AOBPreview originally published online on August 4, 2004
Annals of Botany 2004 94(3):393-404; doi:10.1093/aob/mch155
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Annals of Botany 94/3, © Annals of Botany Company 2004; all rights reserved
Modelling Ontogenetic Changes of Nitrogen and Water Content in Lettuce
1 Faculty of Civil and Environmental Engineering, Division of Environmental Engineering, Water and Agriculture, Technion, Haifa 32000, Israel, 2 Provincial Research and Advisory Centre for Agriculture and Horticulture, B-8800 Rumbeke, Belgium and 3 Laboratory of Plant Ecology, Ghent University, B-9000, Ghent, Belgium
* For correspondence. E-mail segineri{at}tx.technion.ac.il
Received: 10 November 2003 Returned for revision: 23 March 2004 Accepted: 18 May 2004 Published electronically: 4 August 2004
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ABSTRACT |
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TOP
ABSTRACT
INTRODUCTION• Background and Aims It is well established that the nitrogen content of plants, including lettuce, decreases with time. It has also been observed that water content of lettuce increases between planting and harvest. This paper is an attempt at modelling these observations.
• Methods An existing dynamic model (NICOLET), designed to predict growth and nitrate content of glasshouse lettuce, is modified to accommodate the ontogenetic changes of reduced-nitrogen and water contents (on a dry matter basis). The decreasing reduced-N content and the increasing water content are mimicked by dividing the originally uniform plant into ‘metabolically active’ tissue and ‘support’ tissue. The ‘metabolic’ tissue is assumed to contain a higher nitrogen content and a lower water content than the ‘support’ tissue. As the plants grow, the ratio of ‘support’ to ‘metabolic’ tissue increases, resulting in an increased mean water content and a decreased reduced-N content. Simulations with the new model are compared with experimental glasshouse data over four seasons.
• Key Results The empirical linear relationship between water and reduced-N contents, matches, to a good approximation, the corresponding relationship based on the model. The agreement between the two makes it possible to effectively uncouple the estimation of the ‘ontogenetic’ parameters from the estimation of the other parameters. The growth and nitrate simulation results match the data rather well and are hardly affected by the new refinement. The reduced-N and water contents are predicted much better with the new model.
• Conclusion Prediction of nitrogen uptake for the substantial nitrate pool of lettuce depends on the water content. Hence, the modified model may assist in making better fertilization decisions and better estimates of nitrogen leaching.
Key words: Lactuca sativa L, lettuce, ontogenetic changes, nitrogen uptake, chemical composition, nitrogen content, water content, dynamic model, metabolic and support compartments
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INTRODUCTION |
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When plants are grown to maturity in agricultural stands, an ontogenetic decline of nitrogen content (so called ‘N-dilution’) is generally observed [Greenwood et al. (1990)
– several C3 and C4 crops; Justes et al. (1994) – winter wheat; Sheehy et al. (1998) – rice; Colnenne et al. (1998) – winter oilseed rape; Plénet and Lemaire (2000) – maize; Greenwood and Draycott (1989) – various vegetable crops]. This phenomenon is generally modelled by viewing the plants as comprising two types of tissue. One, ‘metabolically active’, responsible for photosynthesis and nutrients uptake, with a high content of nitrogenous compounds; and the other, consisting of mechanical and vascular ‘support’ elements, with a low content of N-compounds (Caloin and Yu, 1984). Hirose and Werger (1987) and Chen et al. (1993) associated the metabolically active tissue with the sunlit leaves, and the support tissue with the shaded leaves and stems. As plants grow, the mass ratio of sunlit leaves to total plant material decreases. Nitrogen-rich compounds, no longer required in the shaded parts, are re-allocated to the younger leaves (Seligman, 1993), resulting in a decline of nitrogen content with depth in the canopy (Charles-Edwards et al., 1987; Grindlay et al. 1995; Alt et al., 2000) and in the canopy as a whole. This description is inspired by the morphology of ordinary crops, where the young leaves are exposed to solar radiation more than the older leaves. In head-lettuce the young leaves are shaded and yet the same ‘dilution’ curve is evident. One way to treat this apparent inconsistency is to associate, as before, ‘metabolic’ with ‘sunlit’, despite the fact that the sunlit leaves are no longer the young ones. Another option is to assume that the composition of young and old leaves is, in evolutionary terms, a slow-changing trait, compared with leaf morphology (head formation). Finally, it is possible to abandon any attempt at an essential interpretation (for lack of suitable data) and view the model as an instrument, whose task is to produce correct predictions of crop nitrogen content. Our approach here is the last of these, retaining for convenience the description of an ‘ordinary’ crop to develop the lettuce model.
