Fertilizer Management: Computation

Nutrient balance approach

The methods to estimate the fertilizer rates, which have been described so far, are all empirical and therefore, should be used within the same environments where they have been developed. This limitation is partially overcome by methods which are based on the principles of plant nutrition. One of these methods is called INFERS (Kee et al ., 1994) which follows the nutrient balance approach and plant nutrient demand. These are the foundations of modern plant nutrition in the field, and recently have been advanced for dealing with soil nutrient depletion in African agriculture in general (Smaling et al ., 1999; Corley and Tinker, 2003). Although a number of past papers have discussed nutrient balance approach (Hew and Ng, 1968; Ng, 1977), only the INFERS model has been described briefly by Kee et al . (1994) and Corley and Tinker (2003) to illustrate the approach for oil palm.

The nutrient balance approach specifically attempts to balance the nutrient demand with the nutrient supply. In the oil palm agro-ecosystem, the components of nutrient demand are plant nutrient uptake for growth and production, nutrient losses through soil processes such as runoff and leaching (environmental losses) and nutrient immobilization (Figure 1). The components of nutrient supply are precipitation, pruned fronds, applied by-products such as empty fruit bunches. Any shortfall between nutrient supply and demand is met by fertilizer input. Ng (1977) considered the major variables in the nutrient balance sheet to be soil nutrient supply to the oil palm and plant nutrient demand.

Note: POME denotes palm oil mill effluent while EFB denotes empty fruit bunches

Figure 1: Nutrient cycles for nitrogen in oil palm plantations

Plant nutrient demand is the requirement for essential elements by a growing plant (Corley and Tinker, 2003). It can be separated into two processes: growth demand and deficiency demand (Tinker and Nye, 2000). The underlying theory of these two “demands” is quoted verbatim from Corley and Tinker (2003) as follows:

Nutrient amount (content) in palm, XW and uptake rate = 

where is the total nutrient in the palm, is the mass, is the fractional content of the nutrient and t is time. The first term in the uptake rate represents the growth demand because the nutrient percentage remains constant as the plant grows at a rate . However, during the correction of a nutrient deficiency, the second term applies, as the weight is a constant with varying nutrient concentration. In fact, both processes probably occur at the same time. Without the differentials and ignoring change in structure of plant material, a simple approximation for the uptake is:

2 (W 2 – W 1) + W 1 (X 2 – X 1) = X 1 (W 2 – W 1) + W 2 (X 2 – X 1) = X 2 W 2 – X 1 W 1

for times t1 and t2 and the meaning of the terms remains the same.

The main components of growth demand in the oil palm are nutrients immobilized in palm tissue by growth and nutrients exported in the FFB. The major components of deficiency demand are increase in palm nutrient content to correct nutrient deficiency and increase in soil nutrients. Changing the present state in these four components to the optimum level and maintaining the optimum state are the central tenets of INFERS model. That is, these four components, FFB yield, growth (palm size), nutrient concentration in palm (usually the leaf nutrient concentration in Frond 17 is used as an indicator) and soil nutrient concentration, form the targets in INFERS. Since these targets differ according to palm age, environment and economic situation, the palm nutrient requirements will also vary. Coupled with different fertilizer use efficiency, the fertilizer rates required for each field will change accordingly. This is indeed the essence of site-specific fertilizer recommendations. A brief description of INFERS module for computing fertilizer rates using N as an example is provided below. The detailed structure of INFERS is provided by Kee et al. (1994) and Corley and Tinker (2003) while the research which supports the model has been well described by Corley and Tinker (2003).

Since INFERS is based on the principle of plant demand and nutrient supply, the four targets to be achieved or maintained must be set correctly. The first target is usually based on the site yield potential using a model called ASYP (Kee et al., 1999). The growth rate is based on the increasing dry weight of Frond 17 as determined from its dimension (Corley et al., 1971) with palm age. It should be noted that the growth rate of oil palm and the maximum frond dry weight depend on the environment. This information is freely available from many experiments conducted on oil palm in Malaysia. The target for the leaf nutrient concentration in Frond 17 may be based on single nutrient critical levels for different environment and palm age or TLC method as described earlier. Since four targets are used in the model, the computed fertilizer rates are less sensitive to changes in leaf nutrient concentration compared to the earlier methods discussed above. The target for soil nutrient contents depends on the soil nutrient classification table (Table 1) or user’s preference for nutrient buildup, maintenance or depletion although INFERS does not in principle aim to deplete soil nutrients.

Table 1: Classification of soil nutrient status for oil palm

The main nutrient demand in the oil palm agroecosystem is probably by the plant. The plant nutrient demand can be separated into four components: canopy, trunk, root and FFB. The equations to calculate the palm N demand are shown below. The figures in subscript, 1 and 2, denote time 1 (present state) and time 2 (a year later).

