Soil Science Society of America Journal 65:414-423 (2001)
© 2001 Soil Science Society of America
DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION
Simple
A model for simulation of plant emergence predicting the effects of soil tillage and sowing operations
C. Dürr,
J.-N. Aubertot,
G. Richard,
P. Dubrulle,
Y. Duval and
J. Boiffin
INRA, Unité d'Agronomie, rue Fernand Christ, 02007 Laon Cedex, France
Corresponding author (durr{at}laon.inra.fr)
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ABSTRACT
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A model predicting seedling emergence is described and applied to sugarbeet (Beta vulgaris L.). The input variables are the soil surface texture, soil temperature, rainfall, aggregate size distribution and position in the seedbed, sowing depths, characteristics of the seeds (initial seed mass distribution, germination time, and hypocotyl elongation distributions). A three-dimensional seedbed layer is created where the aggregates and seeds are placed. Soil water content is assumed not to limit sugarbeet emergence (sowing conditions in northern Europe). The time needed to reach the soil surface is calculated using germination thermal time, soil temperature, the presence or absence of aggregates, and the hypocotyl elongation function. The ability of seedlings to break through the soil surface is a function of crust development and moisture. The seedling growth after emergence is calculated with reference to seed mass distribution, emergence delay, and the presence or absence of mechanical obstacles. The emergence prediction was tested in field experiments with four seedbeds, from fine earth to cloddy structure, and a sowing depth of 17 to 35 mm. The predicted number and sizes of clods encountered by seedlings and the calculated hypocotyl length were not significantly different from measured ones. Predicted germination times were longer than the observed ones (differences <5°C d); final rates were well predicted. Predicted vs. measured final emergence rates differed by less than 10%; changes with time differed from 15 to 30°C. This was due to the hypocotyl elongation functions, which must be improved. Further improvements will be to predict soil water content variations and effects on emergence via water stress and soil strengthening.
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INTRODUCTION
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THERE IS A GREAT NEED to be able to predict the effects of soil tillage, seedbed preparation, and sowing techniques on crop establishment. These technical changes are costly for growers, but their effects are not easy to predict. They cause changes in the physical conditions of the seedbed and in seed placement (Aubertot et al., 1999), which interact with seed treatment, seed characteristics, and cultivars, to determine the features of the crop stand. These effects also depend greatly on the climatic sequences that follow seed sowing. Conventional experiments comparing the plant populations and the final yields for different management techniques are time consuming and expensive. A simulation tool that predicts seedling emergence and early growth could be used to estimate the major effects of changes in the seedbed layer or in the seed characteristics, under several simulated climatic scenarios. Its output variables could be used to initialize crop growth models, in which the variations in crop establishment are often poorly taken into account (Brisson et al., 1998; Guérif et al., 1999).
Few emergence models have been developed (Bouaziz and Bruckler, 1989a, 1989b, 1989c; Finch-Savage and Phelps, 1993; Mullins et al., 1996), and the effects of soil structure on seedling growth are not always taken into account in those models. When they are, indirect variables are used to describe soil structure effects, such as an index of tortuosity representing the increase in the seedling path to the surface and the percentage of the soil surface occupied by clods larger than a given size to predict the percentage of seedlings blocked under clods (Bouaziz and Bruckler, 1989c), or several layers of different mechanical impedance influencing the root and shoot growth rate (Mullins et al., 1996). None of these models gives a representation of the spatial variation in aggregate size and organization in the seedbed, which are greatly altered by soil tillage and sowing operations. We describe a model that simulates the emergence and early growth of seedlings and its application to sugarbeet, taking into account the differences in aggregate number, shape, and spatial organization; the seed placement, resulting from tillage and sowing operations; the variations within the seed population; and the climatic variations with time and among sites. Variations in soil water content are not represented as this was considered not to be a major limiting factor for sugarbeet, in the light of conditions in the sugarbeet cropping area of northern Europe, especially because of earlier sowing dates (Durrant et al., 1988; Duval and Boiffin, 1994). The process chart of the model is described and its evaluation in field experiments was carried out to test the ability of the seedbed generator to represent the seedbed spatial arrangement and its effects on emergence.
