwave Upwelling (Lup): Uses gvf_lup after thermal delay smoothing:

Lup = TsWaveDelay(gvf_lup, ...)    [smoothed across timesteps]

References

Primary UMEP Citation:

  • Lindberg F, Grimmond CSB, Gabey A, Huang B, Kent CW, Sun T, Theeuwes N, Järvi L, Ward H, Capel-Timms I, Chang YY, Jonsson P, Krave N, Liu D, Meyer D, Olofson F, Tan JG, Wästberg D, Xue L, Zhang Z (2018) "Urban Multi-scale Environmental Predictor (UMEP) - An integrated tool for city-based climate services." Environmental Modelling and Software 99, 70-87. doi:10.1016/j.envsoft.2017.09.020

GVF Model:

  • 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." International Journal of Biometeorology 52(7), 697-713.