# Predicting Soybean Yield at the Regional Scale Using Remote Sensing and Climatic Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.1.1. Khabarovsk District Area

^{2}). The region displays monsoon features and is characterized by moderately cold winters with little snow, and warm, excessively moist summers. The alluvial and meadow alluvial soils of the Amur River valley (i.e., Khabarovsk suburbs and the Russian part of Big Ussuriyskiy island) are very suitable for agriculture [30]. Plenty of moisture, sunlight, and good soil conditions allow cultivating soybean [31]. The Khabarovsk District is the leading agricultural municipality of the Khabarovsk Territory. The total arable land in the Khabarovsk region in 2018 amounted to more than 28,000 ha or almost 35% of the arable land throughout the Khabarovsk Territory.

#### 2.1.2. Experimental Sites

#### 2.2. Data Acquisition and Processing

#### 2.2.1. Approximation of Annual NDVI Curves for Soybean and Arable Land in the Khabarovsk District

- m—start of the vegetation period, week number;
- n—end of the vegetation period, week number;
- $NDV{I}_{i}^{pred}$—predicted NDVI for the ith week;
- $NDV{I}_{i}^{obs}$—observed NDVI for the ith week.

- $NDV{I}_{max}^{pred}$—predicted maximum NDVI value;
- $NDV{I}_{i}^{avg}$—average NDVI value in the ith week.

#### 2.2.2. Regression Model

- y—average annual soybean yield estimation by municipality, t/ha;
- x
_{1}—the maximum NDVI value from the 15th to the 30th weeks by the mask of the municipality’s arable land; - x
_{2}—Selyaninov hydrothermal coefficient (SHC) [43], calculated as follows:

- x
_{3}—duration of the growing season as of the 30th week (average temperature above 10 °C); - x
_{4}—total soil temperature as of the 30th week (layer 0–10 sm), °С; - x
_{5}—average soil humidity as of the 30th week (layer 0–10 sm), %; - x
_{6}—photosynthetically active radiation (GJ∙m^{2}), calculated as follows:

^{2}).

_{3}) for the corresponding calendar weeks can be calculated by adding up all of the remaining days for 30 calendar weeks to the already achieved number of vegetation days. This is due to the fact that according to the observations in 2010–2019 in June–July, only three days were observed in total with an average daily temperature below 10 °C (8 June 2018; 16 June 2014; and 12 June 2011). In any case, even when days with temperatures below 10 °C appear, further recalculation of the yield forecast by the model will allow to adjust the yield value.

^{2}), RMSE, and MAPE between modeled and observed data.

- n—observation period duration (years);
- ${y}_{i}^{pred}$—predicted yield in the ith year;
- ${y}_{i}^{obs}$—observed yield in the ith year.

^{2}

_{cv}), cross-validated root mean square error (RMSE

_{cv}), cross-validated mean absolute percentage error (MAPE

_{cv}), and cross-validated absolute percentage error (APE

_{cv}) values using a leave-one-year-out cross-validation, which leaves out one year at a time, permitting a comparison between the observed and predicted yield at that year. These statistics calculated using Formulas (4), (10) and (11).

## 3. Results

#### 3.1. NDVI Seasonal Dynamics for Different Crops in the Experimental Fields in 2014–2018

_{max}(NDVI maximum) for soybean in 2018 was 0.852.

#### 3.2. NDVI Seasonal Dynamics for the Arable Land in the Khabarovsk District in 2014–2018

#### 3.3. Mathematical Model for Calculating Soybean Yield in the Khabarovsk District

_{1}), and the values of the climatic characteristics (x

_{2}–x

_{6}).

