Numerical approaches for 1D morphodynamic modelling

Existing methods for solving 1D morphodynamical systems have been reviewed and new, improved approaches have been identified. Usually the flow equations and the bed-updating equation are solved at separate time steps, using a quasi-steady approach. In this paper we have investigated the simultaneous (or coupled) solution of the equations. The schemes tested are the Lax–Wendroff and the Roe schemes, both with and without flux-limiting methods. Furthermore the discretisation of source terms has been investigated and has shown to be important.     

Mathematical modelling of volcanic tsunamis

The height of widespread tsunami runup about the Bay of Plenty from various volcanic scenarios involving eruptions at White Island is shown to be insignificant in all cases considered, except for Krakatoa‐type explosions. The problem of localised inundation remains unanswered. Some definitions describing volcanic tsunami risk, introduced recently by J. Latter (Bulletin volcanologique 1982), are briefly mentioned. All numerical calculations assumed cylindrical symmetry and used a flux‐corrected Lax‐Wendroff algorithm to solve the modified shallow water equations of Peregrine.     

A three-dimensional hydrodynamic model of estuarine circulation with an application to Southampton Water, UK

A three-dimensional hydrodynamic model has been developed to simulate water mass circulation in estuarine systems. This model is based on the primitive equation in Cartesian coordinates with a terrain-following structure, coupled with a Mellor–Yamada 2.5 turbulence scheme. A fractional-step method is applied and the subset of equations is solved with finite volume and finite element methods. A dry–wet process simulates the presence of the tidal flat at low water. River inputs are introduced using a point-source method. The model was applied to a partially mixed, macrotidal, temperate estuary: Southampton Water, UK. The model is validated by comparisons with sea surface elevation, ADCP measurements and salinity data collected in 2001. The mean spring range 2(M₂ + S₂) and the mean neap range 2(M₂ − S₂) are modelled with an error relative to observation of 12 and 16%, respectively. The unique tidal regime of the system with the presence of the ‘young flood stand’ corresponding to the slackening conditions occurring at mid flood and ‘double high water’ corresponding to an extension of the slackening conditions at high tide is accurately reproduced in the model. The dynamics of the modelled mean surface and bottom velocity closely match the ADCP measurements during neap tides (rms of the difference is 0.09 and 0.01 m s⁻¹ at the bottom and at the surface, respectively), whereas at spring the difference is greater (rms of the difference is 0.25 and 0.20 m s⁻¹ at bottom and surface, respectively). The spatial and temporal variation of the degree of stratification as indicated by salinity distributions compares well with observations.     

A preliminary study of age and growth of the monkfish Lophius upsicephalus (Pisces: Lophiidae) on the Agulhas Bank,South Africa

The sagittal otoliths of Lophius upsicephalus, although extremely variable in shape, were found to be the only structures suitable for age estimation. The annuli are multi-ringed zones separated by "wider than normal" opaque zones. They are difficult to interpret, especially those of fish older than nine years. Periodicity of annulus formation could not be determined by standard methods. By inference, annulus formation could be related to feeding habits and reproductive seasonality. The growth in length (sexes combined) is best described by

Length-at-age = 733,7 (1 – e^{?0,1054 (t + 1,879)})mm.

There is a significant difference in growth by mass between the sexes. The respective equations describing growth by mass (in g) for males and females are:

Weight-at-age = 8616 (1 – e^{?0,1054 (t + 1,879)})^2,805 and

Weight-at-age = 9499 (1 – e^{?0,1054 (t + 1,879)})^2,890.     

Origin and decomposition of sinking particulate organic matter in the deep water column inferred from the vertical distributions of its δN, δ and δ

Sinking particles were analyzed for their nitrogen isotopic ratio δ¹⁵N) of total particulate nitrogen (PN), stable carbon isotopic ratio (δ¹³C) and radioactive isotopic ratio (δ¹⁴C) of total particulate organic carbon (POC), at three different latitudinal (temperate, subpolar and equatorial) and geomorphological (trench, proximal abyssal plain and distal abyssal plain) sites in the western North Pacific Ocean using year-long time series sediment trap systems, to clarify the common vertical trends of the isotopic signals in deep water columns. Although the δ¹⁵N and δ¹³C values of sinking particulate organic matter (POM) were partly affected by the resuspension of sedimentary POM from the sea floor, especially in the trench, the changes in δ¹⁵N and δ¹³C values owing to the resuspension could be corrected by calculation of the isotopic mass balance from δ¹⁴C of sinking POC. After this correction, common downward decreasing trends in δ¹⁵N and δ¹³C values were obtained in the deep water columns, irrespective of the latitudes and depths. These coincidental isotopic signals between δ¹⁵N and δ¹³C values provide new constraints for the decomposition process of sinking POM, such as the preferential degradation of ¹⁵N- and ¹³C-rich compounds and the successive re-formation of the sinking particles by higher trophic level organisms in the deep water column.     

