Soil Science Society of America Journal 65:244-246 (2001)
© 2001 Soil Science Society of America
DIVISION S-8-NUTRIENT MANAGEMENT & SOIL & PLANT ANALYSIS
Comparison of Gross Nitrogen Mineralization Rates by Zero-Order Models
Shigeru Takahashi
Toyama Agricultural Research Center, Soils and Fertilizer Section, 1124-1 Yoshioka, Toyama, 939-8153, Japan
Corresponding author (shigeru{at}agri.pref.toyama.jp)
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ABSTRACT
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Several zero-order models for estimating gross N mineralization rate (M) using 15N have been proposed. In a comparison of the Ms estimated with some experimentally determined values, different models sometimes gave substantially different results. Although the Ms are estimated by using changes in NH4–N (NH4–14N + NH4–15N) and NH4–15N, a comprehensive comparison based on model equations is lacking. I compared four zero-order models to clarify the extent of the difference in estimated Ms between models under different conditions of changes in NH4–N and NH4–15N. The ratio of M by one model equation to M by another is expressed by 
and 
, where AT is NH4–N, AL is NH4–15N, and the subscripts 1 and 2 denote the initial and final values, respectively. Ranges of R and r are R > 0 and 0 < r < 1, respectively, and R > r. The farther r is from 1, the more different the estimated Ms are. Estimation of M must be done with caution when r 
0.2 since model differences increase uncertainties in estimates.
Abbreviations: C, NH4–N consuming rate • I, gross N immobilization rate • M, gross N mineralization rate
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INTRODUCTION
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NITROGEN MINERALIZATION is the transformation of organic N to inorganic NH4–N and the principal natural process by which soil N is made available for plants. There are continuous processes that produce and consume NH4–N in the soil. Plant roots, heterotrophs, and nitrifiers compete for NH4–N. Simple measurements of the changes in pool size of NH4–N are not very informative to understand the flows of N into and out of the pool. Thus, estimates of the gross rates of N transformation are needed.
Many zero-order models for estimating rates of N transformation have been proposed. Smith et al. (1994) characterized seven zero-order models of gross N mineralization rate (M) (Kirkham and Bartholomew, 1954; Blackburn, 1979; Tiedje et al., 1981; Shen et al., 1984; Nishio et al., 1985; Guiraud et al., 1989; Barraclough, 1991) by expressing analytical solutions in a standard format. Smith et al. (1994) indicated that models used by Barraclough (1991), Blackburn (1979), and Nishio et al. (1985) are alternative expressions of the model by Kirkham and Bartholomew (1954), and the expressions used by Tiedje et al. (1981) and Guiraud et al. (1989) are essentially the same models.
In a comparison of the Ms estimated with some experimentally determined values, different models sometimes gave substantially different results (Bjarnason, 1988; Smith et al., 1994). Bjarnason (1988) and Smith et al. (1994) compared not only M but also the N immobilization rate (I). There are many NH4–N consuming processes, for example, immobilization, nitrification, and gaseous loss. Ammonium-N consuming processes that are taken into consideration are different depending on the models. This may cause a difference in I. Therefore, in this study, I focused on M. In any zero-order model, the M is estimated by using changes in NH4–N (NH4–14N + NH4–15N) and NH4–15N. As far as I know, however, a comprehensive comparison based on model equations is lacking. The objectives of this study were to compare four zero-order models for estimating M (Kirkham and Bartholomew, 1954; Tiedje et al., 1981; Shen et al., 1984; Yamamuro, 1988), and to clarify the extent of the difference in estimated M between models under different conditions of changes in NH4–N and NH4–15N.
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MATERIALS AND METHODS
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The nomenclature is as follows: AL is NH4–15N, AU is NH4–14N, AT is 
, M is the gross mineralization rate. The subscripts 1, 2, and a denote the initial and final values and the arithmetic mean of a pool at two consecutive sampling times, respectively; 
t denotes an interval of time.
M by each model is expressed as follows:
Kirkham and Bartholomew (1954)
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Shen et al. (1984)
 | (2) |
Tiedje et al. (1981)
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Yamamuro (1988)
 | (4) |
The derivation of Eq. [1] to [3] from the original expressions was made by Smith et al. (1994).
