Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

Modelling the growth and movement of cyanobacteria in river systems

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes and rivers. In this article, a new deterministic model is introduced which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the four major factors that affect the cyanobacterial bloom formation in freshwaters: light, nutrients, temperature and river flow. The model consists of two sub-models: a vertical migration model with respect to growth of cyanobacteria in relation to light, nutrients and temperature; and a hydraulic model to simulate the horizontal movement of the bloom. This article presents the model algorithms and highlights some important model results. The effects of nutrient limitation, varying illumination and river flow characteristics on cyanobacterial movement are simulated. The results indicate that under high light intensities and in nutrient-rich waters colonies sink further as a result of carbohydrate accumulation in the cells. In turbulent environments, vertical migration is retarded by vertical velocity component generated by turbulent shear stress. (c) 2006 Elsevier B.V. All rights reserved.

Safety and quality and stage of distribution

Let 0 denote the level of quality inherent in a food product that is delivered to some terminal market. In this paper, I characterize allocations over 0 and provide an economic rationale for regulating safety and quality standards in the food system. Zusman and Bockstael investigate the theoretical foundations for imposing standards and stress the importance of providing a tractable conceptual foundation. Despite a wealth of contributions that are mainly empirical (for reviews of these works see, respectively, Caswell and Antle), there have been relatively few attempts to model formally the linkages between farm and food markets when food quality and consumer safety are at issue. Here, I attempt to provide such a framework, building on key contributions in the theoretical literature and linking them in a simple model of quality determination in a vertically related marketing channel. The food-marketing model is due to Gardner. Spence provides a foundation for Pareto-improving intervention in a deterministic model of quality provision, and Leland, building on the classic paper by Akerlof, investigates licensing and minimum standards when the information structure is incomplete. Linking these ideas in a satisfactory model of the food markets is the main objective of the paper.

The real-time optimisation of DNO owned storage devices on the LV network for peak reduction

Energy storage is a potential alternative to conventional network reinforcementof the low voltage (LV) distribution network to ensure the grid’s infrastructure remainswithin its operating constraints. This paper presents a study on the control of such storagedevices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, wherethe objective is to achieve the greatest peak reduction in demand, for a given storagedevice specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-pointcontroller and bench marked against a control algorithm with a perfect forecast. A specificcase study, using storage on the LV network, is presented, and the results of each algorithmare compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.

Sistemas de dunas do parque das Dunas e Barreiras do Inferno/Natal (RN: levantamento geológico /geofísico, elaboração do modelo deterministico e avaliação da vulnerabilidade/suscetibilidade