A study of numerical model equations of circulations in East China Sea

Recently many authors have attepmted to model circulations in East China Sea by numerical means, for example, Xi et al^1),2). (henceforth Ref.[1] is referred to as A and[2] as B respectively), Yuan et al. and Chio. We had raised questions in regard to the correctness of the governing equations used in A, as well as their choice of boundary conditions. Comparing numerical solution of A with that of B which employed a correct form of governing equations (but with an incorrect value for the bottom friction coefficient), B asserted that the governing equations used in A were correct. It is, therefore, appropriate to have a discussion on the formulation of proper equations.     

长牡蛎F3 代快速生长选育群体生长特性的研究

采用模型拟合方法研究了长牡蛎(Crassostrea gigas)F3代快速生长选育群体不同时期各生长性状的发育规律。结果表明,长牡蛎幼虫期壳高(SH)、壳长(SL)对日龄(t)的回归遵循Logistic模型,生长方程分别为SH=455.612/(1+9.500e-0.142t),R2=0.999;SL=462.476/(1+8.026e-0.108t),R2=0.996。幼虫期壳高与壳长成直线相关,回归方程为SL=0.76SH+18.82,R2=0.994。长牡蛎养成期各生长性状呈现明显的季节变化,壳高(SH)、壳长(SL)、壳宽(SW)和总质量(TW)对月龄(X)的多项式回归方程分别为SH=-0.0297X4+1.0365X3-12.0220X2+57.6500X-68.9260,R2=0.985;SL=-0.0173X4+0.5893X3-6.5702X2+30.2420X-34.4150,R2=0.986;SW=-0.0068X4+0.2620X3-3.2806X2+16.9170X-22.1410,R2=0.956;TW=-0.0219X4+0.8234X3-10.1680X2+50.7040X-85.4110,R2=0.972。壳高、壳长、壳宽与总质量均呈幂函数相关,回归方程分别为SH=23.645TW0.3213,R2=0.998;SL=12.337TW0.3776,R2=0.995;SW=6.611TW0.3589,R2=0.981。     

A chemical model for the major electrolyte component of seawater based on the Brønsted-Guggenheim hypothesis

The Brønsted-Guggenheim hypothesis of specific ionic interaction is used to develop a chemical model for the major electrolyte components in seawater (Na⁺---K⁺---Mg²⁺---Ca²⁺---Cl⁻---SO₄²⁻ at 25°C and 1 atm total pressure. The model is shown to be in essential agreement with models based on the Bjerrum ion-association hypothesis (e.g., Garrels and Thompson, 1962), with calculations based on the ionic hydration and cluster expansion theories of electrolyte solutions, and with available experimental evidence.The Brønsted-Guggenheim model is computationally simpler than the currently accepted Bjerrum model and results directly in the conventional total single-ion activity coefficients that are most commonly required for calculations in seawater equilibria. The simple form of the equations should enable the model to be extended quite readily to cover a wide range of temperature, pressure and solution composition. However, applications are at present restricted by the availability of the appropriate interaction coefficients.     

Excretion and respiration rates of the scyphomedusa <Emphasis Type="Italic">Aurelia aurita</Emphasis> from the Inland Sea of Japan

