The general way of a yield estimation using remote sensing data is a regression modeling based on cumulative NDVI vegetation index. Usually, the other additional factors are also included in the model to enhance a yield estimation accuracy, for example, weather conditions during the vegetation season or particular crop type information. Nevertheless, such factors as soil characteristics were not properly investigated and it is still an open question whether they should be included in modeling process or not. This article reveals the regression modeling accuracy dependency on the additional soil characteristics for winter wheat yield estimation using cumulative NDVI. We analyzed several groups of factors obtained from different data sources such as remote sensing images, geoinformation systems and meteorological data. These factors were used to construct primarily yield models without soil factors. The best two models were chosen as the basic models and then they were modified to take into account the additional soil characteristics. Finally, the comparison of the basic models with the modified models including soil parameters was made. We investigated such soil parameters as soil fertility score derived from a ten-year-old soil map and the results of the current agrochemical inspections. The comparison of basic and modified models was made for the winter wheat fields located in Samara region, Russia. The experiments showed that regression models give better determination coefficient and root mean square error if the additional soil characteristics are used for modeling. Moreover, the older data obtained from soil maps and reference book of the soil fertility score delivers better prediction than the current agrochemical inspection data. Therefore, there is no need to know lots of soil parameters for successfully winter wheat yield modeling. The results of this research can be applied to forecasting winter wheat yield in Samara region.
Traditional yield prediction agricultural methods require a vast amount of ground truth measurements that makes these methods very expansive in use. To provide automated yield prediction without ground truth measurements the geoinformation systems (GIS) and remote sensing data (RS data) can be used. RS data provide objective information about agricultural crop growth whereas GIS contains effective instruments for additional parameters calculation based on graphic and semantic information about the field. Therefore, the development of simultaneous GIS and RS data for agricultural purposes remains a very promising research area.
Existing GIS and RS data yield prediction approaches are highly connected with the traditional
methods used in agriculture that mainly utilize linear regression modeling and simulation modeling to
find the relation between the observed factor values and the yield [
In our research, we apply cumulative NDVI [
The article is structured as follows. Section 2 describes the factor groups used to construct the basic soil independent models and the general model equation. Section 3 reveals the details of two approaches to the cumulative NDVI estimation and the process of optimal factor set selection. Section 4 contains the results of the experimental evaluation of soil fertility impact on yield regression modeling. 2. Problem statement Generally, regression modeling is used to find the relation between the expectation of the dependent random variable y and the set of independent variables x1, x2 ,..., xn called factors. The type of regression function is determined according to the heuristic assumptions about the relationship between the observed independent parameters and dependent variable. In the present article, we regard a linear regression model in which the dependent variable y corresponds to the winter wheat yield: n y ai xi a0 i1 where a ,i 0,..., n are the coefficients of the model.
i
We consider several sets of factors for the model (1). The first set (basic set of factors (BSF)) contains factors extracted from the farmer data in GIS, meteorological services and RS data. BSF includes such subgroups of factors as:
1) the remote sensing factors. These factors are calculated using NDVI time series obtained by RS data. They include cumulative and maximum NDVI values for the period of the most active vegetation as well as the vegetation period duration and the vegetation start date. The following equation explains the process of factor extraction: , (2) where r is the cumulative NDVI value, (t) is the average NDVI value for the particular field at the date t , r is the relative date of the vegetation period beginning, T is the vegetation period duration; 2) the bioclimatic factors. These factors are obtained from meteorological services. This subgroup contains such factors as maximum and minimum temperature for the vegetation period, maximum and minimum humidity during the vegetation period and climate zone in which the field is located; 3) the data of agricultural producers join such factors as crop cultivar, seeds reproduction, farmer identifier, date of seeding and geographical coordinates of the field object centroid. The factors of these group are obtained from the GIS database.
The second set of factors (SFS) contains soil fertility factors determined by the GIS soil maps.
These factors are the soil fertility score and the humus content. The soil fertility score was determined
according to the reference study [
The third factor set (TSF) is constructed as a combination of the soil fertility parameters according to the agrochemical survey data. TSF incorporates such factors as average humus, phosphorus, sulfur and potassium contents in the field soil. The agrochemical survey data were obtained from the semantic information of the agrochemical surveys map in GIS.
