doi: 10.15389/agrobiology.2019.1.84eng

*UDC 633: 57.087: 51-76*

**EXPERIENCE WITH THE USE OF MATHEMATICAL STATISTICS METHODS FOR ASSESSMENT OF AGRICULTURAL PLANTS STATUS**

**V.M. Bure ^{1, 2}, A.F. Petrushin^{1}, E.P. Mitrofanov^{1}, O.A. Mitrofanova^{1, 2}, **

V. Denisov^{3}

* ^{1}Agrophysical Research Institute*, 14, Grazhdanskii prosp., St. Petersburg, 195220 Russia, e-mail vlb310154@gmail.com (✉ corresponding author), apetrushin@agrophys.ru, mjeka@agrophys.ru, omitrofa@gmail.com;

^{2}*Saint Petersburg State University,*7/9, Universitetskaya nab., St. Petersburg, 199034 Russia;

*, Herkaus Manto 84, LT-92294 Klaipeda, Lithuania, e-mail vitalij.denisov@ku.lt*

^{3}Klaipeda UniversityORCID:

Danilova T.N. orcid.org/0000-0001-6926-6155

Tabynbayeva L.K. orcid.org/0000-0001-9721-6737

*Received September 28, 2018*

Solving problems related to the assessment of the status of agricultural plants during the growing season, allows us to effectively use fertilizers, obtain favorable yields, improve the quality characteristics of plants, as well as the ecological condition of the field. To solve such problems of precision farming, the use of various methods of mathematical statistics is becoming an increasingly promising direction. The aim of our work was to assess the state of agricultural plants using an approach based on the combined use of kriging and binary regression methods, as well as the determination of nitrogen planting using the NDVI (Normalized Difference Vegetation Index) index. The studies were carried out at the site of an experimental agricultural field located on the territory of the branch of the Agrophysical Institute (Menkovo, Leningrad region) in 2015. With the help of aerial photographs taken from the automatized unmanned aerial vehicle complex Geoscan-401 (Geoscan Group of Companies, Russia), a set of NDVI (Normalized Difference Vegetation Index) vegetation index values was obtained at arbitrary points of the plot. A number of ground-based measurements were also conducted on the studied area of the field. The proposed approach to assessing the state of agricultural plants consisted in the joint use of two methods of mathematical statistics: ordinary kriging and logistic regression. A preliminary variogram analysis was carried out, and a variogram model was constructed. After this, the kriging method was used to calculate a series of predicted values of the parameter being studied. At the next stage, the threshold value of the parameter for the study area was established, and also a dummy variable was entered, taking the value 1 if the parameter value exceeded the threshold, and 0 otherwise. Then a logit model was built, in which one of the factors was a series of estimates of the parameter of interest, obtained using the ordinary kriging method. The input data for building logit models were as follows: *N*(*x _{i}*)

**is the NDVI value at the location**

*x*,

_{i}*i*= 1.78; variable

*T*= 1, if

*N*(

*x*) ≥ 0.46, otherwise

_{i}*T*= 0; the variables

*X*and

*Y*are the coordinates of the observations, are considered as explanatory variables;

*N*(

_{pred}*x*) is

_{i}**parameter values, predicted using the kriging method at the observed points. All calculations were performed using the R programming language. As a result of the experiment, three logit models were built with the dependent variable**

*T*: in the first model, the explanatory variables

*X*and

*Y*; in the second model —

*X*,

*Y*and

*N*; in the third model

_{pred}*N*. Testing showed that when adding the

_{pred}*N*variable, the logit model works better (2 times less than the erroneous determination of the level of the parameter under study). The results obtained suggest that adding in the binary regression factors a set of values predicted by the kriging method can significantly improve the accuracy of calculations.

_{pred}Keywords: plant status, Normalized Difference Vegetation Index, NDVI, kriging, binary regression, language R.

