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1.
Scales in transport of water to roots are compared with the length and volume scales by using the concepts associated with the representative elementary volume (REV). The possibility of a mismatch between model scale and system scale when using a Darcy‐Buckingham‐based model to describe soil water transport to a single root is evaluated. In the absence of a mismatch, the replication requirements for evaluating the Darcy‐Buckingham‐based model near a single root are discussed by using a synthesis of the elementary scales involved, including those for soil, plant and roots, and of the measurement device. By using REV scales from lattice‐Boltzmann simulations, the effective half‐root mean distance and the available measurement techniques, the evaluation of Darcy‐based single root uptake models is possible in roughly 50% of the combinations of soil‐ and root‐system properties. On the basis of an assessment of the scale characterizing natural soil variability, the number of replicates required to assess the average root water uptake profile near a single root is large, and either requires miniaturization of the measurement methods for the hydraulic transport characteristics, or very homogeneous (artificial) growing media with little variability. Variability of water uptake per unit root length will increase the number of samples required.  相似文献   

2.
Two plant species, tomato (Lycopersicon esculentum Mill.) and bitter gourd (Momordica charantia), were used for in‐depth studies on the dynamics of silicon (Si) uptake and translocation to the shoots and compartmentation of Si in the roots. The experiments were conducted under controlled environmental conditions in nutrient solutions, which were partly amended with 1 mM Si in the form of silicic acid. At harvest, xylem exudates were collected, and Si concentrations and biomass of roots and shoots were determined. Mass flow of Si was calculated based on the Si concentration of the nutrient solution and transpiration determined in a parallel experiment. Plant roots were subjected to a fractionated Si analysis, allowing attributing Si to different root compartments. Silicon concentrations in the roots compared to the shoots were higher in tomato but lower in bitter gourd. A more ready translocation from the roots to the shoots in bitter gourd was in agreement with Si concentrations in the xylem exudates which were higher than in the external solution. In tomato, the xylem‐sap Si concentration was lower than in the nutrient solution. Calculated Si mass flow to the root exceeded Si uptake in tomato, which was consistent with the measured accumulation of Si in the root water‐free space (WFS). In contrast, Si concentration in the root WFS was lower than in the nutrient solution in bitter gourd, reflecting the calculated Si depletion at the root surface based on the comparison of Si mass flow and Si uptake. Within the roots, more than 80% of the total Si was located in the cell wall and less than 10% in the cytoplasmic fractions in tomato. In bitter gourd, between 60% and 70% of the total root Si was attributed to the cell‐wall fraction whereas the proportion of the cytoplasmic fraction reached more than 30%. Our results clearly confirm that tomato belongs to the Si excluders and bitter gourd to the Si‐accumulator plant species for which high Si concentrations in the cytoplasmic root fraction appear to be characteristic.  相似文献   

3.
Plant fine roots are subject to continual turnover, i.e., old roots die during the plant life cycle and are quickly replaced by new roots. New roots grow partly into undepleted soil areas and can take up nutrients at a higher rate than old roots. This is one possible advantage of root turnover. It has been shown that root turnover of several plant species increases when P and/or K supply is limited, indicating an efficiency mechanism. The objective of this study was to assess the maximum benefit for nutrient uptake by root turnover and to determine which soil or plant properties influence this process. Based on a data set of field‐grown faba beans, a sensitivity analysis with a transport and uptake model was performed, i.e., several input parameters were systematically varied to assess their importance for nutrient uptake of a root system with and without fine‐root turnover. The calculations were based on the assumptions that all new roots grow into undepleted soil areas and that no inter‐root competition occurs. Model calculations indicated that a root system with a high but realistic turnover rate can take up twice the amount of P or K compared to a stable root system without any turnover. This benefit on uptake is higher at low concentrations of these nutrients in soil solution, low soil water content, or high maximum inflow. However, measured uptake under poor conditions of nutrient supply is often higher than calculated uptake, even when root turnover is taken into account. This indicates that root turnover might be an efficiency mechanism, but not the only one.  相似文献   