We conducted our research in several stages. First of all, we selected an optimal subset of the basic factor set (OBSF). OBSF was determined as the subset of significant factors of the model (1) which delivers the highest value of the determination coefficient (R2). We further refer the regression model estimated for the OBSF as Model 1. In other words, the Model 1 is a name of the general soilindependent regression model estimated using OBSF. Then, in order to get the soil-dependent models, we combined OBSF with two other factor sets SSF and TSF and estimated the regression models for the resulting factor sets. The regression models obtained for OBSF and SSF are further referred as Model 2, while the regression models estimated using OFBSS and TSF are referred as Model 3. Model 2 and Model 3 are the names of the received soil dependent regression models. Finally, the comparison of soil-dependent and soil-independent models was made.
We applied the least square method [
The first approach requires the NDVI threshold T to be given. This threshold is used to achieve the minimum min and maximum max relative dates for which the NDVI value is greater than the threshold T . Therefore, the vegetation beginning date r and the vegetation period duration T are defined as follows:
r min , T max min . (3) (4)
The second approach defines the vegetation period symmetrically around the maximum of NDVI value. Thus, for given vegetation period duration T , we obtain the vegetation beginning parameter in the following way
r tmax T 2 , where tmax argmax t . Figure 2 shows the scheme of the second approach.
t (5)
The proposed approaches determine two different subgroups of remote sensing factors. The factors corresponding to the first approach are cumulative NDVI value r , vegetation beginning date r and vegetation period duration T . The factors formed as a result of the second approach include cumulative NDVI value r , the date of maximum NDVI value tmax and half-width of the vegetation period T 2 .
We tested several values of the NDVI threshold T for the first approach and several values of T 2 for the second approach. Nine BSFs corresponding to different remote sensing factors were formed. A complete list of the BSFs considered and their names are given in Table 1.
According to the different BSFs, nine regression models were estimated and the optimal BSF was
chosen. The whole process of the optimal BSF selection is described as follows:
1. The independent categorical variables such as farmers identifier, seeds reproduction and others
are previously converted in a set of binary variables taking values 0 or 1 depending on the
chosen category.
2. Then all factors are normalized to get zero expectation and unit variance.
3. The normalized factors and the dependent variable values are processed by the least square
method (LSM) to define the unknown regression coefficients in the expression (1).
4. For each of the BSFs, an adequacy of the constructed regression models is checked by testing
the standard LSM hypotheses [
5. The significant factors of regression models tested for adequacy are taken as optimal basic sets of
factors if corresponding regression model has the R2 value greater or close to 0.8.
4. Experimental research
The experimental study was conducted using the remote sensing and GIS data obtained for the season
from April 1 till August 31, 2015. The farmers provided the field boundary information and semantics
that includes wheat cultivar, seed reproduction, farmer identifier and crop yield in the observation
period in the Agricultural GIS of Samara Region. The total number of fields used in experiments was
127. Climate zones and geographical coordinates of the field center were extracted by means of
spatial queries from the vector layer in GIS. The climate zone parameter was defined as the index
taking values from 1 to 3 according to the following notation [
The factors based on remote sensing data were calculated using NDVI vegetation index time series.
We applied the algorithm described in [
Climate data such as air temperature, relative humidity and precipitation were extracted from the weather archives of the following weather stations: Kinel-Cherkassy village (No. 548621) with coordinates 53°0'0"N47°0'0"E, Sernovodsk settlement (No. 496568) with coordinates 53°0'0"N92°0'0"E, Krasnoarmeyskoye village (No. 824366) with the coordinates 52°0'0"N 7°0'0"E. To estimate the climate factors we applied the measurements of the nearest to the field meteorological station among the considered ones.
As for the soil fertility factors, the soil fertility score was defined corresponding to the soil type
marked on the soil map and the reference book [
We used 127 fields to estimate the coefficients of the Model 1 that describes the soil independent regression model. 20 fields were used to estimate the coefficients of the Model 2 that describes the soil map-based model. And 32 fields were used to estimate the coefficients of the Model 3 that describes the model based on the agrochemical inspection data. The difference between the sample set size is explained by the various number of available data for each of the information sources used to extract the factors. The RMSE error was estimated for the same sample sets. The multiple linear regression coefficients estimation and the model adequacy verification was made using MATLAB software.
