Application of Adjoint Approach to Oil Spill Problems

Adjoint method is applied to various oil spill problems. A three-dimensional model for describing the dispersion of a quasi-passive substance (a pollutant or a nutrient) and its adjoint model are considered in a limited sea region. Direct and adjoint estimates are used to get dual (equivalent) estimates of the mean concentration of the substance in important zones of the region. The role of dual estimates is illustrated with a few examples. They include such oil spill problems as the search of the most dangerous point of the oil tanker route, the oil dispersion with a climatic velocity, and the dependence of the oil concentration estimates on the oil spill rate. One more example is the application of optimal bioremediation strategy for cleaning a few zones polluted by oil. In this case, instead of oil, the model describes the dispersion of a nutrient released to marine environment. Balanced, unconditionally stable second-order finite-difference schemes based on the splitting method for the solution of the dispersion model and its adjoint are suggested. The main and adjoint difference schemes are compatible in the sense that at every fractional step of the splitting algorithm, the one-dimensional split operators of both schemes satisfy a discrete form of Lagrange identity. In the special unforced and non-dissipative case, each scheme has two conservation laws. Every split one-dimensional problem is solved by Thomas’ factorization method.     

New international long-term ecological research on air pollution effects on the Carpathian Mountain forests,Central Europe

An international cooperative project on distribution of ozone in the Carpathian Mountains, Central Europe was conducted from 1997 to 1999. Results of that project indicated that in large parts of the Carpathian Mountains, concentrations of ozone were elevated and potentially phytotoxic to forest vegetation. That study led to the establishment of new long-term studies on ecological changes in forests and other ecosystems caused by air pollution in the Retezat Mountains, Southern Carpathians, Romania and in the Tatra Mountains, Western Carpathians on the Polish-Slovak border. Both of these important mountain ranges have the status of national parks and are Man & the Biosphere Reserves. In the Retezat Mountains, the primary research objective was to evaluate how air pollution may affect forest health and biodiversity. The main research objective in the Tatra Mountains was to evaluate responses of natural and managed Norway spruce forests to air pollution and other stresses. Ambient concentrations of ozone (O(3)), sulfur dioxide (SO(2)), nitrogen oxides (NO(x)) as well as forest health and biodiversity changes were monitored on densely distributed research sites. Initial monitoring of pollutants indicated low levels of O(3), SO(2), and NO(x) in the Retezat Mountains, while elevated levels of O(3) and high deposition of atmospheric sulfur (S) and nitrogen (N) have characterized the Tatra Mountains. In the Retezat Mountains, air pollution seems to have little effect on forest health; however, there was concern that over a long time, even low levels of pollution may affect biodiversity of this important ecosystem. In contrast, severe decline of Norway spruce has been observed in the Tatra Mountains. Although bark beetle seems to be the immediate cause of that decline, long-term elevated levels of atmospheric N and S depositions and elevated O(3) could predispose trees to insect attacks and other stresses. European and US scientists studied pollution deposition, soil and plant chemistry, O(3)-sensitive plant species, forest insects, and genetic changes in the Retezat and Tatra Mountains. Results of these investigations are presented in a GIS format to allow for a better understanding of the changes and the recommendations for effective management in these two areas.     

Challenges in quantifying biosphere-atmosphere exchange of nitrogen species

Recent research in nitrogen exchange with the atmosphere has separated research communities according to N form. The integrated perspective needed to quantify the net effect of N on greenhouse-gas balance is being addressed by the NitroEurope Integrated Project (NEU). Recent advances have depended on improved methodologies, while ongoing challenges include gas-aerosol interactions, organic nitrogen and N(2) fluxes. The NEU strategy applies a 3-tier Flux Network together with a Manipulation Network of global-change experiments, linked by common protocols to facilitate model application. Substantial progress has been made in modelling N fluxes, especially for N(2)O, NO and bi-directional NH(3) exchange. Landscape analysis represents an emerging challenge to address the spatial interactions between farms, fields, ecosystems, catchments and air dispersion/deposition. European up-scaling of N fluxes is highly uncertain and a key priority is for better data on agricultural practices. Finally, attention is needed to develop N flux verification procedures to assess compliance with international protocols.     

