Fertilizer Recommendation Equation

1.      Introduction

In crop production, applying the right amount of fertilizer is undoubtedly one of important things to be done for ensuring the achievement of the optimum crop yield.  Considering the Liebig’s Law of the minimum, it is clear that following the lack of moisture, the low fertility comes as the second limiting factor which can lead to the low yield potential in the production of crops. Besides, in plant nutrition, for preventing or correcting a deficiency in a particular plant nutrient element. The supply of such nutrient is essential [1]. For achieving this, there is a need to utilize fertilizers. This brings us to the recommendation of fertilizers and this should be done in the right way for ensuring better crop response to the applied nutrient in the form of a fertilizer.

As mentioned by [2], there are three types of fertilizer recommendation philosophies based on soil tests: (1) maintenance philosophy; (2) nutrient sufficiency philosophy; and (3) consideration of cation balance. From research results it was found that the nutrient sufficiency philosophy is agronomically and economically sound compared to others.

The fertilizer requirement can be related to nutrient status as shown by soil analysis, to soil type, previous crop, to the organic manure use, and to crop features such as variety and yield level. Based on scientific considerations including carrying out a series of field experiments, and taking into account crop removal of nutrients. Fertilizer recommendations are formulated at different levels including but not limited to national and local level by responsible coordinating agency [3].

According to [4], for field crops, nutrient recommendations have evolved over the years on the basis of observations and controlled field studies. For instance, in Michigan, previously used tabular data for fertilizer recommendations were converted into recommendations equations in 1981. During the mid-1990s, specialists in soil fertility from Ohio, Michigan and Indiana elaborated recommendations through developing a set of common nutrients for soya bean, corn, alfalfa and wheat. The conceptual model used for those recommendations is followed for recommendations of potassium and phosphorus.

Since fertilizer recommendations are specific to the area and crop, only general guidelines will be given here. They must be modified to fit soil type, the climate, and the yield goal of the farmer for a particular area. It is important for a farmer to have realistic yield goals when planning a fertilizer program [2].

2.      Fertilizer Recommendations Equations

Actual recommendations for fertilizers are computed using one of three relationships. One is applicable to buildup, another for maintenanceand a third for drawdown:

2.1.            Equations used to calculate the recommended amount of P₂O₅, in pounds per acre, when the soil test is in each zone

2.1.1.      Mineral Soils

ü  Buildup zone: lb P₂O₅ /a = ((CL – ST) x 5) + (YP x CR), when ST is < CL

ü  Maintenance zone: lb P₂O₅ /a = (YP x CR), when ST is ≥ CL and ≤ ML

ü  Drawdown zone: lb P₂O₅ /a = {YP x CR} x {[(CL + PL + DDL) – ST] ÷DDL},

when ST > ML and < (ML + DDL)

where:

CL = critical soil test value (ppm),    

ML = maintenance limit,

ST = soil test value (ppm),

YP = yield potential or goal,

CR = nutrient removal in harvested portion of crop (lb/unit of yield),

PL = maintenance plateau length, and

DDL = drawdown length; recommendation is phased to zero

2.1.2.      Organic Soils

ü  Buildup zone: lb P₂O₅ /a = ((CL – ST) x 2) + (YP x CR), when ST is < CL

ü  Maintenance zone: lb P₂O₅ /a = (YP x CR), when ST is ≥ CL and ≤ ML

ü  Drawdown zone: lb P₂O₅ /a = {YP x CR} x {[(CL + PL + DDL) – ST] ÷DDL},

when ST > ML and < (ML + DDL)

2.2.            Equations used to calculate the amount of K₂O, in pounds per acre, when the soil test is in each zone

2.2.1.      Mineral Soils

ü  Buildup: lb K₂O /a = {(CL – ST) x [(1 + (0 .5 x CEC)]} + (YP x CR), when ST is < CL

ü  Maintenance: lb K₂O /a = (YP x CR), when ST is ≥ CL and ≤ ML

ü  Drawdown: lb K₂O /a = {YP x CR} x {[(CL + PL + DDL) – ST] ÷DDL},

when ST > ML and < (ML + DDL)

where:

CL= critical soil test (ppm); for mineral soils, CL = 75 + (2.5 x CEC)

CEC = cation exchange capacity (me/100g soil,

ML = maintenance limit,

ST = soil test value (ppm),

YP = yield potential or goal,

CR = nutrient removal in harvested portion of crop (lb/ unit of yield),

PL = maintenance plateau length, and

DDL = drawdown length; recommendation is phased to zero

2.2.2.      Organic Soils

ü  Buildup: lb K₂O /a = [(CL – ST) x 1.5] + (YP x CR), when ST is < CL

ü  Maintenance: lb K₂O /a = (YP x CR), when ST is ≥ CL and ≤ ML

ü  Drawdown: lb K₂O /a = {YP x CR} x {[(CL + PL + DDL) – ST] ÷DDL},

when ST > ML and < (ML + DDL) [4]

