One-box Model Research Articles

Dissolved silica budget in the North basin of Lake Lugano

We studied the dissolved silica cycle in the water column of the North basin of Lake Lugano, Switzerland/Italy. Lake Lugano is a meromictic, eutrophic lake, permanently stratified below 100-m depth. A one-box model was used to calculate a silica mass-balance over 1993, based on various lake measurements, such as sediment traps, sediment cores, water analysis and biota countings. We found that the North basin of Lake Lugano is at steady state as far as dissolved silica is concerned. The primary source of dissolved silica in the lake is river input (about 80%), with diffusion from bottom sediments and groundwater input also playing a role. Atmospheric input is negligible. The main export of dissolved silica occurs via biogenic uptake by diatoms and final burial of their frustules in the bottom sediment. Loss of dissolved silica through the lake outflow only represents 15% of the total output. Of the total amount of Si exported to the lake bottom through diatom sinking, less than 20% is re-supplied to the surface water by diffusion. Thus, the lake acts as an important permanent sink for silica. The long residence time of dissolved silica in the lake (7 years) is related to the strong physical stratification of the lake. Only about 10% of the standing stock are available to phytoplankton uptake.

Dynamic Behavior of Fluorescent Whitening Agents in Greifensee: Field Measurements Combined with Mathematical Modeling of Sedimentation and Photolysis

The dynamic behavior of the two fluorescent whitening agents (FWAs) that are currently used in laundry detergents in Switzerland (DAS 1, a diaminostilbene, and DSBP, a distyrylbiphenyl) has been evaluated quantitatively during 1 year for Greifensee, a small lake in Switzerland, by using a one-box model and simulation software (MASAS) for modeling organic pollutants in lakes. Both the one-box model and the one-dimensional simulation were based on (i) independently evaluated processes affecting the fate of FWAs and (ii) measured FWA concentrations in the lake. The relevant processes were derived from literature data and from measurements in the lake and in its tributaries. Besides loading from tributaries, only photodegradation (responsible for 53% and 81% of the elimination of DAS 1 and DSBP, respectively), sorption/sedimentation (20% and 9%), and flushing (27% and 10%) were found to be relevant for FWAs in Greifensee. In particular, no evidence was found for other degradation processes such as biodegradat...

A biomineralization model for the incorporation of trace elements into foraminiferal calcium carbonate

Measurements of Sr Ca of benthic foraminifera show a linear decrease with water depth which is superimposed upon significant variability identified by analyses of individual foraminifera. New data for Cd Ca support previous work in defining a contrast between waters shallower and deeper than ∼ 2500 m. Measured element partition coefficients in foraminiferal calcium carbonate relative to sea water (D) have been described by means of a one-box model in which elements are extracted by Rayleigh distillation from a biomineralization reservoir that serves for calcification with a constant fractionation factor (α), such that D = (1 − f α) (1 − f) , where f is the proportion of Ca remaining after precipitation. A modification to the model recognises differences in element speciation. The model is consistent with differences between D Sr, D Ba and D Cd in benthic but not planktonic foraminifera. Depth variations in D for Sr and Ba are consistent with the model, as are differences in depth variation of D Cd in calcitic and aragonitic benthic foraminifera. The shallower depth variations may reflect increasing calcification rates with increasing water depth to an optimum of about 2500 m. Observations of unusually lower D Cd for some deep waters, not accompanied by similar D Sr or D Ba, may be because of dissolution or a calcification response to a lower carbonate saturation state.

Primary production estimation from continuous oxygen measurements in relation to external nutrient input

In experimental ditches gross and net production were estimated from continuous dissolved oxygen measurements for individual days over a two year period. There are two series of three ditches: the first is dominated by benthic algae, and the second by submerged macrophytes. Each series receives three different levels of external nutrient (N,P) loading, referred to as reference, medium-loaded and highest-loaded level. Generally, there were no vertical oxygen gradients, and a one-box model satisfied. For periods with O 2-stratification a two-box model has been developed. This model assumes that primary production only occurs in a well mixed top layer. In both series, the cumulative gross primary production over two years was positively related to the level of external nutrient input. In the ditches dominated by benthic algae, a continuous increase in cumulative net systems production, that was positively related to the level of external nutrient input, was observed. In the macrophyte ditches, the cumulative net systems production was positively related to the level of nutrient input during the first half year, but after that showed an irregular pattern. The maximum, areal daily gross productions during the summer, corrected for temperature, increased from 1990 to 1991 in all ditches dominated by benthic algae, but decreased in all macrophyte ditches. The accumulation of biomass in the ditches with benthic algae was calculated from the cumulative net production, and showed a good agreement with measured values in the reference ditch, but yielded higher values than measured in the medium-loaded and highest-loaded ditches. Reaeration was calculated using a system specific, empirical wind-reaeration relationship. The wind speed was on average higher during the afternoon than during the rest of the day. High wind speeds thus coincide with high oxygen saturations, and the use of a variable reaeration coefficient during a day results in higher gross and net production estimates than the use of a constant value throughout a day.