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Process Chart of the Simulation Model
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Basic Principles of SIMPLE
The simulation process is outlined in Fig. 1
. The output variables are the germination and emergence changes with time and final rates, and the seedling growth parameters until the first pair of leaves appears. The input variables are the seedlot characteristics (seed mass distribution, germination time distribution, and parameters of the hypocotyl elongation function), soil and climatic characteristics and other conditions resulting from the tillage and sowing operations (aggregate-size distribution and spatial organization in the seedbed and sowing depth distribution). A seedbed generator creates three-dimensional seedbeds using the input variables describing the aggregate shape, number, and spatial organization. The seeds are placed from a sowing depth distribution table. A soil temperature file is given with hourly data intervals. Dynamic submodels are used to simulate the processes at daily intervals, including a physical model characterizing the changes with time in the soil surface state and biological submodels working on individual seeds. This model does not presently consider that the soil offers resistance, except when the surface layer is crusted. It does not predict soil temperature and water content, or the effects of water stress on germination and emergence. The shoot growth does not depend on the root growth. The seed characteristics are sampled n times in the distribution tables describing the seed population (seed mass, germination time, elongation rate). The biological submodels are then reiterated n times to generate the distribution of the predicted variables. The code is written in C programming language and runs on a personal computer with reasonable calculation times (133 MHz, 1 min for a fine seedbed to 
6 h for a cloddy seedbed).
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Fig. 1. Process chart of the simulation model SIMPLE. Italics = models. Roman = variables. Shaded = n iterations
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Submodel Characteristics
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Seedbed Generator and Sowing Simulation
The seedbed layer is described as a parallelepiped, including the seeds and a given number of clods: x = sowing line width, y = length on the sowing line, and z = distance between the surface and the bottom of the seedbed. The numerical structure of the simulated seedbed is divided into two parts, and the model only deals with equations. First, the dimensions of the volume are defined. Second, variables describing the number, size, position, and orientation of each aggregate in the seedbed are listed. The length of the simulated seedbed y was chosen with respect to clod sizes (maximum size order: 10 cm) and with respect to the time the simulation takes using a personal computer. The numbers of clods belonging to a [min, max] grade, obtained by taking soil samples down to the bottom of the seedbed (5 cm for sugarbeet seedbeds) and sieving them through circular apertures (min, lowest; max, largest sieve aperture), are the input variables. This information is transformed to represent clods of each grade by a geometrical object of a given shape and size. The mean intermediate axis l of sieved clods is close to (3min + max)/4 for a given grade (Aubertot et al., 1999). This value is used to give an l value to each graded clod. Aggregates are described by several authors (Dexter, 1985; Perfect et al., 1997; Aubertot et al., 1999) according to their longest L, intermediate l, and shortest axis h, with aspect ratios (l/L, h/L; Addiscott and Dexter, 1994) constant whatever the clod size (Addiscott and Dexter, 1994; Perfect et al., 1997; Aubertot et al., 1999). Measured values of aspect ratios (Addiscott and Dexter, 1994; Perfect et al., 1997; Aubertot et al., 1999) are very close to the theoretical values (0.79, 0.63) calculated by Dexter (1985). Thus, those theoretical values were used to calculate L and h axis values from the l axis value. Clods were assumed to have an ellipsoidal shape. This is more realistic than a spherical shape, and influences the hypocotyl length and the probability for seedlings to encounter a clod. The seedbed generator positions the clods one by one, beginning with the largest ones, down to 5-mm aggregates. The position (x, y, z) of the clod center is chosen at random in a volume according to variables describing the clod spatial organization: percentage of clods visible from the soil surface, degree of burial of the visible clods, and lateral distribution across the row (Fig. 2 and 3)
. The seedbed generator first determines if the clod is to be visible or not; a clod is visible if its volume is not completely included in the parallelepiped representing the soil volume. Three classes of visible clods per grade are defined: (i) on the soil surface, which is defined as 5% of a given clod volume included in soil; (ii) superficially buried (5–50% of the clod volume included in soil); and more than one-half buried. A set of default values is given for these proportions as they did not vary in observed field experiments, in contrast with the total number of visible clods (Aubertot et al., 1999). If the clod is visible, its degree of burial is chosen according to its size and those default proportions. Its lateral location is also chosen according to three possible positions across the row: central, intermediate, and external. If the clod is not visible, it is uniformly positioned within the volume since no specific spatial organization was found for clods buried in seedbeds (Aubertot et al., 1999). A buried clod is freely orientated, whereas a visible clod is orientated to be in an equilibrium position (angle between the longest axis L or the intermediate axis l and the horizontal plane <20°).