The total nitrogen content of plants is conveniently divided into nitrate (inorganic) and reduced (organic) nitrogen. The ratio nitrate-N : reduced-N has a wide range, from essentially zero (N-stressed plants; Broadley et al., 2003, Linker et al., 2004) to one or more (Table 1). The ‘critical’ nitrogen content, as traditionally plotted in N-dilution curves and believed to be required for maximum growth (Ulrich, 1952), seems to include all the reduced-N and possibly part of the nitrate-N. The extra nitrate, if any, is often considered to result from ‘luxury consumption’ (Justes et al., 1994; Grindlay, 1997). Whatever the definition of the components, excessive nitrate concentration is considered as posing a health hazard (European Commission, 1999).
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Information regarding the ontogenetic changes of water content of plants is scant compared with information about nitrogen content. All annual plants end up dry, but during the vegetative phase of lettuce (and possibly of other crops), the water content seems to increase. Heinen et al. (1991)
reported a significant increase, from 14·2 to 24·7 kg[water] kg–1[DM], and quoted Hansen (1976) as having observed a similar increase, from about 14·5 to about 25·3 kg[water] kg–1[DM]. With the ‘metabolic’/‘support’ model in mind, this implies that (during vegetative growth) the ‘support’ tissue contains more water than the ‘metabolic’ tissue, possibly due to relative abundance of vascular tissue. Results in support of the findings of Heinen and Hansen were also obtained in an experiment conducted recently in Beitem, Belgium (Bleyaert and Breugelmans; unpubl. res., 2001; next section). These new data clearly show that the ontogenetic decrease in reduced-N content is associated with a parallel increase in water content (Fig. 1).
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Note, in passing, that we follow here the current convention (see list of references), where ‘content’ is preferred over ‘concentration’ to express mass of substance on dry mass basis. One exception is dry matter content, which is expressed on fresh mass basis.
Before moving on, it seems instructive to contrast the negative correlation of Fig. 1 with the positive correlation of Fig. 2, where water content is proportional to reduced-N content. This figure, based on recent laboratory data for relatively small isolated lettuce plants, shows that both reduced-N content and water content of N-stressed plants (bottom left) are considerably lower than those of normal plants (top right). In fact, the dry matter content (DMC) of highly N-stressed lettuce may become three to four times higher than the normal level of 4–6 % (on fresh-mass basis). These results are in agreement with earlier data, obtained during the growth of young seedlings, a stage termed ‘steady-state’ by Ingestad and Ågren (1988), and ‘balanced exponential growth’ by Thornley (1997). During this early stage of growth the composition of the seedlings is time-invariant and growth is exponential. If the plants are N-stressed, the N : C ratio decreases (Oscarson et al., 1989; Ingestad and Ågren, 1992) as does the water content (Oscarson et al., 1989), resulting in the pattern of Fig. 2.
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The data in Figs 1 and 2, for the young, unstressed plants, should coincide. However, in Fig. 1 these are clustered around [2·5, 15], while in Fig. 2 they are clustered around [3, 20]. This discrepancy may be attributed to different lettuce cultivars, different growing conditions (Fig. 1 in soil, Fig. 2 in hydroponics) or, most likely, to different chemical analysis methods.
This paper is an attempt to model quantitatively the data of Fig. 1, by modifying a previously developed dynamic lettuce model, NICOLET (Seginer, 2003a), which is valid for the initial stage of growth, where composition is time-invariant (Fig. 2). The modification extends the validity of the model to a later stage of vegetative growth where ontogenetic composition-changes take place. We assume here, following Caloin and Yu (1984), that viewing the plant as comprising distinct metabolic and support components is essentially correct, and that the trend shown in Fig. 1 is real.
