947 resultados para Canopy gaps


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Tasaikäisen metsän alle muodostuvilla alikasvoksilla on merkitystä puunkorjuun, metsänuudistamisen, näkemä-ja maisema-analyysien sekä biodiversiteetin ja hiilitaseen arvioinnin kannalta. Ilma-aluksista tehtävä laserkeilaus on osoittautunut tehokkaaksi kaukokartoitusmenetelmäksi varttuneiden puustojen mittauksessa. Laserkeilauksen käyttöönotto operatiivisessa metsäsuunnittelussa mahdollistaa aiempaa tarkemman tiedon tuottamisen alikasvoksista, mikäli alikasvoksen ominaisuuksia voidaan tulkita laseraineistoista. Tässä työssä käytettiin tarkasti mitattuja maastokoealoja ja kaikulaserkeilausaineistoja (discrete return LiDAR) usealta vuodelta (1–2 km lentokorkeus, 0,9–9,7 pulssia m-2). Laserkeilausaineistot oli hankittu Optech ALTM3100 ja Leica ALS50-II sensoreilla. Koealat edustavat suomalaisia tasaikäisiä männiköitä eri kehitysvaiheissa. Tutkimuskysymykset olivat: 1) Minkälainen on alikasvoksesta saatu lasersignaali yksittäisen pulssin tasolla ja mitkä tekijät signaaliin vaikuttavat? 2) Mikä on käytännön sovelluksissa hyödynnettävien aluepohjaisten laserpiirteiden selitysvoima alikasvospuuston ominaisuuksien ennustamisessa? Erityisesti haluttiin selvittää, miten laserpulssin energiahäviöt ylempiin latvuskerroksiin vaikuttavat saatuun signaaliin, ja voidaanko laserkaikujen intensiteetille tehdä energiahäviöiden korjaus. Puulajien väliset erot laserkaiun intensiteetissä olivat pieniä ja vaihtelivat keilauksesta toiseen. Intensiteetin käyttömahdollisuudet alikasvoksen puulajin tulkinnassa ovat siten hyvin rajoittuneet. Energiahäviöt ylempiin latvuskerroksiin aiheuttivat alikasvoksesta saatuun lasersignaaliin kohinaa. Energiahäviöiden korjaus tehtiin alikasvoksesta saaduille laserpulssin 2. ja 3. kaiuille. Korjauksen avulla pystyttiin pienentämään kohteen sisäistä intensiteetin hajontaa ja parantamaan kohteiden luokittelutarkkuutta alikasvoskerroksessa. Käytettäessä 2. kaikuja oikeinluokitusprosentti luokituksessa maan ja yleisimmän puulajin välillä oli ennen korjausta 49,2–54,9 % ja korjauksen jälkeen 57,3–62,0 %. Vastaavat kappa-arvot olivat 0,03–0,13 ja 0,10–0,22. Tärkein energiahäviöitä selittävä tekijä oli pulssista saatujen aikaisempien kaikujen intensiteetti, mutta hieman merkitystä oli myös pulssin leikkausgeometrialla ylemmän latvuskerroksen puiden kanssa. Myös 3. kaiuilla luokitustarkkuus parani. Puulajien välillä havaittiin eroja siinä, kuinka herkästi ne tuottavat kaiun laserpulssin osuessa puuhun. Kuusi tuotti kaiun suuremmalla todennäköisyydellä kuin lehtipuut. Erityisen selvä tämä ero oli pulsseilla, joissa oli energiahäviöitä. Laserkaikujen korkeusjakaumapiirteet voivat siten olla riippuvaisia puulajista. Sensorien välillä havaittiin selviä eroja intensiteettijakaumissa, mikä vaikeuttaa eri sensoreilla hankittujen aineistojen yhdistämistä. Myös kaiun todennäköisyydet erosivat jonkin verran sensorien välillä, mikä aiheutti pieniä eroavaisuuksia kaikujen korkeusjakaumiin. Aluepohjaisista laserpiirteistä löydettiin alikasvoksen runkolukua ja keskipituutta hyvin selittäviä piirteitä, kun rajoitettiin tarkastelu yli 1 m pituisiin puihin. Piirteiden selitysvoima oli parempi runkoluvulle kuin keskipituudelle. Selitysvoima ei merkittävästi alentunut pulssitiheyden pienentyessä, mikä on hyvä asia käytännön sovelluksia ajatellen. Lehtipuun osuutta ei pystytty selittämään. Tulosten perusteella kaikulaserkeilausta voi olla mahdollista hyödyntää esimerkiksi ennakkoraivaustarpeen arvioinnissa. Sen sijaan alikasvoksen tarkempi luokittelu (esim. puulajitulkinta) voi olla vaikeaa. Kaikkein pienimpiä alikasvospuita ei pystytä havaitsemaan. Lisää tutkimuksia tarvitaan tulosten yleistämiseksi erilaisiin metsiköihin.