Understanding Natural Systems through Simple Dynamical Systems Modeling

Undergraduate students at all levels are encouraged to “think critically.” We work toward this goal by connecting the theoretical concepts of computer modeling to a simple physical model constructed in lab . Students build a physical representation of a one-box model, consisting of reservoir, input, and output. They observe the steady-state system, then perturb the system by instantaneously doubling the rate of input. Students observe the response of the system as it arrives at a new steady state with increased input, output and volume. Students then construct a computer model of the same system, and observe that the computer produces results analogous to their observations. In subsequent exercises they modify their models in order to study more complicated systems. There are several advantages to this approach. 1) Students gain confidence in computer modeling by working with a system that they already understand well. 2) Computer modeling is a creative exercise in which students must both analyze a situa...

Estimating australian forest fire danger under conditions of doubled carbon dioxide concentrations

The most appropriate indices with which to quantify Australian bushfire danger are the McArthur fire danger meters. These meters use meteorological information to produce a fire danger index that is directly related to the chance of a fire starting - and to the severity of a fire once it has started. The Mark 5 forest-fire danger meter uses air temperature, relative humidity and wind speed, plus a drought factor that is calculated using daily rainfall and temperature information. Three years of daily data generated from the CSIRO four-level general circulation model, and thirty years of daily data generated from the CSIRO nine-level model were used to estimate the daily McArthur forest fire danger index for simulations corresponding to present conditions, and to those corresponding to doubled atmospheric CO2. The performance of these models with respect to fire danger was tested by comparing the fire danger index for Sale (in the Eastern part of Victoria, South-eastern Australia) calculated from analysis of daily climatological data with the modelled annual cumulative forest fire danger index for the grid point that was representative of Sale. Data from both models for all Australian grid points were also examined. Both models predict an increase in fire danger over much of Australia for their doubled CO2 scenarios. The results from the models confirm that annually averaged daily relative humidity is the single most important variable in the estimation of forest fire danger on an annual basis, yet the models tend to produce relative humidities that are slightly too low so that the fire danger is overestimated. A simple one-box model of evaporation indicates that the value of relative humidity to be expected under an altered climatic regime depends on the modelled relation between actual and potential evaporation, the present values of relative humidity and evaporation rate, as well as on the expected changes in wind speed.

A Simple Heuristic Model of Nutrient Cycling in an Estuary

Three decades of discussion and study have not resolved the apparent discrepancy between N-limitation of primary production and the ability of marine ecosystems to fix N. We use a simple model as a heuristic tool to examine controls on nutrient cycling in a shallow estuary, with Tomales Bay, California as the prototype. The model is a steady-state, one-box model with inputs and losses of nutrients and organic matter, and terms representing N-fixation and denitrification. The physical description of the system is deliberately kept simple to permit a focus on the key biogeochemical reactions. Growth of autotrophs in the model can be limited either by dissolved inorganic nitrogen (DIN) or dissolved inorganic phosphorus (DIP). Nitrogen-fixation is controlled by the availability of DIP or limited by excess amounts of DIN. Model results demonstrate that, for a system with a long residence time, autotroph biomass and total organic matter are controlled primarily by the rate of delivery of P to the system, either as DIP or in organic matter. Increasing the delivery rate of DIN raises autotroph biomass slightly but has little effect on total organic matter. This is because the rates of input of P as DIP or organic matter control the N-fixation rate, and denitrification limits the build-up of DIN in the system. Thus, denitrification and N-fixation act as opposing negative feedbacks, insuring that the supply of N remains roughly commensurate with that of P. When exchange with the ocean is increased, reducing residence time, the relative importance of DIN input increases relative to that of DIP.

