994 resultados para OXIDE EMISSIONS
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Research networks provide a framework for review, synthesis and systematic testing of theories by multiple scientists across international borders critical for addressing global-scale issues. In 2012, a GHG research network referred to as MAGGnet (Managing Agricultural Greenhouse Gases Network) was established within the Croplands Research Group of the Global Research Alliance on Agricultural Greenhouse Gases (GRA). With involvement from 46 alliance member countries, MAGGnet seeks to provide a platform for the inventory and analysis of agricultural GHG mitigation research throughout the world. To date, metadata from 315 experimental studies in 20 countries have been compiled using a standardized spreadsheet. Most studies were completed (74%) and conducted within a 1-3-year duration (68%). Soil carbon and nitrous oxide emissions were measured in over 80% of the studies. Among plant variables, grain yield was assessed across studies most frequently (56%), followed by stover (35%) and root (9%) biomass. MAGGnet has contributed to modeling efforts and has spurred other research groups in the GRA to collect experimental site metadata using an adapted spreadsheet. With continued growth and investment, MAGGnet will leverage limited-resource investments by any one country to produce an inclusive, globally shared meta-database focused on the science of GHG mitigation.
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The biogenic production of NO in the soil accounts for between 10% and 40% of the global total. A large degree of the uncertainty in the estimation of the biogenic emissions stems from a shortage of measurements in arid regions, which comprise 40% of the earth’s land surface area. This study examined the emission of NO from three ecosystems in southern Africa which cover an aridity gradient from semi-arid savannas in South Africa to the hyper-arid Namib Desert in Namibia. A laboratory method was used to determine the release of NO as a function of the soil moisture and the soil temperature. Various methods were used to up-scale the net potential NO emissions determined in the laboratory to the vegetation patch, landscape or regional level. The importance of landscape, vegetation and climatic characteristics is emphasized. The first study occurred in a semi-arid savanna region in South Africa, where soils were sampled from 4 landscape positions in the Kruger National Park. The maximum NO emission occurred at soil moisture contents of 10%-20% water filled pore space (WFPS). The highest net potential NO emissions came from the low lying landscape positions, which have the largest nitrogen (N) stocks and the largest input of N. Net potential NO fluxes obtained in the laboratory were converted in field fluxes for the period 2003-2005, for the four landscape positions, using soil moisture and temperature data obtained in situ at the Kruger National Park Flux Tower Site. The NO emissions ranged from 1.5-8.5 kg ha-1 a-1. The field fluxes were up-scaled to a regional basis using geographic information system (GIS) based techniques, this indicated that the highest NO emissions occurred from the Midslope positions due to their large geographical extent in the research area. Total emissions ranged from 20x103 kg in 2004 to 34x103 kg in 2003 for the 56000 ha Skukuza land type. The second study occurred in an arid savanna ecosystem in the Kalahari, Botswana. In this study I collected soils from four differing vegetation patch types including: Pan, Annual Grassland, Perennial Grassland and Bush Encroached patches. The maximum net potential NO fluxes ranged from 0.27 ng m-2 s-1 in the Pan patches to 2.95 ng m-2 s-1 in the Perennial Grassland patches. The net potential NO emissions were up-scaled for the year December 2005-November 2006. This was done using 1) the net potential NO emissions determined in the laboratory, 2) the vegetation patch distribution obtained from LANDSAT NDVI measurements 3) estimated soil moisture contents obtained from ENVISAT ASAR measurements and 4) soil surface temperature measurements using MODIS 8 day land surface temperature measurements. This up-scaling procedure gave NO fluxes which ranged from 1.8 g ha-1 month-1 in the winter months (June and July) to 323 g ha-1 month-1 in the summer months (January-March). Differences occurred between the vegetation patches where the highest NO fluxes occurred in the Perennial Grassland patches and the lowest in the Pan patches. Over the course of the year the mean up-scaled NO emission for the studied region was 0.54 kg ha-1 a-1 and accounts for a loss of approximately 7.4% of the estimated N input to the region. The third study occurred in the hyper-arid Namib Desert in Namibia. Soils were sampled from three ecosystems; Dunes, Gravel Plains and the Riparian zone of the Kuiseb River. The net potential NO flux measured in the laboratory was used to estimate the NO flux for the Namib Desert for 2006 using modelled soil moisture and temperature data from the European Centre for Medium Range Weather Forecasts (ECMWF) operational model on a 36km x 35km spatial resolution. The maximum net potential NO production occurred at low soil moisture contents (<10%WFPS) and the optimal temperature was 25°C in the Dune and Riparian ecosystems and 35°C in the Gravel Plain Ecosystems. The maximum net potential NO fluxes ranged from 3.0 ng m-2 s-1 in the Riparian ecosystem to 6.2 ng m-2 s-1 in the Gravel Plains ecosystem. Up-scaling the net potential NO flux gave NO fluxes of up to 0.062 kg ha-1 a-1 in the Dune ecosystem and 0.544 kg h-1 a-1 in the Gravel Plain ecosystem. From these studies it is shown that NO is emitted ubiquitously from terrestrial ecosystems, as such the NO emission potential from deserts and scrublands should be taken into account in the global NO models. The emission of NO is influenced by various factors such as landscape, vegetation and climate. This study looks at the potential emissions from certain arid and semi-arid environments in southern Africa and other parts of the world and discusses some of the important factors controlling the emission of NO from the soil.
