Can smarter nitrogen fertilizers be designed?

Field Crops Research 94 (2005) 54–66 www.elsevier.com/locate/fcr

Can smarter nitrogen fertilizers be designed? Matching nitrogen supply to crop requirements at high yields using a simple model John E. Sheehya,*, P.L. Mitchellb, Guy J.D. Kirkc, Anaida B. Ferrera a

Crop, Soil and Water Sciences Division, International Rice Research Institute, DAPO 7777, Metro Manila, Philippines b Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK c National Soil Resources Institute, Cranfield University, Silsoe, Bedfordshire MK45 4DT, UK Received 21 April 2004; received in revised form 23 November 2004; accepted 24 November 2004

Abstract There are numerous difficulties in modeling the uptake of nitrogen by roots. To help make progress a very simple model based on experimental results was constructed. The uptake of nitrogen was described by a first-order equation in which the uptake parameter combined the effects of root size and the uptake per unit root size. The loss of nitrogen was modeled using a similar equation. Using the model, the hypothesis that fertilizer nitrogen losses from high-yielding irrigated rice could be almost eliminated by delivering the precise amounts of nitrogen required to support growth at any given time was demonstrated to be false. The model was used to compute the effects of applying a constant amount of fertilizer nitrogen in eight ways (splits), and also the effects of a slow-release and of an ‘ideal’ fertilizer. Counter to intuition, the practicable limit to recovery of fertilizer nitrogen was about 57%, for the high rates of nitrogen considered here and with the values for the model parameters used here. This arises because it is necessary to have a certain concentration of nitrogen in the available soil pool (freely-exchangeable plus solution nitrogen) from which the crop can take up the nitrogen it needs, and concurrently the available soil pool will lose nitrogen at a rate controlled by various biophysical processes. # 2004 Elsevier B.V. All rights reserved. Keywords: Model; Nitrogen; Slow-release fertilizer; Rice; Fertilizer recovery

1. Introduction Large quantities of nitrogen are required to achieve yield potentials of crops. It has been shown that to * Corresponding author. Tel.: +63 2 580 5600; fax: +63 2 580 5699. E-mail address: [email protected] (J.E. Sheehy).

achieve maximum yield, there has to be a ‘critical’ nitrogen concentration in the biomass (Greenwood et al., 1990; Sheehy et al., 1998). The critical nitrogen content of an indica rice yielding 11.6 t ha
1 in the dry season in the Philippines was estimated to be 276 kg N ha
1 and the measured nitrogen content was 292 kg N ha
1 (Sheehy et al., 2000). However, as much as 70% of fertilizer nitrogen applied to the

0378-4290/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fcr.2004.11.008

J.E. Sheehy et al. / Field Crops Research 94 (2005) 54–66

irrigated rice crop, in the form of urea, can be lost to the crop (Dobermann et al., 2002; Vlek and Byrnes, 1986), much of it in the form of ammonia (De Datta and Patrick, 1986; De Datta, 1995), although some of it will remain in the soil. The half-life of urea fertilizer in the irrigated system is about 6 days during the first 10 days following transplanting; thereafter it is about 3 days (Sheehy et al., 2004a). Consequently, urea fertilizer is usually supplied on a number of occasions during the growing season (Peng and Cassman, 1998). Such management practices incur labor costs (Dawe et al., 2004), and given the short half-life of urea in the soil system are likely to produce optimum concentrations only briefly. Controlled-release fertilizers have been designed to improve the efficiency with which crops capture nitrogen and to reduce losses to the environment (Shoji and Gandeza, 1992; Shaviv and Mikkelsen, 1993). These fertilizers release their contents into the root environment at rates governed by temperature, physical processes and the properties of the casing surrounding the fertilizer (Jarrell and Boersma, 1979). Intuitively, one thinks that much more of a controlledrelease fertilizer ought to be recovered in the crop, perhaps approaching 100% if the rate of release can be matched to the requirements of the crop. Nonetheless, the changing relationship between the amount of fertilizer required by the plants and the amount required in the root environment is obscure, adding to the difficulties in planning optimum fertilizer strategies. Slow-release fertilizers are much more expensive than conventional ones. The major objective of the work described in this paper was to test the following hypothesis, applicable to high-yielding irrigated rice. Can fertilizer nitrogen losses be almost eliminated by delivering the precise amounts of nitrogen required to maximize the daily rate of plant growth in optimum growing conditions? The delivery system could be a smart fertilizer or fertilizer regime. To test the hypothesis, a simple mechanistic model linking nitrogen uptake by the crop to the quantities of nitrogen in the available soil pool was built. Crop growth, crop duration and nitrogen use are influenced by weather, other environmental conditions, and soil properties. Here, we consider the particular example of irrigated tropical rice growing in the dry season and reaching maturity in about 100 days. We did this partly because of the

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importance of the system for food production in Asia and partly because of the availability of experimental data.