Three-dimensional simulations of the impact of Southern Ocean nutrient depletion on atmospheric CO2 and ocean chemistry

Surface nutrient concentrations in the Southern Ocean are an important indicator of the atmosphere-ocean chemical balance that played a key role in ice-age reduction of atmospheric pC0, and would play a role in any Fe fertilization scenario for increasing oceanic uptake of anthropogenic CO,. The response of the ocean and atmosphere to a scenario of extreme depletion of Southern Ocean surface nutrients by an increase in the organic matter flux to the deep ocean is examined with a three-dimensional model of ocean circulation coupled to a one-box model of the atmosphere. After 100 yr, the increase in the organic matter flux is 6-30 Gt C yr-l-about twice the global new production determined by the same model for the present ocean. The removal of nutrients from surface waters of the Southern Ocean reduces the nutrient content of the near-surface and intermediate depth waters of the entire ocean, resulting in a 0.5-l .9 Gt C yr-’ reduction of low-latitude new production. The deep circumpolar waters, enriched in nutrients by regeneration of organic matter, spread into the deep and bottom waters of the remainder of the ocean, giving an overall downward shift of nutrients from surface and intermediate to circumpolar and deep waters. The oceanic total C distribution is also shifted downward, resulting in uptake of atmospheric CO, of 46-85 ppm (98-181 Gt C) in the first 100 yr. The oxygen content shifts upward in the water column, approximately mirroring the downward shift of nutrients. Some of the oxygen shifted to the upper ocean escapes to the atmosphere. As a consequence, the global average oceanic content of oxygen, presently 168 pmol kg-l, is reduced by 6-20 pmol kg-l, with anoxia developing in the southwestern Indian Ocean. CO2 is unusual compared to other atmospheric gases because most of the combined atmosphere-ocean inventory (98.5%) is in the ocean. By contrast, oxygen, a more typical atmospheric gas, has only 0.6% of its atmosphere-ocean inventory in the ocean. CO2 is m 30 times as soluble as oxygen, due mainly to hydrogen bonding with water molecules; however, the primary reason for the large amount of CO2 in the ocean is that it reacts with water to form HCO,and Acknowledgments This work was supported by the U.S. Department of Energy under contract DEFG 02-90ER611052, by the National Science Foundation (OCE 9012333), and by GFDWNOAA through the generosity of K. Bryan and J. Mahlman. The perturbation approach for modeling total C was developed in collaboration with U. Siegenthaler. The collaboration of J.L.S. with F. Joos and U. Siegenthaler in earlier high-latitude, nutrient-depletion studies gave us considerable insight into how to go about our threedimensional experiment and how to interpret the results. B. Flannery was the first member of our group to do a nutrient-depletion experiment (summer 1989), following the basic modeling approach developed by R. Najjar. Collaboration of J.C.O. with R. Najjar, R. Slater, and K. Dixon aided in modeling and analysis. COS2-. Only + 1% of the dissolved inorganic C is in the non-ionic CO, form (e.g. Broecker and Peng 1982). Another important contributor to reduced atmospheric CO, levels results from the distribution of total inorganic CO2 (i.e. the sum of the concentrations of C02, and HC03and C032ions), which is IV 12% lower at the surface than at depth. Part of this surface-to-deep difference is due to what is referred to as the “solubility pump” (Volk and Hoffert 1985). CO, is more than twice as soluble in the cold, high-latitude waters which sink to form the deep waters of the ocean, than it is in warm, low-latitude waters (Weiss 1974). However, the primary source of the surface to deep difference is the “biological pump” (Volk and. Hoffert 19 8 5). Photosynthesis produces organic C from CO, in the euphotic zone of the ocean, depleting surface nutrients to near-zero levels over most of the surface ocean. Although most of the photosynthetically produced organic C is recycled in the euphotic zone, -30% either sinks to the deep ocean or is transported there by circulation before being regenerated to CO,.

Kinetic and equilibrium approaches to estuarine chemistry

A one-box model is used to examine the relationship between freshwater residence time ( T) and the time constant (half-life, t 1 2 ) for a first-order chemical reaction in an estuary. Higher and lower limits of the ratio t 1 2 /T appropriate for conservative or chemical equilibrium modelling, respectively, are derived. These limits depend also on the equilibrium constant for the reaction and the initial reactant and product concentrations. For intermediate values of this ratio, the system can be described quantitatively only by using a kinetic model. Systematic inter-estuarine variability in the distributions of dissolved metals as a function of estuarine size (or hydrodynamic turnover time) is predicted by this model when the potential for sorptive particle-water exchanges is examined. However, this deduction, which is based on kinetic criteria alone, is not confirmed by evidence in the literature. Indeed, the model is contradicted in that dissolved metals appear to be most interactive in some, but not all, small estuaries and least interactive in large estuaries. It follows that the thermodynamic drive for metal interactions to occur is a necessary additional consideration. Gross thermodynamic disequilibrium with respect to particle-water metal exchange, which in turn generates highly non-conservative dissolved metal distributions, is most readily generated in small, highly dynamic systems through enhanced internal mobility of estuarine resuspendable sediment.

