EVALUATION OF THE WHEAT CROP AND PRODUCTION ESTIMATION BASED ON REMOTE SENSING

. Based on remote sensing, the study analyzed the dynamics of a wheat crop using regression analysis to estimate production in relation to the NDMI, NDVI, MSAVI and NBR indices. The wheat crop considered in the study, was located in the area of Sacalaz, Timis county, Romania. Seven series of satellite images were taken, between February and June 2021. Based on the spectral information, the NDMI, NDVI, MSAVI and NBR indices were calculated and series of 595 values were obtained for each index. Very strong correlations were recorded between NBR and NDMI (r=0.999***), between MSAVI and NDVI (r=0.994***), between NBR and MSAVI (r=0.919**), between NDVI and NDMI ( r=0.911) and between NBR and NDVI (r=0.909**). Polynomial equations described the variation of NBR in relation to NDMI (R 2 =0.987), in relation to MSAVI (R 2 =0.794) and in relation to NDVI (R 2 =0.795). The variation of indices in relation to time, during the study period, was described by polynomial equations of the 2nd and 3rd degree, under statistical accuracy conditions (R 2 =0.854 for NDMI; R 2 =0.919 for NDVI; R 2 =0.956 for MSAVI, and R 2 =0.873 for NBR). Through the regression analysis, the wheat production was predicted, based on the calculated indices, and in different combinations of indices. The highest level of accuracy in the prediction of wheat production was recorded in the case of using the NDMI and NBR indices (p<0.001, RMSPE=0.24847), followed by the analysis variant in which the NDVI and MSAVI indices were considered (p=0.0002, RMSEP=1.59084) and the analysis variant in which NDVI and NBR indices were used (p=0.00081, RMSEP=5.20218). Graphical models, in 3D format and in the form of isoquants, have described the variation of wheat production in relation to the NDMI, NDVI, MSAVI and NBR indices.


INTRODUCTION
Specific indices, calculated based on satellite images, are important for the assessment of the spatial variability of the territory and the classification of areas (Li et al., 2018;Popescu et al., 2020;Singh et al., 2022), the description of the vegetation and agricultural crops (Weiss et al., 2020), the description of some phenomena in crops, such as plant lodging, the presence of weeds, diseases or plant pests (Chauhan et al., 2019;Guan et al., 2022).
The response of plants to certain stress factors was evaluated and appreciated based on specific indices, calculated on the basis of satellite images, such as water stress (Ahmad et al., 2021;Safdar et al., 2023), salinity stress (Scudiero et al., 2016;Tian et al., 2020), sau or other conditions and stress factors (Galieni et al., 2021;Skendžić et al., 2023).
The monitoring of agricultural crops during the vegetation period is important because it facilitates obtaining information, such as spectral data, which faithfully reflects the vegetation state of the crops in relation to the environmental conditions, and the applied technologies (Omia et al., 2023;Wu et al., 2023).
Such information is useful for timely interventions in order to adjust some crop parameters, to obtain the planned productions (Ma et al., 2022;Abdul-Jabbar et al., 2023).
Of particular importance is the possibility of estimating the production of agricultural crops, based on the information obtained from satellite images, respectively based on various calculated indices (Ali et  The usefulness of these studies for obtaining information on crops, for monitoring and control, for decisions on some interventions is important in the context of managing agricultural inputs, optimizing technologies and yields (Awad, 2019;Sishodia et al., 2020;Weiss et al., 2020;Gumma et al., 2021).
In wheat crop, imaging analysis based on different types of images (satellite, aerial or terrestrial) was frequently used to analyze and characterize the state of plant vegetation in relation to soil, climatic and technological conditions (Constantinescu et al., 2018;Sala et al., 2020;Cheng et al., 2022) The estimation of wheat production based on remote sensing techniques has also been the subject of numerous studies, which have developed statistical safety estimation models (Aranguren et al., 2020;Cheng et al., 2022;Saad El Imanni et al., 2022).
The present study considered the use of techniques based on remote sensing to monitor a wheat crop during the growing season and formulate production predictions based on spectral information and specific calculated indices.

MATERIAL AND METHODS
The study evaluated the dynamics of a wheat crop based on the satellite images taken from the Sentinel 2 system and the specific indices calculated.The wheat crop, the Anapurna variety, was located in the agricultural area of Sacalaz locality, Timis county, Romania, figure 1.The study took place during the 2020-2021 agricultural year.The wheat crop technology was in non-irrigated system.Fertilization was done with a complex (NPK, 20:20:0) 250 kg ha -1 when preparing the land for sowing.In the spring, there were applied 200 kg ha -1 of urea (first nitrogen fertilization) and 150 kg ha -1 of ammonium nitrate (second nitrogen fertilization).Wheat production was 7700 kg ha -1 , under the study conditions.
In order to evaluate the dynamics of the wheat crop, several satellite images were taken during the vegetation period from March to June, at nine different calendar dates (image acquisition date -Iad; Iad 1 to Iad 9).From the analysis of the series of satellite images, the spectral values were obtained, and based on them, specific indices considered in the evaluation of the wheat crop and production estimation were calculated: NDMI (Wilson and Sader, 2002), equation (1); NDVI (Rouse et al., 1973), equation (2); MSAVI (Qi et al., 1994), equation (3); NBR (Key and Benson, 2005), equation ( 4). (1) The data obtained for the considered indices and the time factor, between the moments of taking the images (Iad 1 to Iad 9), were analyzed for statistical safety and the presence of variance.
Appropriate mathematical and statistical analysis was used to analyze data series (calculated indices, time, production results), obtaining appropriate mathematical and graphical models (Hammer et al., 2001;Wolfram Alpha, 2020;JASP, 2022).

