Methods of Determining Fertilizer Doses

Last updated: June 22, 2025

All methods for determining fertilizer doses are based on data from long-term or occasional field and production experiments, and differ in the completeness and accuracy with which they reflect the relationships among plants, soils, and fertilizers.

Methods and their modifications for determining fertilizer doses can be divided into:

methods of generalizing the results of experiments with empirical fertilizer doses;
methods of generalizing the results of experiments using nutrient balances.

All the listed methods for optimizing fertilizer doses make it possible to predict the yield of agricultural crops. But despite this, they require improvement in terms of an integrated approach that takes into account crop growing conditions and the economic payback of fertilizers.

Methods Based on Generalizing Data with Empirical Fertilizer Doses

Generalization of the results of field experiments conducted under the methodological guidance of the Geographic Network of Experiments VNIIUA in all soil-climatic zones with different crops made it possible to determine the effectiveness of individual types of fertilizers on different soil types and the doses of organic and mineral fertilizers for the main crops on various soil types and subtypes. Subsequently, doses were differentiated within soil differences taking into account the nutrient supply of predecessors and varietal characteristics of crops. Based on generalizations of experimental results, doses, optimal timing, and methods of fertilizer application before sowing, at sowing, and after sowing were also developed for the main crops in all soil-climatic zones.

According to data from the Geographic Network of Experiments VNIIUA and the agrochemical service CINAO, for the main soil-climatic zones of Russia on predominant soil types with an average content of mobile phosphorus and exchangeable potassium, optimal doses of macronutrients for the main crops, as well as doses and methods of applying micronutrients, have been recommended. Regional research institutions offer more specific recommendations for crops, types, subtypes, and soil differences, indicating planned yield levels, soil cultivation levels, and combinations with doses of organic fertilizers.

In each complex of specific natural and economic conditions of territories, based on the results of at least 7–10 reproducible experiments with one crop or variety, regional institutions of the Geographic Network of Experiments and the Agrochem Service determine quantitative indicators of fertilizer efficiency:

yield increase from the optimal dose;
removal of elements per unit of main and by-product and coefficients of utilization of elements from soil and fertilizers;
return coefficients or intensity of element balance;
correction coefficients to doses depending on soil class;
standards of mineral fertilizer costs for obtaining a unit of increase and the yield as a whole;
optimal levels of nutrient content in soil;
standards of fertilizer costs per unit change in the content of mobile forms of elements in soil;
main indicators of product quality;
economic indicators of fertilizer efficiency;
mathematical models characterizing the relationship between crop productivity, soil fertility, fertilizer doses, weather, and agronomic factors;
levels of environmental restrictions in fertilizer application.

Based on the results, specific recommendations for doses and ratios of fertilizers are developed; however, even in this case, correction of doses is necessary for a specific enterprise, agrocenosis, and field.

This same group of methods includes calculations of doses based on standards of mineral fertilizer costs for the entire yield using the formula:

Д = У \cdot Н_1 \cdot К_n

or for the yield increase:

Д = ΔУ \cdot Н_2 \cdot К_n,

where

Д: — dose of N, P₂O₅, K₂O for the desired yield or increase, kg/ha a.i.;
У and ΔУ: — respectively, the desired yield or increase, t/ha;
H₁ and H₂: — standards of fertilizer costs per unit of yield and increase, kg a.i.;
K_n: — correction coefficient for soil class by phosphorus and potassium supply; when calculating nitrogen doses, K_n = 1.

Standards of fertilizer costs and correction coefficients to fertilizer doses are indicated in regional recommendations of RI, agricultural experimental stations, centers, and stations of the Agrochem Service.

The third direction of the group of methods based on generalizing data with empirical fertilizer doses is the search for mathematical relationships between yield and fertilizer doses. The first such attempt was made in 1905 by the German scientist E. A. Mitscherlich, who proposed the following equation:

\lg (А - У) = \lg А - С_x,

where

А: — maximum possible yield;
У: — actual yield;
С: — proportionality coefficient characterizing the relationship between yield and fertilizer dose;
х: — fertilizer dose.

The fourth direction of this group of methods is the development of regression models based on the planning, conduct, and statistical evaluation of the results of multifactorial experiments with empirical fertilizer doses. To determine the quantitative relationship between yield and fertilizer doses, the best mathematical model proved to be an equation with powers 0.5 and 1 for factors and 0.5 for pairwise interactions:

У = а_0 + а_1N^{0,5} + a_2N + a_3P^{0,5} + a_4P + a_5K^{0,5} + a_6K + a_7(NP){0,5} + a_8(NK)^{0,5} + a_9(PK){0,5},

where

У: — yield;
а₀: — free term of the equation;
a₁, a₂, …, a₉: — terms of the equation characterizing the action and interaction of factors;
N, P, K: — fertilizer doses.

The fifth direction of this group of methods is the development of mathematical computer models for determining optimal fertilizer doses for crops taking into account functional dependence on many environmental factors:

$$У = f(x_n),$$

where

У: — yield;
x_n: — variable factors affecting yield, for example, doses and ratios of fertilizers, soil class and soil texture, weather conditions, varietal characteristics, predecessors, etc.

Various research institutions, based on generalized results of field experiments, analyses, and observations, have developed software packages for determining fertilizer doses. Thus, CINAO developed the software package “RADOZ” (an abbreviation of the words “rational doses”), which was modernized into RADOZ-2, later into RADOZ-3. The modernization is associated with an increase in the number of factors affecting crop yields.

The practical application of any of these methods and modifications makes it possible to avoid gross errors in fertilizer use. However, they are determined empirically without taking into account the biological needs of crops for nutrients and do not answer the question about the state of the soil; according to them, despite correction coefficients, it is impossible to quantitatively assess the balance of elements without special calculations.

Methods Based on Generalizing Data Using Balance Calculations

In this group of methods, the determination of optimal fertilizer doses is based on the biological characteristics of crops and varieties in consuming nutrients to create planned high-quality yields while simultaneously regulating soil fertility for specific natural-economic conditions. The consumption by crops of nutrients from soil and fertilizers is determined from the results of field and production experiments, which turns the field method from empirical into analytical, making it possible to move from stating yield increases to predicting their effectiveness.

This group of methods is promising primarily for regions with sufficient moisture and irrigated agriculture, where the limiting factor for high and stable yields is a lack of nutrients, and fertilizer supply is sufficiently high — not less than 100 kg/ha a.i.

A detailed characterization of soils is available in soil and agrochemical maps, which should be present on every farm. The use of soil nutrients by specific crops is determined by utilization coefficients (CUP) or by correction coefficients to doses depending on the fertility of a specific soil.

Differences in effective fertility and cultivation of soils can also be taken into account through differentiated balance coefficients of utilization of mineral and organic fertilizers of relative balance indicators, that is, return coefficients, balance intensity, and difference coefficients of fertilizer utilization.