The current work was developed on the dune systems of the Parque das Dunas and Barreira do Inferno. These places are located in the cities of Natal and Parnamirim (RN, Brazil), respectively. This project has the purpose of developing the deterministic model on a specific blowout at Parque das Dunas, based in the geophysical interpretations of the lines gotten with the Ground Penetration Radar and the planialtimetric acquisitions of the topographical surface of the land. Also analyses of the vulnerability/susceptibility of these dune systems had been done in relation to the human pressures. To develop its deterministic model, it is necessary to acquire inner and outer geometries of the cited blowout. In order to depict inner geometries underneath the surface are used the GPR observing the altimetric control for topographical correction of the GPR lines. As for the outer geometries, the geodesic GPS gives us the planialtimetric points (x, y and z points) with milimetric precision, resulting in high-resolution surfaces. Using interpolation methods of the planialtimetric points was possible create Digital Elevations Models (DEM´s) of these surfaces. As a result, 1,161.4 meters of GPR lines were acquired on the blowout at the Parque das Dunas and 3,735.27 meters on the blowout at the Barreira do Inferno. These lines had been acquired with a 200 MHz antenna, except the 7 and 8 lines, for which we had been used a 100 MHz antenna. The gotten data had been processed and interpreted, being possible to identify boundary surfaces of first, second and third order. The first order boundary surface is related with the contact of the rocks of the Barreiras Group with the aeolian deposits. These deposits had been divided in two groups (Group 1 and Group 2) which are related with the geometry of stratum and the dip of its stratifications. Group 1 presented stratum of sigmoidal and irregular geometries and involved bodies where the reflectors had presented dips that had varied of 20 to the 28 degrees for the Parque das Dunas blowout and of 22 to the 29 degrees for the Barreira do Inferno blowout. Usually, it was limited in the base for the first order surface and in the top for the second order surface. Group 2 presented stratum of trough, wedge or lens geometries, limited in the base for the second order vi surface, where the corresponding deposits had more shown smoothed reflectors or with dips of low angle. The Deterministic and Digital Elevation Models had been developed from the integration and interpretation of the 2D data with the GOCAD® program. In Digital Elevations Models it was possible to see, for the localities, corridor or trough-shaped blowouts. In Deterministic Model it was possible to see first and second order boundary surfaces. For the vulnerability/susceptibility of the dune systems it was applied the methodology proposal by Boderè al (1991); however the same one did not show adequate because it evaluates actual coastal dunes. Actual coastal dunes are dunes that are presented in balance with the current environmental conditions. Therefore, a new methodology was proposal which characterizes the supplying and activity sedimentary, as well as the human pressures. For the methodology developed in this work, both the localities had presented a good management. The Parque das Dunas was characterized as a relic dune system and the Barreira do Inferno was characterized as a palimpsestic dune system. Also two Thematic Maps had been elaborated for the environmental characterization of the studied dune systems, with software ArcGis 8.3, and its respective data bases

Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Uma abordagem probabilística do número de reprodução básica em modelos epidemiológicos com aplicação na ferrugem do eucalipto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Metallicities for six nearby open clusters from high-resolution spectra of giant stars [Fe/H] values for a planet search sample

We present a study of the stellar parameters and iron abundances of 18 giant stars in six open clusters. The analysis was based on high-resolution and high-S/N spectra obtained with the UVES spectrograph (VLT-UT2). The results complement our previous study where 13 clusters were already analyzed. The total sample of 18 clusters is part of a program to search for planets around giant stars. The results show that the 18 clusters cover a metallicity range between -0.23 and +0.23 dex. Together with the derivation of the stellar masses, these metallicities will allow the metallicity and mass effects to be disentangled when analyzing the frequency of planets as a function of these stellar parameters.

Modelos determinístico y probabilístico para la estimación de la carga de nitratos en una cuenca rural

En este trabajo se desarrolló un modelo probabilístico que utiliza la teoría de la función de densidad de probabilidades derivada para estimar la carga media anual de nitratos transportada por el escurrimiento superficial, utilizando una relación funcional entre el escurrimiento y la carga de nitratos. El modelo determinístico hidrológico y de calidad de agua denominado Simulator for Water Resources in Rural Basins - Water Quality (SWRRB-WQ) fue utilizado para estimar la carga de nitratos en el escurrimiento superficial. Este modelo emplea como variable de entrada la precipitación diaria observada en la Estación del Aeropuerto de Olavarría durante el período 1988 a 2002. Para la calibración del modelo se aplicó una nueva metodología que estima la incertidumbre en los valores observados. Ambos modelos probabilístico y determinístico se aplican en una subcuenca rural del arroyo Tapalqué (provincia de Buenos Aires, Argentina) y finalmente se comparan los valores de la carga de nitratos estimados con los dos modelos con las observaciones realizadas en la sección del arroyo motivo de este estudio. Los resultados muestran que la carga media de nitratos obtenida con el modelo probabilístico es del mismo orden de magnitud que los valores medios observados y estimados con el modelo hidrológico y de calidad de agua SWRRB-WQ.

