The choice of optimal lag for Kriging interpolation of NWP model forecast
Treść / Zawartość
In this paper a Kriging method is reviewed and a way of its application in numerical weather prediction is proposed. The basic principles of the Kriging are shown; the main advantage is its accuracy, but at the same time a disadvantage is its large computational complexity. The construction stage of the variographical model is highlighted, as it is the most important stage and has a significant impact on the accuracy of interpolation. The algorithm for the construction of the variographical model is described. Special attention is paid to averaging an experimental variogram by introducing a special interval, called “lag”. Precisely this issue, according to the authors has a significant impact on the effectiveness of the practical application of Kriging for the interpolation of meteorological parameters. The advantages of averaging an experimental variogram by the administration of lag are presented, and the error that arises in this case is estimated. A theoretical study for the determination of the optimal lag was conducted. The lag proposed for the determination is guided by the criteria of accuracy and the economy of computer time. The twocriteria problem is solved, and the formula, which makes it possible to determine the optimal lag on these criteria, is received. An example shown here is the application of the obtained results for solving the applied task associated with meteorological parameters forecast by the COS MO model.
- ArcGIS Resources, 2013, Help of ArcGIS 10.1, http://resources.arcgis.com (data access 17.08.2016)
- Armstrong M., 1984, Common problems seen in variograms, Mathematical Geology, 16 (3), 305-313
- DeMers М.N., 1999, Fundamentals of Geographic Information System, John Wiley and Bong Inc., 512 pp.
- De Morsier G., Fuhrer O., Kaufman P., Schubiger F., 2015, Developing a 1.1 km Model Setup at MeteoSwiss: Impact of changing the boundary conditions, [in:] COS MO/CLM/AR T User Seminar 2015, Book of Abstracts, Offenbach, Germany, 3
- Doms G., 2013, A description of the Nonhydrostatic Regional COSMO-Model, www.cosmo-model.org (data access 17.08.2016)
- Gunes H., Sirisup S., Karniadakis G.E., 2006, Gappy data: to Krig or not to Krig?, Journal of Computational Physics, 212 (1), 358-382, DOI : 10.1016/j.jcp.2005.06.023
- Kanevskiy M.F., Demyanov V.V., Savelyev E.A., Chernov S.Y., Timonin V.A., 1999, An elementary introduction to geostatics (in Russian), VINI TI, Series Problems of the Environment and Natural Resources, 11, 136 pp.
- Katsalova L.M., V.M. Shpyg, 2013, Kriging-interpolation in weather forecast, (in Ukrainian), Scientific Papers of UHMI, 264, 3-9
- Katsalova L.M., V.M. Shpyg, 2014, Variographic models of meteorological parameters distribution on the territory of Ukraine for Kriging-interpolation, (in Ukrainian), Scientific Papers of UHMI, 266, 20-26
- Koshel S.М., Musin О.R., 2000, Digital simulation methods: Kriging and radial interpolation, (in Russian), Newsletter GIS Association, 4-5 (26-27), 32-33
- Matheron G., 1967, Kriging or polynomial interpolation procedures?, Mathematical Geology Transactions, 70, 240-244
- Oliver M.A., 1990, Kriging: a method of interpolation for Geographical Information Systems, International Journal of Geographic Information Systems, 4 (3), 313-332, DOI : 10.1080/02693799008941549
- Roache P.J., 1985, Computational fluid dynamics, (in Russian), Albuquerque: Hermosa Publishers, 616 pp.
- Samarsky A.A., Gulin A.V., 1989, Numerical methods, (in Russian), Nauka, 432 pp.
- Samarsky A.A., 1982, Introduction to numerical methods, (in Russian), Nauka, 552 pp.
- Stein M.L., 1999, Interpolation of spatial data: some theory for kriging, Springer Series in Statistics, Springer-Verlag, New York, USA , 249 pp.
- Will A., Weiher S., Blahak U., 2015, Overview of the interpolation methods. Analysis of the main error sources and first improvements in int2lm, [in:] COS MO/CLM/AR T User Seminar 2015, Book of Abstracts, Offenbach, Germany, 2