We measured the ammonium excretion, phosphate excretion and respiration rates of the scyphomedusa Aurelia aurita from Ondo Strait, in the central part of the Inland Sea of Japan, at 28 and 20°C. The rates measured at 28°C were converted to those at 20°C using the Q₁₀ values, i.e. 1.56, 1.57 and 2.80, for ammonium excretion, phosphate excretion and respiration rates, respectively. The composite relationships between metabolic rates and wet weight of a medusa (WW, g, range 11–1330 g) at 20°C were expressed by the following allometric equations. For ammonium excretion rate (N, μmoles N medusa⁻¹d⁻¹): N = 0.497WW ^1.09, phosphate excretion rate (P, μmoles P medusa⁻¹d⁻¹): P = 0.453WW ^0.84, and respiration rate (R, μmoles O₂ medusa⁻¹d⁻¹): R = 96.9WW ^1.06. Mean O:N ratios (i.e. atomic ratios of 16.9 and 11.0 at 28 and 20°C, respectively) indicated that the metabolism of A. aurita medusae was protein-dominated. These metabolic parameters enabled us to estimate the nitrogen and phosphorus regeneration rates of an A. aurita medusa population typical of early summer in the Ondo Strait (means of water temperature, medusa individual weight and population biomass: 20°C, 200 g WW and 50.8 g WW m⁻³, respectively). Regenerated nitrogen and phosphorus were equivalent to 10.0 and 21.6% of phytoplankton uptake rates, respectively, nearly twice that estimated for mesozooplankton, demonstrating that A. aurita medusae are key components of the plankton community, influencing the trophic and nutrient dynamics in the Ondo Strait during early summer.     

Pb and Po, manganese and iron cycling across the O2/H2S interface of a permanently anoxic fjord: Framvaren, Norway

Vertical profiles of dissolved and particulate ²¹⁰Po and ²¹⁰Pb were measured across the redox transition zone at Station F1 in Framvaren Fjord, Norway. In this fjord, a sharp decrease in pH above the O₂/H₂S interface facilitates the aerobic dissolution of MnO₂. In contrast, Fe(II) concentrations begin to increase only at the O₂/H₂S interface depth. Activity profiles reveal that dissolved ²¹⁰Po and ²¹⁰Pb are sequestered efficiently by particulates in surface waters. As polonium-210 and lead-210 activities descend down into the aerobic manganese reduction (AMR) zone, they are remobilized during the reductive dissolution of the carrier phase oxyhydroxides. Both ²¹⁰Po and ²¹⁰Pb are highly enriched at the O₂/H₂S interface where an active community of microbes, such as anoxygenic phototrophs (e.g., Chromatium, Chlorobium sp.), thrives. The coincident peaks in ²¹⁰Po, ²¹⁰Pb and microbial biomass suggest a strong biological influence on the behavior of these radionuclides. There is a strong covariance between the vertical distribution of Mn and Pb, indicating that their redox cycling is closely coupled and is likely microbially mediated.     

Seasonal variation of Mn adsorption on to calcareous surfaces in the English Channel, and its implication on the manganese distribution coefficient

Dissolved and particulate manganese in seawater samples derived from the English Channel has been analyzed using graphite furnace atomic absorption (GFAAS), and inductively coupled plasma atomic emission (ICP—AES) spectroscopies. Because of the high contents of carbonate minerals found in the suspended matter samples, the English Channel constitutes an ideal field area for the study of the Mn²⁺/Ca²⁺/CaCO₃ system. Owing to the chemical speciation of particulate manganese and the combined use of the X-ray diffraction and electron spin resonance spectroscopy we have shown the importance of the carbonate phase in the stabilization of manganese (II). This has been confirmed by p-pH measurements in the field. All these studies have also indicated that: (1) manganese is associated with calcite in the form of a solid solution, Mn_xCa_1−xCO₃; and (2) significant increases in the concentrations of particulate manganese, especially in offshore waters, occur in summer. This seasonal phenomenon has been attributed to the proliferation of coccolithophorids, which are known to be covered with calcified skeletons at high specific surface areas. To appraise the implication of the coccolithophorid-blooms phenomenon on the Mn²⁺/Ca²⁺/CaCO₃ system, we have used the manganese distribution coefficient, D_i, between the liquid phase and CaCO₃ particles. Overall we have shown that: (1) D_i in summer (i.e. when coccoliths considered as very fine-grained calcite are abundant) is much higher than that obtained in winter; and (2) in the vicinity of the French coast, D_i does not vary significantly even in summer. This is because of the high content of chalk-derived particles found in the near-shore waters.     