Predicting EQ-5D from the Parkinson's disease questionnaire PDQ-8 using multi-dimensional Bayesian network classifiers

The impact of the Parkinson's disease and its treatment on the patients' health-related quality of life can be estimated either by means of generic measures such as the european quality of Life-5 Dimensions (EQ-5D) or specific measures such as the 8-item Parkinson's disease questionnaire (PDQ-8). In clinical studies, PDQ-8 could be used in detriment of EQ-5D due to the lack of resources, time or clinical interest in generic measures. Nevertheless, PDQ-8 cannot be applied in cost-effectiveness analyses which require generic measures and quantitative utility scores, such as EQ-5D. To deal with this problem, a commonly used solution is the prediction of EQ-5D from PDQ-8. In this paper, we propose a new probabilistic method to predict EQ-5D from PDQ-8 using multi-dimensional Bayesian network classifiers. Our approach is evaluated using five-fold cross-validation experiments carried out on a Parkinson's data set containing 488 patients, and is compared with two additional Bayesian network-based approaches, two commonly used mapping methods namely, ordinary least squares and censored least absolute deviations, and a deterministic model. Experimental results are promising in terms of predictive performance as well as the identification of dependence relationships among EQ-5D and PDQ-8 items that the mapping approaches are unable to detect

Evaluación de la seguridad al deslizamiento de una presa de fábrica en un cimiento con una familia de discontinuidades y con un criterio de rotura con ley de fluencia no asociada