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rnNitric oxide (NO) is important for several chemical processes in the atmosphere. Together with nitrogen dioxide (NO2 ) it is better known as nitrogen oxide (NOx ). NOx is crucial for the production and destruction of ozone. In several reactions it catalyzes the oxidation of methane and volatile organic compounds (VOCs) and in this context it is involved in the cycling of the hydroxyl radical (OH). OH is a reactive radical, capable of oxidizing most organic species. Therefore, OH is also called the “detergent” of the atmosphere. Nitric oxide originates from several sources: fossil fuel combustion, biomass burning, lightning and soils. Fossil fuel combustion is the largest source. The others are, depending on the reviewed literature, generally comparable to each other. The individual sources show a different temporal and spatial pattern in their magnitude of emission. Fossil fuel combustion is important in densely populated places, where NO from other sources is less important. In contrast NO emissions from soils (hereafter SNOx) or biomass burning are the dominant source of NOx in remote regions.rnBy applying an atmospheric chemistry global climate model (AC-GCM) I demonstrate that SNOx is responsible for a significant part of NOx in the atmosphere. Furthermore, it increases the O3 and OH mixing ratio substantially, leading to a ∼10% increase in the oxidizing efficiency of the atmosphere. Interestingly, through reduced O3 and OH mixing ratios in simulations without SNOx, the lifetime of NOx increases in regions with other dominating sources of NOx
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The Brazilian Amazon is one of the most rapidly developing agricultural areas in the world and represents a potentially large future source of greenhouse gases from land clearing and subsequent agricultural management. In an integrated approach, we estimate the greenhouse gas dynamics of natural ecosystems and agricultural ecosystems after clearing in the context of a future climate. We examine scenarios of deforestation and postclearing land use to estimate the future (2006-2050) impacts on carbon dioxide (CO(2)), methane (CH(4)), and nitrous oxide (N(2)O) emissions from the agricultural frontier state of Mato Grosso, using a process-based biogeochemistry model, the Terrestrial Ecosystems Model (TEM). We estimate a net emission of greenhouse gases from Mato Grosso, ranging from 2.8 to 15.9 Pg CO(2)-equivalents (CO(2)-e) from 2006 to 2050. Deforestation is the largest source of greenhouse gas emissions over this period, but land uses following clearing account for a substantial portion (24-49%) of the net greenhouse gas budget. Due to land-cover and land-use change, there is a small foregone carbon sequestration of 0.2-0.4 Pg CO(2)-e by natural forests and cerrado between 2006 and 2050. Both deforestation and future land-use management play important roles in the net greenhouse gas emissions of this frontier, suggesting that both should be considered in emissions policies. We find that avoided deforestation remains the best strategy for minimizing future greenhouse gas emissions from Mato Grosso.