1. Nutrient demand of the canopy

Canopy N growth demand (g N/palm) = 0.155* (Pinnae N (%)1) (Frond17 dry weight (g)2– Frond17 dry weight (g)1)

Canopy N deficiency demand (g N/palm) = (0.155 * (Frond17 dry weight (g)2) – 236.817)* (Pinnae N (%)2 – Pinnae N (%)1)

where Frond 17 dry weight is measured using the non-destructive method of Corley et al . (1971) and Pinnae N is obtained from the standard leaf nutrient analysis adopted by the oil palm industry in Malaysia (Foster, 2003).

2. Nutrient demand of the trunk

Trunk N growth demand (g N/palm) = 0.01 * Trunk N concentration (%)1(Trunk dry weight (g)2 – Trunk dry weight (g)1)

Trunk N deficiency demand (g N/palm) = 0.01 * Trunk dry weight (g)2(Trunk N concentration (%)2 – Trunk N concentration (%)1)

The trunk N concentration (%) is estimated by the linear-plateau model as follows:

  • Trunk N concentration (%) = 1.369 – 0.117 (age (yr)) for palm <= 8.5 years old
  • Trunk N concentration (%) = 0.351 for palm > 8.5 years old

The trunk dry weight is estimated by the equations proposed by Corley and Bruere (1981) as follows:

  • Trunk volume (cm3) = ? x d2x h /4
    where d = trunk diameter (cm), usually measured at 1m above the ground
    h = trunk height (cm), usually measured to Frond 41
  • Trunk density (g/cm3) = 0.083 + 0.0076 (age (yr))
  • Trunk dry weight (g) = Trunk volume x Trunk density

The above equations indicate that for palm above 8.5 years old, a constant value for growth demand of trunk may be used since height increment, diameter and N concentration in the trunk are constants and increase in trunk density is relatively small. Also, there is no deficiency demand due to constant trunk N concentration.

3. Nutrient demand of the roots

The N concentration in the roots of oil palm is relatively constant across palm age and soil types at about 0.39 %. Thus, oil palm roots are assumed to have no deficiency demand.

The growth demand of the oil palm roots is calculated using an empirical equation based on root:shoot ratio as follows:

Root:shoot ratio = 1.92 (Palm age (yr))-1.11

The difference in root weights between year 1 and year 2 is multiplied by the constant root N concentration to give the root N demand. It should be noted that the above equation to compute the root weight is based on palms with relatively good nutrition. It is known that root:shoot ratio tends to be higher for palms in poor nutritional state.

4. Nutrient demand of the FFB

At present, it is assumed that the N concentration of FFB is not affected by palm age or nutrition, and remains constant at 3.195 g N per kg FFB. Therefore, there is only growth demand by the production of FFB as follows:

FFB N growth demand (g N/palm) = FFB (kg)2 x 3.195

The soil nutrient demand generally involves two soil processes; soil nutrient build-up and soil nutrient losses. Soil nutrient build-up may be necessary if the soil nutrient status is low or where the soil activity ratio indicates nutrient imbalance as discussed earlier. The soil nutrient losses in the oil palm agroecosystem mainly arise from erosion, runoff and leaching. Corley and Tinker (2003) consider these losses as environmental losses or demand. The erosion and runoff losses can be estimated using the model suggested by Morgan et al. (1984) and leaching losses by Burn’s model (Burns, 1974). Although these sub-models are built into INFERS model, they require many state variables and parameters, and therefore are beyond the scope of this paper. In general, soil N losses through the above processes should not exceed 10 % if the fertilizer is properly applied and correctly timed. N volatilization losses from urea or urea based fertilizers can be considered as part of soil N demand but they are usually taken into account after computing the final fertilizer rate assuming no losses initially. That is, if one expects volatilization losses to be about 30 %, then the final N fertilizer rate is adjusted 30 % upwards.

The major nutrient supply in the oil palm agroecosystem is shown in Figure 3. INFERS assumes that nutrient supply from the atmospheric and rainfall deposition is small and no decrease in soil or plant nutrient content is expected unless done on purpose. For example, it is sometimes necessary to deplete, say soil exchangeable Ca and Mg which may be too high and causing poor K uptake as in ultrabasic soils or the palms on peat soils have too high N and too low K, by the appropriate fertilizer withdrawal. Similarly, the residual value of large dressings of phosphate rock and ground magnesium limestone (Goh et al., 1999b) can be up to three years’ demand and these nutrients can probably be omitted in such cases (Corley and Tinker, 2003). The nutrient supply from by-products such as empty fruit bunches (EFB) and palm oil mill effluent (POME) is well known and can be easily accounted for.

The computations of nutrient balance are subject to errors as in all mathematical and statistical models, and depend on reasonable or achievable targets. Thus, to prevent over manuring, INFERS has set a maximum N uptake rate of 1180 g per palm per year as measured under good environmental conditions.