En España existen del orden de 1,300 grandes presas, de las cuales un 20% fueron construidas antes de los años 60. El hecho de que existan actualmente una gran cantidad de presas antiguas aún en operación, ha producido un creciente interés en reevaluar su seguridad empleando herramientas nuevas o modificadas que incorporan modelos de fallo teóricos más completos, conceptos geotécnicos más complejos y nuevas técnicas de evaluación de la seguridad. Una manera muy común de abordar el análisis de estabilidad de presas de gravedad es, por ejemplo, considerar el deslizamiento a través de la interfase presa-cimiento empleando el criterio de rotura lineal de Mohr-Coulomb, en donde la cohesión y el ángulo de rozamiento son los parámetros que definen la resistencia al corte de la superficie de contacto. Sin embargo la influencia de aspectos como la presencia de planos de debilidad en el macizo rocoso de cimentación; la influencia de otros criterios de rotura para la junta y para el macizo rocoso (ej. el criterio de rotura de Hoek-Brown); las deformaciones volumétricas que ocurren durante la deformación plástica en el fallo del macizo rocoso (i.e., influencia de la dilatancia) no son usualmente consideradas durante el diseño original de la presa. En este contexto, en la presente tesis doctoral se propone una metodología analítica para el análisis de la estabilidad al deslizamiento de presas de hormigón, considerando un mecanismo de fallo en la cimentación caracterizado por la presencia de una familia de discontinuidades. En particular, se considera la posibilidad de que exista una junta sub-horizontal, preexistente y persistente en el macizo rocoso de la cimentación, con una superficie potencial de fallo que se extiende a través del macizo rocoso. El coeficiente de seguridad es entonces estimado usando una combinación de las resistencias a lo largo de los planos de rotura, cuyas resistencias son evaluadas empleando los criterios de rotura no lineales de Barton y Choubey (1977) y Barton y Bandis (1990), a lo largo del plano de deslizamiento de la junta; y el criterio de rotura de Hoek y Brown (1980) en su versión generalizada (Hoek et al. 2002), a lo largo del macizo rocoso. La metodología propuesta también considera la influencia del comportamiento del macizo rocoso cuando este sigue una ley de flujo no asociada con ángulo de dilatancia constante (Hoek y Brown 1997). La nueva metodología analítica propuesta es usada para evaluar las condiciones de estabilidad empleando dos modelos: un modelo determinista y un modelo probabilista, cuyos resultados son el valor del coeficiente de seguridad y la probabilidad de fallo al deslizamiento, respectivamente. El modelo determinista, implementado en MATLAB, es validado usando soluciones numéricas calculadas mediante el método de las diferencias finitas, empleando el código FLAC 6.0. El modelo propuesto proporciona resultados que son bastante similares a aquellos calculados con FLAC; sin embargo, los costos computacionales de la formulación propuesta son significativamente menores, facilitando el análisis de sensibilidad de la influencia de los diferentes parámetros de entrada sobre la seguridad de la presa, de cuyos resultados se obtienen los parámetros que más peso tienen en la estabilidad al deslizamiento de la estructura, manifestándose además la influencia de la ley de flujo en la rotura del macizo rocoso. La probabilidad de fallo es obtenida empleando el método de fiabilidad de primer orden (First Order Reliability Method; FORM), y los resultados de FORM son posteriormente validados mediante simulaciones de Monte Carlo. Los resultados obtenidos mediante ambas metodologías demuestran que, para el caso no asociado, los valores de probabilidad de fallo se ajustan de manera satisfactoria a los obtenidos mediante las simulaciones de Monte Carlo. Los resultados del caso asociado no son tan buenos, ya que producen resultados con errores del 0.7% al 66%, en los que no obstante se obtiene una buena concordancia cuando los casos se encuentran en, o cerca de, la situación de equilibrio límite. La eficiencia computacional es la principal ventaja que ofrece el método FORM para el análisis de la estabilidad de presas de hormigón, a diferencia de las simulaciones de Monte Carlo (que requiere de al menos 4 horas por cada ejecución) FORM requiere tan solo de 1 a 3 minutos en cada ejecución. There are 1,300 large dams in Spain, 20% of which were built before 1960. The fact that there are still many old dams in operation has produced an interest of reevaluate their safety using new or updated tools that incorporate state-of-the-art failure modes, geotechnical concepts and new safety assessment techniques. For instance, for gravity dams one common design approach considers the sliding through the dam-foundation interface, using a simple linear Mohr-Coulomb failure criterion with constant friction angle and cohesion parameters. But the influence of aspects such as the persistence of joint sets in the rock mass below the dam foundation; of the influence of others failure criteria proposed for rock joint and rock masses (e.g. the Hoek-Brown criterion); or the volumetric strains that occur during plastic failure of rock masses (i.e., the influence of dilatancy) are often no considered during the original dam design. In this context, an analytical methodology is proposed herein to assess the sliding stability of concrete dams, considering an extended failure mechanism in its rock foundation, which is characterized by the presence of an inclined, and impersistent joint set. In particular, the possibility of a preexisting sub-horizontal and impersistent joint set is considered, with a potential failure surface that could extend through the rock mass; the safety factor is therefore computed using a combination of strength along the rock joint (using the nonlinear Barton and Choubey (1977) and Barton and Bandis (1990) failure criteria) and along the rock mass (using the nonlinear failure criterion of Hoek and Brown (1980) in its generalized expression from Hoek et al. (2002)). The proposed methodology also considers the influence of a non-associative flow rule that has been incorporated using a (constant) dilation angle (Hoek and Brown 1997). The newly proposed analytical methodology is used to assess the dam stability conditions, employing for this purpose the deterministic and probabilistic models, resulting in the sliding safety factor and the probability of failure respectively. The deterministic model, implemented in MATLAB, is validated using numerical solution computed with the finite difference code FLAC 6.0. The proposed deterministic model provides results that are very similar to those computed with FLAC; however, since the new formulation can be implemented in a spreadsheet, the computational cost of the proposed model is significantly smaller, hence allowing to more easily conduct parametric analyses of the influence of the different input parameters on the dam’s safety. Once the model is validated, parametric analyses are conducting using the main parameters that describe the dam’s foundation. From this study, the impact of the more influential parameters on the sliding stability analysis is obtained and the error of considering the flow rule is assessed. The probability of failure is obtained employing the First Order Reliability Method (FORM). The probabilistic model is then validated using the Monte Carlo simulation method. Results obtained using both methodologies show good agreement for cases in which the rock mass has a nonassociate flow rule. For cases with an associated flow rule errors between 0.70% and 66% are obtained, so that the better adjustments are obtained for cases with, or close to, limit equilibrium conditions. The main advantage of FORM on sliding stability analyses of gravity dams is its computational efficiency, so that Monte Carlo simulations require at least 4 hours on each execution, whereas FORM requires only 1 to 3 minutes on each execution.

