Estimate daily snowmelt, basin meltwater discharge and snow water equivalent (SWE) depletion in a mountain catchment using the classic degree-day method. Vary the basin area and initial SWE to size reservoir inflow and assess snowmelt flood risk.
Parameters
Daily mean air temperature T
°C
Mean air temperature for the target day
Melt factor a
mm/(°C·day)
Bare ground 4-8, forest 2-4, glacier 5-12 are typical
Base temperature T_base
°C
Effective threshold for net melt (usually 0 °C)
Snow depth h_s
cm
Snow water equivalent SWE
mm
Water depth obtained by melting the full snowpack
Basin area A
km²
Elevation lapse rate Γ
°C/100m
Air-temperature drop per 100 m of elevation gain
Results
—
Degree-day value (°C·day)
—
Daily melt (mm/day)
—
Meltwater discharge (m³/s)
—
30-day cumulative melt (mm)
—
SWE depletion (day)
—
Snow density (g/cm³)
—
Mountain basin — snow, stream and reservoir
Raising the air temperature or melt factor thins the snowpack and intensifies the meltwater stream into the reservoir. The colour scale tracks the daily melt intensity.
Daily melt vs air temperature (seasonal sweep)
Cumulative melt and remaining SWE over 30 days
Theory & Key Formulas
$$M = a \cdot (T - T_{base}) \text{ when } T \gt T_{base},\quad SWE = \rho_s \cdot h_s$$
M: daily snowmelt (mm/day), a: melt factor (mm/(°C·day)), T: daily mean air temperature (°C), T_base: base temperature for net melt (usually 0 °C), SWE: snow water equivalent (mm), ρ_s: snow density (g/cm³), h_s: snow depth (cm).
Q: basin meltwater discharge, A: basin area (km²), t_deplete: days required to exhaust the current SWE at the present melt rate.
Snowmelt degree-day method — snowmelt hydrology
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So the degree-day method predicts mountain snowmelt from air temperature alone? That sounds way too simple to be useful.
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It does sound suspicious, but here's the trick: in a mountain basin more than 90% of the variability in seasonal snowmelt is explained by air temperature. Melting needs energy, and the energy fluxes that drive it — shortwave radiation, longwave radiation, turbulent fluxes, even rain heat — are all strongly correlated with surface air temperature. That's why the simple linear law M = a·(T − T_base) still anchors the snow modules of HBV, SRM, SWAT and HEC-HMS, which run in pretty much every operational forecast centre in the world.
🙋
Got it! So if I crank up the melt factor a, the discharge goes up too. How do you actually pick a value for a in real life?
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Great question. The literature gives ranges like 4-8 mm/(°C·day) for bare ground, 2-4 for forest and 5-12 for glacier ice, but a also drifts upward as the season progresses because albedo drops. In production hydrology you calibrate a against measured streamflow — for a typical Japanese mountain catchment like the upper Tone River, you end up around 3-4 on a seasonal mean. Try the slider here: moving a by 1 unit shifts the melt by about 5 mm/day, so you can see how sensitive the discharge is to this single parameter.
🙋
You also output "SWE depletion days". Is that what reservoir operators actually look at?
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Yes — it's a primary decision metric. If on 1 April your snow pillow shows SWE = 200 mm and today's melt is 17.5 mm/day, you have roughly 11 days of meltwater left in the snowpack. Hydropower operators and irrigation agencies recompute this every day, because the snowpack often fills 40-60% of a high-altitude reservoir like Kurobe or Okutadami during the melt season. The tool's "30-day cumulative melt" and "SWE depletion" numbers are exactly the variables that feed into those operational decisions.
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The snow density readout is interesting too. What's actually different between fresh and old snow?
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Snow is mostly air, and it compacts over time. Fresh snow is ρ_s = 0.05-0.15 g/cm³, settled mid-winter snow 0.30-0.45, and ripe melt-season snow 0.40-0.55. The tool back-calculates ρ_s = SWE/(h_s·10) and flags any value below 0.05 or above 0.6 as physically suspect — if you enter 10 cm of depth with 200 mm SWE, density would be 2.0 g/cm³, denser than ice, which is almost certainly a typo. In the field, SWE itself is measured with snow pillows, sampling tubes, or satellite passive microwave instruments like AMSR2.
🙋
What does the elevation lapse-rate slider actually drive? I don't see it move the headline numbers.
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Sharp eye. The lapse rate Γ is used to correct for the elevation distribution of the basin. A real catchment can span 1500 m of relief, so a degree-day model that lumps the whole basin into one temperature ignores the fact that the upper third is still in snow while the lower third has melted out. Production models split the basin into 500-m elevation bands and apply Γ in each band. Here it feeds the verdict text as context; in climate-change studies you sweep Γ to explore "snow-to-rain shift" scenarios.
Frequently asked questions
The degree-day method estimates the daily snowmelt M as a linear function of the difference between the daily mean air temperature T and a base temperature T_base, M = a·(T − T_base), where a is the melt factor. Because air temperature is widely measured even in remote mountain basins, the model is robust and is built into nearly every operational hydrological model (HBV, SRM, SWAT, HEC-HMS). It is less accurate than full energy-balance snowmelt models but requires far fewer inputs.