_{2}and x

_{4}have a high coefficient of variation. The total soil temperature (x

_{4}) in the first 30 weeks of 2014 was 2.5 times higher than the same value in 2016 (769.5 °С and 311.9 °С, respectively). The maximum NDVI values have the least variation—2.4%—while the variability of x

_{3}, x

_{5}, and x

_{6}is in the range of 7–8.5%. In general, 2010, 2011, 2013, and 2015–2017 are characterized by a late start to the growing season (x

_{3}ranged from 71 to 75 days). For 2012, 2014, and 2018, x

_{3}(growing duration) ranged from 82 to 84 days. Similarly, the variable x

_{6}(photosynthetically active radiation) changed during the study period. High PAR values were observed in 2012, 2014, and 2017–2018 and ranged from 0.86 to 0.89 GJ∙m

^{2}. The highest values of the indicators characterizing humidity/aridity were observed in 2011 and 2015. The average relative soil moisture (x

_{5}) was 38.0% and 38.1%, and the Selyaninov hydrothermal coefficient (x

_{2}) was 3.03 and 3.07, respectively.

_{3}and x

_{6}(τ = 0.73), and x

_{2}and x

_{5}(τ = 0.56). Thus, it is advisable to leave only one of the two variables characterizing the degree of aridity (x

_{2}) and to exclude x

_{6}from the regression model. It is also possible to preliminarily characterize the impact of the indicators on soybean yield using the correlation table. Thus, the maximum NDVI value, the duration of the growing season, the total temperature of the soil, and the PAR are all directly related to the average crop yield. Conversely, soil moisture and SHC are inversely related to soybean yield.

_{5}and x

_{6}were excluded during the correlation analysis, and variables x

_{2}and x

_{4}were automatically excluded during stepwise model construction as insignificant indicators. As a result, the multiple regression equation, which characterizes the dependence of soybean yield in the Khabarovsk District on the variables included in the model, constructed according to the data of 2010–2018, has the following form:

^{2}) is 0.72. The standardized values of the regression coefficients are approximately equal, which indicates the same effect of the predictors on soybean yield (Table 7). All of the coefficients of the regression equation are significant (p < 0.05).

^{2}

_{cv}, RMSE

_{cv}, and MAPE

_{cv}values obtained using a leave-one-year-out (2010–2019) cross-validation procedure (Table 8). APE

_{cv}was mainly within 8% (except 2013 and 2015).

#### 3.4. Soybean Yield Prediction in Other Municipalities of Far East Based on Proposed Model

^{2}values, and the p-values.

^{2}values, and the p-values for some regions (i.e., the Khabarovsk, Vyasemskiy, Tambovskiy, Mikhailovskiy, and Khankaiskiy districts) are quite satisfactory. The early forecasting method development for soybean and other crops for different territories is a priority area for future research.

## 4. Discussion

^{−1}for the different regions of Argentina. Using early NDVI values in soybean analysis is, in our opinion, quite a difficult task.

_{1}is the maximum NDVI value, and x

_{2}is the total soil temperature in the 10–40 cm layer during the vegetation season (before the 30th week). The model’s determination coefficient (R

^{2}= 0.68) is slightly less than the corresponding coefficient for our equation from Section 3. Thus, this equation proves the relationship between soil temperature in deep layers and soybean yield. Further study of the influence of soil characteristics on crop yields looks promising.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Observed and approximated weekly Normalized Difference Vegetation Index (NDVI) composites (15th–42nd calendar weeks) for the experimental soybean fields in the Khabarovsk District in (

**a**) 2014; (

**b**) 2015; (

**c**) 2016; (

**d**) 2017; (

**e**) 2018.

**Figure 4.**Observed and approximated weekly NDVI composites (15th–42nd calendar weeks) for the experimental fields in the Khabarovsk District in 2018: (

**a**) Soybean fields; (

**b**) oat fields; (

**c**) spring wheat fields; (

**d**) forage grass fields; (

**e**) total (arable land model).

**Figure 5.**The NDVI seasonal variation curves for crops grown in the experimental fields in 2018 (the maximum NDVI values are marked with stars).

**Figure 6.**Observed and approximated weekly NDVI composites (15th–42nd calendar weeks) for the arable land in the Khabarovsk District in (

**a**) 2014; (

**b**) 2015; (

**c**) 2016; (

**d**) 2017; (

**e**) 2018; (

**f**) 2014–2018 (average).

**Figure 7.**Actual and approximated values of the weekly NDVI composites for the arable land in the Khabarovsk District in 2019: (

**A**) Parameters calculated from the NDVI composites in 2019; (

**B**) parameters calculated from the averaged NDVI composites in 2014–2018.

**Figure 8.**Deviation of the weekly forecasted maximum NDVI values from the actual maximum, % (Khabarovsk District, 2019).