There are many methods and modifications of balance calculations for determining optimal fertilizer doses.

Table. Difference coefficients of nutrient utilization from organic and mineral fertilizers differentiated by soil fertility in the Non-Chernozem zone (averages over the rotation of crop rotations), %.

Soil fertility (class)	N		P₂O₅		K₂O
Soil fertility (class)	organic	mineral	organic	mineral	organic
1	40-50	55-65	45-55	35-45	75-85
2	45-55	60-70	50-60	40-50	80-90
3	50-60	65-75	55-65	45-55	85-95
4	55-65	70-80	60-70	50-60	90-100
5	60-70	75-85	65-75	60-70	95-105
6	70-80	80-90	70-80	70-80	100-110

Example.

It is necessary to determine the optimal doses of mineral fertilizers in combination with 20 t/ha of semi-rotted manure containing 0.4% N, 0.2% P₂O₅, and 0.5% K₂O to obtain 4.0 t/ha of grain with a grain:straw ratio of 1:1.5, winter wheat of the Mironovskaya 808 variety on sod-podzolic medium loamy limed soil with phosphorus and potassium content (according to Kirsanov) of 70 and 100 mg/kg, respectively (3rd class), and pH_salt 6.2 (6th class), predecessor — vetch-oat mixture, under which N₆₀P₆₀K₆₀ was applied.

Cartograms of soil supply with hydrolyzable and mineral nitrogen are usually not compiled due to the high variability of these indicators even within one month; therefore, soil supply with hydrolyzable nitrogen is determined analytically or approximately by the content of organic matter, total nitrogen, phosphorus, or potassium that is at a minimum. Since the nitrogen content in humus averages 4%, and, according to generalized data from VNIIUA, its hydrolyzable forms account for 4–7%, then with a soil humus content of 2.5%, the total nitrogen content will be 0.1%, and hydrolyzable — 0.004%, or 40 mg/kg. To determine nitrogen supply by the element that is at a minimum according to the accepted soil classification, its content corresponding to the same class as the element at a minimum is used.

In all methods and modifications, the economic removal by the crop or variety of nutrients for creating the planned yield is determined from costs per unit of main and the corresponding amount of by-product from zonal, regional reference books and recommendations. Or a field is selected on the farm where a similar yield level of the variety has already been achieved, samples of grain and straw are taken, and subjected to chemical analysis. With N, P₂O₅, and K₂O content in grain of 2.5, 0.8, and 0.6%, respectively, and in straw of 0.5, 0.2, and 1.2%, economic removal with the planned yield will be:

2,5 \cdot 40 + 0,5 \cdot 60 = 130\ кг\ N,

0,8 \cdot 40 + 0,2 \cdot 60 = 46\ кг\ P_2O_5,

0,6 \cdot 40 + 1,2 \cdot 60 = 96\ кг\ K_2O,

and costs per 1 t of grain with the corresponding amount of straw are, respectively, N 130:4 = 33 kg, P₂O₅ 46:4 = 12 kg, K₂O 96:4 = 24 kg.

Then, using the main methods, calculations of the elementary balance are carried out, for the increase, by relative balance indicators, based on one or a combination of several methods.

Method of Elementary Balance

The method of elementary balance is the most widespread and least accurate method, since it uses coefficients of soil nutrient utilization (CUP) that vary greatly under the influence of many factors and more stable difference coefficients of fertilizer utilization. Calculations are carried out using the formula:

Д = \frac{В_у - З К_п - О К_о - П К_1 - Р К_р}{К_2},}#Расчёт дозы удобрений]

For the above example, the optimal doses by this method against the background of 20 t/ha of manure will be:

Д_N = \frac{130 - 120 \cdot 0,2 - 80 \cdot 0,25 - 60 \cdot 0,05}{0,70} = 118 \approx 120\ кг,

Д_{P_2O_5} = \frac{46 - 210 \cdot 0,05 - 40 \cdot 0,35 - 60 \cdot 0,1 - 10 \cdot 0,5}{0,20} = 21 + 10\ (при\ посеве) = 31 \approx 30\ кг,

Д_{K_2O} = \frac{96 - 300 \cdot 0,1 - 100 \cdot 0,55 - 60 \cdot 0,1}{0,65} = 7,7 \approx 10\ кг,

This method is widespread because it takes into account all items of nutrient input and consumption.

When using the method of elementary balance, the following are taken into account:

removal of nutrients by the crop yield;
content of mobile nutrients in soil;
coefficient of utilization of nutrients from soil;
coefficient of utilization of nutrients from fertilizers;
mass of the arable soil layer or the soil layer for which the calculation is made.

Agrochemical indicators of cartograms of soil supply with nitrogen, phosphorus, and potassium in mg per 100 g of soil are converted to kg/ha by multiplying by a coefficient corresponding to the soil difference and the depth of the calculation layer. For example, for the 0–22 cm arable layer of sod-podzolic soils, it is 30, that is, the mass of 1 ha of the arable layer of sod-podzolic soil is considered equal to 3000 t; for a layer up to 30 cm, the coefficient is 40.

This balance method is also used with clarifications and modifications. The objectivity of the method depends on the reliability of the listed data, which can vary significantly depending on soil properties, weather conditions, doses and forms of fertilizer, timing and method of application, and other factors.

Method of Calculations for the Planned Yield Increase

The method of calculations for the planned yield increase is a more accurate method compared with the previous one, since it takes into account soil nutrient supply using correction coefficients to doses, which depend less on various factors than CUP. However, this method requires knowing the yield without fertilizers, which is best determined from data of experiments with fertilizers, on the basis of which in the case under consideration it is equal to 2.0 t/ha. The yield can also be determined by the element that is at a minimum, using its utilization coefficient (CUP). Calculations are carried out using the formula:

Д = \frac{В_п - О К_о - П К_1 - Р К_р}{К_2} К_3,

where

Д: — dose of N, P₂O₅, and K₂O, kg/ha a.i.;
В_п: — removal of the element with the planned yield increase, kg;
О: — amount of the element in organic fertilizer, kg/ha;
K_о: — difference coefficient of utilization of the element from organic fertilizer, fractions of a unit;
П: — amount of the element in the predecessor’s fertilizer and/or in the predecessor’s post-harvest residues, kg/ha;
K₁: — difference coefficient of utilization of the fertilizer and/or predecessor’s residues, fractions of a unit;
Р: — pre-sowing (row) fertilizer, kg/ha a.i.;
K_р: — difference coefficient of utilization of the pre-sowing fertilizer, fractions of a unit;
K₂: — difference coefficient of utilization of fertilizers applied before sowing, fractions of a unit;
K₃: — correction coefficient to the dose depending on soil class (for the 3rd class for grain, leguminous crops, and grasses it is 1).