The clod position is accepted only if the clod periphery does not overlap the periphery of the other clods already placed in that volume. The generator creates N numerical seedbeds with the same input variables to represent the spatial variations of seedbed structure. (n/N) seeds are sown in each simulated seedbed. The seed i is placed by choosing a sowing depth at random in the sowing depth distribution zi. The coordinate xi is chosen at random in a segment across the row; yi is chosen uniformly in the segment [0, y]. The seed position is redrawn at random if the seed coordinates are inside a clod.
Soil Surface Crusting
This submodel generates a qualitative variable describing the surface state, assumed to be continuous. This variable has only two modes: obstacle to emergence or not. The choice between the two is determined by taking into account the cumulative rainfall and the maximum daily rainfall from the sowing date to the current day (Duval and Boiffin, 1994; Fig. 4)
. These climatic variables are compared with threshold values depending on soil texture to determine if a crust is present or not. If there is a crust, it is considered to be dry and an obstacle if the maximum daily rainfall during the last j days before the considered day is less than a threshold value. Values for this empirical submodel are given for sugarbeet, and silt loams and climatic conditions of the Northern Paris basin (Fig. 4).
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Fig. 4. Flow chart of soil surface degradation and emergence submodel. P = emergence probability of sugar beet seedling. For loamy soils: P = 0.6, CRc = 12 mm, DRc1 = 5 mm, DRc2 = 3.5 mm, d = 3 (from Duval and Boiffin, 1994)
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Predicting Germination Time
Seed imbibition during germination is presently assumed not to be limited by moisture conditions, so that the seedbed water content does not influence germination. This assumption was considered to be valid for the early sowings of sugarbeet in northern conditions. Thermal time (using a 3.5°C threshold value; Gummerson, 1986; Dürr and Boiffin, 1995) is cumulative from the sowing date. This heat sum is compared with the thermal time required for seed i germination, which is drawn at random in the distribution of germination times of the seedlot. If the cumulated thermal time from sowing is equal to the time required for germination of the seed, Gi, then the seed is declared germinated. The reference distribution is obtained by standard tests under laboratory conditions. Germination is recorded at 20°C on three replicates of 100 seeds, laid on a plitted paper in a plastic box and watered with 40 mL of demineralized water. Germinated seeds are counted two times daily.
Estimating the Hypocotyl Path and Length
This submodel calculates the course of the hypocotyl on the basis of the following hypothesis. Clods are assumed to be impenetrable, as mostly observed for sugarbeet, except in very wet conditions. The hypocotyl follows a vertical course if it does not meet aggregates with a diameter >5 mm. This limit value was chosen based on a preliminary experiment showing straight hypocotyls in such sowing conditions, with no difference between the hypocotyl length and the sowing depth. If the hypocotyl runs into an aggregate of diameter >5 mm, it either goes on elongating and grows around the clod, following an arc of ellipse in close contact with the clod, or it stays blocked under the clod and the seedling dies. The choice between the two possibilities is determined by random drawing in a probability table depending on the clod size and position in the seedbed (laid on the soil surface or not, Dürr and Aubertot, 2000, Table 1). The arc length is calculated when the seedling is not blocked, with reference to the point where the seedling touched the ellipsoid. This arc length is a part of the ellipse defined by the intersection of the ellipsoid and the plane containing the vertical force exerted by the hypocotyl due to its negative geotropism, and the ellipsoid reaction, normal to its surface. The arc length is calculated between the point where the seedling touched the ellipsoid and the point of the vertical tangent of the hypocotyl with the ellipsoid.