Defining the spatial impacts of poultry farm ammonia emissions on species composition of adjacent woodland groundflora using Ellenberg Nitrogen Index,nitrous oxide and nitric oxide emissions and foliar nitrogen as marker variables

The marker variables, Ellenberg Nitrogen Index, nitrous oxide and nitric oxide fluxes and foliar nitrogen, were used to define the impacts of NH3 deposition from nearby livestock buildings on species composition of woodland ground flora, using a woodland site close to a major poultry complex in the UK. The study centred on 2 units in close proximity to each other, containing 350,000 birds, and estimated to emit around 140,000 kg N year(-1) as NH3. Annual mean concentrations of NH3 close to the buildings were very large (60 microg m(-3)) and declined to 3 microg m(-3) at a distance of 650 m from the buildings. Estimated total N deposition ranged from 80 kg N ha(-1) year(-1) at a distance of 30 m to 14 kg N ha(-1) year(-1) at 650 m downwind. Emissions of N2O and NO were 56 and 131 microg N m(-2) h(-1), respectively at 30 m and 13 and 80 microg N m(-2) h(-1), respectively at 250 m downwind of the livestock buildings. Species number in woodland ground flora downwind of the buildings remained fairly constant for a distance of 200 m from the units then increased considerably, doubling at a distance of 650 m. Within the first 200 m downwind, trends in plant species composition were hard to discern because of variations in tree canopy composition and cover. The mean Ellenberg N Index ranged from 6.0 immediately downwind of the livestock buildings to 4.8 at 650 m downwind. The mean abundance weighted Ellenberg N Index also declined with distance from the buildings. Tissue N concentrations in trees, herbs and mosses were all large, reflecting the substantial ammonia emissions at this site. Tissue N content of ectohydric mosses ranged from approximately 4% at 30 m downwind to 1.6% at 650 m downwind. An assessment of the relative merits of the three marker variables concludes, that while Ellenberg Index and trace gas fluxes of N2O and NO give broad indications of impacts of ammonia emissions on woodland vegetation, the application of a critical foliar N content for ectohydric mosses is the most useful method for providing spatial information which could be of value to policy developers and planners.     

Spatially Disaggregated Inventories of Soil NO and N2O Emissions for Great Britain

Estimates of soil N₂O and NOemissions at regional and country scales arehighly uncertain, because the most widely usedmethodologies are based on few data, they do notinclude all sources and do not account forspatial and seasonal variability. To improveunderstanding of the spatial distribution of soilNO and N₂O emissions we have developedsimple multi-linear regression models based onpublished field studies from temperate climates.The models were applied to create spatialinventories at the 5 km² scale of soil NOand N₂O emissions for Great Britain. The N₂O regression model described soilN₂O emissions as a function of soil N input,soil water content, soil temperature and land useand provided an annual N₂O emission of 128 kt N₂O-N yr^-1. Emission rates largerthan 12 kg N₂O-N ha^-1 yr^-1 werecalculated for the high rainfall grassland areasin the west of Great Britain.Soil NO emissions were calculated using tworegression models, which described NO emissionsas a function of soil N input with and without afunction for the water filled pore space. Thetotal annual emissions from both methods, 66 and7 kt NO-N yr^-1, respectively, span the rangeof previous estimates for Great Britain.     

A Linear-Programming-Based Strategy for Bioremediation of Oil-Polluted Marine Environments

A linear programming problem is considered with the aim to determine the optimal discharge point and the optimal discharge rate of a nutrient to be released to a marine environment polluted with oil. The objective is to minimize the total discharge of nutrient into the system provided that the concentrations of nutrient will reach critical values sufficient to eliminate oil residuals in certain affected zones through bioremediation. An initial boundary-value 3D problem for the advection–diffusion equation and its adjoint problems are considered to model, estimate, and control the dispersion of nutrient in a limited region. It is shown that the advection–diffusion problem is well posed, and its solution satisfies the mass balance equation. In each oil-polluted zone, the mean concentration of nutrient is determined by means of an integral formula in which the adjoint model solution serves as a weight function. Critical values of these mean concentrations are used as the constraints of linear programming problem. Some additional constraints are posed in order to limit not only the local discharge of the nutrient, but also the mean concentration of this substance in the whole region. Both constraints serve for environmental protection. The ability of the new method is demonstrated by numerical experiments on the remediation in oil-polluted channel using three control zones. The experiments show that the optimal discharge rate can always be got with a simple combination of step functions.     

The Influence of Atmospheric N Deposition on Nitrous Oxide and Nitric Oxide Fluxes and Soil Ammonium and Nitrate Concentrations

The deposition of atmospheric N to soils provides sources of available N to the nitrifying and denitrifying microbial community and subsequently influences the rate of NO and N₂O emissions from soil. We have investigated the influence of three different sources of enhanced N deposition on NO and N₂O emissions 1) elevated NH₃ deposition to woodlands downwind of poultry and pig farms, 2) increased wet cloud and occult N deposition to upland forest and moorland and 3) enhanced N deposition to trees as NO ₃ ^– and NH ₄ ⁺ aerosol. Flux measurements of NO and N₂O were made using static chambers in the field or intact and repacked soil cores in the laboratory and determination of N₂O by gas chromatography and of NO by chemiluminescence analysis. Rates of N deposition to our study sites were derived from modelled estimates of N deposition, NH₃ concentrations measured by passive diffusion and inference from measurements of the ²¹⁰Pb inventory of soils under tree canopies compared with open grassland. NO and N₂O emissions and KCl-extractable soil NH ₄ ⁺ and NO ₃ ^– concentrations all increased with increasing N deposition rate. The extent of increase did not appear to be influenced by the chemical form of the N deposited. Systems dominated by dry-deposited NH₃ downwind of intensive livestock farms or wet-deposited NH ₄ ⁺ and NO ₃ ^– in the upland regions of Britain resulted in approximately the same linear response. Emissions of NO and N₂O from these soils increased with both N deposition and KCl extractable NH ₄ ⁺ , but the relationship between NH ₄ ⁺ and N deposition (ln NH ₄ ⁺ = 0.62 ln N_deposition + 0.21, r ² = 0.33, n = 43) was more robust than the relationship between N deposition and soil NO and N₂O fluxes.     