2.3.            Micronutrients Recommendations

Recommendations for micronutrients are based on crop responsiveness, soil test, and soil pH. Continuing to consider the case of Michigan soils, equations used for the calculation of fertilizer recommendations for some micronutrients are given below:

2.3.1.      Manganese (Mn)

For responsive crops, recommended amounts of manganese (Mn) are based on the (0.1 N HCl) soil test (ST) value and soil pH as shown in following equations:

ü  Mineral soils: Mn rec. = [(6.2 x pH) – (0.35 x ST)] – 36

ü  Organic soils: Mn rec.= [(8.38 x pH) – (0.31 x ST)] – 46

where:

Mn recommendation (Mn rec.) is lb Mn/a (band application only), and ST is soil test value (ppm Mn)

2.3.2.      Zinc (Zn)

For responsive crops, recommended amounts of zinc (Zn) are based on the (0.1 N HCl) soil test (ST) value and soil pH according to the following equations:

Mineral and organic soils: Zn rec = [(5.0 x pH) – (0.4x ST)] – 32

where:

Zn recommendation is lb Zn/a

ST is soil test value (ppm Zn) [4].

2.4.            Nitrogen Fertilizer Recommendations

According to [2], variations in mineralization, denitrification, and leaching rates from one soil to another and from one year to another complicate the use of a soil test for making nitrogen fertilizer recommendations. The recommendations for nitrogen fertilizers are based primarily on yield response data obtained from nitrogen fertilizer rate experiments.

 

The basic equation for the Nitrogen fertilizer recommendation is:

Pounds Nitrogen per acre=YG*Optimum Nitrogen rate

Where, YG equals yield (bushels/acre) and the optimum N rate is the pounds of N needed per bushel of yield to produce the economically optimum yield.

 

For grain crops such as corn the economically optimum nitrogen fertilizer rate is based on a corn/nitrogen price ratio: the price of a bushel of corn divided by the price of a pound of nitrogen fertilizer.

The basic nitrogen fertilizer recommendation for corn is modified by consideration of the previous crop and the manure’s amount to be applied. For example, the equation used in Michigan for corn nitrogen recommendations as pounds per acre is:

       

N=[YG*1.36)-27]-[40+(0.60*%ls)]- (4*fm).

The ls is for legume stand, which is evaluated in terms of number of clover or alfalfa plants per unit area. If the rate for alfalfa stand was very good, 100%, then 100 pounds (40+0.6*100) would be subtracted to account for the nitrogen contribution of the previous alfalfa crop. The fm refers to tons of farm manure to be applied per acre.

2.5.            Examples of Fertilizer Recommendation Calculation

As detailed, below are examples for computing fertilizer recommendations for some macronutrients and micronutrients needed in crop production.

Example 1: For a mineral soil where soybean will be grown ST is 10 ppm, CL is 15 ppm, CR is 0.80 lb P₂O₅/bu, and YP is 40 bu/a. Calculate the recommended amount of P₂O₅ in pounds per acre for achieving the potential yield of soybean?

Calculation:

Since the ST is less than the CL, hence the soil test falls in the buildup zone. Therefore, for the computation of the amount P₂O₅recommended will be given by:

ü  Buildup equation for P: lb P₂O₅/A to apply = [(CL - ST) x 5] + (YP x CR)

= [(15 ppm-10 ppm) *5] +(40bu/a*0.80 lbP₂O₅/bu) = (25+32) lb P₂O₅/a= 57 lb P₂O₅/a

Ø  Since 1pound/acre=1.12085116kg/ha, hence 57 lbP₂O₅/a = (1.12085116*57) kg P₂O₅/ha =63.8852kg P₂O₅/ha

The amount of P₂O₅recommended is equal to 63.8852kgP₂O₅ /ha.

Note:

In general, P soil tests are evaluated as low, medium, high, and very high. Soil tests that are low will require additions of phosphorus fertilizer that exceeds the quantity removed by the crop being grown because phosphorus added in the fertilizer becomes fixed. Soils testing medium in phosphorus will require applications of slightly more than that removed by the crop for adequate yield and growth. When the soil test is high, no yield response is expected to the phosphorus fertilizer. In such case, different approaches to management of fertilizer may be followed. Firstly, a starter fertilizer banded during planting may be used to apply a maintenance amount of phosphorus. The intent is to apply the phosphorus amount that is removed by the growing crops so that the high soil test will be maintained. Alternately, no phosphorus fertilizer is applied and the soil is retested at frequent intervals for determining when phosphorus must be applied again.

When the soil test is very high in P, the probability of phosphorus being lost to surface waters through runoff and erosion is great. For reducing the risk of environmental degradation, phosphorus fertilizer should not be applied to soils testing very high. The soil should be retested frequently to determine when phosphorus levels are reduced to the point at which addition of phosphorus is required again [2].

Example 2: The corn silage will be grown in a mineral soil with STL for potassium is 40 ppm, CEC is 8 meq/100g, CR is 8 lb/ton, and YP is 20 tons/acre. Find the amount of K₂O recommended for achieving the potential yield for the corn silage?

