Meteorological downscaling¶
Downscaling turns coarse weather (ERA5 at ~31 km, or the IFS forecast) into hourly weather for each terrain unit. SnowMapper uses TopoPyScale 2 (TPS2), a reimplementation of the TopoSCALE method (Fiddes & Gruber, 2014). The idea: the coarse model knows the state of the atmosphere above the mountains well. What it lacks is the terrain. So TPS2 reads the atmosphere at each unit's real elevation, then applies the unit's slope, aspect and horizon.
The weather model's own surface sits on its smoothed orography: valleys filled in, peaks cut off. A 3000 m station can sit in an ERA5 cell whose surface is 4500 m.
Temperature¶
Interpolated from the pressure levels (300, 500, 700, 850, 1000 hPa) to the unit's elevation, between the two levels that bracket it. This uses the real vertical temperature profile at each hour, including inversions in the free atmosphere, instead of a fixed lapse rate.
Surface-level effects (valley cold pools, the daily heating of the ground) are not in the pressure levels. See Known limitations.
Pressure¶
From the surface pressure with the hypsometric equation, using the mean temperature of the layer.
Humidity¶
Specific humidity is interpolated from the pressure levels. Relative humidity is recomputed at the unit's temperature and pressure.
Wind¶
The u and v components are interpolated from the pressure levels. A logarithmic wind profile then corrects for surface roughness down to a 10 m reference height. The result is an hourly mean over the unit, not a gust.
Shortwave radiation (sunshine)¶
- The incoming sunshine is split into direct and diffuse parts. The split uses the clearness index (surface radiation divided by top-of-atmosphere radiation) and the Erbs correlation.
-
Direct radiation is corrected for the angle between the sun and the slope, and set to zero when the sun is below the horizon of the unit (terrain shading):
\[ SW_{dir,slope} = SW_{dir}\,\frac{\cos i}{\sin h_\odot}, \qquad \cos i = \sin h_\odot \cos\beta + \cos h_\odot \sin\beta \cos(\phi_\odot - \alpha) \]with sun elevation \(h_\odot\), sun azimuth \(\phi_\odot\), slope \(\beta\), aspect \(\alpha\). 3. Diffuse radiation is scaled by the sky-view factor.
So a south slope at noon in winter receives far more energy than a north slope at the same elevation. This is the main reason the north slope keeps its snow longer.
Longwave radiation¶
The sky's thermal radiation is scaled to the unit's temperature (Stefan–Boltzmann). The part of the sky hidden by terrain is replaced by emission from the surrounding slopes, weighted by (1 − SVF).
Precipitation and its phase¶
Amount. Each unit receives the precipitation of the weather-model cell it lies in. There is no elevation gradient by default: precipitation–elevation relations in high mountains are non-monotonic and vary by season, and a fixed gradient does more harm than good. This is the largest single source of error. See Known limitations.
Phase (rain or snow). Decided by the wet-bulb temperature, not the air temperature. A falling snowflake cools by evaporation towards the wet-bulb temperature. In dry air, snow can therefore reach the ground at air temperatures several degrees above 0 °C, which is common in the arid mountains of Central Asia.
| Wet-bulb temperature | Phase |
|---|---|
| below −0.5 °C | all snow |
| −0.5 to +2.5 °C | mixed, linear transition |
| above +2.5 °C | all rain |
A guard rail forces all-rain when the air temperature exceeds +4 °C, so very dry air cannot produce snow on a warm day.
Forecasts¶
The forecast is downscaled the same way, from the IFS pressure levels. The join with the analysis is cross-faded over 6 hours. See Forecasts.