2. Methods 2.1. The model The properties of roots are affected by differences in maturity, geometry, anatomy, and the local properties of the soil (Robinson, 1994). There are numerous difficulties in modeling the uptake of nitrogen by roots and simultaneous losses from the soil by gaseous emission, leaching and other processes (Tinker and Nye, 2000). To avoid undue complexity, here we model uptake and loss with simple first-order equations according to the scheme shown in Fig. 1. Rice seedlings are transplanted in a paddy field to fixed locations called hills, on a square or rectangular spacing. Commercial crops often have several seedlings per hill, but in these experiments a single plant was used and there were 25 hills m
2. To study the dynamics of nitrogen distribution in rice, a quantity of 15 N, equivalent to several hours of the total daily uptake of nitrogen, was delivered in a small gelatin capsule to a rice hill in a paddy (Sheehy et al., 2004a,b). The gelatin dissolves in a few minutes. In that work, it took about 2 weeks for the 15N to be either absorbed by the plant or become unavailable to it in some way. By labeling and monitoring a series of hills over time, it was possible to measure the dynamics of absorption and loss over a cropping season. To explain their observations, Sheehy et al. (2004a,b) developed a simple theoretical analysis to describe the uptake and the loss of the 15N. Some of that theory, helpful to the development of the current model, is described here. Their results showed that both the net rate of uptake by the plant, and loss from the 15N pool available to the plant, were proportional to the quantity of the 15N present in the soil, Q15s(t), at any time (t). The loss of nitrogen resulted from a combination of effects: temporary immobilization of the label into unavailable nitrogen pools, and physical losses from the soil– floodwater system via denitrification, volatilization and in some cases leaching. The rate of uptake of labeled nitrogen by a plant is written as:

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Fig. 1. A block diagram of the model showing the fluxes of soluble nitrogen into and out from the available soil nitrogen pool (ASNP) and into and out from the plant. The rate at which nitrogen from the fertilizer and other sources enters the ASNP is Rin, comprised of Fi, the rate at which nitrogen from sources other than fertilizer enter the ASNP, and Rf, the rate at which fertilizer nitrogen enters the ASNP. The rate at which nitrogen enters the rice plant (hill) is Rh and Rl is the rate at which nitrogen becomes unavailable to the hill through losses and temporary immobilization; Rhl is the rate at which nitrogen is lost from the hill through the death and detachment of organs.

dQ15h ¼
k15h Q15s ðtÞ; (1) dt likewise, the rate of loss to the plant of label is written as: dQ15l ¼
k15l Q15s ðtÞ; (2) dt where k15h and k15l were the rate parameters describing the uptake and the loss of labeled nitrogen for a given application of 15N. The individual rice hill (here with a single rice plant) was used for reference purposes with respect to the flux of nitrogen to the plant (g hill
1 d
1). To convert from g N hill
1 to the more familiar kg N ha
1, multiply by 250 for 25 hills m
2. Instead of available soil pool concentrations of nitrogen, they used absolute amounts of 15N available to the hill (g hill
1), so that the rate parameter for uptake, k15h, had the units day
1 (d
1) and combined the size of the roots and the efficiency of uptake per unit size into a single parameter. The quantity of labeled nitrogen in the soil (Q15s(t)) at any time (t) can be written as: Q15s ðtÞ ¼ Q15o exp ½
ðk15h þ k15l Þt;

(3)

where Q15o is the initial quantity of labeled nitrogen in the capsule, which is assumed to be released when the capsule is inserted under the hill at time t = 0. The fraction of the labeled nitrogen accumulated by the hill at any time (t), Q15h(t)/Q15o, is obtained by substituting for Q15s(t) from Eq. (3) into Eq. (1) and integrating:


 Q15h ðtÞ k15h ¼ Q15o k15h þ k15l  ½1
exp ð
ðk15h þ k15l ÞtÞ:

(4)

15

The maximum fraction of N recovered by a hill (amax) from an application using the point-placement technique can be calculated by assuming t ! 1 in Eq. (4) which gives the maximum value as: amax ¼

k15h : k15h þ k15l

(5)

However, an exponential model describing the uptake of the 15N suffers the disadvantage that it predicts infinite time taken to achieve the maximum uptake of the isotope. Given the concept of 95% confidence limits for experimental data, it was decided that the model prediction of 95% of maximum uptake would be acceptable as a prediction of practicable maximum uptake and this was achieved in about 2 weeks according to the measurements of Sheehy et al. (2004a). To make progress in this paper, we assume that the kinetics describing the 15N added in the capsules by Sheehy et al. (2004a) can be used to describe all other nitrogen in the available soil pool. The model hinges on the first-order relations for uptake and loss derived from the 15N data being applicable to the rest of the plant-available N. If these relations are in reality nonlinear, or the magnitudes of the rate constants are very different, the conclusions may be wrong. There are a number of important caveats that arise from this assumption and we will address them here.