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The accompanying collective research report is the result of the research project in 1986­90 between The Finnish Academy and the former Soviet Academy of Sciences. The project was organized around common field work in Finland and in the former Soviet Union and theoretical analyses of tree growth determining processes. Based on theoretical analyses, dynamic stand growth models were made and their parameters were determined utilizing the field results. Annual cycle affects the tree growth. Our theoretical approach was based on adaptation to local climate conditions from Lapland to South Russia. The initiation of growth was described as a simple low and high temperature accumulation driven model. Linking the theoretical model with long term temperature data allowed us to analyze what type of temperature response produced favorable outcome in different climates. Initiation of growth consumes the carbohydrate reserves in plants. We measured the dynamics of insoluble and soluble sugars in the very northern and Karelian conditions. Clear cyclical pattern was observed but the differences between locations were surprisingly small. Analysis of field measurements of CO2 exchange showed that irradiance is the dominating factor causing variation in photosynthetic rate in natural conditions during summer. The effect of other factors is so small that they can be omitted without any considerable loss of accuracy. A special experiment carried out in Hyytiälä showed that the needle living space, defined as the ratio between the shoot cylindric volume and needle surface area, correlates with the shoot photosynthesis. The penetration of irradiance into Scots pine canopy is a complicated phenomenon because of the movement of the sun on the sky and the complicated structure of branches and needles. A moderately simple but balanced forest radiation regime submodel was constructed. It consists of the tree crown and forest structure, the gap probability calculation and the consideration of spatial and temporal variation of radiation inside the forest. The common field excursions in different geographical regions resulted in a lot of experimental data of regularities of woody structures. The water transport seems to be a good common factor to analyse these properties of tree structure. There are evident regressions between cross-sectional areas measured at different locations along the water pathway from fine roots to needles. The observed regressions have clear geographical trends. For example, the same cross-sectional area can support three times higher needle mass in South Russia than in Lapland. Geographical trends can also be seen in shoot and needle structure. Analysis of data published by several Russian authors show, that one ton of needles transpire 42 ton of water a year. This annual amount of transpiration seems to be independent of geographical location, year and site conditions. The produced theoretical and experimental material is utilised in the development of stand growth model that describes the growth and development of Scots pine stands in Finland and the former Soviet Union. The core of the model is carbon and nutrient balances. This means that carbon obtained in photosynthesis is consumed for growth and maintenance and nutrients are taken according to the metabolic needs. The annual photosynthetic production by trees in the stand is determined as a function of irradiance and shading during the active period. The utilisation of the annual photosynthetic production to the growth of different components of trees is based on structural regularities. Since the fundamental metabolic processes are the same in all locations the same growth model structure can be applied in the large range of Scots pine. The annual photosynthetic production and structural regularities determining the allocation of resources have geographical features. The common field measurements enable the application of the model to the analysis of growth and development of stands growing on the five locations of experiments. The model enables the analysis of geographical differences in the growth of Scots pine. For example, the annual photosynthetic production of a 100-year-old stand at Voronez is 3.5 times higher than in Lapland. The share consumed to needle growth (30 %) and to growth of branches (5 %) seems to be the same in all locations. In contrast, the share of fine roots is decreasing when moving from north to south. It is 20 % in Lapland, 15 % in Hyytiälä Central Finland and Kentjärvi Karelia and 15 % in Voronez South Russia. The stem masses (115­113 ton/ha) are rather similar in Hyytiälä, Kentjärvi and Voronez, but rather low (50 ton/ha) in Lapland. In Voronez the height of the trees reach 29 m being in Hyytiälä and Kentjärvi 22 m and in Lapland only 14 m. The present approach enables utilization of structural and functional knowledge, gained in places of intensive research, in the analysis of growth and development of any stand. This opens new possibilities for growth research and also for applications in forestry practice.