The conversion of nutrient requirement of oil palm to fertilizer equivalent depends on the expected fertilizer efficiency at the site. Since fertilizer efficiency varies across sites, it is ideal that fertilizer response trials on similar soil types are available in the vicinity. In general, the N fertilizer efficiency in Malaysia varies from 30 to 70 %. This wide range in fertilizer efficiency is due to the very different environments where they were measured e.g. fertile coastal clays to infertile Malacca series soils. In reality, the average fertilizer efficiency over three years or more within a site is relatively similar. Therefore, the fertilizer efficiency at a site may be estimated from past fertilizer history and nutrient uptake rate as a first approximation as described step-by-step below.

1. Figure 2 shows a hypothetical response curve of nutrient uptake to fertilizer input. It generally follows a modified Mitscherlich equation or a linear-plateau model. Under an ideal situation, we should know three points:

  • Point A: Nutrient uptake without fertilizer input i.e. soil nutrient supply
  • Point C: Targeted nutrient uptake at the correct fertilizer rate
  • Point B: Average last two to three years nutrient uptake at applied fertilizer rates

Point A and point C are usually unknown from past historical data although point A can be estimated using Foster’s soil based system as discussed earlier. However, point B and the targeted nutrient uptake line are known.

Figure 2: A hypothetical response curve of N nutrient uptake to N fertilizer input and a method to predict the N fertilizer rate for the following year

2. Point B can be calculated based on the model described earlier using the actual yield, dry weight and nutrient concentration in Frond No. 17.

3. The targeted nutrient uptake is calculated based on the targeted yield (site yield potential), dry weight and nutrient concentration in Frond No. 17 for the site.

4. We can then draw a tangent passing through point B to the targeted nutrient uptake line. The point where it cuts (point D) gives the estimated fertilizer rate. This generally underestimates the fertilizer requirement due to higher environmental demand (Corley and Tinker, 2003) with increasing fertilizer rate. We have not fully addressed this issue although a 10% higher rate for N and K appears satisfactory.

5. Another problem which has not been solved is the known fact that fertilizer use efficiency (FUE) declines with increasing fertilizer rate. It generally follows a declining exponential model, FUE = exp(-kF), where F is the fertilizer rate (kg/palm/yr) and k is a constant. This constant is mainly affected by fertilizer sources and environment.

6. This method avoids the necessity to estimate the fertilizer use efficiency and soil nutrient supply directly. However, it is highly dependant on a reasonable starting value (point B) and the targets to avoid over fertilization.

7. A reasonable point B can be obtained if one follows the six tools available to monitor palm health, and changes in soil nutrients and fertilizer use efficiency as listed below:

  • Leaf nutrient status
  • Soil nutrient status
  • Nutrient deficiency symptoms
  • Vegetative growth rate and canopy sizes (Classification)
  • Yield (site yield potential)
  • Fertilizer efficiency

An example showing the computation of N fertilizer rate (kg AC/palm/year) using INFERS model for the low N scenario as provided in the earlier illustrations of fertilizer recommendation systems is given below. The required variables measured in 1993 and 1994, and targets for 1995 are given in Table 2 and the calculated nutrient uptake and fertilizer rate are shown in Table 3. For simplicity, it is assumed that the soil N status is satisfactory and therefore, soil N demand is equaled to zero.

Table 2: Measurements made on oil palm planted in 1979 on Batang (lateritic) Family soil to demonstrate INFERS model

Table 3: Computed N uptake and N fertilizer rate based on variables in Table 16 using INFERS model

The calculated N fertilizer rate is similar to that of Foster’s system but it is the only known fertilizer recommendation system for oil palm that accounts for both deficiency ad growth demands explicitly. It also avoids the problem of dilution or concentration effect of leaf nutrient due to changing canopy sizes. The relatively low N fertilizer rate in the present example is due to the relatively high soil N supply as shown by the past historical data. In general, higher N rate is recommended to account for the decline in fertilizer use efficiency with increasing fertilizer rate due to higher N environmental losses if the first approximation method is used as discussed above. This implies that the model tends to underestimate the fertilizer requirements of oil palm when the initial fertilizer rates are far below the optimum rates. However, the error gets smaller as the recommended fertilizer rates move towards the optimum rates and from experience, the model outputs converge within 3 years under the worst scenario.

INFERS model requires at least 3 targets as discussed above, and if they are wrongly set, then the estimated fertilizer rates will be incorrect. Thus, it requires the agronomist to know the fields well, have a good understanding of oil palm physiology and agronomy, be aware of the management practices and resources available, and have the ability to judge the reliability of the data for the model and decision making including the impact of spatio-temporal variation.

Goh, K.J. (2005). Fertilizer recommendation systems for oil palm: estimating the fertiliser rates. In: Chew, P.S. and Tan, Y.P. (eds) Proceedings of MOSTA Best Practices Workshops – Agronomy and Crop Management. Malaysian Oil Scientists’ and Technologists’ Association (MOSTA): 235-268.

Note: The full list of references quoted in this article is available from the above paper.


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