J.E. Sheehy et al. / Field Crops Research 94 (2005) 54–66

The placement of a 15NH4 capsule in the soil leads to the following considerations. (1)

(2)

(3)

(4)

(5)

(6)

15

NH4 will rapidly equilibrate with 14NH4 in the soil solution and on the soil exchange complex (between which there is rapid exchange, and probably a roughly linear relationship between their concentrations). The available soil pool is the nitrogen in the soil solution plus the nitrogen that is freely exchangeable with it. The freely-available 15NH4 will slowly exchange with 14NH4 fixed in soil minerals, and 15N will also slowly exchange with 14N in organic matter through microbial action. Some 15N may be lost by diffusion to the floodwater and volatilization as NH3, or by diffusion to and nitrification in the rhizosphere or floodwater–soil interface and subsequent denitrification. ‘Loss’ of 15N by isotopic exchange between freely-available and slowly-available pools is necessarily first-order, but the kinetics of the bulk immobilization of added N and other loss processes may be quite different. Isotopic exchange between rapidly-available and slowly-available pools will produce a corresponding decrease in the ratio 15N/14N in the rapidlyavailable pool. Hence, the 15N may not behave as a simple tracer for 14N uptake. The rate coefficients for uptake and loss of 15N from applications made at 5 cm depth and from applications made at the soil surface (beneath the floodwater) were not significantly different (Sheehy et al., 2004a), suggesting that the sum of the rates of the loss processes at the soil and floodwater surfaces are comparable to the sum of the loss processes deeper in the soil. However, the agreement may be a coincidence and we are fortunate to be able to take advantage of it.

These problems do not invalidate the model. Firstorder relations are a rational starting point and the 15N data are evidently indicative of the values of the rate constants. Later in the paper, we compare the model predictions with experimental observations and we investigate the consequences of changing the values of the rate parameters in a sensitivity analysis.

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The rate of total nitrogen absorption by the hill (Rh, g hill
1 day
1) can be written as: Rh ¼ kh Qs ðtÞ; and its loss (Rl, g hill
1 day
1) is:

(6)

(7) Rl ¼ kl Qs ðtÞ; where Qs is the quantity of nitrogen available to the hill in the available soil pool surrounding the roots and has the units g hill
1; and kh and kl are the rate parameters and have the units day
1. We will assume that kh = k15h and kl = k15l. The equation of mass continuity for the soil N pool (Qs) can be written as: dQs ¼ Fi
k h Q s
k l Q s ; (8) dt where Fi is the rate at which nitrogen enters the pool from sources other than fertilizer. If it is assumed that a quantity of nitrogen is supplied as fertilizer to the available soil pool then Eq. (8) can be used to calculate the daily uptake and loss of nitrogen numerically in the following form: Qi ¼ Qi
1 þ Qf
kh ðQi
1 þ Qf Þ Dt
k1 ðQi
1 þ Qf Þ Dt þ Fi Dt;

(9)

where Qi is the quantity in the available soil pool on day i, Qi
1 the quantity on the preceding day and Qf is the quantity of fertilizer added on day i
1 and Dt = 1 d. Once we have values for kh and kl, Eq. (9) can be used to predict the uptake and ‘loss’ of nitrogen for various ways of splitting the nitrogen delivered to the crop, and those predictions can be compared with observed values as a test of the model. Mishra and Kirk (1994) reviewed the work on losses of ammonia from irrigated rice and calculated a single rate constant that worked well in their model. Here, we follow that example and calculate a mean value of kl (0.105 d
1) from measurements shown in Table 1. We assume kl to be a constant for tropical rice paddies because we do not have enough data to establish values at different crop ages or different values for the wet and dry seasons. Having a value of kl, we can now calculate a value for kh by re-arranging Eq. (5): kl : (10) kh ¼ 1=ðamax ðtÞ
1Þ A sequence of measurements of the maximum fractions of 15N recovered by rice hills (amax), made in a dry season experiment (Sheehy et al., 2004b), are

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Table 1 Values of the rate parameter (kl) obtained from equations fitted to time courses of 15N accumulation (Qh(t) = amax(1
exp(
bt)), amax = k15h/(k15h + k15l), and Qh(t)/Q0 = [kh/(kh+kl)][1–exp (
(kh + kl)t)], r2 > 0.86) DAT (days)

kl (d
1)

10 35 17 35 45 55

0.07 0.08 0.14 0.06 0.11 0.17

The first two values were obtained in the wet season of 2002 and the others in the dry season of 2001. The overall mean value of kl is 0.105 d
1.

