The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

Planejamento de recursos hídricos de áreas rurais degradadas: aplicação do modelo SWAT em bacia hidrográfica experimental na região Noroeste do Estado do Rio de Janeiro.

A degradação ambiental do Noroeste do Estado do Rio de Janeiro tem se intensificado nas últimas décadas devido às práticas agrícolas não preservacionistas. Esta situação, que decorre do uso inadequado do solo, tem implicado em mudanças na oferta hídrica em grau variável nos municípios da região com prejuízos econômicos nas atividades dos pequenos e médios proprietários rurais e na qualidade de vida. A abordagem para enfrentar problemas deste tipo depende da participação efetiva das instâncias de governo e dos órgãos responsáveis pela gestão dos recursos hídricos. No âmbito da hidrologia os modelos hidrológicos com base no uso e ocupação do solo são ferramentas que podem auxiliar com ótimo custo e benefício a geração de informações em bacias hidrográficas, instrumentadas ou não. Os modelos são úteis ao planejamento e à tomada de decisão por possibilitarem a previsão de vazões e simulação de cenários sobre o uso do solo e qualidade da água. Neste sentido, o presente estudo pretende dar sua contribuição ao avaliar a adequabilidade do modelo SWAT simular o processo chuva-vazão na microbacia experimental de Santa Maria e Cambiocó, com 13,5 km2, localizada na região hidrográfica do rio Muriaé, afluente do rio Paraíba do Sul. O SWAT tem sido empregado em bacias agrícolas nos EUA, na Europa e, atualmente, na China, sudeste asiático e Irã, entre outros países, e na última década maior inserção no meio acadêmico brasileiro. A versão 2005 do modelo foi utilizada por meio da sua interface SIG para simular as vazões médias diárias com base na precipitação medida no intervalo de 15 minutos no período de 2005/2006. As vazões simuladas foram comparadas com as vazões observadas no exutório da microbacia. Foram testadas as ferramentas de análise de sensibilidade e autocalibração. O método de calibração manual foi usado para o ajuste por tentativa e erro. Os parâmetros ajustados corresponderam ao CN2 e ESCO. Os valores obtidos na calibração para os coeficientes estatísticos R2, NSE, PBIAS e RSR foram 0,80, 0,80, 7,02 e 0,45, respectivamente, indicando escore muito bom, o que foi confirmado pela inspeção dos hidrogramas. As saídas validadas para período diferente da calibração forneceram para os mesmos coeficientes os valores 0,84, 0,80, 25,92 e 0,44. Os dois primeiros, com escore muito bom. O valor de PBIAS, no limite do satisfatório, e RSR, muito bom. O desempenho permitiu concluir que a simulação com o SWAT foi adequada. Em relação às pesquisas que têm sido realizadas no Brasil os valores obtidos para os indicadores foram semelhantes, indicando a capacidade do modelo para novos estudos nesta microbacia que considerem os usos consuntivos e cenários de uso do solo.

Model structure and uncertainty for stochastic non-point source modelling applications

The uncertainty associated with a rainfall-runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions. © 2011 Copyright IAHS Press.

A non-linear perturbation model considering catchment wetness and its application in river flow forecasting

A non-linear perturbation model for river flow forecasting is developed, based on consideration of catchment wetness using an antecedent precipitation index (API). Catchment seasonality, of the form accounted for in the linear perturbation model (the LPM), and non-linear behaviour both in the runoff generation mechanism and in the flow routing processes are represented by a constrained nan-linear model, the NLPM-API. A total of ten catchments, across a range of climatic conditions and catchment area magnitudes, located in China and in other countries, were selected for testing daily rainfall-runoff forecasting with this model. It was found that the NLPM-API model was significantly more efficient than the original linear perturbation model (the LPM). However, restric tion of explicit nan-linearity to the runoff generation process, in the simpler LPM-API form of the model, did not produce a significantly lower value of the efficiency in flood forecasting, in terms of the model efficiency index R-2. (C) 1997 Elsevier Science B.V.

Evaluation of two hybrid metric-conceptual models, for simulating phosphorus transfer from agricultural land in the river enborne, a lowland UK catchment