For the above example, by this method the optimal doses of mineral fertilizers against the background of 20 t/ha of manure will be:

Д_N = \frac{65 - 80 \cdot 0,25 - 60 \cdot 0,05}{0,70} \cdot 1,0 = 60\ кг,

Д_{P_2O_5} = \frac{23 - 40 \cdot 0,35 - 60 \cdot 0,1 - 10 \cdot 0,5}{0,20} \cdot 1,0 = 0 + 10\ (при\ посеве) = 10\ кг,

Д_{K_2O} = \frac{48 - 100 \cdot 0,55 - 60 \cdot 0,1}{0,65} \cdot 1,0 = 0\ (калий\ не\ нужен).

In the above methods, when calculating fertilizer doses for the planned yield or increase, it is necessary to take into account the fertilization of the preceding crop. If preceding crops were grown on fertilized soils, then to the soil nutrients calculated from the crop yield in the current year, the aftereffect of applied fertilizers is added at the rate of 10–15% of the initial amount of the active ingredient in them.

For example, on unfertilized soil, 200 c/ha of green mass of maize is obtained, by which 50 kg N, 20 kg P₂O₅, and 70 kg K₂O are removed. Maize is placed after sugar beet, under which 150 kg of nitrogen, 80 kg of P₂O₅, and 150 kg of K₂O were applied; 15% of this amount will be 22.5 kg N; 12 kg P₂O₅, and 22.5 kg K₂O. Thus, placing maize after sugar beet, one can obtain approximately 300 c/ha of green mass without additional fertilizer application. With a planned yield of 50 t/ha, the calculated dose for the formation of an additional 20 t of green mass will require an additional 50 kg N, 20 kg P₂O₅, and 70 kg K₂O.

Calculation of Optimal Doses Using Balance Coefficients of Fertilizer Utilization Differentiated by Soil Fertility

Calculation of optimal doses using balance coefficients of fertilizer utilization differentiated by soil fertility is the best method, since it allows simultaneous regulation of soil nutrient supply. Calculations for obtaining the planned yield are carried out using the formula:

Д = \frac{В_у - ОК_1}{К_2}

where

Д: — dose of N, P₂O₅, and K₂O, kg/ha a.i.;
B_у: — economic removal of the element with the planned yield, kg/ha;
О: — amount of the element in organic fertilizer, kg/ha;
K₁: — difference coefficient of utilization of the fertilizer and/or predecessor’s residues, fractions of a unit;
K₂: — difference coefficient of utilization of fertilizers applied before sowing, fractions of a unit.

Against the background of 20 t/ha of manure, the doses of mineral fertilizers will be:

Д_N = \frac{130 - 80 \cdot 0,45}{0,9} = 104 \approx 100\ кг,

Д_{P_2O_5} = \frac{ 46 - 40 \cdot 0,45 }{0,8} = 35\ кг,

Д_{K_2O} = \frac{ 96 - 100 \cdot 0,7 }{ 0,95 } = 26 \approx 30\ кг.

Calculations of Optimal Fertilizer Doses Using Return Coefficients or Balance Intensity

Calculations of optimal fertilizer doses using return (compensation) coefficients or balance intensity are more complex, since by these indicators it is difficult to take into account the effect of fertilizers over years: for this, additional indicators are introduced, for example, coefficients of distribution of fertilizer action over years, which are derivatives of difference coefficients and have the same disadvantages.

Methods for Determining Fertilizer Doses Taking into Account Annual Increase in Soil Fertility and Nutrient Removal by the Yield

Example.

D = 80 kg/ha — amount of fertilizer (a.i.) that will be applied annually to the soil;
L = 4 years — number of years after the survey;
B = 30 kg/ha — average annual nutrient removal, kg/ha;
K = 50% (0.5) — share of the nutrient element going to replenish soil nutrient reserves in the arable layer, from the value characterizing a positive balance;
M — planned increase in the content of the nutrient element, mg per 100 g of soil in the arable layer.

The content of nutrient elements in the arable layer equivalent to 1 mg per 100 g of soil, equivalent to 30 kg of phosphorus in the arable layer, is:

M = \frac{Л·К·(Д - В)}{ 30 } = \frac{4 \cdot 0,5 \cdot (80 - 30)} { 30 } = 3,3

that is, over 4 years the phosphorus reserves in the soil increase by 3.3 mg per 100 g of soil, or annually by 0.8 mg per 100 g of soil. Using this formula, the dose of phosphorus fertilizer (kg/ha) is determined provided that the average phosphorus removal by the yield is 30 kg/ha per year and its content in the soil should increase, for example, over 5 years by 4 mg/100 g (M):

M = \frac{ 30М }{ К \cdot Л } + В = \frac{ 30 \cdot 4 }{ 0,5 \cdot 5 } + 30 = 78\ кг\ д.\ в./га

This method makes it possible to determine the fertilizer dose both for the planned yield and for the rate of increase in soil nutrient reserves and its cultivation.

According to the method of N. N. Mikhailov, fertilizer doses for grain crops on soils with low nutrient content, and for row crops on soils with medium content, are calculated for the planned yield taking into account the increase in soil fertility.

Table. Possible removal of phosphorus and potassium from soil.

Content of mobile P₂O₅ and K₂O in soil	Nutrients assimilated by plants from soil, kg/ha
Content of mobile P₂O₅ and K₂O in soil	P₂O₅	K₂O
Very low	0-10	up to 45
Low	10-20	45-90
Medium	20-40	90-180
High	40-80	180-360
Very high	more than 80	more than 360

Calculations of phosphorus and potassium requirements for obtaining the planned yield of winter rye are presented in the table.

Table. Requirement and supply of phosphorus and potassium when planning a winter rye yield of 40 c/ha.

Indicators	P₂O₅	K₂O
Soil supply	low	low
Required for yield formation, kg	48	112
Possible removal from soil, kg	10	45
Required to be provided by fertilizers	38	67
Provision by 20 t of manure	25	72
Required to be provided by mineral fertilizers	13	provided

Nitrogen in this case is better optimized by the N_MIN method.

This method, although it takes into account soil fertility when calculating nutrient requirements for the planned yield, also does not differ in high accuracy, since too wide ranges of phosphorus and potassium utilization by plants from soil are used. Also, rather relative coefficients of nutrient utilization from organic and mineral fertilizers are accepted.

Over a crop rotation, nitrogen from mineral fertilizers is used on average by 60%, phosphorus — by 35%, and potassium — by 75%. Nitrogen and phosphorus from organic fertilizers are used by 50%, potassium — by 75%. Systematic determination of nitrogen, phosphorus, and potassium content in the yield makes it possible to annually correct utilization coefficients and compile more reliable nutrient balances.