shown in Fig. 2a. The data suggested that amax varied during the growing season and an empirical equation was used to describe them:   ! lnðt=bÞ 2 amax ðtÞ ¼ a exp
0:5 ; (11) g where a = 0.68  2.2, b = 43.3  1.2, g = 0.73  0.05 and the coefficient of determination r2 = 0.75. In fitting the curve, it was assumed that immediately following transplanting, the roots would not absorb nitrogen because of transplanting shock and the rate parameter kh and amax would both be zero at t = 0. The value of kh estimated for each day for the growing season is shown in Fig. 2b, with the maximum value estimated to be about 0.22 at 43 days after transplanting (DAT). Another approach to modeling the nitrogen balance of the soil can be developed if the gross nitrogen content of the hills (plants) is known throughout the growing season. The nitrogen content of the hill (Nh) on any day is the content on the previous day plus the difference between the nitrogen entering the hill through the roots and the amount lost to the hill that day. Losses of nitrogen through root exudation or in gaseous form from the hill were smaller than the measurement errors in the experiments of Sheehy et al. (2004a,b) and are not included in these calculations. The equation of mass continuity can be written for the hill as: dNh ¼ Rh
Rhl ; (12) dt where Rhl is the rate of loss of nitrogen through death and detachment. A gross nitrogen accumulation curve

Fig. 2. (a) The maximum fractional uptake of 15N (amax) from a known amount delivered using a point-placement technique. The line was the curve fitted, amax(t) = a exp (
0.5(ln (t/b)/g)2), r2 = 0.75, to the data (*) which are shown as mean and standard error (n = 6). (b) The value of the rate parameter (kh) used for describing the daily uptake of nitrogen by the roots during the growing season.

can be generated from a sequence of measurements of the nitrogen contents of the hills and the losses of nitrogen through death and detachment determined using 15N (Sheehy et al., 2004b). The equation used to describe the gross nitrogen content of the hill, Nhg (g hill
1), as a function of time (t) is fitted to the data and in a general form can be written as: Nhg ¼ f ðtÞ:

(13)

A specific form is given later (Eq. (21)). The change in the gross nitrogen content of the hill (dNhg/dt) is equal to the uptake of nitrogen from the soil pool, where dNhg ¼ kh Qs ðtÞ: dt

(14)

J.E. Sheehy et al. / Field Crops Research 94 (2005) 54–66

Rearranging Eq. (14), the quantity of freely-available nitrogen in the soil is given as:    dNhg 1 Qs ðtÞ ¼ : (15) kh dt Substituting the value for kh from Eq. (10) in (15) gives the quantity of total nitrogen in the available pool as:     dNhg 1 1 Qs ðtÞ ¼ : (16) kl amax ðtÞ
1 dt To maintain the value of Qs(t) at the optimum value predicted by Eq. (16), we can use the equation of mass continuity (Eq. (8)) to calculate the required input of nitrogen to the pool:   dNhg dQs 1 þ : (17) Rin ðtÞ ¼ amax ðtÞ dt dt where Rin(t) is the quantity of nitrogen, from all sources, entering the pool of available nitrogen so as to maintain the optimum size of the pool. Differentiating Eq. (16) gives:   ( dQs 1 d½ð1=amax ðtÞÞ dNhg ¼ kl dt dt dt )   2 d Nhg 1 þ : (18) amax ðtÞ
1Þ dt2 Substituting for dQs/dt in Eq. (17) allows the rate at which nitrogen must enter the pool surrounding the root to be calculated. 2.2. Calculating the initial quantity of nitrogen (Q0) The initial values for the nitrogen content of the plants and amax resulting from the curve-fitting procedures are very small and generally are not important. However, when ratios of such values are computed, as in Eqs. (16) and (17), large errors can be generated. Unfortunately, in field experiments, few or no data are usually collected during the first 7–10 days following transplanting. After transplanting, rice plants suffer shock and assumptions have to be made concerning the initial conditions for the model, otherwise the first values predicted for Qs can be unrealistic. The soil is not in a steady state between rice cultivations, but the order of magnitude of Qs in the absence of plants can be calculated. For such conditions the equation of mass continuity for the soil N pool (Qs) can be written as:

59

dQs ¼ Fi
kl Qs ; (19) dt where Fi is the rate at which nitrogen enters the pool and kl is the rate constant for loss from the pool. If Fi and kl are assumed to be constants then the steady state value of Qs, obtained by integrating Eq. (19), is: ½Fi
ðFi
kl Q0 Þexp ð
kl tÞ ; (20) kl where Q0 is the initial value of nitrogen in the soil and as t ! 1, Qs ! Fi/kl. Dobermann et al. (2003) in an Asia-wide experiment observed crop nitrogen contents ranging from 7 to 130 kg N ha
1. For unfertilized soils in the Philippines, the typical dry season yield of biomass for a 100-day growing season in the absence of fertilizer nitrogen can range from 5 to 10 t ha
1 and the nitrogen absorbed by the crops can range from about 35 to 100 kg N ha
1 (Cassman et al., 1993). If losses of nitrogen were equal to the uptake of nitrogen, the nitrogen supplied from indigenous and other environmental sources (replenished by biological nitrogen fixation over the year and the recycling of crop residues) would range from 100 to 200 kg N ha
1. We adopted a value at the low end of this range, 125 kg N ha
1. Consequently, a typical value for Fi would be about 5.0 mg N hill
1 day
1 and Qs would be about 48 mg N hill
1, for a value of the rate constant kl equal to 0.105 day
1. The value for the initial quantity of plant-available nitrogen in the soil the day before transplanting was therefore, assumed to be 48 mg N hill
1 (12 kg N ha
1), and fertilizer nitrogen was added to this quantity.

