SSSAJ Grow Your Career with SSSA
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (4)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Agricola
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Related Collections
Right arrow Soil Fertility and Productivity
Right arrow Soil Models
Right arrow Phosphorus
Published in Soil Sci. Soc. Am. J. 68:644-653 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

DIVISION S-8—NUTRIENT MANAGEMENT & SOIL & PLANT ANALYSIS

Predictive Mechanistic Model of Soil Phosphorus Dynamics with Readily Available Inputs

T. V. Karpinetsa, D. J. Greenwoodb and J. T. Ammons*,c

a Dep. of Agrochemistry, All-Russian Institute of Agriculture and Protection of Soil from Erosion, Karl Marks Str., 70-b, Kursk, Russia, 305040
b Horticulture Research International, Wellesbourne, Warwick, CV35 9EF UK
c Dep. of Biosystems Engineering and Environmental Science, Univ. of Tennessee, 2505 E.J. Chapman Drive, Knoxville, TN 37996-4531

* Corresponding author (ammonst{at}utk.edu).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Fertilizer and manure P applications together with cropping practices can have a lasting effect on soil fertility and can result in pollution of waterways. This study was aimed at providing a general model for the long-term changes in soil P extracted with conventional tests. The model maintains three active pools of soil P: extractable soil P (X), absorbed P that is not extractable but interchanges reversibly with X (Y), and mineral P that provides solubility-product type buffering of X (Pbuffer). There is also an input for the net P addition. Equations derived from the model define most of the published patterns of response of X found in long-term field experiments. They underpin a dynamic version of the model that permits annual inputs and calculates the time-course of the various P pools. A method was devised for calibrating the dynamic version from measurements that are usually made in long-term experiments. Models calibrated in this way gave good fits to the data from six soils from four countries. Values of the coefficients indicated that solubility product buffering had a decisive influence on the P economy of some but not all soils. The model gave predictions of X that were in good agreement with measurements in three long-term experiments that were entirely independent of those used for calibrating the model. Other possible methods of calibration are discussed. The model concisely represents key factors affecting the dynamics of X over the long term and has both interpretative and predictive value.

Abbreviations: K1, rate constant for conversion of X to Y • K2, rate constant for conversion of Y to X • K3, rate constant for conversion X to Pbuffer • K4, rate constant for conversion of Pbuffer to X • Pbalance, net annual addition less removal of P • Pinert, the intercept of the linear relationship between Ytotal and X • Pbuffer, soil P that provides long-term buffering • R, fraction of Pbalance that is added to X • subscript st.art., level of soil P created by fertilizer and manure application • subscript st.st., steady stationary state • X, soil P extracted in conventional tests • Y, unextractable P that interchanges with X • Ytotal, the total amount of all forms of soil P


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
POLLUTION OF SURFACE WATER from movement of agricultural soil P is of public concern. If the soil P status is high, there can be considerable movement of P out of soils into waterways (Sims et al., 1998) where it promotes eutrophication. On the other hand, if the soil P status is low, yields can be suboptimal, and the deficiency may need to be rectified by applying fertilizer or manure. The residual effects of past fertilizer and manure practices on soil P can persist for >50 yr (Russell, 1973). Two other factors are also important; in most of the world subsidies for crop production are being reduced, and there is a trend toward more sustainable systems of crop production. All this emphasizes the need for more efficient use of phosphate and for methods of predicting long-term changes of soil P.

Much effort has been devoted to experiments aimed at understanding, amongst other things, adsorption and desorption of P on soil surfaces, solubility product type reactions, aging of soil minerals, diffusion of P within minerals, immobilization and mineralization during soil organic matter metabolism, dissolution of P from inert soil minerals as a result of root and microbial activities, transport of P through soil to the root surfaces, P uptake by the roots, and the dependence of plant growth on plant P concentrations (Larsen, 1967; Wild, 1988; McGechan and Lewis, 2002). Some of these studies form the basis of mechanistic models for calculating the response of single crops to applications of P over the short term. The degree of agreement between model calculation and experimental measurement has generally been quite good (van Noordwijk et al. 1990; Rengel, 1993; Barber, 1995; Claassen and Steingrobe, 1999; Tinker and Nye, 2000; Greenwood et al., 2001a, 2001b). Other mechanistic models have been developed to calculate P leaching and run off from agricultural soils (Sharpley and Williams, 1990; Shirmohammadi et al., 1998; Schoumans and Groenendijk, 2000).

