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Each type of information is assumed to specify the probability
of occurrence of a snowstorm event in the four basic periods.
Further, it is assumed here that in the absence of forecast infor-
mation, road-maintenance personnel base their decisions on
(tailored) climatological information. In effect, climatological
information defines the zero points (or baseline values) on the
scales on which forecast quality and forecast values are
measured. Perfect information, although obviously not avail-
able in the real world, provides a useful upper boundary for
the quality and value of imperfect forecasts.
Conditional and marginal distributions characterizing forecast
quality for the wake-up, pre-salt, and maintenance-2 periods are
related to this maintenance-1 period forecast information.
2
To
facilitate the comparison of snowstorm event probabilities for
the three types of information, the marginal probabilities of snow-
storm events initiating in the four basic periods are required.
Results
As previously noted, it is assumed that the goal of Swedish
road-maintenance authorities is to minimize total expected
expenses on each occasion on which a snowstorm constitutes
a threat to traffic safety and highway maintenance in the
Jönköping district. The value of snowstorm forecasts of a spec-
ified level of quality is determined as the difference in total
expected expense between the situation in which the
wakeup/pre-salt decisions are based on climatological infor-
mation, and the situation in which these decisions are based on
forecast information.
Optimal strategies
When the wakeup and pre-salt decisions are based on climato-
logical information, it is always optimal for central authorities to
Table 3: Marginal probabilities of snowstorm-event
occurrence in four basic periods for three types of information
Period
Climatological
Forecast
Perfect
(Event: hours)
information information information
Wake-up (x1: 0-1)
0.060
0.025
0.000
Pre-salt (x2: 1-4)
0.399
0.150
0.000
Maintenance-1 (x3: 4-6)
0.266
0.550
0.720
Maintenance-2 (x4: 6-12) 0.275
0.275
0.280
Source: Liljas, E., and Murphy, A.H.
Table 4: Expected expense and expected value associated
with optimal strategies for different types of meteorological
information for Jönköping district in south-central Sweden
Type of
Expected expense
Expected value
Information
(1,000 SEK)
(1,000 SEK)
Per snowstorm Per year
Per snowstorm Per year
Climatological
10,285
205,700
0
0
Forecast
9,806
196,120
479
9,580
Perfect
8,955
179,100
1,330
26,600
Source: Liljas, E., and Murphy, A.H.
A snowplough (Swedish: plogbil) during a snowstorm in Sweden
Photo: Kerstin Ericsson