Qs ¼

2.3. Model runs We used the model to quantify the uptake and loss of nitrogen by a rice crop with 300 kg N ha
1 applied as fertilizer, which is the amount necessary to achieve high yields with adequate protein content. There were eight runs of the model with the fertilizer divided equally between different numbers of occasions (splits) during the 100-day crop duration. The number of splits was 3, 5, 10, 13, 15, 20, 50 or 100, starting on the day before transplanting. The three splits were applied at the conventional times, i.e. day before transplanting (
1 DAT), about 10 days before panicle initiation (30 DAT) and the start of flowering (60

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DAT). Other splits were applied at equal intervals from transplanting, e.g. for five splits, 60 kg N ha
1 was applied the day before transplanting and at 20, 40, 60 and 80 DAT. The calculations were made using Eq. (9) and the values of Q0 and Fi described above. The sensitivity of the predictions to the values of the rate parameters, kh and kl, was examined. Varying them independently affects amax (Eq. (5)) but they can also be varied so that amax remains constant, although that has little effect on the model predictions. Two sensitivity analyses were made: (1) halving kl while keeping kh unchanged (for all the fertilizer splits), and (2) increasing kh by 50% and keeping kl unchanged (for the 15-split treatment). The first analysis corresponded to the net loss of 14N being apparently less than net loss of 15N owing to the isotopic composition of the soil pools. The second analysis simulated the effects of a larger or more efficient root system in the best split treatment. We made further runs of the model to simulate use of slow-release fertilizers. Shoji and Gandeza (1992) showed the nitrogen dissolution rate from a delayed release POC-urea fertilizer in water at 25 8C; it had a 100-day release period (POC-urea-S100). The same calculations as above were made for 300 kg N ha
1 from a slow-release fertilizer based on the release pattern of POC-urea-S100, and from the pattern of an ‘ideal-release’ fertilizer (Fig. 3). The ‘ideal’ pattern of release was shaped to the temporal pattern of kh.

Fig. 3. The daily amounts of nitrogen released by a slow-release fertilizer (Shoji and Gandeza, 1992) (– –), and for an ‘‘ideal’’ fertilizer (- - -) calculated from the temporal distribution of the kh values.

Next, we took a different approach and used Eqs. (16–18) to calculate the quantity of nitrogen in the available soil pool and the daily rate of input necessary to maintain that quantity at its optimum value for a desired rate of uptake by the plant. Again, the data of Sheehy et al. (2004b) were used to describe the gross nitrogen content of the average hill, Nhg, in g hill
1 as a function of time (t): Nhg ¼

a ; ð1 þ ðt=bÞc Þ

(21)

where the parameter values were a = 1.35  0.05 g hill
1, b = 47.23  1.45 day, c =
3.36  0.20. Differentiating Eq. (21) gives the desired gross daily rate of nitrogen uptake, dNhg/dt.

3. Results 3.1. Comparing predictions with observations Peng and Cassman (1998) compared rates of nitrogen uptake by irrigated rice crops given various nitrogen treatments. They applied no basal nitrogen, but different quantities of nitrogen at mid-tillering (21 DAT), panicle initiation (42 DAT) and flowering (72 DAT) broadcast into the ricefield floodwater, and measured the uptake of nitrogen in the crop. To evaluate the performance of the model, Eq. (9) was used to predict the uptake of nitrogen from their treatments using the values of kh and kl calculated in this paper and the results are shown in Fig. 4. Initially, the model overestimated the nitrogen taken up following the application at 21 DAT, probably because the rate parameters used are calculated for a root system supplied with adequate nitrogen during early growth. The change in the predicted rate of absorption, following the simulated application of nitrogen, closely resembles that observed experimentally by Peng and Cassman (1998). They reported absorption rates of 9.4 kg N ha
1 day
1 for the 4 days following the application of 100 kg N ha
1 at panicle initiation and the rate estimated here for the 4 days following panicle initiation is 9.2 kg N ha
1 d
1. Given that the model was not ‘calibrated’ in any way, the agreement between predictions and observations suggests that the magnitudes of the 15N rate parameters were appropriate for 14N.