Predicting Emergence Time
The changes in hypocotyl length with time are represented by a Weibull function
 | (1) |
where Li is the hypocotyl length of the seedling i, and t is thermal time cumulated from germination at the seed depth level. Five sets of values are given to the parameters a, b, and c, which represent the observed variations in hypocotyl elongation (Table 2). The elongation of the seedling i depends on its germination time Gi (Table 2). The parameters of the functions and their frequencies were established by sowing germinated seeds belonging to five ranges of time to germination: <35, 30 to 35, 35 to 40, 40 to 45, >45°C d. Five seeds were sown per pot (7.5-cm diam., 11-cm height), filled with white sand (bulk density 1.47 g cm-3), raised to 0.2 g g-1 water content with a nutrient solution for young seedlings (Saglio and Pradet, 1980; at one-half concentration). Fifty to one-hundred seeds per germination range were sown. Growth temperature was 15°C. Hypocotyl length was measured one or two times a day without seedling destruction. Seedling were extracted at the end of the experiment to measure their individual sowing depth, which was thereafter added to each hypocotyl measurement, to have the total hypocotyl length. The results of these experiments are given as default values in the model as these experiments are time consuming and cannot be performed for each studied seedlot. A submodel determines the time (thermal time from sowing and Day of Year) at which the seedling reaches the soil surface with reference to the thermal time (base 3.5°C) cumulative from germination, the estimated hypocotyl length, and the hypocotyl elongation rate. When this time is calculated, two successive tests are done. If the age of the seedling, expressed as thermal time from sowing, is greater than 175°C d (base 3.5°C), the seedling is considered to be dead. If not, if there is no crust or a wet crust, the seedling emerges. Its emergence time Ei is the time calculated to reach the soil surface. If there is a dry crust, only a given proportion of seedlings can break through it (Fig. 4, Duval and Boiffin, 1994). The fate of each seedling i reaching the soil surface under these conditions is drawn at random using this probability. If it does not emerge, then thermal time is cumulated until the next day and the state of the crust is once more determined. This procedure is reiterated as long as the seedling has not emerged and its age remains below the threshold value determining seedling death. Emergence time is equal to the cumulated thermal time needed to reach the soil surface and to wait for breaking through the crust. If the crust is not rewetted before the thermal time for death is reached, the seedling fails to emerge and is considered dead.
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Table 2. Elongation function parameters for the sugarbeet hypocotyl, and distribution of these functions according to germination thermal times (% seedlings)
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The reasons for seedlings finally not emerging are nongerminating seeds, seedlings with hypocotyls too short to reach the soil surface, or seedlings blocked under a clod or under a dry crust.
Predicting Early Growth
This submodel is based on the hypothesis that seedling growth is exponential until the first pair of true leaves appear (Dürr and Boiffin, 1995):
 | (2) |
with DWi dry mass of seedling i (mg), TTi the cumulated soil thermal time (°C d) from emergence time of seedling i, DWoi the seedling dry mass at emergence, and RGRi, the seedling relative growth rate (mg mg-1 °C-1). DWoi depends on the initial seed mass (Dürr and Boiffin, 1995). A linear relationship was found in experiments done by these authors, using a given seedlot (cv. Véga, Menesson triploid genotype):
 | (3) |
with SDWi = seed i dry mass (mg, without its teguments; r = 0.82; n = 167).
RGRi depends on the emergence time, that is, the duration of the seedling growth under the soil surface, calculated as thermal time from sowing (TTsi)
 | (4) |
with d = 0.0149, e = 0.0385, and f = 0.00024. RGRi is decreased if the hypocotyl meets an obstacle before emergence (d = 0.0126, estimated from Dürr et al., 1992; Dürr and Boiffin, 1995; Tamet et al., 1996).