Balance data make it possible to more accurately calculate the dose of mineral fertilizers depending on specific conditions and the goal set. Fertilizer doses calculated for obtaining the planned yield and a given content of nutrients in soil are determined by the formula:

Д = \frac{В}{К_1} + \frac{(С_З - С_ф)К_2}{К_3 t},

where

Д: — dose of the nutrient, kg/ha;
В: — removal of nutrients by the planned yield, kg/ha;
K₁: — coefficient of nutrient utilization taking into account aftereffect;
С_З: — given content of the nutrient in soil, mg/100 g;
С_ф: — actual content of the nutrient in soil, mg/100 g;
K₂: — coefficient for converting mg/100 g to kg/ha;
K₃: — coefficient of fertilizer consumption for increasing the nutrient content in soil;
t: — time over which it is planned to obtain the given nutrient content in soil.

Example.

It is necessary to obtain 4 t/ha of winter wheat grain and to achieve, after 10 years, an actual phosphorus content (С_ф) of 10 mg per 100 g of soil. With a grain yield of 4 t/ha, winter wheat removes 48 kg/ha P₂O₅ (В). To determine the phosphorus dose, the removal (48 kg/ha) is divided by the coefficient of its utilization by plants from fertilizers taking into account aftereffect, provided that 2/3 of phosphorus is applied with mineral and 1/3 with organic fertilizers; the utilization coefficient is 0.4 (K₁). In this case, 120 kg/ha P₂O₅ will be required.

The average content of mobile phosphorus over 10 years (t) is increased to 10 mg, or by 5 mg per 100 g of soil (С_З), which corresponds to 150 kg/ha (5 mg · 30).

According to long-term research data, about 0.4 of the amount of phosphorus (K₃) applied above the dose for the planned yield goes to increasing the amount of its assimilable forms in soil. To achieve the given level of mobile phosphorus content in soil over 10 years, it will be required to apply 375 kg/ha P₂O₅ (150 kg:0.4), or on average per year while maintaining the planned yield level — 37.5 kg/ha. Taking this amount into account, the required dose calculated for obtaining the planned yield and the given nutrient content will be equal to 157.5 kg/ha (120 + 37.5):

Д = \frac{48}{0,4} + \frac{(10 - 5) \cdot 30}{0,4} = 120 + 37,5 = 157,5\ кг/га\ P_2O_5.

Calculation of Fertilizer Doses by Soil Score Evaluation

T. N. Kulikovskaya recommends calculating fertilizer doses by soil score evaluation. Based on experimental data, the price of a point of arable land, kg of product per point, has been developed.

Table. Price of a point of arable land, kg of product per point.

Crop	Sod-podzolic soils				Peat-bog
Crop	sandy loam	sandy loam underlain by moraine	sandy loam underlain by sand	sandy	Peat-bog
Winter rye	33	33	36	30	44
Winter wheat	36	34	28	25	36
Barley	39	38	35	25	43
Oats	33	30	30	28	35
Potato	260	250	245	240	262
Flax (fiber)	7,8	7,0	—	—	—
Sugar beet	290	—	—	—	330

Example.

Planned winter wheat yield is 50 c/ha of grain. Soil is sandy loam, arable land score Б_п = 58, price of a point for winter wheat Ц_бп = 34 kg.

Agrochemical properties of the soil:

pH = 6.0;
humus = 1.8%;
P₂O₅ = 14 mg per 100 g of soil;
K₂O = 12 mg per 100 g of soil;
bulk density = 1.3 g/cm³;
mass of 20 cm arable layer = 2600 t.

Correction coefficient for agrochemical properties K = 1.23.

First, the yield that can be obtained due to the effective fertility of the soil is determined:

У = Б_П \cdot Ц_{бп} \cdot К = 58 \cdot 34 \cdot 1,23 = 24,2\ ц/га.

Consequently, when fertilizers are applied, the grain increase will be 25.8 c/ha (50-24.2) (table).

Table. Calculation of fertilizer doses for the planned winter wheat yield of 5 t/ha of dry matter per 1 ha.

Indicators	N	P₂O₅	K₂O
Planned grain yield increase, c/ha	25.8
Removed per 1 c of grain, kg	3.5	1.2	2.5
Total removal for the increase, kg/ha	90.3	30.9	64.5
Coefficient of utilization from mineral fertilizers, %	60	25	45
Required to apply taking into account the utilization coefficient, kg/ha	150.5	123.6	143.3

Thus, to obtain 50 c of grain, N₁₅₁P₁₂₄K₁₄₃ is applied, or a total of 418 kg/ha NPK.

According to research of the Belarusian RI of Soil Science and Agrochemistry, the payback of mineral and organic fertilizers has been determined for various soils.

Table. Payback of fertilizers by yield, kg of product per 1 kg NPK and 1 t of organic fertilizers.

Crop	1 kg NPK on soils				1 t of organic fertilizers
Crop	loamy	sandy loam	sandy	peat-bog	1 t of organic fertilizers
Winter rye	6,3	6,0	5,0	5,9	10-14
Winter wheat	7,2	6,0	—	6,0	12-18
Barley	6,5	6,2	4,5	6,0	7-12
Oats	5,7	5,4	4,5	5,8	10-12
Potato	30	30	28	35	100
Flax (fiber)	1,4	1,3	—	—	—
Sugar beet	35	33	—	30	120

Using the payback indicators of a unit of nutrients, the fertilizer dose for the additional yield of 2580 kg of winter wheat grain is calculated. Thus, per 1 kg of NPK applied to sandy loam soil, 6 kg of grain is obtained; for 2580 kg, 430 kg/ha will be required (2580:6). Knowing the optimal ratio of nutrients, which for winter wheat is N:P:K = 1.0:0.9:1.2, they find, respectively — for 50 c/ha of grain, N₁₃₉P₁₂₅K₁₆₆.

The calculation method is based on a large amount of experimental data, and the dose largely meets the biological characteristics of the crop.

Method for Determining the Actually Possible Yield (APY)

Method for determining the actually possible yield (APY) by nutrient content in soil was proposed by Ermokhin, Neklyudov, and Krasnitsky in 2000. The method is based on the fact that the content of nutrients in soil is a limiting factor and determines the obtaining of the APY.

The approach of the method makes it possible to assess the natural fertility of the soil and determine the possible yield without fertilizers, and then predict the effectiveness of fertilizers.

The authors propose the following formula for calculation:

ДВУ_{ПВП} = \frac { mhdК_п } { H } ,

where

ДВУ_пвп: — actually possible yield due to soil nutrients (without fertilizers), t/ha;
m: — content in soil of the nutrient that is at a minimum, mg/100 g;
h: — depth of the arable layer, cm;
d: — bulk density of the arable layer, g/cm³;
K_n: — coefficient of utilization by plants of the nutrient from soil;
Н: — consumption of the nutrient by plants for creating a unit of main product taking into account by-product, kg/t.

In addition to the content of nutrients in soil, it is necessary to know the ratio of elements participating in yield formation and their availability to plants.

For the conditions of Western Siberia, the ratio of nutrients in soil has been determined that characterizes balanced nutrition and makes it possible to determine which element is in the first minimum.