J.E. Sheehy et al. / Field Crops Research 94 (2005) 54–66

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Fig. 4. A comparison between the predictions of the model (lines) and measured uptake of nitrogen by irrigated rice for the three different nitrogen treatments used by Peng and Cassman (1998). The first treatment (~) was 100, 100, 40 kg N ha
1, the second (*) was 100, 50, 40 kg N ha
1, and the third (*) was 100, 0, 40 kg N ha
1. The first application was made on 21 DAT (A1), the second on 42 DAT (A2) and the third on 72 DAT (A3).

3.2. Model predictions The losses of nitrogen from the system declined from 230 to 215 kg N ha
1 as the number of splits increased (Fig. 5a). The uptake of nitrogen increased from 190 kg N ha
1 for the 3-splits to 208 kg N ha
1 for the 15-splits and then declined to 203 kg N ha
1 for the 100-splits (Fig. 5a). The sum of the total uptake by the plant and the total lost are always less than the total amount of nitrogen available (437 kg N ha
1: 12 kg N ha
1 initial value, 125 kg N ha
1 from the soil and 300 kg N ha
1 fertilizer). This is because different amounts of nitrogen are left in the soil pool after harvest in each of the treatments. When the value of kl was halved while keeping kh unchanged, the losses of nitrogen from the system declined from 172 to 152 kg N ha
1 as the number of splits increased (Fig. 5b). The uptake of nitrogen increased from 262 kg N ha
1 for the 3-splits to 278 kg N ha
1 for the 15-splits and then declined to 269 kg N ha
1 for the 100-splits. The effect of decreasing kl was to reduce the losses from 52 to 37% and to increase the uptake from about 48 to 63%; the maximum value of amax increased by 19%. The second sensitivity analysis was conducted for the 15split treatment only. The effect of increasing kh by 50% was to reduce the losses by 16% and to increase

Fig. 5. The predicted loss and uptake of nitrogen from the available soil pool for eight different ways of splitting 300 kg N ha
1 of fertilizer. The amount applied for any split is equal to 300 kg N ha
1 divided by the number of splits in a particular treatment, e.g. for 3 splits 100 kg N ha
1 are applied in each split. The soil supplied 137 kg N ha
1: 12 kg N ha
1 present in the soil at transplanting and 125 kg N ha
1 during the 100 days of crop duration. (a) Main runs of the model, with kh as in Fig. 2b and kl = 0.105 d
1. (b) Sensitivity analysis, with kh unchanged but kl = 0.0525 d
1.

the uptake by 17%; the maximum value of amax increased by 12%. A comparison between the patterns of nitrogen uptake and loss from the 3-split, 15-split, slow-release and ‘ideal-release’ systems is shown in Fig. 6. The ‘ideal-release’ system loses less (190 kg N ha
1) than the other systems (Fig. 5a) and enables a greater uptake (235 kg N ha
1). When calculating the quantity of nitrogen in the available soil pool to maintain an optimum value for the plant (Eqs. (16–18)), the model predicted negative inputs of nitrogen for the first 10 days and extremely large quantities of soil nitrogen ( 400 mg N hill
1).

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38 DAT. On that day, the quantity of nitrogen around the roots is predicted to be 123 mg N hill
1, the rate of loss to be 13 mg N hill
1 day
1 and the rate of uptake by the hill attains its maximum value of 26 mg N hill
1 day
1.

4. Discussion

Fig. 6. The predicted loss and uptake of nitrogen from the available soil pool for a total of 300 kg N ha
1 delivered as 3-splits, 15-splits, as a slow-release fertilizer or as a controlled-release fertilizer with ideal distribution. The soil supplied 137 kg N ha
1: 12 kg N ha
1 present in the soil at transplanting and 125 kg N ha
1 during the 100 days of crop duration.

This was a consequence of the estimates of Rin and Qs being based on ratios of very small values of kh and dNhg/ dt each obtained from curves fitted to data for 10 DAT onwards, i.e. from extrapolation outside the range of the data. After 10 DAT, where the results were not affected by these anomalies, it appeared that the ideal quantity of nitrogen fell throughout the growth duration and that inputs had to follow the temporal pattern of kh (Fig. 7). The model predicted that to maintain the optimum quantity of nitrogen around the roots to enable maximum growth, the maximum daily rate of nitrogen input from all sources reaches 37 mg N hill
1 day
1 at

Fig. 7. The predicted ideal quantity of nitrogen (- - -) in the available soil pool (Qs), and the accompanying rate of nitrogen input (Rin) to that pool (—) for a crop nitrogen uptake defined by Eq. (21).