4.
The soil preference with respect to soil acidity of Asplenium scolopendrium L., Dryopteris filix‐mas (L.) Schott, Pteridium aquilinum (L.) Kuhn as well as of subspecies of the Asplenium trichomanes L. and Polypodium vulgare L. complexes were studied in relation to root cation‐exchange properties. Data were collected for substrate acidity, soil exchangeable cations, and root cation‐exchange capacity. Acidiphilous pteridophytes were characterized by low cation‐exchange capacities. It is unlikely that cation‐exchange properties protect plants from potentially harmful cations such as aluminium or hydrogen, which are abundant under acid soil conditions, through immobilization. It is postulated that cation‐exchange properties are a secondary adaptation to soil acidity, in addition to major adaptations which determine the apparent soil preference. Possibly, a limited variation in cation‐exchange capacity as a function of soil conditions could prevent harmful interactions of soil exchangeable cations with the cation‐exchange sites, such as displacement of cell wall calcium by aluminium or hydrogen ions in acid soils.  相似文献   

5.
A pot experiment was conducted to test the effect of three microbial regimes on the time course of heavy metal uptake in clover and maize from an industrially polluted soil. The three treatments included: (1) an intact flora of bacteria and fungi, including indigenous arbuscular mycorrhizal (AM) fungi together with soil microfauna; (2) the indigenous bacterial/fungal flora except AM fungi, reintroduced into sterilized soil; or (3) the same bacterial/fungal flora plus an AM fungus. For the final harvest, two pot sizes were included to assess the effect of root density. Plant uptake of P and heavy metals varied according to plant species, harvest time and soil treatment. For both plant species, shoot concentration of Zn, Cd and Cu decreased and Ni increased with plant age. Plants growing in sterilized soil with reintroduced AM fungi generally grew better, but contained higher concentrations of heavy metals than those colonized by indigenous AM fungi. Plants with mycorrhiza frequently contained more P, Zn, Cd, Cu and Pb in roots and shoots compared to nonmycorrhizal plants. Elevated root/shoot concentration ratios of P and metals indicate a sequestration of metal phosphates in mycorrhizal roots. Mycorrhizal performance was influenced by root density. At low root densities, metal concentrations in mycorrhizal plants were reduced, whereas it had no effect at high root densities when the entire soil volume was efficiently exploited by roots. We conclude that root density data are essential for interpretations of the influence of AM on metal uptake in plants.  相似文献   

6.
采用盆栽方式,探讨了栽培于腐熟羊粪、沙土、轻粘土中的平邑甜茶[Malus hupehensis(Pamp) Rehd] 幼树的生长、根系形态与营养吸收的特性。结果显示,羊粪处理平邑甜茶幼树新梢生长量最大,主根和侧根粗长、侧根多,对磷、钙及铁的吸收能力较低;沙土处理的新梢生长量最小,侧根细及少,对磷、钾、钙、铁及锌等元素的吸收能力强;粘土处理的新梢生长量和根系特征参数居于羊粪和沙土处理之间。沙土施羊粪后,平邑甜茶幼树新梢生长量增大,主根增粗、增长,侧根增多且粗长,对磷、钾、钙、铁及锌等营养元素的吸收能力明显下降;而粘土施羊粪,植株叶片增多,主根粗度及长度降低,二级侧根增多、增粗,对钾的吸收能力提高。  相似文献   

7.
Abstract

Although models of nitrogen (N) flow in agroecosystems describe total plant N uptake, only limited data on roots exists. Underground dry matter and N distribution patterns in corn (Zea mays L.) were determined by isolating root segments from soil cores collected around plants at anthesis from a Typic Kanhapludult. Samples were collected from two treatments: no‐till with 70 kg N/ha and conventional tillage and planting with crimson clover (Trifolium incarnatum L.) as a N source. Seven soil cores (4.2 cm diameter) per plant were taken to recover roots in the 0‐ to 15‐cm and 15‐ to 30‐cm depth intervals. Sampling positions were at the base of the plant and at distances (perpendicular to the row) of 6, 16, and 27 cm into the trafficked interrow, and 11, 22, and 32 cm into the untrafficked interrow. Underground shoot and root segments were isolated from soil cores by hydropneumatic elutriation. Root distribution patterns in the no‐till treatment were similar in trafficked and untrafficked interrows, but more roots were detected in the untrafficked interrows than in the trafficked interrows in the tillage treatment. Averaged over treatments, 85 % of the root weight and 81% of the root N were in the 0‐ to 15‐cm depth interval. The root: shoot dry matter ratio was 0.27:1 and the root: shoot N content ratio was 0.20:1. Carbon: nitrogen (C:N) ratios were higher in underground shoot (118:1) and coarse root fragments (78:1) than in aboveground shoot (42:1) or fine root fragments (33:1).  相似文献   