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We have studied charge transport in nanometer scale films of polypyrrole (PPy) that were grown electrochemically onto discontinuous ultrathin films of gold. The gold films consisted of 100 nm size islands, separated from each other by nanometer-size gaps. The thickness of PPy can be varied from 30 to 200 nm. The I-V characteristics of these hybrid PPy-Au nanostructures show strong non-linearity at low temperatures, and in particular for the more insulating samples. The hopping transport is further verified from the log / versus V-1/4 plots. Furthermore, the I-V data follow an empirical relation dlog//dV(1/4) similar to T-1/2.

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Tin sulfide (SnS) nanostructures have been synthesized using a simple and low temperature chemical solution method on seeded substrates, and their structural and optical properties have been investigated. The as-grown SnS nanostructures with well-defined facets exhibited good stoichiometry between constituent elements. These nanobox structures are preferentially oriented along the 010] direction by having 100] and 001] orientations as surrounding facets and exhibited Two distinguishable optical band gaps of 1.36 and 1.9 eV. The effect of solution concentration as well as seed layer on the morphology or SnS structures has also been studied, and finally, the growth mechanism of the regular SnS nanobox structures is proposed.

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Research on carbon uptake in boreal forests has mainly focused on mature trees, even though ground vegetation species are effective assimilators and can substantially contribute to the CO2 uptake of forests. Here, I examine the photosynthesis of the most common species of ground vegetation in a series of differently aged Scots pine stands, and at two clear-cut sites with substantial differences in fertility. In general, the biomass of evergreen species was highest at poor sites and below canopies, whereas grasses and herbs predominated at fertile sites and open areas. Unlike mosses, the measured vascular species showed clear annual cycles in their photosynthetic activity, which increased earlier and decreased later in evergreen vascular species than in deciduous species. However, intraspecific variation and self-shading create differences in the overall level of photosynthesis. Light, temperature history, soil moisture and recent possible frosts could explain the changes in photosynthesis of low shrubs and partially also some changes in deciduous species. Light and the occurrence of rain events explained most of the variation in the photosynthesis of mosses. The photosynthetic production of ground vegetation was first upscaled, using species-specific and mass-based photosynthetic activities and average biomass of the site, and then integrated over the growing season, using changes in environmental factors. Leaf mass-based photosynthesis was highest in deciduous species, resulting in notably higher photosynthetic production at fertile sites than at poor clear-cut sites. The photosynthetic production decreased with stand age, because flora changed towards evergreen species, and light levels diminished below the canopy. In addition, the leaf mass-based photosynthetic activity of some low shrubs declined with the age of the surrounding trees. Different measuring methods led to different momentary rate of photosynthesis. Therefore, the choice of measuring method needs special attention.

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Hostility is a multidimensional construct having wide effects on society. In its different forms, hostility is related to a large array of social and health problems, such as criminality, substance abuse, depression, and cardiovascular risks. Identifying and tackling early-life factors that contribute to hostility may have public health significance. Although the variance in hostility is estimated to be 18-50 percent heritable, there are significant gaps in knowledge regarding the molecular genetics of hostility. It is known that a cold and unsupportive home atmosphere in childhood predicts a child s later hostility. However, the long-term effects of care-giving quality on hostility in adulthood and the role of genes in this association are unclear. The present dissertation is part of the ongoing population-based prospective Young Finns study, which commenced in 1980 with 3596 3-18-year-old boys and girls who were followed for 27 years. The specific aims of the dissertation were first to study the antecedents of hostility by looking at 1) the genetic background, 2) the early environmental predictors, and 3) the gene environment interplay behind hostility. As a second aim, the thesis endeavored to examine 4) the association between hostility and cardiovascular risks, and 5) the moderating effect of demographic factors, such as gender and socioeconomic status, on this association. The study found potential gene polymorphisms from chromosomes 7, 14, 17, and 22 suggestively associated with hostility. Of early environmental influences, breastfeeding and early care-giving were found to predict hostility in adulthood. In addition, a serotonin receptor 2A polymorphism rs6313 moderated the effect of early care-giving on later hostile attitudes. Furthermore, hostility was shown to predict cardiovascular risks, such as metabolic syndrome and inflammation. Finally, parental socioeconomic status was found to moderate the association between anger and early atherosclerosis. The new genetic and early environmental antecedents of hostility identified in this research may help in understanding the development of hostility and its health risks, and in planning appropriate prevention. The significance of early influences on this development is stressed. Although the markers studied are individual- and family-related factors, these may be influenced at the societal level by giving accurate information to all individuals concerned and by improving the societal circumstances.