Few models have been developed to calculate the long-term changes in soil P (Jones et al., 1984, 1991; Bhogal et al., 1996). The model developed by Jones et al. (1984) attracts most attention. It is versatile, has a daily time step and can be used to make predictions over several years. It has been incorporated, essentially unaltered, in other models including EPIC, CREAMS, and GLEAMS (Lewis and McGechan, 2002). While we accept many principles of the model, it has drawbacks. Some of the incorporated equations are based on weak evidence, and difficult-to-obtain inputs are required to run the model. Although model predictions are good for some experiments, our regression analysis (D.J. Greenwood, unpublished data, 2002) reveals no significant correlation (r2 = 0.14) between simulated and measured values of labile P in an example data set consisting of 12 experiments on the U.S. Great Plains soils (Sharpley and Williams, 1990). The possibility exists that a vital process may have been omitted from the model. Thus there is no representation of changes associated with P minerals or solubility product reactions, even though these processes have long been considered to be important (Larsen, 1967). The question arises whether the level of detail in which the various processes are treated is appropriate for the long-term simulation of soil P. Interchange between two pools is governed by a rate coefficient of only 0.1 d–1, which is minute compared with the duration of a long-term experiment. Maybe a less detailed model based on principles that have emerged from long-term experiments such as those described by Johnston and Poulton (1992) could have merit. Mathematical analysis of such a model could account for many key phenomena and reveal the shapes of time-course curves of X and the crucial factors that determine differences. It may also lead to simple quantitative relationships that have predictive value and to an easy-to-use dynamic model for calculating long-term changes in the P economy of soil. This study was aimed at exploring these possibilities through the development of a general model for the long-term changes in soil P extracted with conventional tests.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Model Description
Soil P exists in many different forms or pools, and interactions between them are complex. Their definition in terms law of mass action type processes necessitates a very wide range of rate constants, but the experimental determination of all these constants is exceedingly difficult, if not impossible. Therefore, in the proposed model we consider that active soil P exists in just three pools (Fig. 1) : extractable soil P (X), unextractable but active soil P (Y), and soil P that provides long-term buffering (Pbuffer). In addition to active soil P, the soil also contains inactive soil P, which is very inert and doesn't participate in interchange with X.



View larger version (7K):
[in this window]
[in a new window]
  		Fig. 1. Simplified scheme of P transformations in soil, where X is the extractable soil P, Y is the absorbed P that is not extractable but interchanges reversibly with X, Pbuffer is essentially mineral P that provides solubility-product type buffering of X, Pbalance is the difference between P added as soluble-P fertilizers and manures and that removed as crop P. Pbalance is immediately partitioned between X and Y according to the ratio R. The P flow from X into Y and backward is characterized by rate constants K1 and K2. The P flow from X into Pbuffer and backward is characterized by rate constants K3 and K4.

 
Extractable soil P can be determined by any conventional method, as the model treats different measures similarly. In addition, the model takes account of the annual difference, Pbalance, between the sum of the P added as fertilizer and manure and the removal of P during harvest of the crop. Extractable soil P is the central feature of the model, rather than solution P, because it is much more frequently measured and because equilibration between extractable and solution P is very rapid, at least in terms of the time scale of long-term experiments.

First-order rate equations govern the interchange both between X and Y and between X and Pbuffer. We assume that the gains and losses of Pbuffer are small relative to the amount of P in Pbuffer, so that Pbuffer can be regarded as almost constant. Thus whereas Y is very sensitive to gains and losses from X, Pbuffer provides long-term buffering.

We consider that interchange between X and Pbuffer represents solubility-product reactions; although less emphasis has been given to them in recent years, they must, when equilibrium is established, determine soil solution P concentrations (Larsen, 1967). They are typified by reactions in aqueous suspensions of a major soil P mineral hydroxyapatite. Irrespective of the amount of hydroxyapatite in the suspension, the equilibrium concentration remains the same; even if P is removed or added to the solution its concentration will move to the same equilibrium concentration. Many different solubility-product P reactions occur on different microsites in soil. Soil P that provides long-term buffering represents the average of all these different buffers and other long-term processes, such as the net increase or decrease of X from weathering of minerals and gain of X from a continuing loss of soil organic matter. Although the Pbuffer pool cannot be measured directly, its effects can be measured indirectly from the subsequent theory.