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This work reports on the synthesis, characterization and applications of the new cerium(III) beta-diketonate Ce(hdacac)(3)(Hhdacac)(3)center dot 2H(2)O (where hdacac and Hhdacac denote, respectively, the hexadecylpentane-2,4-dionate and hexadecylpentane-2,4-dione ligands) as catalyst for the reduction of automotive emissions. Due to its amphiphilic character, this complex can be solubilized in non-polar fuels, thus generating cerium(IV) oxide particles, which efficiently catalyze the oxidation of diesel/biodiesel soot. The synthesized complex was characterized by microanalysis (C, H), thermal analysis, and infrared spectroscopy. Scanning electron microscopy, X-ray diffractometry, and specific surface area measurements attested that the complex can act as a soluble precursor of homogeneous CeO(2) spherical nanoparticles. The efficiency of this compound as catalyst for the reduction of soot emission was evaluated through static studies (comprising carbon black oxidation), which confirmed that increasing concentrations of the complex result in lower carbon black oxidation temperatures and lower activation Gibbs free energies. Dynamic studies, which embraced the combustion of diesel/biodiesel blends containing different amounts of the solubilized complex in a stationary motor, allowed a comparative evaluation of the soot emission through diffuse reflectance spectroscopy. These analyses provided very emphatic evidences of the efficiency of this new cerium complex for the control of soot emission in diesel/biodiesel motors. (c) 2009 Published by Elsevier B.V.
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Aquest treball s’enfoca cap l’anàlisi de les emissions de gasos amb un potencial impacte negatiu sobre l’entorn que es poden emetre a l’atmosfera durant el compostatge casolà com són el metà i l’òxid nitrós pel seu paper de gasos d’efecte hivernacle i l’amoníac, però sense oblidar el seguiment dels paràmetres del procés en si i la determinació de la qualitat del compost produït. Durant poc més de 6 mesos s’ha simulat un sistema de compostatge casolà tal i com podria donar‐se en un domicili particular i s’ha confirmat la seva eficàcia en la reducció en pes del residu tractat així com l’obtenció d’un producte final altament estable i d’una qualitat més que acceptable. Pel que fa a les emissions de gasos, les quantitats determinades no són menyspreables. L’experiment s’ha realitzat per triplicat. Les emissions són molt erràtiques i no s’han trobat patrons clars en la seva evolució durant el procés de compostatge més enllà d’una certa correlació entre les emissions d’amoníac i la diferència de temperatures entre l’ambient i l’interior dels compostadors. Cal destacat un elevat grau de biaix en la determinació d’emissions gasoses a petita escala, com és el cas del compostatge casolà. Finalment constatar que la generació de lixiviats en el compostatge domèstic pot ser important donat el contingut en aigua de la matèria orgànica tractada a nivell casolà i el limitat accés a material estructurant sec que es té per a compensar‐les.
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The semi-arid region of Chiapas is dominated by N2 -fixing shrubs, e.g., Acacia angustissima. Urea-fertilized soil samples under maize were collected from areas covered and uncovered by A. angustissima in different seasons and N2O and CO2 emissions were monitored. The objective of this study was to determine the effects of urea and of the rainy and dry season on gas emissions from semi-arid soil under laboratory conditions. Urea and soil use had no effect on CO2 production. Nitrons oxide emission from soil was three times higher in the dry than in the rainy season, while urea fertilization doubled emissions. Emissions were twice as high from soil sampled under A. angustissima canopy than from arable land, but 1.2 lower than from soil sampled outside the canopy, and five times higher from soil incubated at 40 % of the water-holding capacity (WHC) than at soil moisture content, but 15 times lower than from soil incubated at 100 WHC. It was found that the soil sampling time and water content had a significant effect on N2O emissions, while N fertilizer and sampling location were less influent.