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THE BEITEM DATA |
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During the years 1999 and 2000, experiments were conducted in the Provincial Research Centre at Beitem, Belgium (latitude 50°54'N, longitude 03°07'W, 30 m a.s.l.), in an attempt to quantify the effect of various environmental treatments (supplementing nitrogen, light, CO2 and heat) on the nitrate content of butterhead lettuce. The crops were soil-grown in glasshouse compartments, following common agricultural practices, except for the environmental treatments. The second-year experiments produced more consistent data than the first year and were, therefore, selected for the present modelling attempt. A detailed description of these experiments is available upon request (Bleyaert and Breugelmans, 2001
; unpubl. res.). Data from experiments where N supply was judged from the results to be ample and for which chemical analyses were available, were used for the current analysis. Since the interest here is not in the effects of the various treatments (which only rarely resulted in significant effects), the data were pooled to produce four distinct data sets, as shown in Table 1. The environmental data were averaged over the two experimental compartments (or four sub-compartments, when appropriate), and the crop data were averaged over the two higher N treatments, over four blocks (replications), as well as over the compartments (climatological treatments). Hence, each point in Fig. 1 and all the averaged fresh mass, dry mass, nitrate content and reduced-N content data (except the initial harvests), are means of at least eight individual determinations. The crops were sampled for analysis five or six times, at approximately uniform intervals of light integral, along the growing period, starting with the day of transplanting and ending at the final harvest.
Table 1 shows that the effects of season and cultivar are partially confounded. Cultivar ‘Flandria’ is associated with spring and summer and cultivar ‘Troubadour’ is associated with autumn and winter (no confounding for seasons within each cultivar). The ‘Flandria’ points in Fig. 1 appear to lie a bit lower than those of ‘Troubadour’. A few apparent irregularities can be found in Table 1 (bold font): (a) the transplants of the spring crop were unusually large; (b) the ‘light efficiency’ of the summer crop was considerably lower than that of the other crops; (c) the reduced-N of the autumn crop is unusually low.
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THE CURRENT NICOLET MODEL |
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Description
The NICOLET model is described and justified in detail elsewhere (Seginer, 2003a
). It consists of three (virtual) compartments, labelled ‘structure’, ‘vacuole’ and ‘excess-carbon’. The soluble organic and mineral constituents of the vacuole complement each other in contributing to the (constant) osmotic potential, while the carbon and organic-N compounds of the other two compartments are osmotically neutral. The structural N : C ratio and the water : structural-carbon ratio are assumed to be constant. The excess-carbon compartment is assumed to contain only ‘dry’ carbon compounds, and is usually activated only when the crop is N-stressed. Since the available Beitem data are for abundant supply of nitrogen, the excess-carbon compartment and the nutrition uptake formulation are omitted from the summary description provided here, as well as from the computations. A few simplifying notational changes have also been introduced. The resulting two-compartment model is a special case of the (original) three-compartment model. It may be obtained from the latter by setting 
= 0 in eqns [27] to [29] of Seginer (2003a). The simplified model is shown in Fig. 3.
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The fluxes are controlled by: (a) the environmental conditions – photosynthesis by light and CO2, and structural growth by temperature; (b) the ground cover of the crop; and (c) attenuation functions, which reflect the inhibition of certain processes. Photosynthesis is modelled as a Michaelis–Menten process, and respiration and growth are formulated as exponential functions of temperature (Q10 = 2). The ground cover, to which all fluxes are proportional, approaches one asymptotically, and the attenuation functions control the flows in times of stress.
If the environmental conditions are constant, the current NICOLET model predicts that the composition of the crop equilibrates with these conditions, namely remains constant with time. This will be changed below, to allow for ontogenetic effects.
System equations
In the following equations, the symbols denoting masses and fluxes are defined in Fig. 3. The environmental conditions I, T and CC are light flux, ambient temperature and CO2 concentration in the air. The parentheses {} enclose the arguments of functions, and t is time. All other symbols are constants, defined in the notation list and explained in Seginer (2003a).
