The paper proposes an original approach for predicting the values ​​of the spatial series. This approach can be used, in particular, to recover missing data. The counter-prediction method was tested on a model of an artificial neural network (ANN), which is sequentially trained on the values ​​preceding the predicted segment of the series on the left and right. The final prediction of the model is the weighted average of the results of these two sets. We have tested the work of the method using the example of predicting the dust content in the snow cover. 256 snow samples were taken with a step of 0.2 m along the line in the area of ​​the dumps of the existing open pit for the extraction of copper ore. To check the accuracy of the models, based on the data obtained, two spatial series were created: a series of measured values ​​(measured values ​​as they are) and a mixed series (randomly mixed values ​​of a series of measured values). The forecast with the minimum errors and the maximum correlation coefficient was obtained for a number of measured values. The least accurate forecast was obtained for a mixed series. RMSE for a series of measured values was 58% less than RMSE for a mixed series, an average value of the correlation coefficient was 0.3 for a series of measured values ​​and -0.06 for a mixed series.

Anastasia S. Butorova
Research Engineer of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS;
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
1st year Postgraduate Student of the Institute of Radio Electronics and Information Technologies – RtF of the Ural Federal University named after B.N. Yeltsin;
19, Mira str., Ekaterinburg, 620002, Russia
e-mail: a.s.butorova@urfu.ru

Alexander P. Sergeev
Candidate of Physical and Mathematical Sciences, Leading Researcher, Acting Head of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS,
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
e-mail: sergeev@ecko.uran.ru

Andrey V. Shichkin
Researcher of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS,
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
e-mail: and@ecko.uran.ru

Alexander G. Buevich
Researcher of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS,
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
e-mail: bag@ecko.uran.ru

Elena M. Baglaeva
Candidate of Physical and Mathematical Sciences, Senior Researcher of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS,
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
e-mail: e.m.baglaeva@urfu.ru

Marina V. Sergeeva
Researcher of the Laboratory of Physics and Ecology of the Institute of Industrial Ecology, UB RAS,
20, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
e-mail: marin@ecko.uran.ru

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