We obtained 9 models for the different BSFs listed in Table 1 and checked their adequacy. The significance level used to test adequacy was equal to 0.05 for all tests. Table 2 shows the determination coefficients evaluated for each of these models. According to table 2, the significant factors of the models based on NDVI06 and NDVI02 BSFs should be taken as the optimal basic sets of factors. However, the model NDVI02 did not pass the Lilliefors test and, thus, it cannot be regarded as the statistically adequate model. The other models passed adequacy verification successfully. Therefore, we selected the model with NDVI04 BSF as an alternative to NDVI06 model. NDVI03 0.7110 NDVI04 0.7162 NDVI05 0.6970 NDVI06 0.8035 NDVI20 0.7972 NDVI30 0.6999 NDVI40 0.6768 NDVI50 0.6405
NDVI60 0.7110
The further results were obtained for two OBSFs determined as the significant factors of the models based on NDVI04 BSF and NDVI06 BSF. The lists of factors included in the OBSF are given below:
1) for the model NDVI06: cumulative and maximum NDVI values during the vegetation period, the vegetation period duration and vegetation beginning date, maximum and minimum temperature during the vegetation period, maximum and minimum humidity during the vegetation period, seeds reproduction, sowing date and geographical coordinates of the field center;
2) for the model NDVI04: cumulative and maximum NDVI values during the vegetation period, the vegetation period duration and vegetation beginning date, maximum and minimum temperature during the vegetation period, maximum and minimum humidity during the vegetation period, the wheat cultivar, farmer identifier, sowing date and the geographical coordinates of the field center.
The other factors were excluded from the OBSF because they were insignificant. In further text, we will reference on OBSF according to the BSF name for which it was constructed.
To obtain soil-dependent models Model 2 and Model 3, we combined two OBSFs defined above with the SSF and TSF. Therefore, four different regression models were obtained. These models were passed the adequacy tests with the significance level 0.05. The R2 value and RMSE corresponding to the obtained soil-dependent models are given in Table 3. improves the crop yield forecasting quality. The best model quality corresponds to the Model 2 which applies SSF and OBSF based on NDVI04 remote sensing factors. This model has the minimum RMSE and maximum determination coefficient among the models considered.
Figures 3-8 illustrates actual and predicted yield values for the different types of regression models and OBSFs. The red color denotes the upper confidence interval for the predicted yield values. The green color denotes the lower confidence interval for the predicted yield values. The blue color denotes the yield value. The experimental results shows that the RMSE of modeling without soil parameters is in the range from 2.7 up to 3 centner per hectare and from 0.5 up to 2.4 centner per hectare with soil parameters. To summarize, we found that additional soil factors enhance the accuracy of regression modeling using NDVI data. We also recommend using soil fertility score and soil maps instead of agrochemical survey data. As for the remote sensing factors estimation, we propose to apply the first approach with the NDVI threshold equal to 0.4.
Model1 NDVI06 Model1 NDVI04
Actual Figure 7. Diagram of actual and forecasted yield values for Model 3 with OBSF NDVI06.
Actual
Figure 8. Diagram of actual and forecasted yield values for Model 3 with OBSF NDVI04.
Actual Figure 3. Diagram of actual and forecasted yield values for Model 1 with BSF NDVI06.
Actual Figure 4. Diagram of actual and forecasted yield values for Model 1 with BSF NDVI04.
Model2 NDVI06
Model2 NDVI04
Actual
Figure 6. Diagram of actual and forecasted yield values for Model 2 with OBSF NDVI04.
Model3 NDVI04
The study presented in this article shows that the accuracy of winter wheat yield regression modeling using the NDVI vegetation index depends on the additional soil characteristics. We regarded several factor groups derived from the remote sensing data and the geoinformation systems to define the optimal basic factor set for the yield modeling without soil factors. Two types of additional soil factors were combined with the optimal basic factor sets, and comparative analysis of soil-dependent and soil -independent models was performed. The analysis was made for the sample fields in Samara region, Russia. As a result, we found that the soil parameters enhance the quality of winter wheat yield modeling and soil fertility score derived from a ten-year-old soil maps is provides more accurate results than the agrochemical inspection data. Therefore, only two parameters such as soil fertility score and soil type might for successfully winter wheat yield modeling instead of variety agrochemical characteristics. We also compared different approaches for the remote sensing factors computation using NDVI time series data. We concluded that the threshold 0.4 effectively determines the vegetation beginning date, vegetation period duration and cumulative NDVI in terms of the yield prediction accuracy. The results of this research can be applied to forecasting winter wheat yield in Samara region. Acknowledgements This work was supported by the RFBR projects No. 16-29-09494 and 18-07-00748.