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MATERIALS AND METHODS
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Model Evaluation
Experiments were carried out to evaluate each step of this model. Seedbeds of varying cloddiness were created. The frequency and dimension of the aggregates encountered, the germination rates, the hypocotyl length path and the emergence rates were the variables on which predictions were compared with measured values. The soil temperature was introduced as an input variable. The soil surface degradation was prevented as the soil surface degradation and emergence through crust submodel had already been tested (Dürr et al., 1996). The submodel for predicting seedling growth parameters after emergence was not tested.
A set of experiments was carried out in March and April 1996 in Mons-en-Chaussée (northeastern France, 49.56°N, 2.56°E) in a silt loam soil (Typic Hapludalf, Luvisol Orthique, 0.74 g g-1 silt, 0.20 g g-1 clay, 0.04 g g-1 sand, in the 0–0.3 m plowed layer), to study emergence in relation to seedbed cloddiness. The soil before sowing was either not plowed (NP), or not plowed and compacted (NPC) under wet conditions (0.22 g g-1 mean soil water content in the 0–0.3 m soil layer) with a tractor (8.0 t) running one time wheel tracks over wheel tracks, with tires inflated at 200 kPa. The seedbed was prepared by a single pass of combined implements (spring tine cultivator and skeleton rollers) at soil water content of 0.19 to 0.21 g g-1 in the 0- to 0.1-m soil layer. Seeds (cv. Roberta, KWS genotype) were sown with a six-row precision pneumatic driller, with 0.16 m between seeds and 0.45 m between rows. Each plot (12 rows, 15 m long) was replicated two times. Plots were protected against soil surface crusting with a perforated plastic grid (5 by 5 mm holes) placed 0.50 m above the soil, to decrease the energy of raindrops falling on the soil. Surface layer and subsurface seedbed samples were sieved to determine their aggregate size distribution (5-, 10-, 20-, 30-, 40-, 50-mm diameters of circular sieve apertures). The sowing depths of 100 to 200 seed positions per plot were recorded (Table 3). The experimental plots were denoted as NP30, NPC25, and NPC35, the number at the end of the code representing the mean sowing depth in millimeters of the plot. The soil temperature was recorded hourly using sensors plugged at the mean sowing depth and connected to a data logger (Grant, Cambridge, UK). The mean daily temperatures were 5 to 15°C throughout the experiments. The soil water content was recorded daily, in the first 10 cm at centimeter intervals and remained at 0.16 to 0.22 g g-1 (-0.1 to -0.05 MPa) throughout the experiments. Bulk densities were measured using metal tubes of known volume (2 cm long, 5-cm diam.) to take soil samples and weigh them after drying at 105°C for 24 h. Measurements were replicated eight times and gave low values: 0.98 ± 0.04 SD, 1.14 ± 0.07 SD, and 1.19 ± 0.08 SD g cm-3 on NP30, NPC25, and NPC35 in the layer surrounding the seeds. Forty seeds were observed each day in each plot to record germination rates. Seedling emergence (800 seed positions for each plot) was recorded once or twice a day. Microprofiles in a vertical plane of the seedbed were observed once emergence had reached its maximum: the seed position in the seedbed and the seedling fate (germinated or not, abnormal without knocking an obstacle, blocked under an aggregate or not) were recorded. The hypocotyl length up to the soil surface was measured for emerged seedlings. The seedbed state around the hypocotyl was carefully recorded, especially the longest axis and position of aggregates met by the hypocotyl.
