Snow Modelling - Rationale
Relationships for 24 hours duration for 2 to 10-year return periods, and
1-24 hours duration for 5 and 10 year return periods are the values of most
interest because the lack of snow damage in the UK indicates that more frequent
events do not cause damage, and high accumulations of intense duration are most
likely to cause damage.
| Duration (hours) |
Frequency | (per year) | Return Period | (years) | ||||||
| B'ham | Eskdalem | B | E | B | E | B | E | B | E | |
| 0.5 | 0.5 | 1 | 1 | 2 | 2 | 5 | 5 | 10 | 10 | |
| 1 | 1.9 | 3.2 | 3.4 | 4.3 | 4.6 | 5.3 | 6.6 | 6.6 | 8.5 | 8.5 |
| 3 | 3.2 | 5.1 | 4.8 | 6.8 | 6.5 | 8.3 | 9.2 | 9.9 | 12.7 | 12.8 |
| 6 | 3.6 | 6.3 | 5.7 | 8.3 | 7.5 | 10.4 | 10.5 | 12.5 | 15.4 | 16.2 |
| 24 | 3.9 | 8.5 | 7.3 | 11.2 | 9.5 | 14.7 | 13.6 | 19.0 | 20.8 | 23.8 |
Combinations of Interest:
1hr - 5 & 10 year return periods 2
3hr - 1, 2, 5 & 10 year return periods 3
6hr - 0.5, 1, 2, 5 & 10 year return periods 4
24hr - 0.5, 1, 2, 5, & 10 year return periods 5
TOTAL 14 sets of relationships
These relationships can be used to estimate snow accumulation return
periods from mean annual snow days, using the relationship calculated for
Birmingham and Eskdalemuir (which has height and geographical space built in to
a certain extent). It should at least give a reasonable estimate which can be
tested (see below) and used to calculate modifications for critical wind speed
outputs in the tree models.
It might be possible to develop a model using multivariate analysis of x,
y, z and snow lie depths, but these are snow lie depths which do not
necessarily reflect snowfall. Although snow lie data is used to test the model
which is developed.
Testing
Firstly the measurements were tested against Birmingham and Eskdalemuir
data to see if there is any relationship between maximum snow depth for
different return periods calculated from meteorological measurements and snow
accumulation. Plots of maximum snow depth for different return periods versus
accumulation should produce a straight line relationship.
Data tested using:
1. Calculated 2-year and 5-year depths from another paper by Jackson (1977)
2. Depths from snow survey reports can be used to test the shorter time
periods of once and twice per year snow depths.
Thus the only snow accumulation not tested is the 10-year.
However, testing may not be perfect because of the discrepancies between
snow accumulation as calculated from detailed records, and snow depth
measurements made from lying snow, which may not be linked to the amount which
has fallen (for example if 10cm is measured, has this fallen, or is it
unmelted, or partially melted snow from previous days?) It may be possible to
use biogeographic zones to adjust the snow lie by factors which reflect the
likelihood of melting between snow falls.
Snow Model Summary
Model - Jackson's 1977 statistical model based on data from 25
meteorological stations over the UK for measurements made between 1941 and
1970, although there was incomplete spatiotemporal coverage. Derived
relationships are assumed to be straight line, although this is not the case
for all stations. However the paper gives no indication of which stations do
not fit the relationships used.
The model essentially provides multiplying factors for calculating the mean
annual number of days with snow falling, and multiplying ratios from which can
be calculated the return periods for
Snow Modelling - ARC/INFO and EXCEL work
Jackson's model to calculate the mean annual number of days with falling sleet or snow, in a winter, has been implemented using ARC/INFO. There are several AMLs which do different combinations of calculations. Excel was used to determine the relationships between snow accumulations in specified durations with different return periods and the number of mean annual snow days predicted by the model. These relationships were determined using Birmingham and Eskdalemuir data (the only stations for which snow accumulation information is given by Jackson).
Thus the model was based on a relationship determined by only two points. The relationships for 2- and 5-year return periods were tested using snow lie data (which should be related to snow fall), from 46 climate stations. The information was provided by another Jackson 1977 paper. Information for other return periods was not available to be used as test data.
Snow fall accumulations for 2- and 5-year return periods for different durations were plotted against the snow lie data. The results produced a rather good relationship (R2=8.2 and 8.5).