The optimal ratio of these elements in the 0–30 and 0–40 cm soil layer is:

$$P_2O_5\ мг/100\ г \approx 10 \cdot NO_3\ мг/100\ г \approx K_2O\ мг/100\ г.$$

The balanced ratio P₂O₅:NO₃ is 10, P₂O₅:K₂O is 1. If the ratio P₂O₅:NO₃ is less than 10, this indicates a phosphorus deficiency; if more than 10, then nitrogen is at a minimum in the soil. The ratio of K₂O and NO₃ is characterized similarly.

To determine which element is at a minimum, the coefficient of action of the element that will be applied as fertilizer is established. The highest coefficient of action (Kd) indicates that this element is at a minimum and will limit the yield of the cultivated crop.

Example.

With soil content of N-NO₃ — 0.7 mg/100 g; P₂O₅ — 10.5 mg/100 g; K₂O — 10.0 mg/100 g; the ratio of nutrient elements will be: P₂O₅:N-NO₃ = 10.5:0.7 = 15; K₂O:N-NO₃ = 10.0:0.7 = 14.3. Consequently, the limiting factor for crop yield on this soil is nitrogen.

When using fertilizers, the authors recommend for soils of Western Siberia to use optimal levels of nutrient content established for grain crops by A. E. Kochergin (mg/100 g): N-NO₃ — 1.5; P₂O₅ — 15.0; K₂O — 15.0.

The coefficient of action of a nutrient can also be determined by another method: by the ratio of optimal and actual nutrient content in soil:

К_{Д_N} = \frac { N-NO_3 (мг/100 г, оптимум) } { N-NO_3 (мг/100 г, фактическое) } = \frac {1,5} {0,7} = 2,14,

К_{Д_{P_2O_5}} = \frac { P_2O_5 (мг/100 г, оптимум) } { P_2O_5 (мг/100 г, фактическое) } = \frac {15} {10,5} = 1,43,

К_{Д_{K_2O}} = \frac { K_2O (мг/100 г, оптимум) } { K_2O (мг/100 г, фактическое) } = \frac {15} {10} = 1,50.

From these data it follows that the limiting factors restricting the yield on this soil are all three nutrients, and to the greatest extent nitrogen, since K_д of nitrogen has the greatest value — 2.14.

For Siberia, Yu. I. Ermokhin et al. (2000) give the following coefficients of nutrient utilization by plants from soil reserves: nitrate nitrogen — 0.6–0.8 (60–80%), mobile phosphorus — 0.1 (10%), exchangeable potassium — 0.2–0.3 (20–30%). Knowing these indicators, the APY (for example, of barley) without fertilizers is determined.

Example.

N-NO₃ = 0.7 mg/100 g;
P₂O₅ = 10.5 mg/100 g;
K₂O = 10.0 mg/100 g;
h = 30 cm;
d = 1.2 g/cm³;
H_n = 35.6 kg/t;
H_P = 12.1 kg/t;
H_K = 25.1 kg/t;
K_{П N} = 0.6;
K_{П P} = 0.1;
K_{П К} = 0.3.
Determine APY, t/ha = ?.

Solution.

Taking into account current nitrification (N_Т = 70 kg/ha), the APY will be for nitrogen:

ДВУ = \frac { (0,7 \cdot 30 \cdot 1,2 + 70) \cdot 0,6 } { 35,6 } = 1,6\ т/га,

for phosphorus:

ДВУ = \frac { (10,5 \cdot 30 \cdot 1,2 \cdot 0,1) \cdot 0,6 } { 12,1 } = 3,1\ т/га,

for potassium:

ДВУ = \frac { (10,0 \cdot 30 \cdot 1,2 \cdot 0,3) \cdot 0,6 } { 25,1 } = 4,3\ т/га,

Consequently, with this soil characteristic, the possible barley yield will be 1.6 t/ha.

Methods for Calculating Fertilizer Doses for the Planned Yield (N. K. Boldyrev)

N. K. Boldyrev in 1962, on the basis of integrated methods of leaf and soil diagnostics, proposed methods for calculating fertilizer doses for the planned yield.

The simplified method for calculating fertilizer doses by the chemical composition of leaves and mobile nutrients in soil is based on establishing the degree of need (С_Н) for a nutrient element using the equation:

$$С_Н = ОС:ФС,$$

where

ОС: — optimal content of the element;
ФС: — actual content of the element.

The degree of need is refined by another element that is in relative excess, or by the optimal ratio between element norms in leaves, taking into account the equalities:

$$\%N(Л) = 12\% Р(Л) = 1,2\% К(Л)\ или\ \%N(Л) = 5,2\% P_2O_5\ (Л) = \%K_2O\ (Л).$$

Equation:

$$\%N = 12 \cdot \%P = 1,2 \cdot \%K = 12 \cdot \%S = 12 \cdot \%Mg = 6 \cdot \%Ca.$$

N. K. Boldyrev called this the equation of optimal balance of elements in leaves of cereal crops in the flowering phase. Optimal ratios of elements have been developed for other agricultural crops.

Table. Indicators of normal levels of element content and optimal ratio between them in leaves of some crops.

Crops	Yield level, c/ha, at value “В”	Time of sampling for analysis (growth phase)	Organ, leaf tier	Content in % of absolutely dry matter			Optimal ratio between elements
Crops	Yield level, c/ha, at value “В”	Time of sampling for analysis (growth phase)	Organ, leaf tier	N	Р	К	N/P	N/K	Р/К
Spring and winter wheat	40 — 45 (0,8)^*	tillering	aboveground part	5	0,43	4,2	12	1,2	10
Barley	50-60 (1,00-1,25)	stem elongation	all leaves	4	0,33	3,3	12	1,2	10
		end of flowering (6–8 days after full heading)	3–4 leaves, counting from the ear	3	0,25	2,5	12	1,2	10
		end of flowering (6–8 days after full heading)	aboveground part	2,1	0,25	2,1	8	1,0	8
Maize for silage	500 (0,8) 800-1000 (1-1,25)	6–8 leaves	aboveground part	4	0,34	3,4	12	1,2	10
Maize for grain	45-50 (0,8)	cob flowering	2 leaves near the cob	3,2	0,27	2,7	12	1,2	10
Maize for grain	80-100(1 -1,25)	cob flowering	aboveground part	2,5	0,21	2,0	12	1,2	10
Sunflower for grain	35-40(1,0)	head formation before flowering	all leaves	3,1	0,25	2,8	12	1,1	11
Perennial cereal grasses	120-140 for 2 cuttings	beginning of flowering	aboveground part	2,6	0,26	2,5	10	1,0	10

Note.

^* In parentheses is the value of the coefficient of action of the balanced element in leaves (CDAEL, or “В”), corresponding to a certain level of plant yield.

N. K. Boldyrev gives three tables with the NPK ratio in leaves in three growth phases: tillering, stem elongation, and end of flowering. In the center of each table, the optimal ratio of elements is given (NPK in leaves in three growth phases). Up and down from the center, imbalance increases, associated with a deficiency of an element (С_Н < 1) or with an excess (С_Н > 1).

