Elements for Life

wake up district personnel and for these road-maintenance

personnel to initiate pre-salting activities. On the other hand, the

optimal strategy given forecast information is to wake-up and

pre-salt given the forecast f=1 and to not wake-up or pre-salt

given the forecast f=0. It is through the difference in optimal

strategies between climatological information and forecast infor-

mation that the latter acquires its positive economic value. Perfect

information leads to the same optimal strategy as forecast infor-

mation.

Forecast-value estimates

The expected expenses associated with optimal strategies

based on climatological, forecast, and perfect information are

indicated – on a per-snowstorm basis and on an annual basis

(assuming 20 snowstorms on average per year) – in Table 4.

Expected forecast value is also listed in this table, under the

assumption that climatological information defines the zero

point on the value scale. The economic value of snowstorm

forecasts (of current quality) is 0.48 million SEK per snow-

storm or 9.60 million SEK for a typical year. Corresponding

estimates for perfect information are 1.33 million SEK and

26.60 million SEK, respectively. Thus, current forecast infor-

mation realizes approximately 36 per cent of the value of

perfect information in the context of this DMP.

Quality/value Relationship

In addition to estimates of the value of forecasts of current quality,

the relationship between forecast quality and forecast value is

also of interest.

The basic quality/value question can be posed

as follows: Given a specific change in the level of forecast quality,

what change can be expected in the level of forecast value?

The availability of a model of the snowstorm/road-mainte-

nance DMP including a submodel that characterizes forecast

quality – makes it relatively easy to evaluate the quality/value

relationship in this context. To simplify this analysis, a scalar

quadratic error measure of forecast quality was introduced.

Various incremental changes (improvements and deteriora-

tions) in forecast quality were postulated, and the

snowstorm/road-maintenance model was used to determine

the optimal strategies and forecast-value estimates corre-

sponding to each level of quality. Relative forecast value V* is

plotted against relative forecast quality Q* in the graph here

(these rescaled quantities are defined in the figure legend). This

diagram reveals that the quality/value relationship is approxi-

mately linear for relatively modest levels of quality but is highly

nonlinear over higher levels of quality. In this regard, the Q*

value for forecasts of current quality is 0.725.

Short discussion of the winter road

maintenance problem

This paper has summarized some results of a decision-analytic

study of the value of short-range snowstorm forecasts in road-

maintenance decisions in the Jönköping district in south-central

Sweden. The study focused on the wake-up/pre-salt decisions

made by central/local road-maintenance authorities, evaluated

a relatively broad range of expenses associated with mainte-

nance activities and snowstorm events, and estimated the

economic benefits – in the context of this DMP – of state-of-

the-art forecasts from the time of initiation of a typical

snowstorm. Specifically, the incremental benefits of basing these

road-maintenance decisions on forecast information – instead

of on climatological information – is approximately 0.5 million

SEK per snowstorm or about 10 million SEK per winter season.

It should be kept in mind that these estimates refer only to the

economic benefits of snowstorm forecasts in decisions involv-

ing main roads in the Jönköping district. The overall annual

economic benefits of forecast information in road-maintenance

decisions relating to both snowstorm and black-ice events for

all major roads in Sweden are estimated – by a rough scaling-

up process – to exceed 300 million SEK.

In evaluating these estimates of benefits, it is also important

to recognize that a relatively sophisticated form of climato-

logical information has been used as a standard of reference in

this study. If road-maintenance authorities only had access to

a relatively rudimentary form of climatological information in

the absence of snowstorm forecasts, then the value of the fore-

cast information of interest here would increase (because the

economic value of the zero point had decreased). Alternatively,

this relatively sophisticated climatology could be viewed as an

intermediate form of information (between the rudimentary

form of climatology and state-of-the-art forecasts) with consid-

erable economic value in its own right.

When looking at the combined result of nowcasting as the

result of mapping of current weather by radar, satellite and

automatic stations (~700) +, forecast information, and the

assumption that the user optimised the economic outcome

with efficient decision-making, a figure on the order of 100

million euros was saved in Sweden each winter. Of this, 60 per

cent came from improved decisions due to better mapping by

weather radar, satellite images and automated weather stations

(AWS); 40 per cent came from the forecasts for the next 12

hours. Potential to improve the outcome by increasing fore-

cast quality was postulated. A clear conclusion was that an

effective decision-making process is important in order to

improve the outcomes of weather services to save lives, health,

the environment and money.

[

] 113

Quality/value relationship for snowstorm/road-maintenance DMP.

Q* and V* are rescaled measures of quality and value, respectively,

where Q* = 0 and V* = 0 for climatological information and Q* =

1 and V*=1 for perfect information. Q* 0.725 and V* = 0.360 for

state-of-the-art snowstorm forecasts

Source: Liljas, E., and Murphy, A.H.

0.5

1.0

Forecast value V*

0.5

1.0

Forecast quality Q*