Relationship between cadmium and phosphate in the northwest Pacific Ocean

The relationship between Cd and PO₄ in the Kuroshio and Oyashio regions and the Okhotsk Sea was examined. The resultant equations are as follows: Cd (ng l^–1)=37.0 PO₄ (M)+2.6; Cd(ng l^–1)=32.1 PO₄ (M)+1.2 and Cd (ng l^–1)=34.1 PO₄ (M)+7.9, respectively. These results are in good agreement with previously reported studies, and indicate that during removal from surface waters to deeper waters by biological assimilation and regeneration in deeper waters Cd and PO₄ maintain the same ratio in the open ocean. The relationship between Cd and PO₄ in coastal waters, however, differed from that in the open ocean.     

The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C

The pK₁^* and pK₂^* for the dissociation of carbonic acid in seawater have been determined from 0 to 45°C and S = 5 to 45. The values of pK₁^* have been determined from emf measurements for the cell:

Pt](1 − X)H2 + XCO2|NaHCO3, CO2 in synthetic seawater|AgC1; Ag

where X is the mole fraction of CO₂ in the gas. The values of pK₂^* have been determined from emf measurements on the cell:

Pt, H2(g, 1 atm)|Na2CO3, NaHCO3 in synthethic seawater|AgC1; Ag

The results have been fitted to the equations:

lnK^*₁ = 2.83655 − 2307.1266/T − 1.5529413 lnT + (−0.20760841 − 4.0484/T)S^0.5 + 0.08468345S − 0.00654208S¹

InK^*₂ = −9.226508 − 3351.6106/T− 0.2005743 lnT + (−0.106901773 − 23.9722/T)S^0.5 + 0.1130822S − 0.00846934S^1.5

where T is the temperature in K, S is the salinity, and the standard deviations of the fits are σ = 0.0048 in lnK₁^* and σ = 0.0070 in lnK₂^*.Our new results are in good agreement at S = 35 (±0.002 in pK₁^*and ±0.005 in pK₂^*) from 0 to 45°C with the earlier results of Goyet and Poisson (1989). Since our measurements are more precise than the earlier measurements due to the use of the Pt, H₂|AgCl, Ag electrode system, we feel that our equations should be used to calculate the components of the carbonate system in seawater.     

Consumption,absorption efficiency,respiration and excretion in the South African abalone Haliotis midae

Feeding periodicity, consumption rate, absorption efficiency, respiration rate and ammonia excretion were measured as functions of wet body mass in abalone collected from the western and southern Cape coasts. A well developed diel feeding rhythm was evident, consumption being restricted to the period 16h00–08h00. Food intake averaged 8,1 per cent of wet flesh mass·d^?1 at 14°C and 11,4 percent at 19°C. The daily consumption rate was related to body mass by the relationships C(g) = 0,54 W(g)^0,67 at 14°C and C(g) = 0,35 W(g)^0,77 at 19°C. Absorption efficiency averaged 37 per cent and was independent of body size. Equations relating respiration rate to wet body mass were R(m? O₂·h^?1) = 0,03 W(g)^0,83 at 14°C and R = 0,03 W(g)^0,94 at 19°C. No significant differences were detected between day and night rates or between fed and starved individuals. The rate of ammonia excretion (μmole·h^?1) was related to wet body mass (g) by the equations U = 0,22 W^0,43 at 14°C and U = 0,03 W^0,85 at 19°C.     

Distribution and contribution of major phytoplankton groups to carbon cycling across contrasting conditions of the subtropical northeast Atlantic Ocean