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Nitrogen fertilizers increase the nitrous oxide (N2O) emission and can reduce the methane (CH4) oxidation from agricultural soils. However, the magnitude of this effect is unknown in Southern Brazilian edaphoclimatic conditions, as well as the potential of different sources of mineral N fertilizers in such an effect. The aim of this study was to investigate the effects of different mineral N sources (urea, ammonium sulphate, calcium nitrate, ammonium nitrate, Uran, controlled- release N fertilizer, and urea with urease inhibitor) on N2O and CH4 fluxes from Gleysol in the South of Brazil (Porto Alegre, RS), in comparison to a control treatment without a N application. The experiment was arranged in a randomized block with three replications, and the N fertilizer was applied to corn at the V5 growth stage. Air samples were collected from a static chambers for 15 days after the N application and the N2O and CH4 concentration were determined by gas chromatography. The topmost emissions occurred three days after the N fertilizer application and ranged from 187.8 to 8587.4 µg m-2 h-1 N. The greatest emissions were observed for N-nitric based fertilizers, while N sources with a urease inhibitor and controlled release N presented the smallest values and the N-ammonium and amidic were intermediate. This peak of N2O emissions was related to soil NO3--N (R² = 0.56, p < 0.08) when the soil water-filled pore space was up to 70 % and it indicated that N2O was predominantly produced by a denitrification process in the soil. Soil CH4 fluxes ranged from -30.1 µg m-2 h-1 C (absorption) to +32.5 µg m-2 h-1 C (emission), and the accumulated emission in the period was related to the soil NH4+-N concentration (R² = 0.82, p < 0.001), probably due to enzymatic competition between nitrification and metanotrophy processes. Despite both of the gas fluxes being affected by N fertilizers, in the average of the treatments, the impact on CH4 emission (0.2 kg ha-1 equivalent CO2-C ) was a hundredfold minor than for N2O (132.8 kg ha-1 equivalent CO2-C). Accounting for the N2O and CH4 emissions plus energetic costs of N fertilizers of 1.3 kg CO2-C kg-1 N regarding the manufacture, transport and application, we estimated an environmental impact of N sources ranging from 220.4 to 664.5 kg ha-1 CO2 -C , which can only be partially offset by C sequestration in the soil, as no study in South Brazil reported an annual net soil C accumulation rate larger than 160 kg ha-1 C due to N fertilization. The N2O mitigation can be obtained by the replacement of N-nitric sources by ammonium and amidic fertilizers. Controlled release N fertilizers and urea with urease inhibitor are also potential alternatives to N2O emission mitigation to atmospheric and systematic studies are necessary to quantify their potential in Brazilian agroecosystems.
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Among the greenhouse gases, nitrous oxide (N2O) is considered important, in view of a global warming potential 296 times greater than that of carbon dioxide (CO2) and its dynamics strongly depend on the availability of C and mineral N in the soil. The understanding of the factors that define emissions is essential to develop mitigation strategies. This study evaluated the dynamics of N2O emissions after the application of different rice straw amounts and nitrate levels in soil solution. Pots containing soil treated with sodium nitrate rates (0, 50 and 100 g kg-1 of NO−3-N) and rice straw levels (0, 5 and 10 Mg ha-1), i.e., nine treatments, were subjected to anaerobic conditions. The results showed that N2O emissions were increased by the addition of greater NO−3 amounts and reduced by large straw quantities applied to the soil. On the 1st day after flooding (DAF), significantly different N2O emissions were observed between the treatments with and without NO−3 addition, when straw had no significant influence on N2O levels. Emissions peaked on the 4th DAF in the treatments with highest NO−3-N addition. At this moment, straw application negatively affected N2O emissions, probably due to NO−3 immobilization. There were also alterations in other soil electrochemical characteristics, e.g., higher straw levels raised the Fe, Mn and dissolved C contents. These results indicate that a lowering of NO−3 concentration in the soil and the increase of straw incorporation can decrease N2O emissions.
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ABSTRACT Livestock urine and dung are important components of the N cycle in pastures, but little information on its effect on soil nitrous oxide (N2O) emissions is available. We conducted a short-term (39-day) trial to quantify the direct N2O-N emissions from sheep excreta on an experimental area of ryegrass pasture growing on a Typic Paleudult in southern Brazil. Four rates of urine-N (161, 242, 323, and 403 kg ha-1 N) and one of dung-N (13 kg ha-1 N) were applied, as well as a control plot receiving no excreta. The N2O-N emission factor (EF = % of added N released as N2O-N) for urine and dung was calculated, taking into account the N2O fluxes in the field, over a period of 39 days. The EF value of the urine and dung was used to estimate the emissions of N2O-N over a 90-day period of pasture in the winter under two grazing intensities (2.5 or 5.0 times the herbage intake potential of grazing lambs). The soil N2O-N fluxes ranged from 4 to 353 µg m-2h-1. The highest N2O-N fluxes occurred 16 days after application of urine and dung, when the highest soil nitrate content was also recorded and the water-filled pore space exceeded 60 %. The mean EF for urine was 0.25 % of applied N, much higher than that for dung (0.06 %). We found that N2O-N emissions for the 90-day winter pasture period were 0.54 kg ha-1 for low grazing intensity and 0.62 kg ha-1 for moderate grazing intensity. Comparison of the two forms of excreta show that urine was the main contributor to N2O-N emissions (mean of 36 %), whereas dung was responsible for less than 0.1 % of total soil N2O-N emissions.