We consider that most reversible P processes responsible for changes in extractable and unextractable P that take place after P addition and withdrawal may be represented by the interchange between X and Y. These processes include adsorption and desorption, reversible reactions on particle surfaces, solid-state diffusion into and out of particles (Barrow, 1983), mineralization and immobilization of P in soil organic matter, a loss of P from the top to the subsoil, and gain of P from the subsoil possibly mediated by plant roots.

The size of the Y pool can be determined quantitatively from the linear relationship between total soil P (Ytotal) and X that occurs when equilibrium is reached in long-term experiments (Thomas, 1964; Mattingly et al., 1970; Johnston and Poulton, 1992):

[1]
where n is the gradient and Pinert is the intercept on the total soil P axis. This equation permits separation of the X and Y pools from Pbuffer. As it is assumed that Pbuffer is virtually independent of X and remains almost constant, we consider that part of Pinert consists of Pbuffer and the remainder of Pinert consists of inactive P, which plays no part in any interchange. Total soil P is the sum of X, Y, and Pinert, so that Y can be defined as

[2]
For each year, the difference between additions and removals of P, Pbalance, is added to soil. The processes that take place after such addition are too complex to be modeled in detail. We therefore consider that a fraction R of the Pbalance is added to X, and the remainder to Y. Depending on the amount of added P and the time scale, R will have a value within the limits 0 < R ≤ 1. After soluble fertilizer P has been incorporated in moist soil, there is, during subsequent incubation at 25°C, an initial phase during which X generally declines rapidly for few days or weeks (Javid and Rowell, 2002). Thereafter X only declines slowly. Eventually the distribution of fertilizer P between X and Y will tend toward that originally in the soil. Thus when we model the long-term affects of Pbalance that is applied only once a year, we consider it is reasonable to assume that Pbalance distributes between X and Y according to the amounts already there. It means that the amount of Pbalance added to the X pool is RPbalance, and to the Y pool is (1 – R) Pbalance where R = X(t)/[X(t)+Y(t)] and (t) indicates at time t. This approximation is supported by the linear relationships found in long-term experiments between X and Pbalance (Barber, 1979; McCollum, 1991; Johnston and Poulton, 1992; Kamprath, 1999) and the proportional relationship between X and Y that follows from the summation of Eq. [1] and [2]. There are, however, circumstances when setting R = 1 (all the added P goes into X) may be more appropriate. An example is in modeling the short-term changes that take place after incorporation of a single heavy application of P fertilizer. The transfer from X to Y under these conditions is also analyzed in terms of the model. No distinction is made in any of the modeling between organic and fertilizer P inputs in view of the similarity of the effects of fertilizer P and farmyard manure P on X found in long-term experiments (Mattingly et al., 1970; Johnston and Poulton, 1992).

The model is concerned with changes in P pools in the surface layer, usually 15 to 30 cm, of arable soils, from which crop roots generally extract most of their P. We define rate of change in terms of first-order rate coefficients according to the Fig. 1. Over the time interval {Delta}t, the increase in X, {Delta}X, and the increase in Y, {Delta}Y, can be represented by

[3]

[4]

Below we use these equations: (i) to reveal the relationships for calibrating the rate coefficients K1, K2, K3, and K4 from the results of long-term trials; (ii) to elucidate the patterns change in X following a single heavy application of P fertilizer; and (iii) to obtain an algorithm for calculation the annual soil P dynamics.

Relationships for Calibration of Rate Coefficients from the Results of Long-Term Trials
A possible way of calibrating the rate coefficients in the model is to consider the stationary states of P in soil. Inspection of Eq. [3] and [4] reveals that a stationary state, in which {Delta}X/{Delta}t = {Delta}Y/{Delta}t = 0, can occur in two different ways depending on Pbalance. When Pbalance is 0, as can occur in fallow soils or under climax vegetation, there is neither a net input nor removal of P. After equilibrium is established, we consider the corresponding stationary state to be the steady-stationary state. If fertilizer P is added to soil at a constant rate over a long period, then according to Eq. [3] and [4] there are an infinite number of stationary states depending on the values of Pbalance. The equilibria that are reached when Pbalance!=0 are regarded as pseudo-equilibria. Levels of extractable P that are reached with different values Pbalance in long-term trials, when equilibrium has been reached, provide a basis for calibrating rate coefficients from measurements usually made in long-term field experiments.

