With CairnGorm Mountain officially closing for the season with the end of regular lift served snowsports at close of play on Sunday 6th June it’s time to total up this year’s fantasy lift league!
The results of the Fantasy Lift League for the 2010 season can be found by visiting the thread in the forum. The actual lift league can be found in the forum thread.
If you want to just see the nice graph of the snow making model, jump to the foot of this post!
For the 2010 competition a new extra was added, in the form of virtual snowmaking for the Sheiling Trainer Tow using ‘virtual’ Ratnik Sky Giant IV guns with AA nozles. The specs of these guns are as follows (with AA nozzles):
Start-up Temperature: -1.3c Wetbulb
Flow Rate (AA Nozzles): 2.72lps (at lowest quoted water pressure on gun specification).
Obviously not all the water that comes out of a gun will convert to snow and not all of the snow will land were you want it, so to keep calculations simple and to some extent account for these factors the following two assumptions will be used:
- Only machine made snow is counted. The calculation ignores natural snow inputs.
- A snow density of 0.5kg/l will be used, a so called ‘technical snow density’ value of 0.4kg/l is used for packed piste snow, so this figure gives a pessimistic conversion factor that we’ll use to account for the fact not all the water lands as snow, nor does all the snow go where it’s wanted.
- Snowmaking aims to provide a run that is 300m long, by 20m wide (inc uptrack) at a minimum average depth of 30cm for the Sheiling Tow to be counted as ‘Open’.
Snow loss from thaw conditions was calculated using a basic degree day ablation model, adjusted to use the average temperature returned from the database where the the AWS (Automatic Weather Station) recorded data every 5 minutes - rather than calculate an approximate average based on the Tmin and Tmax (Maxium Daily Temperature).
At it’s most basic a degree day ablation model is:
M = Df*(Tmax -Tm)/2
Where M is the melt rate (water equivalent in mm day -1), Df is the degree day factor (mm °c -1 day -1), Tmax is the max daily temperature (°c ) and Tm is critical temperatre for melt to occur (°c).
Within Day Temperature variation
An important aspect of Scotland’s climate is the variation of temperature within the day where the free air temperature may lie above 0°c for part of the day and fall below 0°c for the rest. Thus it is often the case that snow fall and snow melt will occur within the same day and similarly with a snow making system it is possible that there maybe at least some albation during the same day as when snow making was in progress.
This scenario could occur due to afternoon daytime maxima climbing above 0°c or due to a change in weather systems, such as a warm front sweeping in possibly overnight.
Thus applying a degree day ablation model on a full day basis increases the scope for considerable error in modelling as noted by (Dunn, 2000). Dunn, introduced an extra factor Fm (fraction of the day where T > Tm). Thus:
M = Fm*Df*(Tmax -Tm)/2
However, both the average temperature and the Fm value used by Dunn et. al. was an approximation derived from daily temperature values and day length.
Adaption for use with AWS data
With the availability of AWS data sampled at 5 minute intervals throughout the day with weather stations situated at the foot of the Sheiling Trainer Tow and at the SSC Hut at the same elevation as the top of the Sheiling Tow, it is possible to accurately calculate the actual Fm value and to derive from SQL queries an actual rather than guestimated average temperatre for the period where T > Tm.
Calibrating a Degree Day Model for the Cairngorms?
Work previously done by Dunn et. al. as part of research into modelling catchment dynamics in the upper Dee catchment provides values to calibrate the degree day model. Though these have been used for the Sheiling ‘virtual snow making’ calculations, a couple of notes of caution:
- The snow density of machine groomed on-piste snow will be substantially higher than natural snow for the majority of the snow season.
- Machine made snow is naturally denser and more thaw resistant due to crystal structure than fresh natural snow.
- Thus ideally the Degree Day Factor should be re-calibrated specifically for modeling machine made and on-piste snow on CairnGorm Mountain.
The values provided by Dunn et. al. are as follows:
Degree Day Factor (Df): 9.5 mm °c -1 day -1
Critical Melt Temperature (Tm) +1.8°c
Modelling Accumulated Depth
For the ‘fantasy lift league’ to keep the modelling as simple as possible natural snow inputs were not considered and the model was based soley on the accumulation and ablation of machine made snow, using a uniform snow density of 500gl-1 for both freshly made snow added and for the actual snow depth loss calculated from the mm of meltwater equivilent from the degree day ablation model.
Combining the modelled daily snow making hours with the daily ablation rate it was possible to calculate the new snow made and total up an accumulated depth of machine made snow for each scenario (based on number of guns). When the accumulated depth exceed 120cm for any scenario only 1/4 of the available snowmaking hours were used beyond that point.
Where the accumulated machine made snow depth in any scenario exceeded 200cm at midnight no snow would be made that day or following days until one started with a depth below the 200cm threshold.
The graph below shows the modelled accumulated machine made snow depth from 4th November 2009 till 20th May 2010 (Series numbers correspond to number of Ratnik Sky Giant IV Snow Guns used in the model):
Accumulated Machine Made Snow - Modelled Depth
The graph shows some interesting implications of different numbers of guns in the scenario outlined above given the target depth constraints specified. While the 2 gun scenario significantly out performs the 1 gun scenario, giving 31 days more cover > 30cm than 1 gun, there is only a small difference between 2,3 guns (3 extra days) and 4 guns (10 extra days over 2 guns). While the 5 gun scenario gives a further 20 day jump over the 4 gun scenario, as can be seen on the graph, keeping the snow depth above the 30cm mark through the milder period in the 1st half of May while all other scenarios see snow depth fall below 30cm or reach 0.
Some further thoughts…
The Degree Day Factor (Df): 9.5 mm °c -1 day -1 used may be overly pessimistic in terms of a managed snowsports scenario, a Df of 3 - 4 mm °c -1 day -1 would be commonly used within an Alpine Set Up.
However a degree day model does not try to be accurate day to day, but to average out conditions experienced so that it is accurate over a longer time period. Basically such a model does not take account of the difference between a calm, dry day with +7°c and a day with driving rain, storm force winds and +7°c where the snow melt as we know only too well in Scotland would be markedly higher. The Df must account for both scenarios.
On the flip side, it is likely the snow making modeling was over optimistic in terms of the % of water pumped through a gun that is actually converted to snow which lands where it is supposed to. Much work is needed to advance the calibration of such modeling for real use in snow making research in the Scottish Highlands.
REFERENCES:
S.M Dunn, S.J. Langan, R.J.E. Colohan “The impact of variable snow pack accumulation on a major Scottish water resource” - The Scienece of the the Total Environment 265 p181-194 (2000)