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RESULTS AND DISCUSSION
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Here, R and r are the ratios of changes in NH4–N and NH4–15N during t, respectively. Equations [1] to [4] are expressed by using 
and 
as follows
 | (5) |
 | (6) |
 | (7) |
 | (8) |
M must be >0; thus, R > r. From Eq. [5] through [8], the ratio of M by one model to M by another is expressed
 | (9) |
 | (10) |
 | (11) |
 | (12) |
 | (13) |
 | (14) |
When R = 1, MK is expressed as follows instead of Eq. [1] (Kirkham and Bartholomew, 1954).
 | (15) |
When 
is substituted for Eq. [8], MY is expressed by Eq. [15]. And when ,
 | (16) |
These results mean that 
, and Eq. [13] represents this ratio.
The ratio of any of the above two models is expressed by R and r except for MY/MS. MY/MS is related to only r. Equations [9] through [14] indicate that M by one model could be converted to M by another. These relationships using several values of R and r are plotted in Fig. 1
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Equations [2] and [3] are quite similar. Shen et al. (1984) multiplied by (ATa/ALa), while Tiedje et al. (1981) divided by (AL/AT)a.
 | (17) |
From Eq. [17], MS > MT when R > 1 and MS < MT when R < 1 since R > r > 0 (Fig. 1).
As indicated above, MS and MT are based on the arithmetic means of AL and AT. While Yamamuro (1988) assumed exponential decrease in AL with time; that is, 
, where k was a rate constant. Mean of AL (ALA) during 
is as follows
Therefore,
 | (18) |
Equation [18] is the same as Eq. [13]. The deviations between MY and MS would be derived from the difference in the treatment of a decrease in AL. Under the assumptions adopted by Kirkham and Bartholomew (1954)—no remineralization, nitrification, or gaseous loss, and M and I are constant—AL decreases like exponentially with time rather than linearly, and the arithmetic mean of AL is approximate of the true mean of AL (Bjarnason, 1988). Bjarnason (1988) stated that use of the model equation of Shen et al. (1984) is, therefore, restricted to shorter t compared with the model equation of Kirkham and Bartholomew (1954).
The deviations between models is quite small in case of r 
1 (Fig. 1). Mineralization supplies AU, while NH4–N consuming processes remove both AU and AL. 
, where C is the NH4–N consuming rate. When r 1, C is very small and M approaches (AT2 - AT1)/t. Therefore, estimated M by any model becomes nearly the same value. The large deviations between models occurred at very low values of r. Among them, MY/MK and MT/MS showed relatively small deviations except for 
across a range of r compared with the ratio of other pairs. This would be related to the treatment of a decrease in AL. Estimation of M must be done with caution when r 0.2 since model differences increase uncertainties in estimates. This may be the case when the time interval is long or the NH+4–N consuming rates (e.g., the nitrification rate or immobilization rate) are fast.
Received for publication January 5, 2000.
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REFERENCES
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- Shen, S.M., G. Pruden, and D.S. Jenkinson. 1984. Mineralization and immobilization of nitrogen in fumigated soil and the measurement of microbial biomass nitrogen. Soil Biol. Biochem. 16:437–444.
- Smith, C.J., P.M. Chalk, D.M. Crawford, and J.T. Wood. 1994. Estimating gross nitrogen and immobilization rates in anaerobic and aerobic soil suspensions. Soil Sci. Soc. Am. J. 58:1652–1660.[Abstract/Free Full Text]
- Tiedje, J.M., J. Sorensen, and Y.-Y.L. Chang. 1981. Assimilatory and dissimilatory nitrate reduction: Perspective and methodology for simultaneous measurement of several nitrogen cycle processes. Ecol. Bull. 33:331–342.
- Yamamuro, S. 1988. A theoretical approach to the fate of nitrogen in paddy field by using an NH4–15N tracer technique. Jpn. J. Soil Sci. Plant Nutr. 59:538–548.
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ABSTRACT
INTRODUCTION
and symbols were plotted at 0.05, 0.2, 0.4, 0.6, 0.8, and 0.95. (See text for details.)