Steady-State Equilibrium, Pbalance = 0
At this steady state, termed the steady stationary state, X = Xst.art. and Y = Yst.art., so that from Eq. [3] and [4], when Pbalance = 0, {Delta}X(t)/{Delta}t = 0 and {Delta}Y(t)/{Delta}t = 0

[5]

[6]
The last equation permits the calculation of the relationship between Xst.st. and Yst.st. as a function of the rate constants K1 and K2

[7]
By adding Eq. [5] and [6], we define Pbuffer as a function of Xst.st. and rate constants K3 and K4.


[8]
If Eq. [8] is taken into account, we may rewrite Eq. [3] as

[9]
The term (K4Pbuffer) in this equation is replaced with (K3Xst.st.) which facilitates calibration as parameter Xst.st. can be readily measured whereas K4 cannot.

Pseudo-Equilibriums Pbalance != 0
When Pbalance is not 0 (positive or negative) then some stationary artificially created level of extractable and unextractable soil P forms (Xst.art. and Yst.art.) may be maintained by P fertilization. At this stationary state X = Xst.art and Y = Yst.art.

Adding Eq. [3] and [4], when {Delta}X(t)/{Delta}t = 0, {Delta}Y(t)/{Delta}t = 0 and Pbalance != 0, gives

[10]
or

[11]
Substitution of Pbuffer of Eq. [8] in Eq. [11] gives

[12]
This equation gives the value of X that may be maintained by an annual P balance,

[13]

Equation [7] and the linear relationship between Ytotal and X (Eq. [1]) permit the rate constants K1, K2, K3, and Xst.st. to be calibrated from measurements made on long-term field experiments by a procedure that will be described in the Calibration section.

Short-Term Changes in Extractable Soil Phosphorus Following a Single Heavy Application of Phosphorus Fertilizer
The short-term changes in X that take place following the application of P fertilizer can be analyzed in terms of the model. The period for which such analysis applies will be increased by application of high rates of fertilizer and by factors such as drought and low temperatures that impede chemical reactions between fertilizer and soil. The amount of X in most soils is many times less than that of Y. Thus, immediately after incorporation of fertilizer, there is a considerable increase in X relative to the amount already there, whereas the increase in Y relative to the amount there will be negligible. It is therefore reasonable to make the approximation that in the short-term Y remains at its initial value. On this basis, an approximate relationship for the kinetics of change in X after such perturbation may be derived from the Eq. [3] and [4].

First consider a soil at its stationary state and that the levels of extractable and unextractable soil P are Xst.st. and Yst.st., respectively. Suppose also that the soil is fallow (i.e., Pbalance = 0), then it follows from Eq. [3] that

[14]
If an amount of fertilizer P, m, is incorporated into this soil and all the m is immediately converted into X, substitution in Eq. [3] gives

[15]
Subtraction of Eq. [14] from Eq. [15] gives:

[16]
Integration with the boundary condition that m = Mo when t = 0 gives

[17]
Equation [17] predicts that, after the addition of P, its extractable amount should decline in a negative exponential manner.

As m = X – Xst.st., it follows from Eq. [16] that

[18]
This equation predicts that there is a linear relationship between the initial level of X after large P fertilization and the fall in that level over any time interval. The growth and harvest of crops should seldom affect the nature of the relationships because, over wide range of values of X, P uptake would generally be expected to be either constant or approximately linearly related to X. This is because, as a close approximation, crop P uptake is related to X by a split leg function consisting of two straight lines, one of which has a positive gradient while the other is almost horizontal. Only at the intersection between the two lines should the Eq. [18] fail, because it is only then that P uptake is neither constant nor linearly related to X.

