VLASOV A.N. VOLKOV-BOGORODSKY D.B., CUROCHKINA V.A., BLAS I. C.
institute Of Applied Mechanics, Ras, Moscow, Russia
Moscow State University Of Civil Engineering, Moscow, Russia
Federal Hydrological Institute, Koblenz, Germany

The optimization problem of a measuring network on coastal seawater areas is actually for the countries with the advanced coastal line subject to influence of flows, ebbs and wind fluxes, including Russia.

The problem of optimal location of the measuring devices tracing a level of a water surface in the area of Northern sea, adjoining to Wilhelmshaven port in the Jade river bay at northern coast of Germany is considered.

Specific property of this area is intensive navigation and small sea depth that causes necessity to contain a network of measuring stations. These stations represent expensive objects in exploitation. Therefore there is a necessity of optimization of their arrangement with the purpose of more precise definition of a sea water level.

Solving of the optimization problem is based on the great volume of the given measurements for a long time monitoring on a big water area, but at quite limited number of measuring devices. In a considered case the network of stations for monitoring a sea water level will consist of 8 points. On the basis of these data was constructed model of approximation of a water surface in the whole monitoring region.

At the decision of the optimization problem for criterion of accommodation of tracing points in the water area was accepted average curvature of an approximating surface for the estimated value. It means that devices should stand in the most critical places for the estimated characteristic, where it is subject to the strongest change, i.e. in places of the greatest average curvature to a water surface.

An important point is not only optimization of an arrangement of measuring devices, but also an estimation of stability of measuring system in relation to the casual emissions caused by influence natural and man-caused factors. In the present work this estimation was carried out with the hope of regression analysis and comparison of its results with the actual data.

For the considered period of time change of a sea water level essentially influences area depths that emphasize importance of the reliable control over a seawater surface.

Though between all monitoring points there is a high degree of correlation, nevertheless- errors under estimation of the maximal and minimal values of a water level can achieve significant meaning. Hence, the level of a water surface as the random variable, does not submit to the normal law of distribution. It is observed also anomalous values of an error at the estimation of the maximal and minimal values of levels of a surface. The error in a definition of minimal value was higher then for maximal.

The represented analysis of correlation of maximal and minimal water levels and error estimation were carried out on the basis of the averaging period equal to one year. Quite same analysis can be earned out for the averaging period equal to one month. The received results for average values, dispersions and correlation factors are similar to the results received for year averaging period, but are rather higher. The most error of estimation was more then two time accurate. This implies that for a forecast of maximal and minimal values of water levels it is necessary to take into account seasonal fluctuations.

The executed calculations have shown, that year by year, the locations of extreme values of average curvature of a surface can be a few displaced, remaining in some small area. Hence, it is necessary to take analysis with all accessible set of measuring data for definition of places of a desirable arrangement of devices, with base of averaging on all period of monitoring with consideration of the fractional periods of averaging, such as annual and can be monthly. For this purpose it is necessary to construct levels of average curvature of maximal and a minimal water surfaces for all period of monitoring and to define on them places of preferable accommodation of measuring devices.

Conclusions
1. The level of fluctuations of a water surface in considered region is significant and essentially influences water sea depth in this area.
2. The minimal and maximal values of a water level do not submit to the normal law of distribution.
3. At the solving of a forecasting problem of a water level it is necessary to take into account not only long cycles, such as year, solar, etc., but also seasonal.

References
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2. Pogorelov A. V. Differential geometry. //M.: Nauka, 1974, 176p (In Russia)
3. Jensen J., Mudersbach С Long-term changes of the water levels along the German North-Sea coastline. //Littoral 2002. 22-26 September. Porto. Portugal.
4. Buhmann M.D. Multivariate cardinal interpolation with radial-basis functions. //Constructive approximations 1990. V. 6. P. 225-255.
5. VemzelE.S. Probability theory. //M.: Nauka, 1969. 576p (In Russian)

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