Table. Ratio between nitrogen and phosphorus (% P) in leaves (tillering, stem elongation, and end of flowering phase) as a basis for assessing nutrition conditions and determining the degree of need (С_Н) and fertilizer norms for cereal crops (according to N. K. Boldyrev).

Reference point number from the optimum center (1-OC)	N/P ratio	С_Н		Conditions of nitrogen and phosphorus nutrition and their balance
Reference point number from the optimum center (1-OC)	N/P ratio	N	P
7	22,5-24	0,5	2,0	strong phosphorus deficiency with large excess of nitrogen
6	20	0,6	1,7
5	18	0,7	1,5
4	16	0,75	1,3	medium phosphorus deficiency with medium excess of nitrogen
3	14	0,8	1,2	medium phosphorus deficiency with medium excess of nitrogen
2	13	0,9	1,1	ratio close to normal
1-OC	12	1	1	balanced N and P nutrition
2	11,2	1,1	0,9	ratio close to normal
3	10	1,2	0,8	medium nitrogen deficiency with medium excess of phosphorus
4	9,0	1,3	0,75	medium nitrogen deficiency with medium excess of phosphorus
5	8	1,5	0,66	strong nitrogen deficiency with slight excess of phosphorus
6	7,1	1,7	0,6
7	6,0	2	0,5

Table. Ratio between nitrogen and potassium (% K) in leaves as a basis for assessing nutrition conditions, determining the degree of need (С_Н) and fertilizer norms for cereal crops (according to N. K. Boldyrev).

Reference point number from the optimum center (1-OC)	N/K ratio	С_Н		Conditions of nitrogen and potassium nutrition and their balance
Reference point number from the optimum center (1-OC)	N/K ratio	K	N
7	2,25-2,4	2,0	0,5	strong potassium deficiency with large excess of nitrogen
6	2,0	1,7	0,6
5	1,8	1,5	0,7
4	1,6	1,3	0,75	medium potassium deficiency with medium excess of nitrogen
3	1,4	1,2	0,8	medium potassium deficiency with medium excess of nitrogen
2	1,3	1,1	0,9	ratio close to normal
1-OC	1,2	1,0	1,0	balanced N and K nutrition
2	1,12	0,9	1,1	ratio close to normal
3	1,0	0,8	1,2	medium nitrogen deficiency with medium excess of potassium
4	0,9	0,75	1,3	medium nitrogen deficiency with medium excess of potassium
5	0,8	0,66	1,5	strong nitrogen deficiency with slight excess of potassium
6	0,71	0,6	1,7
7	0,6	0,5	2

Table. Ratio between potassium (% K) and phosphorus (% P) in leaves as a basis for assessing nutrition conditions, determining the degree of need (С_Н) and fertilizer norms for cereal crops (according to N. K. Boldyrev).

Reference point number from the optimum center (1-OC)	K/P ratio	С_Н		Conditions of phosphorus and potassium nutrition and their balance
Reference point number from the optimum center (1-OC)	K/P ratio	P	K
7	20	2,0	0,5	strong phosphorus deficiency with large excess of potassium
6	18	1,8	0,56
5	16	1,6	0,63
4	14	1,4	0,7	medium phosphorus deficiency with medium excess of potassium
3	12,5	1,2	0,8
2	11,2	1,1	0,9	ratio close to normal
1-OC	10	1	1	balanced K and P nutrition
3	8	0,8	1,25	medium potassium deficiency with medium excess of phosphorus
4	7,1	0,7	1,4
5	6,3	0,6	1,6	strong potassium deficiency with slight excess of phosphorus
6	5,6	0,56	1,8
7	5	0,5	2

Knowing the values of С_Н, determined by the equation С_Н = ОС:ФС or from tables, it is possible to calculate the fertilizer dose.

If С_Н < 1, then the plants do not need this element and the dose is not calculated. When the value of С_Н is from 1.1 to 3–4, the indicator is included in the formula:

Д\ (кг/га) = C_Н \cdot М_Н,

where

Д: — dose of active ingredient (a.i.);
М_Н: — minimum dose (kg a.i.) used in the main fertilizer, the value of which is established in field experiments.

The value of М_Н in the main fertilizer for grain crops, maize, and peas is usually 30 kg/ha a.i., for potato and vegetables — 45 kg/ha a.i. under normal growing conditions for obtaining yields up to 40 c/ha of grain, 250 c/ha of potato, and 500 c/ha of cabbage. Under irrigation conditions, the minimum dose (МН) can be 1.5–2 times higher. In the integrated method of leaf diagnostics, the dose of the deficient element is corrected by other main elements that are in some excess or deficiency.

Example.

Calculation of the nitrogen norm for obtaining 40 c/ha of spring wheat grain.

For the tillering phase, the optimal content in leaves is N = 5%, P = 0.43%, K = 4.2%. The coefficient of action of the balanced element (nitrogen) in leaves B = 0.5 for a yield of 32–40 c/ha, 0.63 — for a yield of 41–50 c/ha, and 0.8 — for 55–60 c/ha. The nitrogen requirement of spring wheat per 1 c of grain with straw is 4 kg. The coefficient of utilization from mineral fertilizers is N — 63%, P₂O₅ — 20%, and K₂O — 63%. The minimum nitrogen norm N_MIN = 45 kg.

For the end of flowering phase, the optimal content of elements in leaves is N = 3%, P = 0.25%, K = 2.5%. The coefficient of action of elements in leaves (B) for yields of 40 c/ha is 0.8, for yields up to 50 c/ha of grain — 1.0, for yields of 51–60 c/ha — 1.25. The remaining indicators are the same as for the tillering phase.

The actual indicators of the chemical composition of leaves of the unfertilized variant in the tillering phase are N = 3.92%, P = 0.46%, K = 4.3%; in the end of flowering phase N = 2.10%, P = 0.29%, K = 3.74%.

Then, for the tillering phase, the degree of need for nitrogen will be:

C_НN = \frac { 5,0 \%N_{(опт)} } { 3,92 \%N_{(факт)} } \cdot \frac { 0,46 \%P_{(факт)} } { 0,43 \%P_{(опт)} } = 1,4.

For the end of flowering phase, the degree of need for nitrogen will be:

C_НN = \frac { 3,0 \%N_{(опт)} } { 2,1 \%N_{(факт)} } \cdot \frac { 0,29 \%P_{(факт)} } { 0,25 \%P_{(опт)} } = 1,7.

This degree of need of wheat for nitrogen should be corrected taking into account the deficiency of phosphorus in leaves or soil, if this deficiency cannot be overcome. Taking into account that CH N = 1.7,

C_НN = \frac { 5,0 \%N_{(опт)} } { 3,1 \%N_{(факт)} } \cdot \frac { 0,26 \%P_{(факт)} } { 0,43 \%P_{(опт)} } = 1,7 \cdot 0,6 = 1,02.