8.
In nitrogen-loaded areas, many forest stands show a positive growth response to the increased nitrogen input. However, with extensive soil acidification and cation leakage, damage in forest stands is frequently observed, in particular in mature forest stands. The most important soil-mediated factors which cause a reduction in fine-root growth and mycorrhizal development are: (i) high nitrogen/cation ratios and (ii) aluminium (Al) toxicity, viz. elevated Al/cation ratios, leading to an increased sensitivity of the root systems to environmental stress. Extensive data on fine-root growth in response to experimental manipulation of plant nutrients in the forest soil are available from many large-scale field experiments in Sweden. It is concluded from the data that Al toxicity should be considered as a predisposing factor for forest decline on SW Swedish sites, reducing root function and inhibiting nutrient uptake. A chronically high nitrogen deposition is furthermore likely to produce longer-lasting damage symptoms on fine roots and their function. Aluminium-induced deficiencies of important cations in the forest trees may contribute to forest decline. In SW Swedish forest stands, potassium deficiency is likely to be another important predisposing factor.  相似文献   

9.
Aerated solution culture is frequently used for studying plant growth. Few comparisons have been made of root growth in solution with that found in soil. The objective of this study was to compare root growth and root hair development in these two mediums. Corn (Zea mays L.) grown in aerated solution at two temperatures (18 and 25°C) and three P concentrations (2, 10, and 500 μmol L‐1) was compared with that in three soils, Raub (Aquic Argiudoll) and two Chalmers (Typic Haplaquoll) silt loams, in a controlled climate chamber over 21d. Corn plant weight and root growth were similar in solution culture and Raub soil when grown at an air and soil temperature of 18°C. At 25°C both yield and root growth were greater in Raub soil, even though P uptake by corn was 7‐fold greater in solution culture. The same difference was found when corn grown at 25°C in solution culture at 3 different P concentrations was compared with that grown in Chalmers soil at two P levels. Percentage of total root length with root hairs, root length and density and consequently root surface area, were all greater in the Chalmers soil than in solution culture. An increase in soil P, resulted in a decrease in root hair growth. No such relationship was found in solution culture. Although the recovery and measurement of plant roots and root hairs is more convenient in solution culture, results from this study indicate that the usefulness of solution culture for determining those factors which control root growth and root hair development in soil is limited.  相似文献   

10.
Fifty-six sites throughout the Wimmera region of Victoria were sampled to 1 m depth, and 1:5 extracts analysed for pH, conductivity and cation content. The relationship between conductivity measured in saturated extracts and 1:5 extracts at five sites was used to calculate cation concentrations expected if saturated extracts had been prepared. Soils were generally alkaline and cations at depth were dominated by sodium. The ratio of sodium to calcium varied from <2.6 (10% of samples) to >85.5 (10%) to a maximum of 247.1. It exceeded 12.8 in 40% of samples, and exceeded 45.6 in 20% of samples, levels which are likely to reduce root growth and ability of roots to exclude sodium. Higher ratios were associated with depth, pH and conductivity. The ratio of magnesium to calcium exceeded 1 in 80% of samples, 2 in 55% of samples, 3 in 30% of samples and the maximum measured was a ratio of 7.6, suggesting plant growth may be reduced. The issues of extrapolating from experiments in solution culture to soil, and errors likely in using 1:5 extracts are discussed.  相似文献   