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Fire is an important driver of the boreal forest ecosystem, and a useful tool for the restoration of degraded forests. However, we lack knowledge on the ecological processes initiated by prescribed fires, and whether they bring about the desired restoration effects. The purpose of this study was to investigate the impacts of low-intensity experimental prescribed fires on four ecological processes in young commercial Scots pine (Pinus sylvestris) stands eight years after the burning. The processes of interest were tree mortality, dead wood creation, regeneration and fire scar formation. These were inventoried in twelve study plots, which were 30 m x 30 m in size. The plots belonged to two different stand age classes: 30-35 years or 45 years old at the time of burning. The study was partly a follow-up of study plots researched by Sidoroff et al. (2007) one year after burning in 2003. Tree mortality increased from 183 stems ha-1 in 2003 to 259 stems ha-1 in 2010, corresponding to 15 % and 21 % of stem number respectively. Most mortality was experienced in the stands of the younger age class, in smaller diameter classes and among species other than Scots pine. By 2010, the average mortality of Scots pine per plot was 18%, but varied greatly ranging from 0% to 63% of stem number. Delayed mortality, i.e. mortality that occurred between 2 and 8 years after fire, seemed to become more important with increasing diameter. The input of dead wood also varied greatly between plots, from none to 72 m3 ha-1, averaging at 12 m3 ha-1. The amount of fire scarred trees per plot ranged from none to 20 %. Four out of twelve plots (43 %) did not have any fire scars. Scars were on average small: 95% of scars were less than 4 cm in width, and 75% less than 40 cm in length. Owing to the light nature of the fire, the remaining overstorey and thick organic layer, regeneration was poor overall. The abundance of pine and other seedlings indicated a viable seed source existed, but the seedlings failed to establish under dense canopy. The number of saplings ranged from 0 to 12 333 stems ha-1. The results of this study indicate that a low intensity fire does not necessarily initiate the ecological processes of tree mortality, dead wood creation and regeneration in the desired scale. Fire scars, which form the basis of fire dating in fire history studies, did not form in all cases.

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Although previous research has recognised adaptation as a central aspect in relationships, the adaptation of the sales process to the buying process has not been studied. Furthermore, the linking of relationship orientation as mindset with adaptation as a strategy and forming the means has not been elaborated upon in previous research. Adaptation in the context of relationships has mostly been studied in relationship marketing. In sales and sales management research, adaptation has been studied with reference to personal selling. This study focuses on adaptation of the sales process to strategically match it to the buyer’s mindset and buying process. The purpose of this study is to develop a framework for strategic adaptation of the seller’s sales process to match the buyer’s buying process in a business-to-business context to make sales processes more relationship oriented. In order to arrive at a holistic view of adaptation of the sales process during relationship initiation, both the seller and buyer are included in an extensive case analysed in the study. However, the selected perspective is primarily that of the seller, and the level focused on is that of the sales process. The epistemological perspective adopted is constructivism. The study is a qualitative one applying a retrospective case study, where the main sources of information are in-depth semi-structured interviews with key informants representing the counterparts at the seller and the buyer in the software development and telecommunications industries. The main theoretical contributions of this research involve targeting a new area in the crossroads of relationship marketing, sales and sales management, and buying and purchasing by studying adaptation in a business-to-business context from a new perspective. Primarily, this study contributes to research in sales and sales management with reference to relationship orientation and strategic sales process adaptation. This research fills three research gaps. Firstly, linking the relationship orientation mindset with adaptation as strategy. Secondly, extending adaptation in sales from adaptation in selling to strategic adaptation of the sales process. Thirdly, extending adaptation to include facilitation of adaptation. The approach applied in the study, systematic combining, is characterised by continuously moving back and forth between theory and empirical data. The framework that emerges, in which linking mindset with strategy with mindset and means forms a central aspect, includes three layers: purchasing portfolio, seller-buyer relationship orientation, and strategic sales process adaptation. Linking the three layers enables an analysis of where sales process adaptation can make a contribution. Furthermore, implications for managerial use are demonstrated, for example how sellers can avoid the ‘trap’ of ad-hoc adaptation. This includes involving the company, embracing the buyer’s purchasing portfolio, understanding the current position that the seller has in this portfolio, and possibly educating the buyer about advantages of adopting a relationship-oriented approach.