Measuring Aerosol and Heavy Metal Deposition on Urban Woodland and Grass Using Inventories of 210Pb and Metal Concentrations in Soil

The deposition of aerosols to trees has proved very difficult to quantify, especially in complex landscapes. However, trees are widely quoted to be efficient scavengers of particles from the atmosphere, and a growing proportion of the pollutant burden in the atmosphere is present in the aerosol phase. In this study, the deposition of aerosols onto woodland and grass was quantified at a range of locations throughout the West Midlands of England. The sites included mature deciduous woodland in Edgbaston, and Moseley, and mixed woodland at sites within Sutton Park, a large area of semi-natural vegetation. Aerosol deposition to areas of grassland close to the woodland at each site was also measured. Detailed inventories of ²¹⁰Pb in soils within the woodland and in grassland soils, together with concentrations in the atmosphere and precipitation, provided the necessary data to calculate the long-term (about 40 years) annual deposition of sub-micron aerosols onto grassland and woodland. The soil inventories of ²¹⁰Pb under woodland exceeded those under grass, by between 22% and 60%, with dry deposition contributing 24% of the total input flux for grass and 47% for woodland. The aerosol dry deposition velocity to grassland averaged 3.3 mm s^-1 and 9 mm s^-1 for woodland. The large deposition rates of aerosols onto woodland relative to grass or other short vegetation (× 3), and accumulation of heavy metals within the surface horizons of organic soils, leads to large concentrations in soils of urban woodland. Concentrations in the top 10 cm of these woodland soils averaged 252 mg kg^-1 for Pb with peaks to 400 mg kg^-1. Concentrations of Cd averaged 1.4 mg kg^-1, Cu, 126 mg kg^-1, Ni 23 mg kg^-1 and Zn 173 mg kg^-1. The accumulated Pb in urban woodland soils is shown to be large relative to UK emissions.     

Dual oil concentration estimates in ecologically sensitive zones

Propagation of the oil spilling from a damaged oil tanker is considered in a limited sea area. Direct and adjoint estimates of the average oil concentration in special zones are derived by using solutions of the 2-D main and adjoint oil transport problems, respectively. The dual estimates complement each other nicely in studying the oil spill consequences. While the direct estimates are preferable to get a comprehensive idea of the oil spill impact on the whole area, the adjoint ones are specially useful and economical when the accident site-dependence or/and the oil spill rate-dependence of the oil concentration is/are studied only in a few ecologically sensitive zones. Indeed, each adjoint estimate explicitly relates the average oil concentration in a zone to the oil spill rate using the adjoint solution values at the accident site. Being independent of the two parameters (the accident site and oil spill rate), the adjoint solution can be found for each zone regardless of a concrete accident and used repeatedly for various possible values of these parameters. Several examples explain how to decide between two estimates.Thanks to special boundary conditions, the main and adjoint problems are both well-posed according to Hadamard (1923). The dual estimates can be generalized to the three dimensions. The balanced, absolutely stable and compatibie main and adjoint 3-D numerical algorithms by Skiba (1993) can easily be adapted to the problem discussed here.     

Emissions of NO and N2O from soils

Nitric oxide (NO) and nitrous oxide (N₂O) fluxes were measured from agricultural, forest and moorland environments, using chamber techniques. Maximum emissions of NO and N₂O were measured from the agricultural soils shortly after fertiliser application (7 ng NO-N m^–2 s^–1 and 91 ng N₂O-N m^–2 s^–1). For the non-agricultural soils the NO flux ranged from –0.3 to 0.5 ng NO-N m^–2 s^–1 and the N₂O flux ranged from 1 to 2.7 ng N₂O-N m^–2 s^–1. Emissions, however, were increased 2 to 7 fold when N deposition (uplands) and N fixation (alder plantations) contributed to the pool of soil available N. The best predictors of the NO emission were soil NO ₃ ^– and soil temperature, accounting for 60% of the variability observed. The prediction of N₂O was less successful. Only 30% of the variability could be explained by the soil NO ₃ ^– and the soil moisture content, soil temperature did not have a significant effect on the N₂O emission.