The relation between trophic regime and phytoplankton composition and function in oceanic systems is well accepted in oceanography. However, the relative dynamics and carbon cycling contributions of different phytoplankton groups across gradients of ocean richness are not fully understood. In this work we investigated phytoplankton dynamics along two transects from the NW African coastal upwelling to open-ocean waters of the north Atlantic subtropical gyre. We adopted a pigment-based approach to characterize community structure and to quantify group-specific growth and grazing rates and associated carbon fluxes. Changes in pigment cell concentration during the incubation experiments due to photoadaptation were corrected to obtain reliable rates. The oceanic region was dominated by Prochlorococcus (PRO) (45±7% of total chlorophyll a) while diatoms dominated in upwelling waters (40±37%). Phytoplankton grew faster (μ=0.78±0.26 d⁻¹) and free of nutrient limitation (μ/μ_n=0.98±0.42) in the coastal upwelling region, with all groups growing at similar rates. In oceanic waters, the growth rate of bulk phytoplankton was lower (μ=0.52±0.16 d⁻¹) and nutrient limited (μ/μ_n=0.68±0.19 d⁻¹). Diatoms (0.80±0.39 d⁻¹) and Synechococcus (SYN) (0.72±0.25 d⁻¹) grew faster than Prymnesiophyceae (PRYMN) (0.62±0.26 d⁻¹) and PRO (0.46±0.18 d⁻¹). The growth rates of PRO and SYN were moderately nutrient limited (μ/μ_n=0.81 and 0.91, respectively), while the limitation for diatoms (μ/μ_n=0.71) and PRYMN (μ/μ_n=0.37) was more severe. Microzooplankton grazing rate was higher in upwelling (0.68±0.32 d⁻¹) than in oceanic waters (0.37±0.19 d⁻¹), but represented the main loss pathway for phytoplankton in both systems (m/μ=0.90±0.32 and 0.69±0.24, respectively). Carbon flux through phytoplankton, produced and grazed, increased from offshore to coastal (∼2 to ∼200 μg C L⁻¹ d⁻¹), with diatoms dominating the flux in the upwelling region (52%) while PRYMN (40%) and PRO (30%) dominated in the open ocean.     

Sea-bed Mixing and Particle Residence Times in Biologically and Physically Dominated Estuarine Systems: a Comparison of Lower Chesapeake Bay and the York River Subestuary

Biologically dominated lower Chesapeake Bay and the physically dominated York River subestuary are contrasted in terms of the dynamics of sediment mixing, strata formation and sea-bed particle residence times. Two lower bay sites were examined; both are located within the bay stem plains and are characterized by muddy sand and an abundance of large, deep-dwelling organisms. X-radiographs indicate extensive biological reworking of sediments, with no long-term preservation of physical stratification.²¹⁰Pb profiles reveal low sediment accumulation rates at both lower bay sites (<0·1 cm year⁻¹), but significant differences in biological mixing depths (25vs40 cm) and biodiffusivity (>80vs6–30 cm²year⁻¹). In contrast, the York River site, located within a partially-filled palaeochannel, is predominantly mud with a depauperate benthic community dominated by small, short-lived, shallow-dwelling organisms. Although²¹⁰Pb accumulation rates at the York River site (<0·2 cm year⁻¹) are similar to those measured in the lower bay, there is little bioturbation. In addition, transient bed forms at the York River site form laterally persistent, linear ridges and furrows sub-parallel to the channel, spaced 10–20 m apart. These observations, coupled with evidence of episodic erosion and deposition from radioisotope and porosity profiles, and X-radiographs, suggest that the upper 60–120 cm of the sea-bed are dominated by physical mixing. Deep mixing and low accumulation rates result in long residence times of particles in the mixed upper portion of the sea-bed (10²year) at both locations, despite different mixing controls [i.e. biological (diffusive)vsphysical (advective)].     

缢蛏混养对三疣梭子蟹-日本囊对虾综合养殖系统理化环境和小型底栖动物的影响

滤食性贝类在生态系统中可通过自身生理活动促进系统的物质循环和能量流动,进而影响养殖环境。为从养殖系统底质环境角度为综合养殖系统优化提供依据,建立了4个实验生态系统,即在三疣梭子蟹-日本囊对虾养殖系统中混养3个不同密度的缢蛏(由低到高分别表示为PMB₁,PMB₂,PMB₃),并以三疣梭子蟹-日本囊对虾养殖系统(PM)为对照。通过对不同养殖系统底泥理化性质及小型底栖动物丰度、生物量的比较分析,探究缢蛏不同混养密度对养殖系统底质环境的影响。结果显示,总体而言,试验期间缢蛏高密度混养系统PMB₃底泥pH与氧化还原电位(ORP),显著高于其他系统,而底泥有机质含量显著低于其他系统。从小型底栖动物群落物种组成来看,不同养殖系统中线虫在丰度上占主要优势,占总丰度的35.9%~42.7%;介形类在生物量上占最大优势,占总生物量的74.2%~81.1%,PMB₃总丰度和总生物量显著高于其他系统。较高混养密度下,缢蛏能通过滤食残饵、粪便等有机物减少底泥有机物质的积累,改善底质环境,提高小型底栖动物丰度和生物量。本试验条件下,根据养殖系统底质环境变化特征,缢蛏放养密度34.7×10⁴ ind./hm²为最优放养密度。     