Crop | Soybean | Wheat | Oat | Potato | Forage Grasses | The Rest of the Crops | Total |
---|---|---|---|---|---|---|---|

Sown area, ha | 16,976 | 1382 | 1748 | 1692 | 4568 | 1833 | 28,200 |

Percentage | 60.2 | 4.9 | 6.2 | 6.0 | 16.2 | 6.5 | 100 |

**Table 2.**Parameters of the NDVI curves, the maximum NDVI, mean absolute percentage error (MAPE), and root-mean-square error (RMSE) for the experimental soybean fields in the Khabarovsk District in 2014–2018.

2014 | 2015 | 2016 | 2017 | 2018 | |
---|---|---|---|---|---|

c | 8.2 | 8.7 | 7.5 | 8.0 | 7.6 |

b | 31.0 | 31.3 | 31.4 | 31.4 | 31.5 |

$NDV{I}_{\mathrm{max}}^{pred}$ | 0.819 | 0.753 | 0.858 | 0.825 | 0.852 |

$NDV{I}_{\mathrm{max}}^{obs}$ | 0.819 | 0.753 | 0.859 | 0.826 | 0.854 |

MAPE, % | 8.5 | 6.0 | 13.9 | 10.2 | 10.9 |

RMSE | 0.043 | 0.029 | 0.063 | 0.048 | 0.05 |

**Table 3.**Parameters of the NDVI seasonal variation curves, the maximum NDVI values, and the errors for crops grown in the experimental fields in the Khabarovsk District in 2018.

Soybean | Spring Wheat | Oat | Forage Grasses | Model (Arable Land) | |
---|---|---|---|---|---|

c | 7.6 | 8.7 | 8.5 | 8.1 | 9.2 |

b | 31.5 | 29.4 | 30.5 | 29.2 | 30.4 |

$NDV{I}_{\mathrm{max}}^{pred}$ | 0.852 | 0.811 | 0.747 | 0.852 | 0.805 |

$NDV{I}_{\mathrm{max}}^{obs}$ | 0.854 | 0.812 | 0.748 | 0.852 | 0.806 |

MAPE, % | 10.9 | 6.5 | 6.2 | 9.1 | 6.6 |

RMSE | 0.05 | 0.035 | 0.029 | 0.052 | 0.032 |

**Table 4.**Parameters of the NDVI approximation curves, the maximum NDVI values, and the model errors for the arable land in the Khabarovsk District in 2014–2018.

2014 | 2015 | 2016 | 2017 | 2018 | Average, 2014–2018 | |
---|---|---|---|---|---|---|

c | 10.4 | 10.3 | 10.4 | 10.1 | 10.1 | 10.3 |

b | 29.8 | 30.5 | 29.9 | 29.4 | 29.9 | 29.9 |

$NDV{I}_{\mathrm{max}}^{pred}$ | 0.723 | 0.742 | 0.708 | 0.755 | 0.734 | 0.727 |

$NDV{I}_{\mathrm{max}}^{obs}$ | 0.724 | 0.743 | 0.708 | 0.756 | 0.734 | 0.727 |

MAPE, % | 7.7 | 6.9 | 7.4 | 3.9 | 6.9 | 6.5 |

RMSE | 0.044 | 0.039 | 0.044 | 0.026 | 0.039 | 0.038 |

**Table 5.**Soybean yield (y), maximum NDVI (x

_{1}), and the meteorological indicators for the Khabarovsk District (x

_{2}–x

_{6}) in 2010–2018.

y | x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | |
---|---|---|---|---|---|---|---|