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Using ab initio methods we have investigated the fluorination of graphene and find that different stoichiometric phases can be formed without a nucleation barrier, with the complete “2D-Teflon” CF phase being thermodynamically most stable. The fluorinated graphene is an insulator and turns out to be a perfect matrix-host for patterning nanoroads and quantum dots of pristine graphene. The electronic and magnetic properties of the nanoroads can be tuned by varying the edge orientation and width. The energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO) of quantum dots are size-dependent and show a confinement typical of Dirac fermions. Furthermore, we study the effect of different basic coverage of F on graphene (with stoichiometries CF and C4F) on the band gaps, and show the suitability of these materials to host quantum dots of graphene with unique electronic properties.

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The loss and degradation of forest cover is currently a globally recognised problem. The fragmentation of forests is further affecting the biodiversity and well-being of the ecosystems also in Kenya. This study focuses on two indigenous tropical montane forests in the Taita Hills in southeastern Kenya. The study is a part of the TAITA-project within the Department of Geography in the University of Helsinki. The study forests, Ngangao and Chawia, are studied by remote sensing and GIS methods. The main data includes black and white aerial photography from 1955 and true colour digital camera data from 2004. This data is used to produce aerial mosaics from the study areas. The land cover of these study areas is studied by visual interpretation, pixel-based supervised classification and object-oriented supervised classification. The change of the forest cover is studied with GIS methods using the visual interpretations from 1955 and 2004. Furthermore, the present state of the study forests is assessed with leaf area index and canopy closure parameters retrieved from hemispherical photographs as well as with additional, previously collected forest health monitoring data. The canopy parameters are also compared with textural parameters from digital aerial mosaics. This study concludes that the classification of forest areas by using true colour data is not an easy task although the digital aerial mosaics are proved to be very accurate. The best classifications are still achieved with visual interpretation methods as the accuracies of the pixel-based and object-oriented supervised classification methods are not satisfying. According to the change detection of the land cover in the study areas, the area of indigenous woodland in both forests has decreased in 1955 2004. However in Ngangao, the overall woodland area has grown mainly because of plantations of exotic species. In general, the land cover of both study areas is more fragmented in 2004 than in 1955. Although the forest area has decreased, forests seem to have a more optimistic future than before. This is due to the increasing appreciation of the forest areas.

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By law, rescue services must anticipate and plan future rescue situations so that the emergency measures taken in the event of an accident can be accomplished quickly and effectively. To reach this goal, rescue services planning must be up to date. The development of rescue services is di-rected by the Rescue Act, and guidelines such as the readiness program, based on that law. The guidelines give the basic principles for organizing rescue services. This paper studies the ability of rescuers to reach different locations now, and in the future, and whether this happens within the time constraints required by the readiness program. The time per-spective of the study includes both the current time and the future. Predictions of possible future situations are based on zoning information. The goal of the study is to find out whether there are any gaps in the network of fire stations or if gaps will develop in the near future. The strong growth and increase in the population of the greater Helsinki area, and of surrounding towns, creates many challenges for city planning, including rescue services. This study targets the two towns of Espoo and Kirkkonummi, where fast growth specifically into new housing areas, makes planning of rescue services challenging. Many new options are available for planning due to technological developments. The combined methods of planning and geo-informatics used in this study help to determine the need for new resources in rescue services. By using these methods, the planning of rescue services could be done at least 10 years into the future.

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We point out possibilities for exotic physics in barium bismuthates, from a detailed study of the negative-U, extended-Hubbard model proposed for these systems. We emphasize the different consequences of electronic and phononic mechanisms for negative U. We show that, for an electronic mechanism, the semiconducting phases must be unique, with their transport properties dominated by charge ± 2e Cooperon bound states. This can explain the observed difference between the optical and transport gaps. We propose other experimental tests for this novel mechanism of charge transport.