Algorithm for the Calculation of the Annual Soil Phosphorus Dynamics
This algorithm is concerned with calculating long-term changes in X and Y that occur following additions of Pbalance made only once a year. For the previously described reasons we consider that, for these conditions, the algorithm can best take account of the added P by assuming that it is distributed between X and Y in proportion to the amounts already there. An exact solution of Eq. [3] and [4] cannot be obtained because of interactions between {Delta}X/{Delta}t and {Delta}Y/{Delta}t. But we may develop a dynamic model that updates the levels of X and Y for each year from the annual balance of P, {Delta} Pbalance, by adapting Eq. [4] and [9] to give

[19]

[20]

[21]

[22]

[23]

[24]

[25]

To run this dynamic model the following inputs are needed; initial values of X and Y, annual values of Pbalance, and values characteristic of the soil, namely K1, K2, K3, and Xst.st. The initial value of Y is preferably measured, but may be calculated, as will be described in the calibration section. The above sequence of calculations was repeated with a time step of 1 yr except for USA data where the time step was 0.5 yr. Shorter time steps had little effect on the simulated values of X.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Experiments Used to Develop the Model
Most of the essential features of 14 long-term experiments and data sets and the sources of the information are given in Table 1. The results of the experiments were used to calibrate and test the validity of the model, to check model predictions of the dynamic patterns of X following P fertilization and to provide estimates of the model coefficients characterizing soil P processes in different soils. Other features of the experiments are described below.


View this table:
[in this window]
[in a new window]
  		Table 1. Experimental codes and soil properties.

 
Russian and Ukrainian Experiments
Data from the Nosko experiment were used to calibrate the model, and data from the Brovkin and Barshtein experiments were used to test its validity. In the Nosko experiment the same 32 N, P, K fertilizer treatments were incorporated in soil for each of 24 yr with a crop rotation of sugarbeet (Beta vulgaris L.) and cereals. The Brovkin and Barshtein experiments lasted for 12 and 10 yr and included 17 and 13 different fertilizer treatments, respectively. In every case the active depth of soil was considered to be 30 cm, and Pbalance for each year was assumed to be the average over the entire period of the experiment. The Kasitski microfield experiment was used to test the predicted proportional relationship between the decline of X and its initial value. Initially, 13 different levels of X were created by fertilizer applications. For each of the subsequent 7 yr no P was applied, and some plots were cropped while others were left fallow. Each year measurements were made of X and removal of crop P.

Experiments in Southeast Asia (Phillippines and Indonesia)
The data from the Sitiung experiment were used to calibrate the model, which was tested against data from the Matalom experiment. Both experiments were on acid soils that typify upland farming in Southeast Asia. At Sitiung, zero and four levels of fertilizer P were incorporated in soil for each of two upland rice (Oryza sativa L.) and one soybean crop over a period of 3 yr. The Matalom experiment was identical with that at Sitiung with the exception that there were two soybean crops.

United Kingdom Experiments
The first period of the Saxmundham experiment, referred to as Saxmundham 1, lasted from 1899 until 1964, during which there were eight treatments consisting of different levels of farmyard manure and N and P fertilizers on a four-course rotation. At the end of this period soil samples were taken for analysis. The treatments were then changed for an intermediary period of 5 yr, after which the experiment was modified again and is referred to as Saxmundham 2. There were eight levels of X residual from past treatments, and the site was continuously cropped while no P was applied. Over the subsequent 15-yr crop removals were measured and soil samples taken and analyzed each alternate year. The Ropsley experiment was superimposed on plots of an earlier phase of the experiment that had received either no or different levels of P during cropping from 1978 until 1985. From 1986 until 1996, the treatments consisted of all combinations of the residual effects of these treatments and annual applications of 0, 31, and 44 kg P ha–1. The soil was cropped continuously with winter wheat (Triticum aestivum L.). The amounts of Pbalance and X were measured each year. The relevant treatments of the Wick experiment consisted of incorporating eight levels of fertilizer P supplying between 0 and 3500 kg P ha–1 2.5 yr before the experiment began to allow equilibration. Measurements of X were made then and 351 d later, during which time removal of P from the soil was negligible.

United States of America Experiments
Relevant treatments of the Norfolk experiment were 0, 10, 20, and 40 kg P ha–1 yr–1 applied as superphosphate from 1975 to 1985 followed by no application from 1986 to 1992. Corn (Zea mays L.) and soybean (Glycine max L.) were grown in alternate years from 1975 to 1992. Detailed soil analyses were performed on samples taken in 1975, 1985, and 1992. In our work, total soil P was assumed to be the separate total referred to by Schmidt et al. (1996). The first part of the experiment, from 1975 to 1985, is referred to as Norfolk 1 and the second part as Norfolk 2. In the Davidson experiment, the treatments and data collection were identical with the Norfolk 1. The first part of the experiment is referred to as Davidson 1 and the second part as Davidson 2.