Isotopic and Elemental Variations of Carbon and Nitrogen in a Mangrove Estuary

Variations in elemental and isotopic ratios of suspended particulate matter (SPM) were investigated in the Guayas River Estuary Ecosystem (GREE) that empties into the Gulf of Guayaquil, Ecuador. Detritus in the system was identified on the basis of extremely high carbon:chlorophyll aratios (>1000). This material had mean δ¹³C of −26·4±0·3, δ¹⁵N of +4·8±0·2, and (C:N)_atomicof 14·1±0·9. The isotopic data were comparable to measurements reported for fresh and degrading mangrove leaves, whereas the elemental ratio was comparatively enriched in nitrogen. Isotope measurements of SPM throughout the GREE were more similar to values for riverine material and detritus compared with that for the coastal end-member. Values indicative ofin situproduced algae, sewage and shrimp pond effluent were only found at selected sites. Bacterial bioassays, which were used to document potential sources of dissolved organic matter in the GREE, were isotopically similar to SPM. This correspondence coupled with the relatively low (C:N)_aof SPM could be explained by bacterial immobolization of nitrogen onto detritus. Finally, tidal variations of (C:N)_aand δ¹³C at a brackish mangrove site were similar in magnitude to spatial variations encountered throughout the GREE. Based on these results, the authors caution that care must be taken when samples are taken for food-web studies in these systems.     

Flocculation and phytoplankton cell size can alter Th-based estimates of the vertical flux of particulate organic carbon in the sea

The deficit of ²³⁴Th relative to its radioactive parent ²³⁸U in the surface ocean can yield reliable estimates of vertical Particulate Organic Carbon (POC) fluxes to deeper waters, but only when coupled with an accurate ratio of POC concentration to activity of ²³⁴Th on sinking matter. Assuming a simple partitioning of suspended phytoplankton mass between single cells and flocs, we calculate the ratio of the POC flux estimated from ²³⁴Th deficit to the actual POC flux (p ratio, Smith, J.N., Moran, S.B., Speicher, E.A., in press. The p-ratio: a new diagnostic for evaluating the accuracy of upper ocean particulate organic carbon export fluxes estimated from ²³⁴Th/²³⁸U disequilibrium. Deep-Sea Research I.). The p ratios are calculated under the assumption that particle surface area is correlated with ²³⁴Th activity and particle volume is correlated with POC concentration. The value of the p ratio depends on the relative contributions of single cells and flocs to the vertical flux. When large single cells make up a significant fraction of the vertical flux, p ratios are less than one, meaning POC fluxes estimated from ²³⁴Th deficits underestimate actual POC fluxes. When large single cells are abundant but do not sink fast enough to contribute to vertical POC flux, p ratios are greater than one (up to 3 × overestimate). Factor analysis of the model indicates that altering the extent of flocculation in suspension and changing the density and maximum size of phytoplankton cells have the greatest effects on the p ratio. Failure to measure the properties of flocs when characterizing the ratio of POC to thorium on sinking matter potentially leads to large overestimation of the POC flux (over 20 ×). Failure to characterize the POC to thorium ratio of large particles, by, for example, destruction of phytoplankton cells in pumps, can lead to underestimation of POC flux. Estimates of POC flux should be most reliable in highly flocculated suspensions populated by small cells and rapidly sinking flocs. These conditions are often associated with intense phytoplankton blooms.     

Theoretical considerations about the reactions of calcification in sea water

We examine the concentration variations of the different parameters X of the carbonate system in seawater when calcium carbonate precipitation occurs. Variations are expressed as ∂[X]/∂[Ca²⁺]. Four different cases are considered: spontaneous chemical precipitation; calcification combined with photosynthetic activity under a constant ΔCT/Δ[Ca²⁺] ratio; precipitation under constant p_CO2 and precipitation under constant [Ca²⁺]·[CO₃²⁻] ionic concentration product. The last condition should be maintained by an ecosystem which, thanks to the regulation of its calcifying and photosynthetic activity, would absorb 1 mol of carbon for organic tissue each time 1 mol of CaCO₃ is formed. This stoichiometric ratio would allow the activity of these biological communities to go on in practically closed systems during periods compatible with their growth or development cycles.