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The objective of the thesis is to study cerium oxide thin films grown by the atomic layer deposition (ALD) for soot removal. Cerium oxide is one of the most important heterogeneous catalysts and can be used in particulate filters and sensors in a diesel exhaust pipe. Its redox/oxidation properties are a key factor in soot oxidation. Thus, the cerium oxide coating can help to keep particulate filters and sensors clean permanently. The literature part of the thesis focuses on the soot removal, introducing the origin and structure of soot, reviewing emissions standards for diesel particulate matter, and presenting methods and catalysts for soot removal. In the experimental part the optimal ALD conditions for cerium oxide were found, the structural properties of cerium oxide thin films were analyzed, and the catalytic activity of the cerium oxide for soot oxidation was investigated. Studying ALD growth conditions of cerium oxide films and determining their critical thickness range are important to maximize the catalytic performance operating at comparatively low temperature. It was found that the cerium oxide film deposited at 300 °C with 2000 ALD cycles had the highest catalytic activity. Although the activity was still moderate and did not decrease the soot oxidation temperature enough for a real-life application. The cerium oxide thin film deposited at 300 °C has a different crystal structure, surface morphology and elemental composition with a higher Ce3+ concentration compared to the films deposited at lower temperatures. The different properties of the cerium oxide thin film deposited at 300 °C increase the catalytic activity most likely due to higher surface area and addition of the oxygen vacancies.
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Landwirtschaft spielt eine zentrale Rolle im Erdsystem. Sie trägt durch die Emission von CO2, CH4 und N2O zum Treibhauseffekt bei, kann Bodendegradation und Eutrophierung verursachen, regionale Wasserkreisläufe verändern und wird außerdem stark vom Klimawandel betroffen sein. Da all diese Prozesse durch die zugrunde liegenden Nährstoff- und Wasserflüsse eng miteinander verknüpft sind, sollten sie in einem konsistenten Modellansatz betrachtet werden. Dennoch haben Datenmangel und ungenügendes Prozessverständnis dies bis vor kurzem auf der globalen Skala verhindert. In dieser Arbeit wird die erste Version eines solchen konsistenten globalen Modellansatzes präsentiert, wobei der Schwerpunkt auf der Simulation landwirtschaftlicher Erträge und den resultierenden N2O-Emissionen liegt. Der Grund für diese Schwerpunktsetzung liegt darin, dass die korrekte Abbildung des Pflanzenwachstums eine essentielle Voraussetzung für die Simulation aller anderen Prozesse ist. Des weiteren sind aktuelle und potentielle landwirtschaftliche Erträge wichtige treibende Kräfte für Landnutzungsänderungen und werden stark vom Klimawandel betroffen sein. Den zweiten Schwerpunkt bildet die Abschätzung landwirtschaftlicher N2O-Emissionen, da bislang kein prozessbasiertes N2O-Modell auf der globalen Skala eingesetzt wurde. Als Grundlage für die globale Modellierung wurde das bestehende Agrarökosystemmodell Daycent gewählt. Neben der Schaffung der Simulationsumgebung wurden zunächst die benötigten globalen Datensätze für Bodenparameter, Klima und landwirtschaftliche Bewirtschaftung zusammengestellt. Da für Pflanzzeitpunkte bislang keine globale Datenbasis zur Verfügung steht, und diese sich mit dem Klimawandel ändern werden, wurde eine Routine zur Berechnung von Pflanzzeitpunkten entwickelt. Die Ergebnisse zeigen eine gute Übereinstimmung mit Anbaukalendern der FAO, die für einige Feldfrüchte und Länder verfügbar sind. Danach wurde das Daycent-Modell für die Ertragsberechnung von Weizen, Reis, Mais, Soja, Hirse, Hülsenfrüchten, Kartoffel, Cassava und Baumwolle parametrisiert und kalibriert. Die Simulationsergebnisse zeigen, dass Daycent die wichtigsten Klima-, Boden- und Bewirtschaftungseffekte