Calculation:

First of all, we need to find the value of CL. Given that CL=75+(2.5*CEC) for all crops, therefore the CL=75+(2.5*8 meq/100g) = 95 ppm.

As the ST (40 ppm) is less than the CL (95ppm), therefore the soil test falls in the buildup zone.  

ü  Build up equation for K: lb K₂O/A to apply = [(CL - STL) x ((1 + (0.05 x CEC))] + (YP x CR) = [(95 ppm-40 ppm) *((1+(0.05*8 meq/100g))] + (20 ton/acre*8 lb/ton) = (55+22+160) lb K₂O/a= 237 lb K₂O/acre

Ø  Given that 1pound/acre =1.12085116kg/ha. Therefore 237 lb K₂O/acre =(1.12085116*237)kg K₂O /ha=265.6417kg K₂O /ha

The amount of K₂O recommended is 265.6417kg K₂O/ha.

Example 3: For a mineral soil where potato will be grown, the soil test using 0.1 N HCl indicated the manganese content of 6 ppm at pH 6.3. How much manganese in needed for achieving the potential yield for the potato that will be grown?

Calculation:

Recall that for mineral soils manganese recommendations can be found as follows:

Mn rec. = [(6.2 x pH) – (0.35 x ST)] – 36= [(6.2*6.3) －(0.35*6)] －36 = 37.06－36= 1.06 lb Mn/acre (For band application only).

 Note: Recommended rates of Mn are for band application because Mn is readily bound into unavailable forms when mixed (broadcast and incorporated) with the soil.

Example 4: The soil with a soil test value for manganese content of 2 ppm at pH 6.6 is going to be used for bean production. Elaborate recommendations for manganese application?

Calculation:

 Zinc recommended for mineral and organic soils: Zn rec = [(5.0 x pH) – (0.4x ST)]–32= [(5.0*6.6)–(0.4*2)]-32= (33-0.8)-32= 32.2-32=0.2 lb Zn/acre

Ø  As 1pound/acre =1.12085116kg/ha. Then 0.2 lb Zn/acre =(1.12085116*0.2)kg Zn/ha =0.2242kg Zn/ha

The amount of Zn recommended is equal to 0.2242kg Zn/ha.

Example 5: For a YG of 150 bushels/acre, when corn follows an excellent stand of alfalfa or clover and 10 tons/acre of manure are applied. Calculate the N recommendation?

Calculation:

Recall that N=[YG*1.36)-27]-[40+(0.60*%ls)] -(4*fm).

 

Therefore, the N recommendation is Pounds N/acre=177-100-40=37 lb N/acre

Ø  Since 1pound/acre =1.12085116kg/ha, hence 37 lb N/acre= (1.12085116*37) kg N/ha =41.4715kg N/ha

The amount of Nitrogen recommended is 41.4715kg N/ha.

 

Note:

Sometimes a previous soybean crop is equated to 40 pounds of nitrogen fertilizer. This basic method is also used for making recommendations for small grains and other non-legume crops.

Other factors are used for modifying the recommendation, depending on the crops and conditions.

For legume crops, there is a variation in their nitrogen-fixing efficiency. To avoid possible contamination of ground water, some agricultural experimental stations are becoming more conservative and are eliminating nitrogen recommendations for soybeans. Additionally, the application of nitrogen fertilizer to efficient nitrogen-fixing legumes may reduce the fixation of nitrogen without affecting yields.

Crops grown on organic soils:  Organic soils, histosols, contain a greater amount of total nitrogen than mineral soils. As a consequence, the nitrogen mineralization potential is very high and many crops are grown without using nitrogen fertilizer. These soils require drainage and tend to be wet and cold in the spring leading to a slow rate of mineralization. For such season, some crops respond to small applications of nitrogen fertilizer [2].

2.6.            Conclusion

Considering how the supply of nutrient elements which are insufficient in crop production can contribute in increasing the crop yield. Adequate correction or prevention of nutrient insufficiency by use of fertilizers should be done by following right fertilizer recommendations. The recommended fertilizer amount needs to be computed in the same way as demonstrated in this article. Doing so, a considerable increase in crop yield can be expected in crop production.

 

References

[1]	S. L. Tisdale, J. L. Havlin, J. D. Beaton and W. L. Nelson, Soil Fertility and Fertilizers : An Introduction to Nutrient Management, 6 ed., Upper Saddle River, New Jersey: Prentice-Hall, Inc. & Pearson Education, 1999, pp. 6-12.
[2]	H. D. Foth, Soil fertility, 2 ed., Boca Raton, Florida: Lewis Publishers, 1997, pp. 140-143, 159.
[3]	FAO, Fertilizer and plant nutrition guide, FAO [Food and Agriculture Organization of the United Nations], 1984, pp. 37-40.
[4]	W. Darryl, D. Jon and J. Lee, Nutrient recommendations for field crops in Michigan, Michigan: Michigan State University, Department of crop and soil sciences, 2009, pp. 3-16.

By

Jean Claude Tuyisenge