(i) Carbon balances (used as state equations)
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(iii) Compositional relationships
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(iv) Normalized content of soluble carbon-compounds
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EXTENSION TO INCLUDE METABOLIC AND SUPPORT COMPONENTS |
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Variable r and
The originally uniform plant, with structural N : C ratio r and water : structural-C ratio
(eqns 6 and 7), is now divided into ‘metabolic’ and ‘support’ components. The structural N : C ratios of these components are denoted by r(m) and r(s), where m and s denote ‘metabolic’ and ‘support’, respectively, and r(m) is larger than r(s). The water : structural-C ratios are similarly denoted by (m) and (s), where (m) is smaller than (s).
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is proportional to f{MCs}, which in view of eqns (9) to (12) makes the rate of photosynthesis, and all other metabolic activities, directly proportional to the reduced-nitrogen content of the metabolic compartment. This is in agreement with Ågren's (1985) view of ‘nitrogen productivity’.
Dividing eqn (22) by MCs, the N : C ratio of the structure as a whole is obtained:
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1).
The total water content is, similar to eqn (22)
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(m) and (s) instead of just r and ], but requires no additional state variables. The original, constant-r and constant- formulation, is a special case of the new model and can be obtained by setting r(m) = r(s) = r and (m) = (s) = .
Uptake of nitrogen
Differentiating the osmotica balance, eqn (5), with respect to time, and utilizing eqns (1), (2), (3), (6), (7), (23) and (26), results (Appendix A) in the flux form
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CONVERSION BETWEEN MEASUREMENTS AND MODEL STATES |
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The comparison of model predictions with experimental data requires that the two can be mapped back and forth into each other. The experimental results of Bleyaert and Breugelmans can be expressed in terms of (a) fresh mass per unit ground area, WF, (b) dry mass per unit ground area, WD, (c) molar nitrate content on dry-mass basis, Cnit-N, and (d) molar reduced-N content on dry-mass basis, Cred-N.
From these, the water volume per unit ground area is determined via
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is the density of water. Combining this with eqn (26), an implicit expression for one of the state variables, MCs (eqn 2), is obtained
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From the definition of Cnit-N,
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The inverse conversion requires, in addition, an assumption regarding the conversion of dry matter, such as
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C and N, are determined from the molecular masses of typical compounds. |
ESTIMATING THE PARAMETERS FOR THE ‘METABOLIC’ AND ‘SUPPORT’ COMPONENTS |
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Analysis
Figure 1 shows a negatively sloping linear relationship between water content and reduced-N content. The empirically fitted line may be expressed as
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The ontogenetic model is in general agreement with this observation, as can be shown by eliminating f{MCs}/aMCs between eqns (23) and (26), and multiplying throughout by MCs/WD, to obtain
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Equating eqns (35) and (36), results in
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(m) and (s). Hence, given just the line of Fig. 1, two of the four parameters remain free for fitting. Further information can be extracted from the two ends of the data cluster of Fig. 1 if it is assumed that the lower right data points represent young plants with effectively no support tissue and the upper left data points represent mature plants consisting mainly of support tissue. For these data, utilizing eqns (23) and (26) and assuming the validity of eqn (20) for the young plants (subscript y) and MCs 
for the mature plants (subscript m), the result is
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Since V/MNs is the slope of lines radiating from the origin in Fig. 1, denoting this slope for the young plants by y and that for the mature plants by m, eqns (37) to (40), can be used to evaluate the four ‘ontogenetic’ parameters as follows:
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Evaluation for the Beitem data
The values of A, B, y and m can be read directly from Fig. 1, resulting approximately in
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= 1000 kg[water] m–3, and substituting into eqns (41) to (44), the mean results over the two cultivars and over all seasons become
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SIMULATIONS |
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Variable compositional ratios
The model was fitted to the available data, by changing some of the original NICOLET parameters, selected according to previous experience with the model (Broadley et al., 2003
; Linker et al., 2004). It turns out that the two cultivars require somewhat different values for two of the parameters, 
and 
, as shown in columns 1 and 2 of Table 2. Apparently, ‘Troubadour’ has a somewhat higher photosynthetic efficiency, , and a somewhat lower partitioning to growth, , than ‘Flandria’; however, the differences are rather small and may result from the partial confounding between cultivar and season. The values of the compositional ratios r and are the same for the two cultivars, as derived in the previous section from the common regression line of Fig. 1. All other parameters were the same for all simulations. The results of the simulations are presented in Fig. 4, showing fair to good agreements between the measured and simulated values. The first two variables, dry and fresh mass, are cumulative and are predicted rather well. The last three variables are ratios, with noisier signals and looser fits. The logarithmic scale of the fresh mass and the linear scale of the dry mass together show how the initially exponential growth changes gradually into linear. The model was able to mimic the rather different shapes of the growth curves, resulting from different weather, cultivar and spacing. The prediction of nitrate content, the main focus of the original NICOLET model, is rather sensitive to short (daily) and medium term (weekly) environmental changes. In view of this, the fit to the various trends, including the nearly constant level of the winter experiment, should be considered as rather good.