Whence, the nitrogen dose will be N kg/ha = C_H⋅45 = 1.02⋅45 = 46 kg/ha, instead of 80 kg/ha. This correction is important when determining nitrogen doses for winter and spring crops whose fields have mobile phosphorus or potassium content below the norm.

Thus, the nitrogen dose by the chemical composition of leaves in the tillering phase will be N kg/ha = C_H⋅М_Н = 1.4⋅45 = 63 kg/ha, in the end of flowering phase N kg/ha = С_Н⋅М_Н = 1.7⋅45 = 76 kg/ha, on average — 70 kg/ha.

If we take into account the excess potassium content in leaves compared with the optimal content, then

C_НN = \frac { 3,0 \%N_{(опт)} } { 2,1 \%N_{(факт)} } \cdot \frac { 3,74 \%K_{(факт)} } { 2,50 \%K_{(опт)} } = 1,4 \cdot 1,5 = 2,1,

and the nitrogen dose will be H_n = 2.1⋅45 = 94 kg/ha.

According to the sum of three calculations with corrections for some excess of phosphorus and potassium over two growth phases, the nitrogen norm will average (63 + 76 + 94) : 3 = 78 kg/ha.

By analogy with the integrated method of analytical leaf diagnostics, N. K. Boldyrev recommends calculating fertilizer doses by the content of mobile nutrients in soil, that is, applying the integrated method of soil diagnostics. The method is based on determining the normal nutrient composition of “soil” that ensures obtaining a high yield of grain crops, for example, 40 c/ha of spring wheat grain. They can be called optimal parameters of soil fertility by mobile forms of nutrients.

Table. Indicators of normal nutrient composition of various soil types ensuring the obtaining of 40 c of spring wheat and the corresponding yield level of other crops.

Soil type	Content in soil before sowing (7–10 days before sowing), mg/kg
	N-NO₃	P₂O₅ by				K₂O by
	N-NO₃	Chirikov	Machigin	Kirsanov	Truog	Chirikov	Machigin	Kirsanov	Maslova
Chernozem:
- ordinary	25	180	—	—	200	180	—	—	320
- leached	25	180	—	—	200	180	—	—	—
- carbonate	25	—	25^*	—	—	—	250	—	—
Chestnut	25	—	25	—	—	—	250	—	—
Sod-podzolic medium texture	25	—	—	200	—	—	—	200	—
Peat-bog	125	—	—	1000	—	—	—	1000	—

Note.

^* For the yield level of 50–55 c/ha of winter wheat grain, the content corresponds to 35 mg/kg of soil.

The table is supplemented with indicators of the optimal ratio between elements in soil, which are necessary for subsequent calculated corrections of fertilizer doses by the ratios between mobile nutrients.

Table. Ratio between mobile nutrients in soil as a basis for assessing nutrition conditions and determining the degree of need for fertilizers of cereal crops.

Reference point number from the optimum center	P₂O₅:(N-NO₃) mg/kg	Degree of need С_Н		Characteristics of nitrogen and phosphorus nutrition conditions, their balance
Reference point number from the optimum center	P₂O₅:(N-NO₃) mg/kg	for N	for P₂O₅
7	14,4	2,0	0,5	strong nitrogen deficiency with large excess of phosphorus in soil
6	12,5	1,8	0,56
5	11,2	1,56	0,63
4	10,0	1,4	0,72	medium nitrogen deficiency with medium excess of phosphorus
3	9	1,25	0,8	medium nitrogen deficiency with medium excess of phosphorus
2	8	1,11	0,9	ratio close to normal
1 OCP*	7,2	1,0	1,0	balanced N and P₂O₅ nutrition
2	6,3	0,9	1,14	ratio close to normal
3	5,6	0,8	1,28	medium phosphorus deficiency with medium excess of nitrogen
4	5	0,72	1,44	medium phosphorus deficiency with medium excess of nitrogen
5	4,5	0,63	1,6	strong phosphorus deficiency with large excess of nitrogen
6	4	0,56	1,8
7	3,6	0,5	2,0

Note.

^* OCP — optimum of nutrition by nutrient ratios. Designations:
1 OCP — balanced nutrition determined by the equation: mg/kg P₂O₅ — 7.2⋅Nnit mg/kg K₂O; 2 — weak imbalance of nutrition; 3-4 — medium; 5-7 — strong.

Table. Ratio between potassium and nitrate nitrogen in soil as a basis for assessing nutrition conditions, determining the degree of need CH and norms of the deficient element in fertilizer.

Reference point number from the optimum center	K₂O:(N-NO₃) mg/kg	Degree of need С_Н		Characteristics of potassium and nitrogen nutrition conditions, its balance
Reference point number from the optimum center	K₂O:(N-NO₃) mg/kg	for N	for K₂O
7	14,4	2,0	0,5	strong nitrogen deficiency with large excess of phosphorus in soil
6	12,5	1,3	0,56
5	11,2	1,6	0,63
4	10,0	1,4	0,72	medium nitrogen deficiency with medium excess of phosphorus
3	9,0	1,25	0,80	medium nitrogen deficiency with medium excess of phosphorus
2	8,0	1,12	0,9	ratio close to normal
1 OCP*	7,2	1,0	1,0	balanced K₂O nutrition
2	6,3	0,9	1,14	ratio close to normal
3	5,6	0,8	1,28	medium phosphorus deficiency with medium excess of nitrogen
4	5,0	0,72	1,44	medium phosphorus deficiency with medium excess of nitrogen
5	4,5	0,63	1,60	strong phosphorus deficiency with large excess of nitrogen
6	4,0	0,56	1,80
7	3,6	0,5	2,0

Table. Ratio between mobile phosphorus and exchangeable potassium (according to Chirikov) as a basis for assessing nutrition conditions and determining the degree of need C_Н for the deficient element.

Reference point number from the optimum center	P₂O₅:K₂O mg/kg	Degree of need С_Н		Characteristics of potassium and nitrogen nutrition conditions, its balance
Reference point number from the optimum center	P₂O₅:K₂O mg/kg	for K₂O	for P₂O₅
7	2,0	2,0	0,5	strong nitrogen deficiency with large excess of phosphorus in soil
6	1,8	1,3	0,56
5	1,6	1,6	0,63
4	1,4	1,4	0,72	medium nitrogen deficiency with medium excess of phosphorus
3	1,25	1,25	0,80	medium nitrogen deficiency with medium excess of phosphorus
2	1,12	1,12	0,90	ratio close to normal
1 OCP*	1,0	1,0	1,0	balanced K and P nutrition
2	0,9	0,9	1,12	ratio close to normal
3	0,8	0,8	1,25	medium phosphorus deficiency with medium excess of nitrogen
4	0,72	0,72	1,4	medium phosphorus deficiency with medium excess of nitrogen
5	0,63	0,63	1,6	strong phosphorus deficiency with large excess of nitrogen
6	0,56	0,56	1,8
7	0,5	0,5	2,0

The ratios N:P₂O₅:K₂O in soil characterize the qualitative aspect of plant nutrition and its balance. The ratio between the optimal and actual content of NH and P₂O₅, between NH and K₂O is expressed by quantitative indicators of the degree of need for the deficient element, which are used as correction coefficients for adjusting the fertilizer norm.