auf die Ertragsbildung korrekt abbildet. Berechnete Länderdurchschnitte stimmen gut mit Daten der FAO überein (R2 = 0.66 für Weizen, Reis und Mais; R2 = 0.32 für Soja), und räumliche Ertragsmuster entsprechen weitgehend der beobachteten Verteilung von Feldfrüchten und subnationalen Statistiken. Vor der Modellierung landwirtschaftlicher N2O-Emissionen mit dem Daycent-Modell stand eine statistische Analyse von N2O-und NO-Emissionsmessungen aus natürlichen und landwirtschaftlichen Ökosystemen. Die als signifikant identifizierten Parameter für N2O (Düngemenge, Bodenkohlenstoffgehalt, Boden-pH, Textur, Feldfrucht, Düngersorte) und NO (Düngemenge, Bodenstickstoffgehalt, Klima) entsprechen weitgehend den Ergebnissen einer früheren Analyse. Für Emissionen aus Böden unter natürlicher Vegetation, für die es bislang keine solche statistische Untersuchung gab, haben Bodenkohlenstoffgehalt, Boden-pH, Lagerungsdichte, Drainierung und Vegetationstyp einen signifikanten Einfluss auf die N2O-Emissionen, während NO-Emissionen signifikant von Bodenkohlenstoffgehalt und Vegetationstyp abhängen. Basierend auf den daraus entwickelten statistischen Modellen betragen die globalen Emissionen aus Ackerböden 3.3 Tg N/y für N2O, und 1.4 Tg N/y für NO. Solche statistischen Modelle sind nützlich, um Abschätzungen und Unsicherheitsbereiche von N2O- und NO-Emissionen basierend auf einer Vielzahl von Messungen zu berechnen. Die Dynamik des Bodenstickstoffs, insbesondere beeinflusst durch Pflanzenwachstum, Klimawandel und Landnutzungsänderung, kann allerdings nur durch die Anwendung von prozessorientierten Modellen berücksichtigt werden. Zur Modellierung von N2O-Emissionen mit dem Daycent-Modell wurde zunächst dessen Spurengasmodul durch eine detailliertere Berechnung von Nitrifikation und Denitrifikation und die Berücksichtigung von Frost-Auftau-Emissionen weiterentwickelt. Diese überarbeitete Modellversion wurde dann an N2O-Emissionsmessungen unter verschiedenen Klimaten und Feldfrüchten getestet. Sowohl die Dynamik als auch die Gesamtsummen der N2O-Emissionen werden befriedigend abgebildet, wobei die Modelleffizienz für monatliche Mittelwerte zwischen 0.1 und 0.66 für die meisten Standorte liegt. Basierend auf der überarbeiteten Modellversion wurden die N2O-Emissionen für die zuvor parametrisierten Feldfrüchte berechnet. Emissionsraten und feldfruchtspezifische Unterschiede stimmen weitgehend mit Literaturangaben überein. Düngemittelinduzierte Emissionen, die momentan vom IPCC mit 1.25 +/- 1% der eingesetzten Düngemenge abgeschätzt werden, reichen von 0.77% (Reis) bis 2.76% (Mais). Die Summe der berechneten Emissionen aus landwirtschaftlichen Böden beträgt für die Mitte der 1990er Jahre 2.1 Tg N2O-N/y, was mit den Abschätzungen aus anderen Studien übereinstimmt.
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Little is known about gaseous carbon (C) and nitrogen (N) emissions from traditional terrace agriculture in irrigated high mountain agroecosystems of the subtropics. In an effort towards filling this knowledge gap measurements of carbon dioxide (CO_2), methane (CH_4), ammonia (NH_3) and dinitrous oxide (N_2O) were taken with a mobile photoacoustic infrared multi-gas monitor on manure-filled PE-fibre storage bags and on flood-irrigated untilled and tilled fields in three mountain oases of the northen Omani Al Jabal al Akhdar mountains. During typical 9-11 day irrigation cycles of March, August and September 2006 soil volumetric moisture contents of fields dominated by fodder wheat, barley, oats and pomegranate ranged from 46-23%. While manure incorporation after application effectively reduced gaseous N losses, prolonged storage of manure in heaps or in PE-fibre bags caused large losses of C and N. Given the large irrigation-related turnover of organic C, sustainable agricultural productivity of oasis agriculture in Oman seems to require the integration of livestock which allows for several applications of manure per year at individual rates of 20 t dry matter ha^−1.