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History of HS4CastIn about 1985 we investigated methods to detect the state of road surfaces. We found a method of contactless determination of thin films of water on a road surface. In addition, theoretical computations were carried out to measure the water film thickness and the salt concentration on a road surface. Patents that cover the method of contactless measurement were applied. To recognize the hazardous build-up of ice on a road, it is necessary to know the state of the road in the future. Our primary approach to compute the future road temperature was to solve the differential equation that describes the temperature of the road surface. The so-called boundary conditions contain the influences on the road surface temperature. These influences can be computed if meteorological quantities like the air temperature, wind speed or sun radiation are known. However, to determine the boundary conditions for future times the meteorological data must also be predicted. So it is not enough to measure some meteorological data - they must also be forecast.
Another way of incorporating forecasts into the boundary condition is using the meteorologists' forecasts. However, normally no predictions will exist for a given road measurement site. It turns out that neglecting the local situation at the road site completely leads to large forecast errors. Local phenomena like shading during a certain time-period or the influence of a nearby wood must be taken into account for a correct prediction of the road temperature. So forecasts coming from a meteorological office can only be used in combination with local measurements. Moreover, since normally the meteorologists can only provide forecasts once or twice a day, the forecast model must continue observing the local measurement pattern in the meantime. The (local) prediction of meteorological data is more difficult than the forecast of certain business data. Since weather patterns of consecutive days do not necessarily contain a general trend, it is not always possible to find out the correct periodicity from an analysis of consecutive days. More to the point, it may be possible to find out the correct trend but the time-lag would be much to large for such a forecast method to be of any value. The use of neuronal networks to produce meteorological forecasts was not satisfying. Neuronal networks can only forecast "average" situations easily and cannot be trained during operation. So this method has no on-line learning ability. To forecast meteorological data locally and autonomously for time periods greater than one to three hours (typically up to 12 or even 24 hours), we have developed a new method and incorporated it into the forecast model HS4Cast. Using this method, HS4Cast can produce high-quality forecasts between the intervals when new data arrive from a meteorological office. Even if there are no met-office forecasts at all, HS4Cast is fully operational - it does not rely on external data. |
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To forecast these
meteorological data many methods could be used in principle. Polynomial extrapolation is a
means to do this if you need not look very far into the future (about one to two hours).
The degree of such polynomials can be chosen arbitrarily, but it turns out that any degree
above 2 leads to unwanted instabilities; on the other hand, a polynomial degree of 1
(which is a straight line) or 0 (a horizontal line continuing at the level of the mean
value) obviously isn't very sophisticated and is simply wrong near extremities. 