The focus of this study is on the changes with time of the water and reduced-N content. The model predicts an increase with time of the former (decrease of DMC) and decrease of the latter. This is generally the trend of both data and simulation, but the details of the fit are less clear, partly because several data points are missing and partly because the scatter around the line in Fig. 1 is rather large. Figure 5 summarizes the simulations of water and reduced-N contents. Although the individual trajectories, starting at the lower right and ending at the upper left, do not closely agree with the data, the general behaviour in Fig. 5 is as expected.
Comparison with fixed compositional ratios
The question now is whether the new model produces better predictions than the original NICOLET model, where the water and reduced-N ratios were fixed (single r and ; original model). Selecting mean values for these ratios and adjusting slightly and (Table 2), the results of Fig. 6 were obtained. The figure shows that the trajectories of dry mass, fresh mass and nitrate content, are generally similar to those of Fig. 4. The dry matter and reduced-N contents, however, are rather different. The difference between the models is particularly striking when viewed in terms of the co-ordinates of Figs 1 and 5, as shown in Fig. 7.
Comparison of Figs 5 and 7 shows clearly that the model with fixed compositional ratios cannot capture the changes occurring in water and reduced-N contents as the crop grows.
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DISCUSSION |
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Reduced-N and water contents
The new model, with ontogenetically decreasing reduced-N content and increasing water content, is a refinement of a previous model, NICOLET, which had been designed to predict growth and nitrate content of lettuce. The division of the ‘ontogenetic’ plant model, into ‘metabolic’ and ‘support’ tissue with high and low nitrogen contents, respectively, corresponds well with the morphology and nitrogen distribution of ‘ordinary’ crops. However, the extension of the concept to head lettuce and to water content can at the moment, while detailed data (of individual organs over the growing season) are not available, only be supported by the overall trends, such as shown in Fig. 1.
Figures 1 and 2 show the wide range of possible combinations of water and reduced-N content in lettuce. The negative correlation of Fig. 1 is due to ontogeny, while the positive correlation of Fig. 2 is due to N-stress. It may be of theoretical interest to explore what might be possible and impossible trajectories in the water versus reduced-N plane. The data of Fig. 1 are likely to mark the upper bound of the feasible region, while the data of Fig. 2 are likely to mark the lower bound.
Regarding the rate of ‘maturation’, in the sense of rate of N ‘dilution’ (moving from right to left in Fig. 1), this rate presumably depends on the rate of growth (faster growth leading to faster ‘dilution’). To some extent, however, it may also depend on plant spacing, isolated plants having higher reduced-N content than dense canopies of similar age (Seginer, 2003b).
Perhaps the most noteworthy point regarding the ontogenetic model is the similarity between eqns (35) and (36). The first is an empirical linear relationship between water and reduced-N contents, and the second is the model-formulated relationship, which is approximately linear. The correspondence between the two expressions makes it possible to effectively uncouple the estimation of the ‘ontogenetic’ parameters r(m), r(s), (m) and (s) (utilizing Fig. 1), from the estimation of the other parameters.