Calibration of the Model
The procedure, with few minor differences in detail described below, was the same for all sites. When the soil had been cropped for many years with the same or no application of fertilizer P, an excellent linear relationship was always found between Ytotal and X (Eq. [1]). The intercept on the y-axis was taken as Yinert so that (Ytotal – X – Yinert) is equal to Y. The gradient of Y against X was considered equal to K1/K2 by analogy with Eq. [7], and, if Y had not been measured, the initial value of Y was calculated by multiplying the initial value of X by the gradient K1/K2. This was regarded as a reasonable procedure because, although this equation strictly only applies when Pbalance = 0, the gradient was found experimentally to be constant over a wide range of values of X and thus of Pbalance; there is therefore no reason to believe that it changes when Pbalance = 0. As Xst.st. indicates the X when there is neither input nor removal of P, we estimated X st.st. as the intercept on the X-axis of the linear relationships between X and Pbalance found in long-term experiments.

A strong interaction exists between the effects of K1 and K3 on X, so a special procedure was devised to provide best estimates of the two coefficients. First, with K3 set to zero, the dynamic model (i.e., Eq. [19] through [25]) was run with different values of K1, and the range of values were identified that gave the minimum sum of squares between simulated and measured X. The mean of this range was used for the next step, unless a very wide range of values gave equally good fits, in which case K1 was taken to be one. Using the value of K1 calculated in this way, the model was run again and the (measured X – simulated X) was regressed against simulated X. The gradient was taken to be the provisional estimate of K3, and the 95% confidence limits were noted. Finally, the model was run with values of K3 varying between the confidence limits, and of K1 varying in the range that was identified with K3 set to zero, or between 0 and 3 yr–1, if a very wide range of values gave equally good fits. The values were determined that minimized the sum of squares between simulated and measured X subject to K1 > K3. There was always a well-defined minimum. The validity of the procedure was justified by determining K1 and K3 on data that had previously been generated by the model with known values of the two coefficients.

Data from Saxmundham1 were used to calculate K1/K2 and Xst.st.., and the values of K1 and K3 were obtained by fitting to the Saxmundham2 data. The data from the Norfolk1 experiment was used to calculate K1/K2 and Xst.st., but K1 and K3 were obtained by fitting to the entire data set of Norfolk1 and Norfolk2 experiments. The parameters for Davidson were obtained in a manner similar to that used for the Norfolk data.

To provide a test of the overall reliability of the fitting procedure, we regressed the measured values of X against the values simulated with the model using the parameter values determined as described above (Table 2). As is required for perfect fits, the values of the intercept were not significantly different (P < 0.05) from zero and the gradient not significantly different (P < 0.05) from one for any of the six data sets. Four of the values of r2 exceeded 0.90, and in the other two cases they exceeded 0.74.


View this table:
[in this window]
[in a new window]
  		Table 2. Relationship between the measured and simulated values of extractable soil P.

 

   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Comparison Between Measured and Predicted Values of Extractable Soil Phosphorus
Excellent agreement was found between the measured values of X in the Brovkin and Barshtein experiments and those predicted by the dynamic model (Fig. 2a,b) . For this purpose the model had been calibrated with entirely independent data from the Nosko experiment. Likewise, with the exception of one point, there was good agreement between measured and predicted values of extractable P measured at Matalom (Fig. 2c). For this purpose the model was calibrated with data from an entirely independent experiment at Sitiung. The model, however, gave a poor prediction of the highest level of extractable soil P, probably because the level of applied P was very high, and thus the equilibrium was not reached.



View larger version (13K):
[in this window]
[in a new window]
  		Fig. 2. Comparisons between measured and predicted values of extractable soil P (X) for Brovkin (A), Barshtein (B) and Matalom (C) experiments. Predictions of A and B were with the model after it had been calibrated with data from the Nosko experiment and for C, after the model had been calibrated with the Sitiung experiment. Lines are those for perfect agreement.