The model predicted qualitatively and quantitatively the observations of nitrogen uptake observed by Peng and Cassman (1998) following the second application of three rates of nitrogen fertilizer at panicle initiation (Fig. 4). However, the model overpredicted the observed uptake of nitrogen earlier in the experiment, following the first application of nitrogen at 21 DAT. Consequently, during the first 15 days of the simulation, the values of kh used in the calculations must have been larger than the actual values in the experiments. This is not an unreasonable conclusion because, in contrast to the experiments in which kh was determined, no nitrogen was applied by Peng and Cassman (1998) before transplanting in their experiments. Moreover, loss through volatilization is important during early crop development, but less so as the crop canopy cover increases (Kirk, 2004). If the loss parameter kl was under-estimated by the 15N method, partly because kl was assumed to be a constant, then over-prediction of nitrogen uptake could occur early in crop development. The model was used to simulate the consequences of dividing an overall input of 300 kg N ha
1 of fertilizer into equal amounts delivered at uniformly spaced intervals (splits). The loss of nitrogen decreased asymptotically as the number of splits into which the fertilizer was divided increased (Fig. 5a and b). The uptake of nitrogen increased from 3-splits to 15-splits and then decreased as the number of splits increased further (Fig. 5a and b). In the 3-split system, half of the total loss of nitrogen has occurred in the first 29 days after transplanting, before the second split was applied. Reducing the value of kl by 50% increased simulated uptake from about 48 to 63% and reduced losses from about 51 to 37%. Smaller values of kl may be appropriate for certain soils. In addition, we suggest from this result that values for the uptake and loss of total nitrogen would indicate whether the kl derived from 15N measurements was appropriate for use in calculations of 14N use.

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Slow-release fertilizers deliver nitrogen continuously (Fig. 3), however, the calculations show that the nitrogen released is subject to the same processes governing loss as any other nitrogen in the root environment (Fig. 6). It is clear that matching what is required with what can be supplied requires knowledge of the ideal quantities in the available soil pool to support maximum growth. The model suggested that an ideal fertilizer would have a release pattern that matches the root uptake parameter and would release an amount that would optimize the uptake process. The results shown in Fig. 7 give an indication of the required pattern and amount, but Eqs. (16) and (17) of the model were unable to provide predictions for the first 10 days following transplanting. Nonetheless, using the values of kh and its temporal pattern, the model predicted that an ‘ideal’ fertilizer would reduce losses to a minimum and maximize uptake (Fig. 6). The ‘ideal’ fertilizer resulted in a predicted absorption of 53% of the total nitrogen (soil plus fertilizer) available to it whereas the least effective system (3splits) resulted in a predicted 44% absorption. The much greater cost of controlled-release fertilizers makes it unlikely that poor farmers in Asia would adopt such an ‘ideal’ fertilizer. It is often thought that the optimum quantity of nitrogen required for maximum growth is a function of the activity of the roots and the uptake rate of the crop (Eq. (16)). However, that nitrogen is also subject to the ever-present biophysical processes governing losses of nitrogen. Fertilizer applied to the crop must meet the crop demands for nitrogen, but also it inevitably fuels proportional losses. Much of the nitrogen supplied by the soil is lost as well. For all of the model runs considered here, with 137 kg N ha
1 in total supplied by the soil, approximately 44% is taken up by the crop, 52% is lost and 4% remains in the soil. The model shows that inputs of nitrogen during the periods when kh is relatively small, close to transplanting and maturity, are largely lost to the crop. Paradoxically, the predictions from Eqs. (16–18) suggest that high concentrations are required during the 10 days following transplanting to ensure early uptake of nitrogen when the value of kh is low. The equations suggested that both the rate of uptake and the quantity of nitrogen in the available soil pool decrease soon after panicle initiation. The rate of nitrogen uptake and the uptake parameter per unit root weight decline

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Fig. 8. Root weight of the irrigated crop (circles and bars are mean and standard error (n = 4), the data and line (y = a/(1+(x/b)c)) are from Mnzava and co-workers (2002); the daily value of the rate parameter (kh) for nitrogen uptake per unit root weight (—); and the daily rate of nitrogen uptake per unit root weight (- - -); all values are normalized.

rapidly from about the time of panicle initiation (Fig. 8) and root weight does not increase significantly after flowering. The results suggest that the rate parameter kh and the uptake of nitrogen per unit root weight are largely independent of root age until panicle initiation. The importance of maximizing yield through removing nitrogen limitations and preventing large losses of nitrogen into the environment appear to be irreconcilable goals during the first 10 days following transplanting. However, the work of Wang et al. (1993a,b) suggests that the nitrogen uptake parameter is inversely correlated with plant nitrogen status. Consequently, it may be possible to capture the required nitrogen from lower concentrations in the soil following transplanting, but that possibility needs investigating during the period of early growth. The consequences of a non-linear relationship between uptake and the external concentration of nitrogen could be explored using a Michaelis–Menten relationship (Wang et al., 1993b). However, that would require a more complex and information-rich model. In contrast, the model presented here is very simple and avoids the necessity to characterize the size of the roots and the variations in uptake capacity per unit area or weight, associated with the age profile of the roots. Neither does it involve considerations of the interactions between the soil particles, the available soil pool and the fertilizer nitrogen; all of those factors combine to produce the observed values of kl and kh.