Hybrid wind-diesel power plant valuation and optimization using real option theory and dynamic programming

El sistema de energía eólica-diesel híbrido tiene un gran potencial en la prestación de suministro de energía a comunidades remotas. En comparación con los sistemas tradicionales de diesel, las plantas de energía híbridas ofrecen grandes ventajas tales como el suministro de capacidad de energía extra para "microgrids", reducción de los contaminantes y emisiones de gases de efecto invernadero, y la cobertura del riesgo de aumento inesperado del precio del combustible. El principal objetivo de la presente tesis es proporcionar nuevos conocimientos para la evaluación y optimización de los sistemas de energía híbrido eólico-diesel considerando las incertidumbres. Dado que la energía eólica es una variable estocástica, ésta no puede ser controlada ni predecirse con exactitud. La naturaleza incierta del viento como fuente de energía produce serios problemas tanto para la operación como para la evaluación del valor del sistema de energía eólica-diesel híbrido. Por un lado, la regulación de la potencia inyectada desde las turbinas de viento es una difícil tarea cuando opera el sistema híbrido. Por otro lado, el bene.cio económico de un sistema eólico-diesel híbrido se logra directamente a través de la energía entregada a la red de alimentación de la energía eólica. Consecuentemente, la incertidumbre de los recursos eólicos incrementa la dificultad de estimar los beneficios globales en la etapa de planificación. La principal preocupación del modelo tradicional determinista es no tener en cuenta la incertidumbre futura a la hora de tomar la decisión de operación. Con lo cual, no se prevé las acciones operativas flexibles en respuesta a los escenarios futuros. El análisis del rendimiento y simulación por ordenador en el Proyecto Eólico San Cristóbal demuestra que la incertidumbre sobre la energía eólica, las estrategias de control, almacenamiento de energía, y la curva de potencia de aerogeneradores tienen un impacto significativo sobre el rendimiento del sistema. En la presente tesis, se analiza la relación entre la teoría de valoración de opciones y el proceso de toma de decisiones. La opción real se desarrolla con un modelo y se presenta a través de ejemplos prácticos para evaluar el valor de los sistemas de energía eólica-diesel híbridos. Los resultados muestran que las opciones operacionales pueden aportar un valor adicional para el sistema de energía híbrida, cuando esta flexibilidad operativa se utiliza correctamente. Este marco se puede aplicar en la optimización de la operación a corto plazo teniendo en cuenta la naturaleza dependiente de la trayectoria de la política óptima de despacho, dadas las plausibles futuras realizaciones de la producción de energía eólica. En comparación con los métodos de valoración y optimización existentes, el resultado del caso de estudio numérico muestra que la política de operación resultante del modelo de optimización propuesto presenta una notable actuación en la reducción del con- sumo total de combustible del sistema eólico-diesel. Con el .n de tomar decisiones óptimas, los operadores de plantas de energía y los gestores de éstas no deben centrarse sólo en el resultado directo de cada acción operativa, tampoco deberían tomar decisiones deterministas. La forma correcta es gestionar dinámicamente el sistema de energía teniendo en cuenta el valor futuro condicionado en cada opción frente a la incertidumbre. ABSTRACT Hybrid wind-diesel power systems have a great potential in providing energy supply to remote communities. Compared with the traditional diesel systems, hybrid power plants are providing many advantages such as providing extra energy capacity to the micro-grid, reducing pollution and greenhouse-gas emissions, and hedging the risk of unexpected fuel price increases. This dissertation aims at providing novel insights for assessing and optimizing hybrid wind-diesel power systems considering the related uncertainties. Since wind power can neither be controlled nor accurately predicted, the energy harvested from a wind turbine may be considered a stochastic variable. This uncertain nature of wind energy source results in serious problems for both the operation and value assessment of the hybrid wind-diesel power system. On the one hand, regulating the uncertain power injected from wind turbines is a difficult task when operating the hybrid system. On the other hand, the economic profit of a hybrid wind-diesel system is achieved directly through the energy delivered to the power grid from the wind energy. Therefore, the uncertainty of wind resources has increased the difficulty in estimating the total benefits in the planning stage. The main concern of the traditional deterministic model is that it does not consider the future uncertainty when making the dispatch decision. Thus, it does not provide flexible operational actions in response to the uncertain future scenarios. Performance analysis and computer simulation on the San Cristobal Wind Project demonstrate that the wind power uncertainty, control strategies, energy storage, and the wind turbine power curve have a significant impact on the performance of the system. In this dissertation, the relationship between option pricing theory and decision making process is discussed. A real option model is developed and presented through practical examples for assessing the value of hybrid wind-diesel power systems. Results show that operational options can provide additional value to the hybrid power system when this operational flexibility is correctly utilized. This framework can be applied in optimizing short term dispatch decisions considering the path-dependent nature of the optimal dispatch policy, given the plausible future realizations of the wind power production. Comparing with the existing valuation and optimization methods, result from numerical example shows that the dispatch policy resulting from the proposed optimization model exhibits a remarkable performance in minimizing the total fuel consumption of the wind-diesel system. In order to make optimal decisions, power plant operators and managers should not just focus on the direct outcome of each operational action; neither should they make deterministic decisions. The correct way is to dynamically manage the power system by taking into consideration the conditional future value in each option in response to the uncertainty.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Seasonal dynamics of an aquatic macroinvertebrate assembly (Hydrobiological case study of Lake Balaton No. 2)