2010 | 1.13 | 0.732 | 1.90 | 71.0 | 616.1 | 33.8 | 0.76 |

2011 | 1.19 | 0.742 | 3.03 | 71.0 | 693.9 | 38.0 | 0.76 |

2012 | 1.29 | 0.698 | 2.03 | 84.0 | 502.6 | 33.5 | 0.89 |

2013 | 1.50 | 0.734 | 2.45 | 72.0 | 414.4 | 36.6 | 0.75 |

2014 | 1.47 | 0.724 | 2.58 | 82.0 | 769.5 | 36.9 | 0.89 |

2015 | 1.19 | 0.743 | 3.07 | 73.0 | 663.3 | 38.1 | 0.78 |

2016 | 1.01 | 0.708 | 2.55 | 72.0 | 311.9 | 33.0 | 0.74 |

2017 | 1.58 | 0.756 | 1.56 | 75.0 | 707.2 | 31.6 | 0.86 |

2018 | 1.67 | 0.734 | 2.52 | 82.0 | 621.0 | 30.7 | 0.89 |

$\overline{x}$ | 1.34 | 0.730 | 2.41 | 75.8 | 588.9 | 34.7 | 0.81 |

σ | 0.23 | 0.018 | 0.50 | 5.3 | 149.8 | 2.8 | 0.07 |

V, % | 17.0 | 2.4 | 20.8 | 7.0 | 25.4 | 8.0 | 8.5 |

$\Delta \overline{x}$ | 0.17 | 0.014 | 0.39 | 4.1 | 115.2 | 2.1 | 0.05 |

min | 1.01 | 0.698 | 1.56 | 71.0 | 311.9 | 30.7 | 0.74 |

max | 1.67 | 0.756 | 3.07 | 84.0 | 769.5 | 38.1 | 0.89 |

**Table 6.**Correlation matrix for the dependent and independent variables (significant coefficients (p < 0.05) are highlighted).

y | x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | |
---|---|---|---|---|---|---|---|

y | 1.00 | 0.31 | −0.17 | 0.44 | 0.28 | −0.28 | 0.44 |

x_{1} | 0.31 | 1.00 | 0.14 | −0.18 | 0.37 | 0.20 | −0.03 |

x_{2} | −0.17 | 0.14 | 1.00 | −0.09 | 0.22 | 0.56 | −0.17 |

x_{3} | 0.44 | −0.18 | −0.09 | 1.00 | 0.32 | −0.26 | 0.73 |

x_{4} | 0.28 | 0.37 | 0.22 | 0.32 | 1.00 | 0.11 | 0.28 |

x_{5} | −0.28 | 0.20 | 0.56 | −0.26 | 0.11 | 1.00 | −0.17 |

x_{6} | 0.44 | −0.03 | −0.17 | 0.73 | 0.28 | −0.17 | 1.00 |

b* | Std.Err. of b* | b | Std.Err. of b | t (6) | p-Value | |
---|---|---|---|---|---|---|

Intercept | −8.24543 | 2.644295 | −3.1182 | 0.020632 | ||

x_{1} | 0.738891 | 0.23912 | 9.38573 | 3.037413 | 3.09004 | 0.021387 |

x_{3} | 0.847303 | 0.23912 | 0.03603 | 0.010169 | 3.54342 | 0.012168 |

**Table 8.**Cross-validated coefficient of determination (R

^{2}

_{cv}), root-mean-square error (RMSE

_{cv}), mean absolute percentage error (MAPE

_{cv}), and absolute percentage error (APE

_{cv}), calculated in a one-leave-out cross−validated approach for the regression model.

R^{2}_{cv} | RMSE_{cv} (t/ha) | MAPE_{cv}, % | APE_{cv}, % | |
---|---|---|---|---|

2010 | 0.70 | 0.11 | 6.1 | 3.5 |

2011 | 0.73 | 0.11 | 5.8 | 7.9 |

2012 | 0.73 | 0.12 | 6.5 | 4.9 |

2013 | 0.81 | 0.07 | 4.0 | 22.7 |

2014 | 0.72 | 0.12 | 6.5 | 1.2 |

2015 | 0.79 | 0.10 | 5.1 | 18.3 |

2016 | 0.62 | 0.12 | 6.4 | 2.2 |

2017 | 0.70 | 0.11 | 6.1 | 2.9 |

2018 | 0.68 | 0.11 | 5.7 | 8.2 |

2019 | 0.72 | 0.11 | 6.2 | 5.8 |

$\overline{x}$ | 0.11 | 5.9 | 7.8 | |

$\Delta \overline{x}$ | 0.01 | 0.6 | 5.1 |

**Table 9.**Average RMSE and APE yield values, calculated using approximated NDVI maxima for 22 (June 1)–30 (July 30) calendar weeks in the Khabarovsk District (2010–2019).