REFERENCES

- Bure V.M., Mitrofanova O.A. Analysis of aerial photographs to predict the spatial distribution of ecological data.
*Contemporary**Engineering Sciences*, 2017, 10(4): 157-163 CrossRef - Kim Y., Reid J.F., Han S. On-the-go nitrogen sensing and fertilizer control for site-specific crop management.
*International Journal of Agricultural and Biosystems Engineering*, 2006, 7(1): 18-26. - Blackmer T.M., Schepers J.S. Aerial photography to detect nitrogen stress in corn.
*J. Plant Physiol.*, 1996, 148(3-4): 440-444 CrossRef - Graeff S., Pfenning J., Claupein W., Liebig H.P. Evaluation of image analysis to determine the N-fertilizer demand of broccoli plants.
*Advances in Optical Technologies*, 2008, Article ID 359760 CrossRef - Thenkabail P.S., Lyon J.G., Huete A.
*Hyperspectral remote sensing of vegetation*. CRC Press, MA, USA, 2011. - Franzen D.W., Reitmeier L., Giles J.F., Cattanach A.C. Aerial photography and satellite imagery to detect deep soil nitrogen levels in potato and sugarbeet.
*Proc. of the 4th International Conference «Precision Agriculture»*. St. Paul, MN, 1999: 281-290. - Bure V.M.
*Materialy Mezhdunarodnogo seminara, posvyashchennogo pamyati professora Ratmira Aleksandrovicha Poluektova (Poluektovskie chteniya)*[Proc. International Seminar dedicated to the memory of Prof. Ratmir Alexandrovich Poluektov (Poluektov reading)]. St. Petersburg, 2014: 118-121 (in Russ.). - Debella-Gilo M., Etzelmüller B. Spatial prediction of soil classes using digital terrain analysis and multinomial logistic regression modeling integrated in GIS: Examples from Vestfold County, Norway.
*Catena*, 2009, 77(1): 8-18 CrossRef - Kempen B., Brus D.J., Heuvelink G.B.M., Stoorvogel J.J. Updating the 1:50,000 Dutch soil map using legacy soil data: a multinomial logistic regression approach.
*Geoderma*, 2009, 151(3-4): 311-326 CrossRef - Yakushev V.P., Zhukovskii E.E., Kabanets A.L., Petrushin A.F., Yakushev V.V.
*Variogrammnyi analiz prostranstvennoi neodnorodnosti sel'skokhozyaistvennykh polei dlya tselei tochnogo zemledeliya*[Variogram analysis of agricultural fields spatial heterogeneity for precision farming]. St. Petersburg, 2010 (in Russ.). - Claret M.M., Urrutia R.P., Ortega R.B., Best S.S., Valderrama N.V. Quantifying nitrate leaching in irrigated wheat with different nitrogen fertilization strategies in an Alfisol.
*Chilean Journal of Agricultural Research*, 2011, 71(1): 148-156 CrossRef - Krasilnikov P., Sidorova V. Geostatistical analysis of the spatial structure of acidity and organic carbon in zonal soils of the Russian plain. In:
*Soil geography and geostatistics: concepts and applications*. P. Krasilnikov, F. Carré, L. Montanarella (eds.). European Communities, Luxembourg, 2008: 55-67. - Dulaney W.P., Lengnick L.L., Hart G.F. Use of geostatistical techniques in the design of an agricultural field experimental.
*Proc. of the Survey research methods section*. Alexandria, VA, 1994: 183-187. - Adamsen F.J., Pinter P.J., Barnes E.M. Measuring wheat senescence with a digital camera.
*Crop Science*, 1999, 39(3): 719-724 CrossRef - Panayi E., Peters G.W., Kyriakides G. Statistical modelling for precision agriculture: a case study in optimal environmental schedules for Agaricus Bisporus production via variable domain functional regression.
*PLoS ONE*, 2017, 12(9): e0181921 CrossRef - Isaaks E., Srivastava M.
*An introduction to applied geostatistics*. Oxford University Press, NY, USA, 1989. - Fernandes G.B., Artes R. Spatial dependence in credit risk and its improvement in credit scoring.
*Eur. J. Oper. Res*., 2016, 249(2): 517-524 CrossRef - Dem'yanov V., Savel'eva E.
*Geostatistika. Teoriya i praktika*[Geostatistics. Theory and practice]. Moscow, 2010 (in Russ.). - Webster R., Oliver M.A.
*Geostatistics for environmental scientists, Second edition*. John Wiley and Sons Ltd, Chichester, UK, 2007 CrossRef - Yakushev V.P., Bure V.M., Parilina E.M.
*Binarnaya regressiya i ee primenenie v agrofizike*[Binary regression and its application in agrophysics]. St. Petersburg, 2015 (in Russ.). - Hosmer D., Lemeshow S.
*Applied logistic regression, Second edition*. Wiley, NY, 2000 CrossRef - Bure V.M., Parilina E.M.
*Teoriya veroyatnostei i matematicheskaya statistika: uchebnoe posobie*[Probability theory and mathematical statistics: tutorial]. St. Petersburg, 2013 (in Russ.). - Plant R.E.
*Spatial data analysis in ecology and agriculture using R*. CRC Press, Boca Raton, 2012. - Yakushev V.P., Kanash E.V., Konev A.A., Kovtyukh S.N., Lekomtsev P.V., Matveenko D.A., Petrushin A.F., Yakushev V.V., Bure V.M., Rusakov D.V., Osipov Yu.A.
*Teoreticheskie i metodicheskie osnovy vydeleniya odnorodnykh tekhnologicheskikh zon dlya differentsirovannogo primeneniya sredstv khimizatsii po opticheskim kharakteristikam poseva: prakticheskoe posobie*[Theoretical and methodological basis for the allocation of homogeneous technological zones for the differentiated use of chemicals according to the optical characteristics of sowing: practical guide]. St. Petersburg, 2010 (in Russ.). - Kanash E.V., Osipov Ju.A. Optical signals of oxidative stress in crops physiological state diagnostics.
*Proc. 7th European conference on precision agriculture*. Wageningen, Netherlands, 2009: 81-89. - Goovaerts P.
*Geostatistics for natural resources evaluation*. Oxford University Press, NY, 1997.