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Table 2 Values for the total nitrogen (N) uptake, grain yield, relative efficiency of fertilizer nitrogen uptake and efficiency of uptake of combined soil and fertilizer nitrogen, for different amounts of fertilizer applied to the crop Total applied fertilizer N (kg ha
1)

Total N uptake (kg ha
1)

Grain yield (t ha
1, 14% mc)

Relative efficiency (%)

Total efficiency (%)

0 50 100 200 300 400

55.0 95.0 110.0 170.0 210.0 240.0

4.8 6.1 6.9 8.4 9.8 9.7

na 80 55 58 52 46

40 51 46 50 48 45

The experiment was conducted by Wopereis et al. (1994) in the dry season at Los Ban˜ os in the Philippines. The nitrogen was divided into seven equal applications and applied at approximately 0, 14, 21, 40, 50, 60, and 67 DAT. For the calculation of total efficiency, we assumed the soil N supply was 137 kg N ha
1.

Further work will be necessary to investigate if those parameters vary between different soil types (Purakayastha et al., 1997). Another difficulty in modeling nitrogen uptake arises from the uncertainties relating to the intrinsic capacity of the soil to supply nitrogen. The invention of some simple, direct way of measuring that supply would be of great assistance in improving the management of nitrogen in irrigated rice.

5. Conclusions The hypothesis that losses of fertilizer nitrogen from high-yielding irrigated rice could be almost eliminated by delivering the nitrogen required to support growth at the right time and in the precise quantity was demonstrated to be false. The timing of fertilizer applications has been the subject of much research. It is clear that providing fertilizer to the crop as one initial or a few spread out applications will lead to large losses since the crop cannot take up all the fertilizer available in a short space of time. In the case of nitrogen in particular, the fertilizer does not remain in the soil, unaltered, awaiting uptake by the plant, but is available to other organisms and to physical and chemical processes which result in losses of availability and losses from the rooting zone. It seems obvious that applying the same total amount of fertilizer as numerous, small applications spaced out throughout the crop duration ought to reduce losses greatly, and, in the limit, reduce losses to a negligible amount if the applications were exactly matched to crop needs using a controlled-release fertilizer.

Recovery of fertilizer nitrogen in the crop should then approach 100%. Counter to intuition, the practicable limit to recovery of fertilizer nitrogen is not close to 100%, but a much lower value: 57% in this analysis (the relative efficiency). This arises because it is necessary to have a certain concentration of nitrogen in the available soil pool from which the crop can take up the nitrogen it needs, governed by the rate parameter kh. Concurrently, the available soil pool will lose nitrogen, at a rate controlled by the rate parameter for loss, kl. The efficiency of recovery of soil and fertilizer nitrogen combined is 53%; the efficiency of recovery of soil nitrogen was 44%. Using the experimental data of Wopereis et al. (1994) for a multiple nitrogen split system and different amounts of fertilizer it can be shown that relative efficiency declines from 80 to 46% with increasing yield (Table 2). Although the model greatly simplifies all the nitrogen transformations in the system, the rate parameters were derived from experiments; albeit subject to the imperfections arising from differences between the various fates of 15N and 14N. Furthermore, even with a 50% increase in kh or a decrease of 50% in kl, uptake of total available nitrogen in the most efficient 15-split system was 57 and 64%. The robustness of the conclusion, that fertilizer recovery rates will never approach 100%, even with a perfect controlled-release fertilizer, will need to be tested with other models and other rate parameters obtained from experiments. One general implication of these findings, as fertilizer use increases to provide higher yielding crops, is the fate of the nitrogen not recovered by the

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crop. Losses to the atmosphere may be short-term (ammonia distributed across the landscape by dry and wet deposition) or long-term (from denitrification, as nitrous oxide, a powerful greenhouse gas, or as nitrogen gas). Losses of nitrate in run-off can produce eutrophication in aquatic ecosystems and losses to groundwater may reduce the quality of water for human use. Replacing fertilizer nitrogen by biologically-fixed nitrogen, via a suitable symbiosis, would seem to be the only way of significantly reducing losses of nitrogen during growth. There is a carbon cost associated with biological nitrogen fixation (Witty et al., 1983), but its impact on yield in the field can be negligible (Sheehy et al., 1991). Progress towards biological nitrogen fixation in rice is slow at present (Dixon et al., 2000; Fischer, 2000; de Bruijin et al., 1995) and it is hoped that the results presented in this paper will encourage more research in that area.

Acknowledgements For the painstaking gathering of data used in this paper we are grateful to Paquito Pablico, Moses Mnzava and Abigail Elmido.

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