 
Test of Model Predictions of Dynamic Patterns in Extractable Soil Phosphorus Following Phosphorus Fertilization
The Wick and Kasitski experiments had a series of plots that initially had different levels of X and were then either left fallow or cropped, during which X fell. According to Eq. [18] the fall over any period, {Delta}m/{Delta}t, should be linearly related to the initial value of X. Figure 3 shows that a linear relationship fitted each of the data sets, whether the soil was left fallow or was cropped, and thus supported the theory. Similar support was provided by the Saxmundham 2 experiment. In addition, the time course of the decline in X for eight separate treatments was accurately calculated by the dynamic version of the model (Fig. 4) despite the coefficients, Xst.st. and K1/K2, having been derived from data obtained in an earlier experiment.



View larger version (16K):
[in this window]
[in a new window]
  		Fig. 3. Relationships between the rate of changes in extractable soil P ({Delta}m/{Delta}t) and the initial levels of extractable soil P (X) for a fallow soil in (A) the Wick experiment and for a fallow and a cropped soil in (B) the Kasitski experiment.

 


View larger version (15K):
[in this window]
[in a new window]
  		Fig. 4. Effect of annual cropping and removing all the aboveground plant material on the bicarbonate extractable soil P (X). No fertilizer or manure was applied during the entire period of the experiment. Symbols are measurements and curves are simulations. The initial values of X were the result of previous treatments and only data for alternate treatments are presented. The experimental data was taken from the Saxmundham 2 experiment (Table 1).

 
Measured Values of the Coefficients Characterizing Soil Phosphorus Processes in the Dynamic Model
Table 3 summarizes the values for six soils from four countries. Intersoil variation in parameter values is considerable. Thus K3 is very small for the Nosko and Sitiung experiments but very large for the Ropsley experiment. There was a significant improvement (P < 0.01) in the fit of the model to the experimental data by using the fitted value of K3 over what could be obtained by setting it to zero, in the case of Ropsley and Saxmundham, but not for the other data sets. Over all experiments, K2 = 0.157K1 (r2 = 0.78), which indicates that intersite variation in K2/K1 is not large. The influence of the coefficients K1, K2, K3, and Xst.st. on X after 10 yr without cropping is given in Fig. 5 for two contrasting soils. In both, increase in K1 decreased X and increase in K2 had the reverse effect. Change in both K3 and Xst.st. had a substantial effect on X on the Ropsley soil but virtually no effect on the Nosko soil.


View this table:
[in this window]
[in a new window]
  		Table 3. Values of the inputs to the model for the indicated data sets.

 


View larger version (18K):
[in this window]
[in a new window]
  		Fig. 5. Sensitivity of the calculated extractable soil P to variations in parameter values. Simulations were over a 10-yr period with an initial value of X of 30 mg kg–1 and the input coefficients set at 0.5, 1.0, 1.5, and 2.0 times the default values, while the others remained at their default values; these are those given in Table 3. In these analyses the initial value of Y was fixed for a given soil at the initial value of X(default value of K1)/(default value of K2) by analogy with Eq. [7].

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Long-term experiments at Rothamsted (Russell, 1973; Johnston and Poulton, 1992) showed that crops removed more than 4.5 kg of P ha–1 yr–1 for up to 70 yr without the 0.5 M NaHCO3–extractable P falling below 3 mg kg–1, and indeed, for many years the extractable P remained roughly constant. In these experiments P was released from the soil reserves that was not available when the levels of X were higher. Similar results have been reported elsewhere (Hooker et al., 1983; Blake et al., 2000; Gransee and Merbach, 2000). The model predicts this phenomenon through buffering controlled by Pbuffer, which is constant for a given soil. As shown in the theory section, the effect of this buffering is proportional to the term, –K3[X(t) – Xst.st.]. When extractable soil P, X(t), is less than Xst.st. this term becomes positive and releases X in amounts that increase as X(t) decreases. As a result, change in X calculated by Eq. [22] can be zero or even reverse its sign when X drops below the steady stationary level for the given soil. The importance of this phenomenon thus depends on K3 and Xst.st., both of which vary from soil to soil.

McCollum (1991) showed that X levels could not be maintained by annual replacement of crop-removed P on an Ultisol; the greater the annual input of P, the higher the level of X that could be maintained. Hooker et al. (1983), Webb et al. (1992), Blake et al. (2000), and Gransee and Merbach, (2000) report similar findings. This phenomenon is quantitatively defined by Eq. [12] and [13] in the model, which shows how soil properties influence the magnitude of the effect. According to Eq. [13], once a substantial level of X has been built up it can only be maintained by subsequent regular applications of P, even when there is no crop P removal. The level required to maintain such a level depends on the level itself, Xst.st. and the rate constant K3.