A complementary experiment was performed in laboratory conditions. A seedbed was created in tanks (58 by 58 by 10 cm3, replicated two times) filled with the same soil as in field experiments, sieved to have aggregates <5 mm, at a bulk density of 0.98 ± 0.02 SD g cm-3. Soil water content was kept at 0.19 g g-1 (-0.05 MPa) by covering the tanks with a plate. Temperature was regulated at 19°C. Seeds were sown at a mean depth of 17 mm, 50 mm in each direction from each other (102 seeds per tank, Véga, same seedlot as for the reference functions in the model). This treatment was denoted as SS17 (sieved soil). The same observations were made on seeds and seedlings as in the other experiments. Simulations were performed using the observed aggregate size distribution and position in the seedbed, the sowing depth distribution of each plot, germination thermal time distribution obtained on a standard test at 20°C (Table 3), and the hypocotyl elongation function distribution obtained on Véga and given as default values in the model. Each seedbed was simulated one-hundred times (N = 100, V = 20 by 8 by 4.5 cm3), and germination and emergence rates were established according to 1000 reiterations of seed sowing, with 10 seeds sown in each virtual seedbed. The statistical criteria used to compare the predicted Pi and observed Oi values of germination and emergence (Smith et al. (1996), n being the number of times germination or emergence were observed in each plot, are: the modeling efficiency, EF
 | (5) |
the root mean square error, RMSE
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and the coefficient of residual mass, CRM
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RESULTS AND DISCUSSION
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Frequency and Dimension of Encountered Clods
The number of seedlings that encountered a clod of a given size observed on microprofiles was compared with that predicted by the model using numerical sowings (Table 4). Results were in good agreement for aggregate grades >10 mm. However, the model for the 5- to 10-mm grade overestimated the number of clods encountered. This could be explained by the fact that smaller clods, especially 5- to 10-mm grade, are less easy to observe than bigger clods on field microprofiles. This difference cannot strongly influence the results of emergence simulation as those small clods block only very few seedlings (Table 1) and very slightly increase the length to the soil surface.
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Table 4. Percentage of seedlings having encountered a clod of a given grade, observed on microprofiles in field experiments (Obs) and simulated (Sim)
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Table 1. Probability that sugarbeet seedlings will be blocked under a given aggregate size and position in the seedbed
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Germination Kinetic and Seedling Path Length to the Surface
The final predicted germination rates were high and in good agreement with the observed values (Fig. 5)
. Differences between observed and simulated germination times were less than 5°C d (EF > 0.85 on all plots, Table 5), but CRM were positive, indicating that the majority of predicted values were less than the measured ones. This has been observed in other experiments when comparing germination rates obtained under field conditions to rates on filter paper. This could be due to a less efficient contact between seeds and plitted paper than in fine earth.
Hypocotyl path length measured in seedbeds was compared with those calculated by the model (Fig. 6)
. The predicted values were not statistically different from the observed ones (Kolmogorov test, P < 0.05). Clods had little effect on the path length: the mean path length is close to the mean sowing depth in each treatment (difference <2 mm). This is consistent with the calculation of the mean increase in the hypocotyl length calculated when it encounters the surface of a sphere in a random point: it ranges from 0.5 to 5.4 mm for sphere diameters ranging from 5 to 50 mm. The time taken to reach the soil surface depends mainly on the sowing depth and the soil temperature, even in sugarbeet cloddy seedbeds. The main effects of clods are on the emergence final rates because seedlings can remain blocked under clods.
Because of the differences between simulated and observed germination rates, changes with time in emergence rates were simulated using observed germination times to test only the effects of elongation rates and clods on the path of the hypocotyl.
Emergence Rates
The final emergence rates on the experimental plots were 85 to 95% (Fig. 7)
. Differences between the predicted and observed emergence rates were <10%. The sources of nonemergence were nongerminating seeds, seedlings with hypocotyls too short to reach the soil surface, and seedlings blocked under clods. NPC35 was the plot in which the difference between observed and predicted values of final emergence rates was the greatest. This was because the model overestimated the frequency of too-short hypocotyls on plots with large sowing depths (NPC35).
The predicted and observed emergence changes with time in the sieved soil experiment (SS17) were very close (EF = 0.99, Table 5), even though the predicted values were slightly less than observed ones (RMSE = 4.9%, CRM = 0.09). In contrast, the predicted changes in emergence with time were systematically greater than the observed values in field experiments. CRM were negative and between -0.2 and -0.4. There was no limitation in water or mineral supplies; temperatures were always in the optimum range during the experiments. The differences could only come from the elongation functions, as germination times used in the simulations were the observed ones. One difference can be that the seedlots and the varieties used were not the same as those used to obtain the reference functions in the model. But, there was almost no difference in the hypocotyl elongation rates of several genotypes (Dürr and Boiffin, 1995). Another difference could be in the mechanical impedance of the seedbeds. Bulk densities were slightly higher in the treatments compacted before seedbed preparation in the field experiments compared with those not compacted (P = 0.05) and were correlated with the seedbed cloddiness, which was also greater for those plots. But they remained low, very close to the SS17 plot, and there were no differences between the three field plots in emergence time correlated with the slight differences in bulk densities. This variable may not be sufficient to estimate the mechanical impedance around the growing hypocotyl. A soil strength measurement in the first few centimeters using a penetrometer might have shown differences between seedbeds.
