From a daily climate series to a peak-water year
The model does three things each year on a ~100 m grid over Dixon: compute the surface mass balance (accumulation minus melt), evolve the glacier geometry as mass is lost, and sum the runoff. Peak water is the year that runoff stops rising. Every equation below is a published parameterization; the parameters tagged cal are what the Calibration station fits.
- MFcal
- melt factor — melt per positive degree-day
- asnow, aicecal
- radiation coefficients over snow and bare ice (a_ice > a_snow)
- I
- potential clear-sky solar radiation from the DEM (slope, aspect, shading, solar geometry) — no radiation sensor needed
- T+
- air temperature on melt days — the temperature itself when T > T₀ (not the excess T − T₀), and 0 below the threshold
Melt responds to warmth and to how much sun a cell's slope and aspect actually receive — the spatial signal that lets the model match snowlines, not just glacier-wide totals. A plain degree-day variant (Melt = DDF·(T − T₀)) runs alongside as a structural-uncertainty check.
MODELING_OPTIONS.md §1 · Hock 1999 (DETIM); DD variant Hock 2003
- pcorcal
- station→glacier precipitation correction factor
- pgradcal
- precipitation increase per metre of elevation (Δz above the station)
- Trs
- rain/snow threshold, fixed ≈ 1–1.5 °C (Hock 1999 / GloGEM) — not fitted
Station precipitation is scaled to the glacier and lifted with elevation; the fraction falling as snow (below the threshold) becomes accumulation. This is the GloGEM accumulation form.
MODELING_OPTIONS.md §5 · Huss & Hock 2015 (GloGEM)
- hr
- normalized elevation, 0 at the head (top) to 1 at the terminus — so the curve peaks (most thinning) at the terminus
- Δh
- the (dimensionless) shape by which each year's volume loss is spread over elevation
Each year's computed volume loss is redistributed by this empirical curve — thinning concentrated at the terminus, near zero at the top — so retreat emerges as low bands run out of ice. Mass-conserving, no free parameters, and validated on Dixon's own 2000–2025 outlines (see Validation).
MODELING_OPTIONS.md §3 · Huss et al. 2010; docs/deltah_hindcast.md
- 1Force the grid: the daily station temperature and precipitation are transferred onto each cell via the fitted lapse + katabatic damping, with CMIP6 monthly bias correction applied to the future forcing.
- 2Melt & accumulate: each cell melts (Hock 1999) and accumulates snow (the rain–snow split) day by day through the year.
- 3Surface mass balance: accumulation minus melt gives each cell's annual balance, and the glacier-wide volume change.
- 4Δh geometry update: the year's volume loss is redistributed by the Huss-2010 curve; cells that run out of ice retreat.
- 5Repeat to 2100 on the new geometry — the shrinking area is the feedback that eventually turns runoff over.
Runoff = melt + rain − refreezing, summed over the initial glacier footprint. Peak water is the year of maximum 11-year rolling-mean runoff (Huss & Hock 2018) — the smoothing that reads the trend rather than a single noisy year — after which the yield enters its permanent decline.