11.
Phosphorus is one of the most limiting macronutrients for plant productivity in agriculture worldwide. The main reasons are the limited rock phosphate reserves and the high affinity of phosphate (P) to the soil solid phase, restricting the P availability to the plant roots. Plants can adapt to soils low in available P by changing morphological or/and physiological root features. Morphological changes include the formation of longer root hairs and a higher root : shoot ratio both parameters increasing the root surface which provides the shoot with P. This may be successful if the P availability in soil, i.e., the P concentration of the soil solution is not extremely low (> 1–2 µM P). If the P concentration of the soil solution is lower, the diffusive flux to the root surface will be very low and may not satisfy the P demand of the shoots. Under these conditions plants have developed strategies to increase the rhizosphere soil solution concentration by secreting mobilizing agents. The most effective way of P mobilization is the release of di‐ and tricarboxylic acid anions, especially oxalate and citrate. Citrate can accumulate in the rhizosphere up to concentrations up to 80 µmol g?1 soil. Cluster root formation is an efficient way of carboxylate accumulation in the cluster root rhizosphere improving P mobilization. Cluster roots strongly improve the acquisition of the mobilized P. Considering a single root, around 80–90% of the mobilized P diffuses away from the root. From the rhizosphere of cluster roots, most of the mobilized P is taken up by the cluster roots. Both, the strong accumulation of carboxylates in and the effective P uptake from the cluster‐root rhizosphere are the basis of the unique ability of P acquisition by cluster root‐forming plants. Plants that do not form cluster roots, e.g., red clover, can also accumulate carboxylates in the rhizosphere. Red clover accumulates high quantities of citrate in the rhizosphere soil. Model calculations show that the release of citrate by red clover roots and its accumulation in the rhizosphere strongly improve P acquisition by this plant species in various soils. Similar results are obtained with alfalfa. In sugar beet, oxalate release can strongly contribute to P acquisition. In summary, P acquisition can be strongly improved by the release of carboxylates and should be taken as a challenge for basic and applied research.  相似文献   

12.
黄土区植物根系对营养元素在土壤剖面中迁移强度的影响   总被引:12,自引:2,他引:12  
不同植物群落根系对土壤元素迁移具有显著影响,不同基因型植物细根的特殊剖面分布特征,是其适应和改善土壤养分物理化学逆境的生理生态学基础。采用原状土柱淋滤实验装置及大型挖掘剖面壁法,在陕北黄土丘陵沟壑区研究并定量分析了不同径级根系对黄土中营养元素K、Na、Ca、Mg、Cu、Mn、Fe、Si、Al迁移强度的影响,旨在探索土壤养分生物有效性的提高途径。结果表明,不同植被类型土壤营养元素淋溶迁移的剖面差异并非完全取决于土壤中元素或矿物含量的大小,而是主要受制于直径1mm的须根根系在剖面中的缠绕分布特征。不同植被类型土壤中营养元素的迁移强度随土层深度增加呈递减规律。不同植物根系对黄土中营养元素迁移强度的影响具有显著差异,其大小顺序为:林地草地农地。林、草地土壤中元素迁移强度序列有明显变异的临界土层深度分别在30cm和10cm处。在林、草地和农地土层中常量元素水迁移强度序列为CaNaMgKSiAl,微量元素基本为CuMnFe。植物根系对营养元素迁移能力的影响具有明显的区域范围,随着直径1mm有效根密度和根量的增大,根系对土壤元素迁移强度的影响显著增强。  相似文献   

13.
Abstract

In soil solutions the sum of cations is equivalent to that of anions. Anions are soluble or precipitated as less soluble salts. Therefore, the sum of soluble anions are responsible for the sum of cations in the soil solution. Soluble nitrate anions are unstable as they immobilize in biological materials. Hydrogen carbonate is excreted from plant roots and decomposes into carbon dioxide and carbonate. Carbonate reacts with hydrogen ions and forms complexes and ion pairs with calcium ions. Sulphate and chloride are more stable in the soil solution as anions.

Chloride ions were found to increase the activity of cations in the soil solution and to increase uptake of cations through the entire growth period. Increased absorption of cations increased yield. In temperate climate regions the surplus of chloride leaches from the root zone during winter.  相似文献   

14.
Water uptake by roots and resulting water redistribution along the soil profile depend on soil hydraulic properties and root distribution, as well as on the physical, chemical, and biological soil–plant interactions that occur in the root zone. The hydraulic properties of the soil in the root zone are difficult to investigate in situ at the needed high spatial resolution, and they still present important open questions. For instance, is there more or less water at the root–soil interface compared to the bulk soil? Neutron radiography (2‐D) and tomography (3‐D) are efficient methods to answer such questions, providing the possibility to image simultaneously water distributions and root structure in situ at high spatial resolution. We planted a lupin and a maize in rectangular boxes filled with sandy soils. The plants were grown for 3 weeks at controlled conditions. Infiltrated water and subsequent water redistribution were imaged for 5 d at regular intervals by means of neutron radiography and tomography. Soil water‐content distributions were quantified from the radiographs after correcting for neutron scattering. The radiographs showed that the water content in the root zone was higher than in the bulk soil both during and after infiltration. Similarly, the tomograms showed localized regions of high water content around some locations of the roots, in particular near the tips of the lupin. Local regions of water depletion, which are expected as a consequence of water uptake, were visible along the main root where laterals branched. These results reflect the complexity of soil–plant–water relations, showing the different properties of bulk soil and root zone, as well as the varying moisture gradients along the root system.  相似文献   

