From albedo darkening to radiative forcing and melt
How the atlas converts wildfire-attributable albedo darkening into energy and an upper-bound melt estimate.
Wildfire deposits particles, including black carbon and organic matter, on glacier surfaces. The surface darkens and its albedo decreases. A darker glacier absorbs more incoming solar radiation; this additional energy can melt more ice. The atlas represents that chain in three steps: darkening → radiative forcing → melt.
The energy chain
Δα
darkening
Negative albedo change attributed to wildfire: the difference between with-fire and no-fire counterfactuals.
×
SW
incoming shortwave
Physically downscaled incoming solar radiation (W/m²), not a constant.
=
RF
radiative forcing
Additional absorbed energy in W/m², equivalent to J/s/m².
→
× 92 days ÷ Lf
melt
Energy accumulated over the JJA model window, divided by the latent heat of fusion.
Formulas
RF = −Δα · SW
wildfire radiative forcing (W/m²)
melt =
RF · Δt · 86400Lf
in mm water equivalent
Δt is the 92-day JJA model window, 86400 is the number of seconds per day, and Lf = 334,000 J/kg is the latent heat of fusion of ice. Because 1 kg/m² of water = 1 mm, the result is directly expressed in millimetres water equivalent (mm w.e.).
Interactive calculator
0 → −0.15 (large wildfire deposition signal)
Region × hypsometric-zone JJA range: 164 → 274 W/m²; median 226 W/m²
−Δα · SW = radiative forcing3.19 W/m²
× 92 days · 86400 = energy25.33 MJ/m²
÷ Lf (334 kJ/kg)→ melt
75.8 mm w.e.
potential wildfire-attributable melt over 92 JJA days (upper bound)
Worked example: Athabasca Glacier in 2023
| Term | Value | Meaning |
|---|---|---|
| Δα | −0.0137 | 2023 posterior-mean JJA estimate for Athabasca Glacier from bayes_REGION_mv |
| TopoSCALE SW | 232.8 W/m² | terrain-corrected incoming shortwave, weighted across the glacier's hypsometric bands |
| RF = −Δα·SW | 3.19 W/m² | potential additional absorbed energy |
| × 92 days × 86400 s | 25,327,965 J/m² | energy accumulated during JJA |
| ÷ Lf (334,000 J/kg) | 75.8 mm w.e. | potential meltwater equivalent (1 kg/m² = 1 mm water) |
Why this is an upper bound
Calculation assumptions
- All additional absorbed energy is assigned to melt. The estimate does not partition energy into sensible heat, emitted longwave radiation, sublimation or snowpack warming, and assumes a surface already at 0 °C.
- The calculation applies the estimated darkening continuously across the full 92-day JJA window; it does not resolve its timing within the summer.
- This is melt attributable to wildfire alone, defined by the with-fire minus no-fire contrast, not total glacier melt.
Verified for the current Chapter 1 records. Every atlas value uses the same TopoSCALE terrain-only shortwave recipe as the retained attribution chain. The albedo effects are posterior counterfactual estimates, not direct measurements or causal proof; the energy conversion remains an upper bound.