RESULTS AND DISCUSSIONS
According to the purpose of the study, satellite images were taken at different stages, during the vegetation period of the wheat crop, and spectral values were obtained from the analysis of the images.Based on the calculation formulas, equations (1) to (4), the considered indices were calculated (series of 85 values for each index and date of aquiring the images, table 1, figure 2).The average values calculated for the indices, in relation to the moment of aquiring the images, are presented in table 2. The data obtained for the indices considered, in series of 85 values for each index, were analyzed for the evaluation of statistical safety and the presence of variance in the data series (ANOVA test, Alpha=0.001),table 3. The correlation analysis between the values of the indices and the time in days, over the interval of aquiring the images, led to obtaining very strong correlations between NBR and NDMI (r=0.999***), between MSAVI and NDVI (r=0.994***), between NBR and MSAVI (r=0.919**), between NDVI and NDMI (r=0.911) and between NBR and NDVI (r=0.909**).The values of the correlation coefficient and the statistical safety parameter, resulting from the analysis, are presented in table 4. The high affinity between the values of the NBR and NDMI indices was described by equation ( 5), under statistical safety conditions, according to R 2 =0.987, p=0, with graphic representation in figure 3 (a).In relation to MSAVI, the NBR variation was described by equation ( 6), under conditions of R 2 =0.794, p<0.001, with graphic representation in figure 3 (b).In relation to NDVI, the NBR variation was described by equation ( 7), under conditions of R 2 =0.795, p<0.001.The variation of indices in relation to time (t, days) during the vegetation period was described by polynomial equations under statistical safety conditions, figure 4.  The estimation of wheat production was made based on the values of the calculated indices.Regression analysis was used, and different combinations of indices were considered in the analysis.
Equation ( 8) resulted, and the values of the equation coefficients depending on the indices considered in the analysis are presented in table 5.The statistical accuracy in estimating the production was described by the regression coefficient (R 2 =0.999), by the values of the parameter p and RMSEP, table 5.
Depending on the combinations of indices used in the regression analysis, variable values resulted for the parameter p and RMSEP.The highest level of accuracy in the prediction of wheat production was recorded in the case of using the NDMI and NBR indices (p<0.001,RMSEP=0.24847),followed by the analysis variant in which the NDVI and MSAVI indices were considered (p=0.0002,RMSEP=1.59084) and the analysis variant in which NDVI and NBR indices were used (p=0.00081,RMSEP=5.20218),table 5.
The graphic representation of the production variation in relation to the indices considered, for the most reliable estimates referred to, are presented in figure 5 in relation to the NDMI and NBR indices, and in figure 6 in relation to the NDVI and MSAVI indices.(8) where: Y -wheat production (kg ha -1 ); x , y -indices used (table 5); a, b, c, d, e, f -coefficients of the equation ( 8), table 5.  Evaluation of the dynamic of agricultural crops and production estimation are of interest for an adequate management of the farm.The facilities offered by imaging analysis, based on satellite, aerial and terrestrial images, are already implemented in high-performance management systems at farm level, or structures at different levels in the agri-food chain (Brown, 2015;Bégué et al., 2020).
In order to estimate production, data from different satellite systems, UAV or terrestrial images were used, based on which appropriate indices were calculated and prediction models were found (Hisham et  The use of the NDMI and NBR indices in the regression analysis led to the prediction of the production with the highest level of precision and under conditions of statistical safety.

CONCLUSIONS
The temporal variation of the wheat crop was described by the NDMI, NDVI, MSAVI and NBR indices calculated on the basis of spectral information, in relation to time (days) in the interval February -June 2021.Polynomial equations of degree 2 and 3 were found to describe the variation of the index values, as an expression of the vegetation state of the crop, over the considered time period.Very strong, positive correlations were found between the determined indices, and the interdependence between NBR and NDMI, MSAVI, respectively NDVI was described by models in the form of equations.
Production prediction based on the calculated indices was possible, and the highest level of accuracy in wheat production prediction was recorded in the case of using the NDMI and NBR indices (p<0.001,RMSEP=0.24847).Next as level of precision and safety, the analysis variant in which NDVI and MSAVI indices were considered (p=0.0002,RMSEP=1.59084), and the analysis variant in which NDVI and NBR indices were used (p=0.00081,RMSEP=5.20218).
3D models and in the form of isoquants have been generated to graphically represent the variation of Y production in relation to the indices considered in the analysis.

Figure 1 .
Figure 1.The study area, wheat crop

Figure 3 .
NBR variation in relation to NDMI (a) and in relation to MSAVI (b)

Figure 4 .
Figure 4. Distribution of index values calculated in relation to time (days) and equations with R 2 parameters

YFigure 5 .Figure 6 .
The distribution of wheat production in relation to the NDMI and NBR indices (a) (b) The distribution of wheat production in relation to the NDVI and MSAVI indices al., 2022; Saad El Imanni et al., 2022).Cavalaris et al. (2021) used different indices (NDVI, EVI, NDMI and NDWI) derived from Sentinel-2 for durum wheat yield modeling.In relation to the values of the indices considered (NDMI, NDVI, MSAVI and NBR) and the combinations of indices used in the regression analysis, the estimation of wheat production was possible in the present study, but with different precision and levels of statistical certainty.

Table 1 .
Descriptive Statistics Figure 2. Graphical distribution of index values by size classes

Table 2 .
Average values of the indices in relation to the date of acquiring the images

Table 4 .
Correlation table

Table 5 .
Values of the coefficients of equation (8) and the associated statistical parameters