15.
The aim of this research was to identify and quantify gaps in currents methods and models for predicting the plant availability of selected nutrient and contaminant metals (Cu, Ni, Zn, Cd) in soil. This study investigated relationships between the relative solubility of Cu, Ni, Zn, and Cd determined by six extraction methods with short-term uptake by shoots and roots of wheat (Triticum aestivum). For Cu, Ni, and Cd, relationships between solubility and plant uptake were found to be different for shoots and roots, with Cu and Ni solubility being more closely correlated with root uptake compared with shoot uptake. Correlation coefficients for Cd concentrations in shoot and root tissue for all six solubility methods were poor (r 2?<?0.5), while corresponding results for Zn explained more than 50 % of shoot variation but less than 50 % of root variation. Soil Cu solubility explained up to 85 % of variation in root uptake compared with 42–55 % for shoot uptake. These results clearly demonstrated that purely chemical and passive diffusion mechanisms were inadequate predictors of Cd uptake by shoots and roots, together with Cu uptake by shoots. Thus further attempts at refining soil metal bioavailability assays based solely on chemical extraction without consideration of plant responses are unlikely to improve prediction of plant uptake.  相似文献   

16.
Previous studies describe the suitability of a new type of phosphorus (P) fertilizer, called “rhizosphere‐controlled fertilizer” (RCF), to supply available P to plants while reducing soil phosphorus fixation. In order to explore the involvement of organic acid root exudation in P uptake from RCF, we investigated the relationship between shoot and root P concentrations, and the concentration of the main polycarboxylic organic acids in roots, shoots, and plant exudates. Plant species with different P‐acquisition efficiency (low: maize; medium: chickpea; high: lupin) were grown in hydroponics with three different P fertilizers: The water‐insoluble P fraction of RCF (RCF); Phospal, a slow‐release source of phosphate composed of calcium and aluminum phosphates (PH); monopotassiumphosphate (KP), and a control treatment without P (P–). RCF was as efficient as KP in supplying P to plants in the case of chickpea and lupin, and slightly less efficient than KP in maize. However, P from PH was not available for maize and less available compared to KP and RCF in chickpea and lupin. This variation reflects the different efficiencies in P acquisition for the three plant species. Except in the case of maize, plants receiving KP presented the lowest concentration of organic acids in roots and exudates, while those plants suffering severe P deficiency (P– and PH) showed the highest organic acid concentration. However, RCF had a high concentration of organic acids in roots and exudates, as well as a high P concentration in the shoot indicating that P uptake from RCF is enhanced due to root release and action of specific organic acids.  相似文献   

17.
The soil organic matter plays a key role in ecological soil functions, and has to be considered as an important CO2 sink on a global scale. Apart from crop residues (shoots and roots), left over on the field after harvest, carbon and nitrogen compounds are also released by plant roots into the soil during vegetation, and undergo several transformation processes. Up to now the knowledge about amount, composition, and turnover of these root‐borne compounds is still very limited. So far it could be demonstrated with different plant species, that up to 20 % of photosynthetically fixed C are released into the soil during vegetation period. These C amounts are ecological relevant. Depending on assimilate sink strength during ontogenesis, the C release varies with plant age. A large percentage of these root‐borne substances were rapidly respired by microorganisms (64—86 %). About 2—5 % of net C assimilation was kept in soil. The root exudates of maize were mainly water‐soluble (79 %), and in this fraction about 64 % carbohydrates, 22 % amino acids/amides and 14 % organic acids could be identified. Plant species and in some cases also plant cultivars varied strongly in their root exudation pattern. Under non‐sterile conditions the exuded compounds were rapidly stabilized in water‐insoluble forms and bound preferably to the soil clay fraction. The binding of root exudates to soil particles also improved soil structure by increasing aggregate stability. Future research should focus on quantification and characterization of root‐borne C compounds during the whole plant ontogenesis. Apart from pot experiments with 14CO2 labeling, it is necessary to conduct model field experiments with 13CO2 labeling in order to be able to distinguish between CO2 originating from the soil C pool and rhizosphere respiration, originating from plant assimilates. Such a separation is necessary to assess if soils are sources or sinks of CO2. The incorporation of root‐borne C (14C, 13C) into soil organic matter of different stability is also of particular interest.  相似文献   