Week | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
---|---|---|---|---|---|---|---|---|---|

RMSE | 0.77 | 0.74 | 0.67 | 0.38 | 0.33 | 0.21 | 0.18 | 0.16 | 0.15 |

APE Yield,% | 50.2 | 51.4 | 47.2 | 40.4 | 29.9 | 19.2 | 9.9 | 8.5 | 7.6 |

**Table 10.**NDVI values (observed in ith week); NDVI maxima, soybean yield, and absolute percentage errors in 2019 in the Khabarovsk District, calculated using the approximating function in the 22nd (June 1) to 30th (July 30) calendar weeks.

Week | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
---|---|---|---|---|---|---|---|---|---|

$NDV{I}_{i}$ | 0.523 | 0.606 | 0.652 | 0.686 | 0.709 | 0.716 | 0.724 | 0.730 | 0.712 |

$NDV{I}_{\mathrm{max}}^{pred}$ | 0.701 | 0.758 | 0.768 | 0.768 | 0.761 | 0.745 | 0.736 | 0.733 | 0.712 |

APE NDVI, % | 4.0 | 3.8 | 5.1 | 5.1 | 4.2 | 2.0 | 0.8 | 0.4 | 2.5 |

Calculated Yield, t/ha | 1.36 | 1.90 | 1.99 | 1.99 | 1.93 | 1.77 | 1.69 | 1.66 | 1.47 |

APE Yield,% | 11.5 | 23.4 | 29.0 | 29.0 | 25.1 | 15.2 | 9.7 | 8.0 | 4.3 |

**Table 11.**Average RMSE results for the different municipalities in the Russian Far East (2010–2018). Significant results highlighted bold, insignificant highlighted italics.

Region | District | RMSE (t/ha) | R^{2} | p |
---|---|---|---|---|

Khabarovsk Territory | Khabarovsk | 0.11 | 0.72 | 0.02 |

Vyasemskiy | 0.09 | 0.76 | 0.03 | |

Lazo | 0.10 | 0.15 | 0.06 | |

Jewish Autonomous Region | Oktyabrskiy | 0.06 | 0.74 | 0.07 |

Leninskiy | 0.15 | 0.38 | 0.39 | |

Amur Region | Tambovskiy | 0.05 | 0.94 | 0.01 |

Mikhailovskiy | 0.09 | 0.8 | 0.04 | |

Primorskiy Territory | Khorolskiy | 0.13 | 0.32 | 0.32 |

Khankaiskiy | 0.11 | 0.68 | 0.03 | |

Mikhaylovskiy | 0.16 | 0.01 | 0.95 | |

Chernigovskiy | 0.16 | 0.12 | 0.69 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Stepanov, A.; Dubrovin, K.; Sorokin, A.; Aseeva, T.
Predicting Soybean Yield at the Regional Scale Using Remote Sensing and Climatic Data. *Remote Sens.* **2020**, *12*, 1936.
https://doi.org/10.3390/rs12121936

**AMA Style**

Stepanov A, Dubrovin K, Sorokin A, Aseeva T.
Predicting Soybean Yield at the Regional Scale Using Remote Sensing and Climatic Data. *Remote Sensing*. 2020; 12(12):1936.
https://doi.org/10.3390/rs12121936

**Chicago/Turabian Style**

Stepanov, Alexey, Konstantin Dubrovin, Aleksei Sorokin, and Tatiana Aseeva.
2020. "Predicting Soybean Yield at the Regional Scale Using Remote Sensing and Climatic Data" *Remote Sensing* 12, no. 12: 1936.
https://doi.org/10.3390/rs12121936