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CONCLUSIONS
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The model was evaluated to distinguish the physical and biological effects of several submodels used to predict the emergence of sugarbeet. The evaluation of SIMPLE for situations with no obstacle in the hypocotyl path showed that the biological variations in seed and seedling behavior are correctly described under those conditions by the biological models of germination and elongation that were used and their parameters. The random drawings from distributions describing the seed and seedling population and the seed positions in the seedbed could be used to reproduce the spread of emergence time resulting from these characteristics of seeds and seedbed. The good agreement between observed and simulated values of hypocotyl lengths and number of clods encountered by seedlings indicated that the seedbed generator correctly described variations in aggregate sizes and spatial organization. The main sources of differences from field experiments were the elongation functions, which should be improved. It led to predict faster emergence than reality; the bias was 15 to 30°C d.
The model can be used as a tool for simulating some important effects of soil tillage and sowing operations, that is, the spatial organization of aggregates and of seeds in the seedbed layer. It also gives a spatial prediction of soil surface cloddiness and plant positions. Further planned improvements include the addition of a submodel predicting the changes in temperature and soil water content at depth steps of a few centimeters and according to changes in soil structure. This submodel should incorporate a soil strength–water content relationship that could improve the shoot growth prediction. Germination and emergence in dry conditions could also be predicted, which would widen the use of the model. A more accurate prediction of the dynamics of crust formation, which takes into account the soil surface state as it is described by the seedbed generator and the changes in crust water content and in crack patterns, should also be incorporated.
APPENDIX Symbols Used in Submodels
| Symbol |
Description |
Unit |
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| N |
number of simulated seedbeds |
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| x |
row width |
mm |
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| y |
row length |
mm |
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| z |
seedbed depth |
mm |
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| L |
the longest axis of clod |
mm |
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| l |
the intermediate axis of clod |
mm |
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| h |
the shortest axis of clod |
mm |
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| CRc |
threshold value for cumulative rainfall |
mm |
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| DRc1, DRc2 |
threshold value for daily rainfall |
mm |
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| P |
emergence probability of a seed |
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| d |
number of days for DRc2 comparison with rainfall data |
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| n |
number of simulated seeds |
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| i |
individual seed |
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| (xi, yi, zi) |
seed position in the seedbed layer |
mm |
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| SWi |
mass of the seed i |
mg |
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| Gi |
germination thermal time of the seed i |
°C d |
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| Li |
elongation function of the seed i |
mm |
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| a, b, c |
parameters of the elongation function |
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| Ei |
emergence time of the seed i |
°Cd |
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| RGRi |
cotyledon relative growth rate of seedling i |
mg mg-1 °C d-1 |
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| DWoi |
seedling i dry mass at emergence |
mg |
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| e, f, g |
parameters for prediction of early growth |
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| t |
time |
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| TTi |
cumulative soil thermal time from emergence time |
°C d |
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| TTSi |
cumulative soil thermal time from sowing |
°C d |
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ACKNOWLEDGMENTS
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We thank C. Leforestier, C. Dominiarzick, and P. Régnier for technical assistance and Dr. O. Parkes for checking the English text. This work was supported by ITB (Institut Technique de la Betterave) and by the Biopôle Végétal Picard.
Received for publication January 11, 2000.
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REFERENCES
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- Aubertot, J.N., C. Dürr, K. Kiêu, and G. Richard. 1999. Characterization of sugar beet (Beta vulgaris L.) seedbed structure. Soil Sci. Soc. Am. J. 63:1377–1384.[Abstract/Free Full Text]
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