Cadmium-113m in the water, sediments, and adjacent soils of Lake Michigan

Cadmium-113m entered the environment as a consequence of testing of nuclear weapons in the atmosphere. Earlier we demonstrated that 113mCd can be determined accurately in water, soils, and sediments. In Lake Michigan, the present concentrations of 113mCd are 350 ± 150 μBq l −1 ( n = 16) in the water, and 10.0 ± 5.5 mBq g −1 ( n = 12) in the surficial sediments. The specific activities in water and sediment are statistically indistinguishable from one another and average 9.9 kBq g −1 Cd. The inferred K D is thus 29 ± 20 l g −1. In undisturbed soils near Lake Michigan, the mean 113mCd/ 137Cs activity ratio is 2.0 ± 1.4 × 10 −2 ( n = 4), implying a total 113mCd input to the lake of 2.7 ± 1.3 TBq (corrected for decay to 1984). Using the K D for 113mCd, and taking K D for 137Cs to be 90 ± 6 l g −1, the predicted 113mCd activities are 1.1 ± 1.1 mBq g −1 in sediment, and 120 ± 125 μBq l −1 in water. These values are comparable to the observed activities. Application of a simple one-box model to the observed activities leads to a residence time for Cd of 40 ± 30 years, or about 0.4 times the hydraulic residence time. Resuspension may account for the difference between the 113mCd-based value and an earlier estimate based on a mass balance for stable Cd.

A test of two models of different levels of complexity for predicting changes of phosphorus concentration in a lake's outflow

Abstract The objective of this investigation is to compare the ability of a one-box model and a two-box model to predict the temporal variations of total phosphorus in the outflow of several lakes. The one-box model considers only total phosphorus and treats the lake as well-mixed, all year round. The two-box model considers two phosphorus fractions and the epilimnion and hypolimnion. For five shallow Canadian Shield lakes, some of the temporal variability in lake phosphorus concentrations can be explained on the basis of changes in hydraulic inflows and phosphorus loadings. Both models give roughly similar predictions for shallow lakes with high hydraulic loadings (1–200 m/year) and small variations in total phosphorus concentrations. In comparing the settling and hydraulic outflow mechanisms, a sensitivity analysis shows that both models are more sensitive to the settling rate if the lake's hydraulic loadings are less than 1 m/year, and more sensitive to the outflow rate if the lake's hydraulic loadings are greater than 100 m/year. This analysis suggests a priority for concentrating economic and other resources in conducting field measurement programs for testing phosphorus models.

Mögliche Massnahmen zur Restaurierung des Sempachersees

Since 1954 average orthophosphate and total phosphorus concentrations have increased twenty and eightfold respectively in Lake Sempach. It is demonstrated that the lake is not in steady state with its phosphorus loading and that the net deposition rate of phosphorus is not linearly related to the phosphorus content of the lake. This implies that linear steady state one-box models are unsuitable to describe the phosphorus balance of this lake. Applying a nonlinear dynamic lake model we predict that the defined water quality goals ([P] ⩽30 mg m−3, [O2 ⩾4 mg m−3]) can only be achieved within the next 15 years if the external phosphorus loading is reduced by at least 50% and simultaneously lake-internal measures, such as hypolimnion areation or hypolimnion siphoning are carried into effect.

The Concept of DC Gain in Modeling Secular Variations in Atmospheric14C

A constraint on radiocarbon reservoir models is that the DC gain of a system (system transfer function at zero frequency) should equal the equilibrium ratio of the atmospheric radiocarbon mass to the production rate. The simple one-box model is essentially a “black box” but the value of the single residence time is theoretically equal to the DC gain. Using a sunspot-production rate algorithm as the forcing function, predictions of the one-box model match the14C data from ad 1700 to 1900 better than the 3-box, 5-box and box-diffusion models. The more complex models tend to pile up14C in the atmosphere because their DC gains are too high, and they over-attenuate the de Vries “wiggles”. The DC gains can be reduced to more acceptable levels by adjusting model parameters, particularly the sizes of the ocean reservoirs. Better fits to the “wiggles” are also obtained by parameter adjustment. Water content of deep-sea sediments constitutes an extra reservoir for dead carbon, and should help reduce system DC gain.