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Road transport and infrastructure has a fundamental meaning for the developing world. Poor quality and inadequate coverage of roads, lack of maintenance operations and outdated road maps continue to hinder economic and social development in the developing countries. This thesis focuses on studying the present state of road infrastructure and its mapping in the Taita Hills, south-east Kenya. The study is included as a part of the TAITA-project by the Department of Geography, University of Helsinki. The road infrastructure of the study area is studied by remote sensing and GIS based methodology. As the principal dataset, true colour airborne digital camera data from 2004, was used to generate an aerial image mosaic of the study area. Auxiliary data includes SPOT satellite imagery from 2003, field spectrometry data of road surfaces and relevant literature. Road infrastructure characteristics are interpreted from three test sites using pixel-based supervised classification, object-oriented supervised classifications and visual interpretation. Road infrastructure of the test sites is interpreted visually from a SPOT image. Road centrelines are then extracted from the object-oriented classification results with an automatic vectorisation process. The road infrastructure of the entire image mosaic is mapped by applying the most appropriate assessed data and techniques. The spectral characteristics and reflectance of various road surfaces are considered with the acquired field spectra and relevant literature. The results are compared with the experimented road mapping methods. This study concludes that classification and extraction of roads remains a difficult task, and that the accuracy of the results is inadequate regardless of the high spatial resolution of the image mosaic used in this thesis. Visual interpretation, out of all the experimented methods in this thesis is the most straightforward, accurate and valid technique for road mapping. Certain road surfaces have similar spectral characteristics and reflectance values with other land cover and land use. This has a great influence for digital analysis techniques in particular. Road mapping is made even more complicated by rich vegetation and tree canopy, clouds, shadows, low contrast between roads and surroundings and the width of narrow roads in relation to the spatial resolution of the imagery used. The results of this thesis may be applied to road infrastructure mapping in developing countries on a more general context, although with certain limits. In particular, unclassified rural roads require updated road mapping schemas to intensify road transport possibilities and to assist in the development of the developing world.

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In lake-rich regions, the gathering of information about water quality is challenging because only a small proportion of the lakes can be assessed each year by conventional methods. One of the techniques for improving the spatial and temporal representativeness of lake monitoring is remote sensing from satellites and aircrafts. The experimental material included detailed optical measurements in 11 lakes, air- and spaceborne remote sensing measurements with concurrent field sampling, automatic raft measurements and a national dataset of routine water quality measurements from over 1100 lakes. The analyses of the spatially high-resolution airborne remote sensing data from eutrophic and mesotrophic lakes showed that one or a few discrete water quality observations using conventional monitoring can yield a clear over- or underestimation of the overall water quality in a lake. The use of TM-type satellite instruments in addition to routine monitoring results substantially increases the number of lakes for which water quality information can be obtained. The preliminary results indicated that coloured dissolved organic matter (CDOM) can be estimated with TM-type satellite instruments, which could possibly be utilised as an aid in estimating the role of lakes in global carbon budgets. Based on the results of reflectance modelling and experimental data, MERIS satellite instrument has optimal or near-optimal channels for the estimation of turbidity, chlorophyll a and CDOM in Finnish lakes. MERIS images with a 300 m spatial resolution can provide water quality information in different parts of large and medium-sized lakes, and in filling in the gaps resulting from conventional monitoring. Algorithms that would not require simultaneous field data for algorithm training would increase the amount of remote sensing-based information available for lake monitoring. The MERIS Boreal Lakes processor, trained with the optical data and concentration ranges provided by this study, enabled turbidity estimations with good accuracy without the need for algorithm correction with field measurements, while chlorophyll a and CDOM estimations require further development of the processor. The accuracy of interpreting chlorophyll a via semi empirical algorithms can be improved by classifying lakes prior to interpretation according to their CDOM level and trophic status. Optical modelling indicated that the spectral diffuse attenuation coefficient can be estimated with reasonable accuracy from the measured water quality concentrations. This provides more detailed information on light attenuation from routine monitoring measurements than is available through the Secchi disk transparency. The results of this study improve the interpretation of lake water quality by remote sensing and encourage the use of remote sensing in lake monitoring.

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Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.