In 2002, 2003 and 2004, we took macoinvertebrate samples on a total of 36 occasions at the Badacsony bay of Lake Balaton. Our sampling site was characterised by areas of open water (in 2003 and 2004 full of reed-grass) as well as by areas covered by common reed (Phragmites australis) and narrowleaf cattail (Typha angustifolia). Samples were taken both from water body and benthic ooze by use of a stiff hand net. We have gained our data from processing 208 individual samples. We took samples frequently from early spring until late autumn for a deeper understanding of the processes of seasonal dynamics. The main seasonal patterns and temporal changes of diversity were described. We constructed a weather-dependent simulation model of the processes of seasonal dynamics in the interest of a possible further utilization of our data in climate change research. We described the total number of individuals, biovolume and diversity of all macroinvertebrate species with a single index and used the temporal trends of this index for simulation modelling. Our discrete deterministic model includes only the impact of temperature, other interactions might only appear concealed. Running the model for different climate change scenarios it became possible to estimate conditions for the 2070-2100 period. The results, however, should be treated very prudently not only because our model is very simple but also because the scenarios are the results of different models.

Evaluation of climate change scenarios based on aquatic food web modelling

In the years 2004 and 2005 we collected samples of phytoplankton, zooplankton and macroinvertebrates in an artificial small pond in Budapest. We set up a simulation model predicting the abundance of the cyclopoids, Eudiaptomus zachariasi and Ischnura pumilio by considering only temperature as it affects the abundance of population of the previous day. Phytoplankton abundance was simulated by considering not only temperature, but the abundance of the three mentioned groups. This discrete-deterministic model could generate similar patterns like the observed one and testing it on historical data was successful. However, because the model was overpredicting the abundances of Ischnura pumilio and Cyclopoida at the end of the year, these results were not considered. Running the model with the data series of climate change scenarios, we had an opportunity to predict the individual numbers for the period around 2050. If the model is run with the data series of the two scenarios UKHI and UKLO, which predict drastic global warming, then we can observe a decrease in abundance and shift in the date of the maximum abundance occurring (excluding Ischnura pumilio, where the maximum abundance increases and it occurs later), whereas under unchanged climatic conditions (BASE scenario) the change in abundance is negligible. According to the scenarios GFDL 2535, GFDL 5564 and UKTR, a transition could be noticed.