The melt factor a depends strongly on land cover and season. Common ranges are 4-8 mm/(°C·day) for bare ground and grassland, 2-4 mm/(°C·day) for coniferous forest, and 5-12 mm/(°C·day) for glacier ice. Seasonal mean values of 2-7 mm/(°C·day) are typical. Late in the melt season (May-June) albedo drops and a tends to rise. In practice a is calibrated against observed runoff, and this tool lets you sweep a directly with a slider to feel its sensitivity.
Although ice melts at 0 °C in the lab, real basins use the daily mean air temperature, which averages daytime melting and nighttime refreezing. The effective T_base at which net melt begins typically lies between −2 °C and +2 °C. Forested or shaded slopes tend to calibrate to a higher T_base, while open south-facing slopes calibrate lower. This tool lets you adjust T_base between −5 and +5 °C to match your region.
SWE is the depth of liquid water you would obtain by melting the entire snowpack, expressed in mm: SWE = ρ_s · h_s, where ρ_s is the snow density (g/cm³) and h_s the snow depth (cm). Fresh snow is 0.05-0.15, settled snow 0.30-0.45 and ripe melt-season snow 0.40-0.55. This tool back-calculates ρ_s from your SWE and depth inputs and warns when it falls outside 0.05-0.6 as physically unrealistic. SWE matters far more than depth for runoff forecasting, which is why it is measured directly with snow pillows or passive microwave satellites.
Real-world applications
Reservoir inflow and hydropower scheduling: High-altitude reservoirs such as Kurobe, Okutadami and Tagokura receive 40-60% of their annual inflow during the spring melt. Utilities combine telemetry from snow pillows with degree-day forecasts to schedule generation and spill operations days ahead. The calibration accuracy of a single melt factor directly drives generation revenue and the safety margin against snowmelt floods.
Snowmelt flood and Rain-on-Snow early warning: Combined snowmelt and rainfall events have caused major floods in Hokkaido, Tohoku and the Hokuriku region. Forecast agencies overlay quantitative precipitation forecasts on a baseline degree-day melt to track peak flow 48-72 h ahead. Melting snow also raises pore pressure in steep slopes, triggering landslides and wet-snow avalanches, so monitoring the SWE decline rate is critical for disaster prevention.
Irrigation and paddy water supply: Rice-growing prefectures such as Nagano, Niigata and Yamagata size their May intake structures around the snowmelt peak. SWE observations plus a degree-day forecast tell water managers when and how much meltwater will arrive, so they can plan gate operations on canal headworks. Earlier snowmelt under a warming climate widens the gap with the planting calendar and is an explicit input to long-term planning.
Climate-change impact assessment (snow-to-rain shift): IPCC scenarios project less winter precipitation falling as snow and earlier melt peaks in mountain basins. Driving a degree-day model with future temperature time series lets you compare SWE peaks and melt timing across scenarios, which feeds reservoir re-operation studies and agricultural adaptation planning at agencies such as MRI and NILIM in Japan.
Common pitfalls
The biggest trap is using a single melt factor a for the whole year. In reality a drifts from roughly 2-3 in early spring (March-April) to 4-6 at peak melt (May) and even higher in early summer as the snow surface darkens. A single annual value will under-predict the peak melt discharge and over-predict the tail. Operational practice uses a "variable degree-day factor" that switches monthly or with accumulated degree-days as a trigger.
Next, treating Rain-on-Snow events with the bare degree-day formula. When warm rain falls on a snowpack, sensible and latent heat from the rain dramatically accelerate melt. The pure degree-day model only sees air temperature, so it can under-predict the peak discharge of Rain-on-Snow events by 50% or more. Operationally you either add an energy-balance correction during rain or temporarily double the melt factor during the event.
Finally, blindly trusting degree-day output in a basin without SWE measurements. The model only predicts the melt rate; if your initial SWE is wrong, total melt and depletion days are wrong too. Depth times density gives SWE, but density swings widely across the season, so without on-site observations a ±30% SWE error is normal. Modern best practice combines passive microwave satellites (AMSR2, SMAP), UAV LiDAR snow depth surveys and a degree-day model — only the combined system reaches operational accuracy.
How to Use
Enter mean daily air temperature (°C) and temperature range (±°C) to define thermal conditions; typical alpine valleys range 5–15°C during spring melt season.
Input basin area (km²) and elevation adjustment range to account for lapse rate; use 0.6°C per 100 m for mountain terrain.
Set baseline temperature threshold (°C)—typically 0°C for snow—and historical snow depth (cm); simulator calculates degree-day accumulation, daily melt rate (mm/day), and meltwater discharge (m³/s) for your catchment.
Worked Example
Alpine basin: 45 km² area, mean April temperature 8°C with ±2°C range, baseline threshold 0°C, initial SWE 120 mm, snow density 0.28 g/cm³. Simulator yields degree-day value 8°C·day, daily melt 3.2 mm/day (using melt factor 0.4 mm/°C·day for wet snow), meltwater discharge 12.5 m³/s, 30-day cumulative 96 mm, SWE depletion occurs in 37.5 days. High elevation zones (2400 m) show reduced melt due to 9°C cooler temperatures.
For climate-adjusted runoff forecasting, cascade degree-day outputs into unit hydrograph models; USGS Rocky Mountain basins validate this method within ±15% of observed discharge.
SWE density increases 0.01–0.03 g/cm³/day during ripening phase; monitor hsRange to capture diurnal melt cycles in steep north-facing slopes where temperature swings exceed ±4°C.