Optimal ratios between mobile nutrients in soil are established in field experiments with varying fertilizer doses according to factorial or conventional schemes by determining correlation relationships graphically or by grouping between indicators of ratios of pairs of elements and the yield value. Optimal ratios between mobile nutrients in soil for grain crops on some soil types are expressed by nutrient balance equations.

For ordinary and leached chernozems (Chirikov method for phosphorus and exchangeable potassium), the equality:

$$P_2O_5\ мг/кг\ почвы = 7,2 \cdot N-NO_3\ мг/кг = K_2O\ мг/кг.$$

For carbonate chernozems and chestnut soils (Machigin method for phosphorus and potassium):

$$P_2O_5\ мг/кг\ почвы = N-NO_3 = K_2O : 10.$$

Indicators of the optimal nutrient soil composition and the optimal ratio between mobile nutrients are used to determine fertilizer doses in other calculation methods as well. Calculation of fertilizer doses based on agrochemical soil analysis data is carried out by analogy with the leaf diagnostics method.

The norm of the deficient element is determined by multiplying С_Н by the minimum dose М_Н of the element, equal to 30.

For nitrogen under irrigation conditions, М_Н is differentiated taking into account the planned yield and is: М_Н = 30 for yields up to 36–38 c/ha; М_Н = 45 — for yields of 40–50 c/ha and М_Н = 60 for yields above 60 c/ha. For phosphorus, М_Н under irrigation is 45 kg P₂O₅.

The initial soil analysis data were taken for ordinary chernozem and obtaining the planned spring wheat grain yield under irrigation of 40 c/ha. The humus content in the 0–30 cm layer is 6.0%, the content 7–10 days before sowing of nitrate nitrogen (N-NO₃) is 14.0 mg/kg; P₂O₅ and K₂O (according to Chirikov) — 182 and 1176 mg/kg, respectively. Bulk density of 1 cm³ of the analyzed layer d = 1.05, depth of the analyzed layer h = 30 cm. The mass of the analyzed soil layer in million kg per 1 ha for converting nutrients from mg/kg to kg/ha, that is, the conversion coefficient to the mass of the layer М_c, is determined by the formula:

М_с = \frac {dh}{10},

М_с = \frac {1,05 \cdot 30}{10} = 3,15.

For chestnut soil and under irrigation for nitrate nitrogen, the determination layer 0–60 cm is used at d = 1.2 g/cm³, М_с will be 7.2.

Procedure for determining the fertilizer dose

1. Comparison of actual data on N-NO₃, P₂O₅, and K₂O with optimal indicators — 25, 180, 180 mg/kg, respectively — indicates that wheat plants for a yield of 40 c/ha do not need phosphorus and potassium fertilizers and have a need only for nitrogen.

2. The degree of need of plants for nitrogen is determined by the equation:

C_НN = \frac { N-NO_3\ (мг/кг,\ оптим.) }{ N-NO_3\ (мг/кг,\ факт.) } = \frac {25}{14} = 1,78,

correction for phosphorus:

C_НN = \frac { P_2O_5:N-NO_3\ (мг/кг,\ факт.) }{ P_2O_5:N-NO_3\ (мг/кг,\ оптим.) } = \frac {182:14}{180:25} = 1,7.

C_{H N} with correction for the ratio K₂O and N-NO₃ due to excess exchangeable potassium reaches a very large value.

Correction for potassium:

C_НN = \frac { K_2O:N-NO_3\ (мг/кг,\ факт.) }{ K_2O:N-NO_3\ (мг/кг,\ оптим.) } = \frac {1176:14}{180:25} = 11,6.

Therefore, balancing nitrogen nutrition proceeds by the excess of potassium in soil, when the correction for potassium exceeds 3, С_Н for phosphorus is (180:182) = 0.99, and for potassium С_Н = (180:1176) = 0.15, that is, there is no need for these elements.

3. The dose of nitrogen application in the main fertilizer is determined by the formula:

Д_N\ кг/га = С_Н \cdot М_Н,

where С_Н = 1.8, the minimum dose (М_Н) is 30 kg/ha or 45 kg/ha of nitrogen, H_n kg/ha = 1.8⋅30 = 54, H_n kg/ha = 1.8⋅45 = 81.

These calculated doses, equal to 54 and 81 kg/ha of nitrogen, almost coincide with the optimal doses identified in field experiments. There was no need to apply phosphorus and potassium fertilizers.

Based on long-term research of the Kazakh Agro-Technical University (KATU), carried out by V. G. Chernenok, the soil gradations by P₂O₅ content were adjusted for the conditions of Northern Kazakhstan.

Table. Gradation of dark chestnut and chernozem soils of Northern Kazakhstan by P₂O₅ content and efficiency of phosphorus fertilizers.

Supply class	Supply indicator	P₂O₅ content in the 0–20 cm layer, mg/kg	Fertilizer efficiency	Actual effect from P₆₀, %, average over 12 field-rotations
I	Very low	Up to 15	Very high (30-50%)	—
II	Low	15-25	High (20-30%)	24
III	Medium	25-35	Medium (10-20%)	13
IV	Increased	35-45	Low (5-10%)	6
V	High	More than 45	Absent	0

Application of Balance Calculation Methods

The disadvantage of all balance methods is that they do not take into account predecessors, agrochemical indicators, soil cultivation, and other indicators that affect the coefficient of nutrient utilization by plants from soil and fertilizers. Therefore, they are considered approximate, especially if the data for calculations are taken from reference materials. In practice, they give satisfactory results and streamline fertilizer application.

The task of the above calculation methods is to obtain a yield in the current year using the natural fertility of the soil. Fertilizers compensate for the amount of nutrients that cannot be obtained from the soil. In this case, systematic improvement of fertility and replenishment of nutrient reserves that were spent on yield formation are not envisaged.

Balance calculations of fertilizer doses for the planned yield, taking into account fertility improvement, have variants:

Obtaining high yields with the application of small doses while simultaneously depleting the soil of nutrients.
Obtaining high yields while maintaining effective fertility at the initial level.
Obtaining the maximum possible yields of a given crop while simultaneously increasing effective fertility.

List of Sources

Mineev V. G., Sychev V. G., Gamzikov G. P. et al. (2017). Agrochemistry. Textbook. Edited by Mineev V. G. Moscow: Publishing House of VNIIA named after D. N. Pryanishnikov.
Yagodin B. A., Zhukov Yu. P., Kobzarenko V. I. (2002). Agrochemistry. Edited by B. A. Yagodin. Moscow: Kolos.