Following an application of fertilizer P, the logarithm of X has often been found to decline linearly with time both in field experiments, under crops (Cox et al., 1981; McCollum, 1991), and in laboratory experiments on soil samples (Javid and Rowell, 2002). The model predicts this phenomenon (Eq. [17]), and also reveals that the higher the level of X the greater its decline over a given period. There is a linear relationship between these parameters that is demonstrated by Eq. [18] and Fig. 3. Data presented by Cox et al. (1981), Jones et al. (1991), Webb et al. (1992), and McCollum (1991) also support this relationship. There was also good agreement (Fig. 4) between the experimentally measured exponential decline of X and that calculated by the algorithm, Eq. [19] through [25].

In addition to defining the major patterns of response, the model also provides a new way of elucidating the reasons for differences between soils. There are considerable differences between the fitted values of the parameters characterizing the effects of soil properties on X. For example, the value of K3 for the Ropsley soil is considerable, and X is very sensitive to changes in it. The implication is that this soil contained minerals, such as those formed by past applications of fertilizer that readily release P to plants (Larsen, 1967), and indeed this soil had received much P fertilizer before the start of the experiment discussed in this paper (Bhogal et al., 1996). On the other hand, the fitted value of K3 was negligible for the Nosko and Sitiung soils, and with the same negligible values of K3 good predictions of X were made for the Brovkin, Barshtein and Matalom soils (Fig. 2). A possible explanation is that none of these soils had previously received heavy applications of fertilizer and thus did not contain readily decomposable soil minerals.

For some soils, where K3 can be assumed to be zero, it may be possible to deduce approximate values for the remaining parameters from the published literature and, on this basis, to simulate changes in X using the algorithm Eq. [19] through [25]. For example, Jones et al. (1984) considered that their rate coefficient equivalent to K1 was 0.28 yr–1 for all calcareous soils, which compares with a mean value of 0.26 yr–1 for 17 UK soils (Larsen et al., 1965). A more refined estimate of the value for a particular UK soil could be obtained by taking account of its pH, as a strong correlation was found between K1 and H+ ion concentration. It is possible to calculate K2 from K1 for some soils by interpreting long-term field experimental data with Eq. [7] or even by using a correlation between K2 and K1 like the one referred to earlier in which K2 = 0.157 K1. Thus for such soils, all the parameters are available for calculating change in X with the algorithm Eq. [19] through [25]. There may be other relationships between the required soil parameters and readily available information such as those described by Sharpley et al. (1984). It should generally be possible to calculate the values of the various parameters in the model for a particular soil from the measurements made in a long-term experiment on that soil by the procedures described in the calibration section. The good agreement between predicted and measured values of X (Fig. 2) suggests that the model calibrated in this way will give reliable predictions on soils of similar type to that used for calibrating the model. It should be emphasized that the calibrated model allows calculations of X to be made with inputs of crop P removal and addition of fertilizer and manures that vary each year. Incorporation of this model into short-term models for crop response to fertilizers (Greenwood et al., 2001a) could provide more reliable predictions of fertilizer response and X over many successive years.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
The model enables the time-course of change of X in long-term experiments to be summarized in terms of a few meaningful parameters. It predicts a wide range of previously reported dynamic patterns of response of X and explains them in terms of a simple concept. It also provides a basis for calculating the year-to-year changes in X for soils subjected to different annual inputs and removals of P.


   ACKNOWLEDGMENTS
 
We thank Damian L.J. Hatley for an advance copy of his Thesis.

Received for publication September 19, 2002.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




This article has been cited by other articles:


Home page
 Crop Sci.Home page
D. J. Greenwood, A. M. Stellacci, M. C. Meacham, M. R. Broadley, and P. J. White
Phosphorus Response Components of Different Brassica oleracea Genotypes Are Reproducible in Different Environments
Crop Sci., August 1, 2005; 45(5): 1728 - 1735.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (4)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Agricola
Right arrow Articles by Karpinets, T. V.
Right arrow Articles by Ammons, J. T.
Related Collections
Right arrow Soil Fertility and Productivity
Right arrow Soil Models
Right arrow Phosphorus

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS