# Estimation of Parameters of Biomass State of Sowing Spring Wheat

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Models

- -
- in the time interval before the earing of crops

- -
- in the time interval from the beginning of earing to the full ripening of the grain

_{1m}—the average density of the total biomass of crops over the area of the field, cwt·ha

^{−1}; x

_{2m}—the average density of the wet weight of crops over the area of the field, cwt·ha

^{−1}; the parameters of the state of the biomass in the model (12) are: x

_{1u}—the average density of the total biomass over the field area, cwt·ha

^{−1}; x

_{2u}—the average density of the wet weight of crops over the area of the field, cwt·ha

^{−1}; x

_{3u}—the average density of the mass of ears of crops (harvest) over the area of the field, cwt·ha

^{−1}; external perturbations in both models are: f

_{1}—average daily air temperature, °C; f

_{2}—average daily radiation level, W·(m

^{2}·h)

^{−1}; f

_{3}—average daily precipitation intensity, mm; parameters of the chemical state of the soil: v

_{N}—nitrogen content in the soil, kg·ha

^{−1}; v

_{K}is the potassium content in the soil, kg·ha

^{−1}; v

_{P}—phosphorus content in the soil, kg·ha

^{−1}; v

_{Mg}—content of magnesium in the soil, kg·ha

^{−1}; v

_{4}—moisture content in the soil, mm; y,h—spatial coordinates, m; $t\in ({T}_{1m},{T}_{2m})$—time variable, days, beginning and end of the growing season preceding the heading phase; $t\in ({T}_{1u},{T}_{2u})$—the beginning and end of the growing season from the beginning of earing to the full ripening of the grain, cwt—center (hundredweight)—the unit of mass adopted in Russia is 1 cwt = 0.1 tn.

- -
- in the time interval before the earing of crops

- -
- in the time interval from the beginning of earing to the full ripening of the grain

_{1m}) and in the near infrared range (750–950 nm) (z

_{2m});

_{1u}), in red (625–740 nm)—(z

_{2u}), in near-IR (750–950 nm)—(z

_{3u});

_{1m}—the density of the sowing biomass (yield) for the spatial coordinate $(y,h)$, cwt·ha

^{−1}; x

_{2m}—the density of the sowing wet weight for the spatial coordinate $(y,h),$ cwt·ha

^{−1};

_{1u}—the density of the sowing biomass, cwt·ha

^{−1}; x

_{2u}—the density of the sowing wet mass, cwt·ha

^{−1}; x

_{3u}—the density of the mass of ears, cwt·ha

^{−1}.

^{2}, the number of cyclic variables will be 5000 per hectare of the field area. With a total field area under crops of 500 ha, the total number of elementary plots and cycles of the algorithm will be 2.5 × 106 units. Therefore, for large areas of crops (more than 1000 ha), it is advisable to use approximation schemes for modeling and estimation. The essence of such schemes lies in the fact that, first, the parameters of the sowing state averaged over the area of the field are modeled (estimated), which are then corrected along the field surface by means of a corrective model in the same way for the state of sowing before and after heading (omitting the indices of the phenological state of sowing).

^{2}, the number of cyclic variables will be 5000 per hectare of field area. With a total area of the field under sowing of 500 hectares, the total number of elementary plots and algorithm cycles will be 2.5 × 10

^{6}units. Therefore, for large areas of crops (more than 1000 hectares), it is advisable to use approximation modeling and estimation schemes. The essence of such schemes is that, first, the parameters of the seeding state averaged over the field are modeled (estimated), which are then corrected over the field surface by means of a corrective model in the same way for the seeding state before and after earing (omitting the indices of phenological phases of seeding)

#### 2.2. Estimation Algorithm

**Step1.**From the remote sensing data obtained over the entire area of the field, data on test plots are selected $Z(y,h)=Z(i),i=\mathrm{20...40}$.

**Step2.**Remote sensing data for test areas are averaged $Z\frac{1}{20}{\displaystyle \sum _{i=1}^{20}Z(i)}$.

**Step3.**For each test plot, the estimation algorithm (6) evaluates the state of the crop biomass $\stackrel{\u2322}{{X}}(i),i=\mathrm{20...40}$. The scores obtained are averaged $\stackrel{\u2322}{{X}}=\frac{1}{20}{\displaystyle \sum _{i=1}^{20}\stackrel{\u2322}{{X}}(i)}$.

**Step4.**Determine local variations of remote sensing data $\Delta Z(i)=Z(i)-Z$ and local variations of estimates $\Delta \stackrel{\u2322}{{X}}(i)=\stackrel{\u2322}{{X}}(i)-\stackrel{\u2322}{{X}},i=\mathrm{20...40}$.

**Step5.**From the obtained variations, an array of data is formed, $\{\Delta \stackrel{\u2322}{{X}}(i),\Delta Z(i)\}$ which evaluates the parameter matrix K of the spatial corrector (5).

## 3. Results

#### 3.1. Experimental Research Base

#### 3.2. Results of Approbation of Models and Estimation Algorithms

#### 3.3. The Discussion of the Results

^{2}. First of all, such information is in demand in precision farming systems (TK), in which automated technological machines operate, where elementary sowing areas can be serviced by working bodies independently of each other [17]. This makes it possible to realize high accuracy of control over the state of crops in conditions of large spatial heterogeneity of the agricultural field. Such inhomogeneities are due to the influence of soil heterogeneity, uneven sowing of seeds, differences in the rate of development of individual groups of plants, the presence of a field microrelief, and other reasons. In addition to management tasks in TK systems, such information is in demand in monitoring systems. It is designed to analyze and predict the state of crops, both over the entire area of the field, and in its individual zones and elementary sections. With its help, it is possible to accurately determine areas of low productivity, soil degradation, and stress conditions of crops.

## 4. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Image of an experimental field with sowing of spring wheat at the stage of milky-wax ripeness. Menkovsky branch of the Agrophysical Institute.

**Figure 2.**Dynamics of the field-averaged parameters of reflection of spring wheat sowing in the time interval preceding heading. 1 channel—red, 2 channel—near IR.

**Figure 3.**Estimates of the field-averaged parameters of the biomass of spring wheat sowing in the time interval preceding heading.

**Figure 4.**Dynamics of the reflection parameters of spring wheat sowing in the time interval from heading to grain ripening. 1 channel—green, 2 channel—red, 3 channel—near IR.

**Figure 5.**Estimates of the parameters of the biomass of spring wheat sowing in the time interval from heading to grain ripening.

**Figure 6.**Adjustment of the spatial corrector of estimates of the biomass of spring wheat sowing in the time interval preceding heading.

**Figure 7.**Adjustment of the spatial corrector of estimates of the biomass of spring wheat sowing in the time interval from heading to grain ripening.

**Figure 8.**Distribution of the reflection parameters over elementary areas of the field with sowing of spring wheat in the “green” region of the spectrum.

**Figure 9.**Distribution of the reflection parameters over elementary areas of the field with sowing of spring wheat in the “red” region of the spectrum.

**Figure 10.**Distribution of the reflection parameters over elementary areas of the field with sowing of spring wheat in the “near infrared” region of the spectrum.

**Figure 11.**Distribution of the estimates of the total biomass of spring wheat sowing by elementary plots of the field.

**Figure 12.**Distribution of the estimates of the wet weight of spring wheat sowing by elementary plots of the field.

**Figure 13.**Distribution of the estimates of the weight of ears of spring wheat sowing by elementary areas of the field.

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Mikhailenko, I.M.
Estimation of Parameters of Biomass State of Sowing Spring Wheat. *Remote Sens.* **2022**, *14*, 1388.
https://doi.org/10.3390/rs14061388

**AMA Style**

Mikhailenko IM.
Estimation of Parameters of Biomass State of Sowing Spring Wheat. *Remote Sensing*. 2022; 14(6):1388.
https://doi.org/10.3390/rs14061388

**Chicago/Turabian Style**

Mikhailenko, Ilya Mikhayilovich.
2022. "Estimation of Parameters of Biomass State of Sowing Spring Wheat" *Remote Sensing* 14, no. 6: 1388.
https://doi.org/10.3390/rs14061388