18.
An understanding of the phosphorus, P, uptake characteristics of plant roots is important for developing practices that improve P fertilizer efficiency. Phosphorus uptake by plant roots is influenced by plant root properties and solution P level. Since little information about the nutrient uptake characteristics of spring wheat (Triticum vulgare L.) roots is available, this research was undertaken with wheat to determine the relation between the proportion of the roots supplied with P on P influx and root growth characteristics. An experiment was conducted with wheat plants grown in solution culture in a controlled climate chamber.

Phosphorus uptake kinetics were measured on 30‐day‐old wheat using split‐root experiments. Supplying P to only part of the root system resulted in lower plant P concentration and higher Imax(maximum influx) by the roots. The Imax value of wheat roots was much lower than corn (Zea mays L.) and soybeans (Glycine max L.), but the values of Km (the solution P concentration where influx, In is 1/2 Imax) and Cmin (the solution P concentration where influx, In is 1/2 Imax) were greater than those of both corn and soybean crops grown in similar experiments. Phosphorus concentrations in wheat plant's shoots and roots were higher than those for corn and soybean with the same proportions of roots in P solution. Decreasing the proportion of the roots supplied with P had no statistically significant (p = 0.05) effect on shoot dry weight. This differs from the results for corn and soybeans where it decreased significantly as the proportion of the roots exposed to P decreased. These results indicate that the effect of P placement on P uptake and on plant root growth varied among species.  相似文献   


19.
分层供水和表层施锌对玉米植株生长和锌吸收的影响   总被引:1,自引:0,他引:1  
进行分层水分隔离盆栽试验,模拟田间不同层次土壤中水分含量分布不均条件,研究表层土壤施锌情况下,玉米植株生长和锌吸收以及根系在表层和底层土壤中的分配。结果表明,施锌明显促进了玉米地上部生长。在土壤表层水分充足时,施锌对植株增长效果较明显,有利于玉米利用土壤水分。缺锌条件下,改善土壤水分并未显著提高玉米生物量。表层土壤干旱时,上下层土壤中根系干物重之比减小,底层土壤中根系分布相对增加,当表层土壤水分增加时,根系在表层土壤中干物重显著增加,分布相对增多。施锌并没有影响根系在不同层次土壤中的分配。表层土壤水分对苗期玉米植株锌吸收总量有显著影响,干旱条件下,玉米植株锌吸收总量下降;底层土壤水分供应状况对玉米锌浓度影响不大,但植株中锌向地上部运转增加。尽管施锌没有提高生长早期玉米根系生长和对底层土壤水分的利用,但本研究表明缺锌旱地土壤上如通过灌溉等措施增加了耕层土壤水分,应该注意施用锌肥,否则严重影响玉米生物量和玉米对土壤水分的利用效率。  相似文献   

20.
A model for simulation of wheat root growth under non-optimal conditions has been developed. The following influences on root growth are considered: soil temperature; soil water suction and mechanical resistance dependent on soil density and soil water content; the occurrence of soil cracks. The probability of root tips finding cracks, where unimpeded growth can occur, is given special consideration, including the effect of changes in the crack system with changes in soil water content. Water uptake is calculated, and by use of a transpiration coefficient an estimate of dry-matter production is made. This is partitioned between roots, leaves and stem and later grain. Effects of soil fertility are not yet considered in this model.A sensitivity analysis of the model was made by varying the soil density profile, the occurrence of cracks, sowing date and plant density for several years of weather data. The variability, caused by the fact that only a limited number of root axes was simulated in each run and guided by random numbers, was also investigated.The model can be used to assess the effects of compaction on wheat yield, and also the likely benefits which may be derived from sub-soiling or slit-tillage.The model is written in Digital's VAX FORTRAN language, and a run for one growing season takes less than 10 seconds of CPU-time on a VAX 11/785 computer.  相似文献   

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