Uptake of nitrogen
The new model has the potential advantage of estimating nitrogen uptake more accurately than before. Partitioning the total uptake into structural reduced-nitrogen and vacuolar nitrate, NICOLET treats the former strictly as a function of the size of the plant (as measured by MCs) and the latter as a function of both size and environment. Regarding reduced-N, the new version predicts uptake rates for mature plants which are lower than those predicted by the original model, since in the new model the mature plants recycle much of their structural nitrogen (r(s) < r(n)). On the other hand, the increasing water content ((s) > (n)), results in an increased demand for nitrate to maintain the required osmotic potential. Judging by the potentially large nitrate content of lettuce, changes in the environment may have a significant effect on the uptake of nitrogen.
The accuracy of the uptake calculations depends on the accuracy of the predicted size and nitrogen content of the crop. At the moment, as shown by Fig. 8 (which may be regarded as a cumulative version of Fig. 1), there is some disagreement between model and data with respect to reduced-N accumulation in the crop. According to the model, all the points of Fig. 8 should lie on a single curve, obtained by plotting eqn (25) (times ) against eqn (22). The data, however, show that two of the autumn points are considerably off the trend of the other three seasons (evident also in the reduced-N frames of Fig. 4). This may be blamed on the model (insufficient detail) and/or on the data (insufficient accuracy). An optimistic view would be to emphasize the good agreement of the data of three of the seasons, but definitely more data are required to establish a reliable set of the relevant parameters [r(m), r(s), (m), (s) and a].
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Good estimation of the nitrate content is even more difficult, since it strongly depends on the environmental conditions. Considering the potentially high nitrate content of lettuce, the accuracy of its estimation should also be improved before the model can be used reliably for N-uptake calculations. For that, a good estimate of the ontogenetic change in water content is required.
Further points
The model was able to fit data of different seasons with the same set of (cultivar specific) parameters, even when the differences were as significant as between autumn and winter for the same cultivar (Troubadour; Fig. 4). The fit (Fig. 4) was generally good, despite significant differences in initial size of transplants (Flandria), in light efficiency (Flandria) and in final reduced-N content (Troubadour), as pointed out in conjunction with Table 1.
Comparison of Figs 4 and 6 shows that the new model does not improve significantly the prediction of growth and nitrate content of lettuce. It does, however, improve the prediction of water and reduced-N contents (Figs 5 and 7). Whether this improvement is useful to horticultural practice depends on the effect of these two attributes on lettuce quality and on the ability to make better nitrogen uptake predictions.
Most of the other tests of the NICOLET model have been against data from hydroponics (Broadley et al., 2003; Linker et al., 2004). The present data are of soil-grown lettuce which, however, was assumed to have a plentiful supply of nitrogen. The predictability for the soil-grown lettuce seems as good as for the hydroponics lettuce.
In conclusion, the new model is an improvement, as a comparison of Figs 5 and 7 demonstrates. It has the potential for improving the estimates of nitrogen uptake, thus leading to more accurate calculation of fertilizer needs and leaching potentials.
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APPENDIX A: DERIVATION OF EQN (27) |
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The time derivative of eqn (5) is
 | (A1) |
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 | (A3) |
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APPENDIX B: NOTATION |
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Main symbols
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Subscripts
Compartments
- i, j general compartment indices
- s structure
- v vacuole
- s structure
Constituents
- C carbon
- J general constituent index
- N nitrogen
- J general constituent index
Processes
- g growth
- k general process index
- m maintenance
- p photosynthesis
- u uptake
- k general process index
Superscripts
- (m) metabolically active component of plant
- (s) support component of plant
- (s) support component of plant
Acronyms
- DAP days after (trans)planting
- DM dry matter
- DMC dry matter content
- FMfresh matter
- PAP photosynthetically active photons
- DM dry matter
Notes
- – indicates dimensionless quantities
- {} used exclusively to contain the arguments of functions.
- {} used exclusively to contain the arguments of functions.
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ACKNOWLEDGEMENTS |
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This research has been funded by EU project FAIR6-CT98-4362 (NICOLET). We would like to acknowledge the constructive comments offered by Prof. Gerrit van Straten, Dr Fokke Buwalda and Dr Leo Marcelis, Wageningen University, The Netherlands.
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