Across Europe, elevated phosphorus (P) concentrations in lowland rivers have made them particularly susceptible to eutrophication. This is compounded in southern and central UK by increasing pressures on water resources, which may be further enhanced by the potential effects of climate change. The EU Water Framework Directive requires an integrated approach to water resources management at the catchment scale and highlights the need for modelling tools that can distinguish relative contributions from multiple nutrient sources and are consistent with the information content of the available data. Two such models are introduced and evaluated within a stochastic framework using daily flow and total phosphorus concentrations recorded in a clay catchment typical of many areas of the lowland UK. Both models disaggregate empirical annual load estimates, derived from land use data, as a function of surface/near surface runoff, generated using a simple conceptual rainfall-runoff model. Estimates of the daily load from agricultural land, together with those from baseflow and point sources, feed into an in-stream routing algorithm. The first model assumes constant concentrations in runoff via surface/near surface pathways and incorporates an additional P store in the river-bed sediments, depleted above a critical discharge, to explicitly simulate resuspension. The second model, which is simpler, simulates P concentrations as a function of surface/near surface runoff, thus emphasising the influence of non-point source loads during flow peaks and mixing of baseflow and point sources during low flows. The temporal consistency of parameter estimates and thus the suitability of each approach is assessed dynamically following a new approach based on Monte-Carlo analysis. (c) 2004 Elsevier B.V. All rights reserved.

Teleconnections between Ethiopian summer rainfall and sea surface temperature: part II. Seasonal forecasting

A seasonal forecasting system that is capable of skilfully predicting rainfall totals on a regional scale would be of great value to Ethiopia. Here, we describe how a statistical model can exploit the teleconnections described in part 1 of this pair of papers to develop such a system. We show that, in most cases, the predictors selected objectively by the statistical model can be interpreted in the light of physical teleconnections with Ethiopian rainfall, and discuss why, in some cases, unexpected regions are chosen as predictors. We show that the forecast has skill in all parts of Ethiopia, and argue that this method could provide the basis of an operational seasonal forecasting system for Ethiopia.

Climate change and heat-related mortality in six cities Part 1: model construction and validation

Heat waves are expected to increase in frequency and magnitude with climate change. The first part of a study to produce projections of the effect of future climate change on heat-related mortality is presented. Separate city-specific empirical statistical models that quantify significant relationships between summer daily maximum temperature (T max) and daily heat-related deaths are constructed from historical data for six cities: Boston, Budapest, Dallas, Lisbon, London, and Sydney. ‘Threshold temperatures’ above which heat-related deaths begin to occur are identified. The results demonstrate significantly lower thresholds in ‘cooler’ cities exhibiting lower mean summer temperatures than in ‘warmer’ cities exhibiting higher mean summer temperatures. Analysis of individual ‘heat waves’ illustrates that a greater proportion of mortality is due to mortality displacement in cities with less sensitive temperature–mortality relationships than in those with more sensitive relationships, and that mortality displacement is no longer a feature more than 12 days after the end of the heat wave. Validation techniques through residual and correlation analyses of modelled and observed values and comparisons with other studies indicate that the observed temperature–mortality relationships are represented well by each of the models. The models can therefore be used with confidence to examine future heat-related deaths under various climate change scenarios for the respective cities (presented in Part 2).

Statistical downscaling of river flows

An extensive statistical ‘downscaling’ study is done to relate large-scale climate information from a general circulation model (GCM) to local-scale river flows in SW France for 51 gauging stations ranging from nival (snow-dominated) to pluvial (rainfall-dominated) river-systems. This study helps to select the appropriate statistical method at a given spatial and temporal scale to downscale hydrology for future climate change impact assessment of hydrological resources. The four proposed statistical downscaling models use large-scale predictors (derived from climate model outputs or reanalysis data) that characterize precipitation and evaporation processes in the hydrological cycle to estimate summary flow statistics. The four statistical models used are generalized linear (GLM) and additive (GAM) models, aggregated boosted trees (ABT) and multi-layer perceptron neural networks (ANN). These four models were each applied at two different spatial scales, namely at that of a single flow-gauging station (local downscaling) and that of a group of flow-gauging stations having the same hydrological behaviour (regional downscaling). For each statistical model and each spatial resolution, three temporal resolutions were considered, namely the daily mean flows, the summary statistics of fortnightly flows and a daily ‘integrated approach’. The results show that flow sensitivity to atmospheric factors is significantly different between nival and pluvial hydrological systems which are mainly influenced, respectively, by shortwave solar radiations and atmospheric temperature. The non-linear models (i.e. GAM, ABT and ANN) performed better than the linear GLM when simulating fortnightly flow percentiles. The aggregated boosted trees method showed higher and less variable R2 values to downscale the hydrological variability in both nival and pluvial regimes. Based on GCM cnrm-cm3 and scenarios A2 and A1B, future relative changes of fortnightly median flows were projected based on the regional downscaling approach. The results suggest a global decrease of flow in both pluvial and nival regimes, especially in spring, summer and autumn, whatever the considered scenario. The discussion considers the performance of each statistical method for downscaling flow at different spatial and temporal scales as well as the relationship between atmospheric processes and flow variability.

Deriving global flood hazard maps of fluvial floods through a physical model cascade

Global flood hazard maps can be used in the assessment of flood risk in a number of different applications, including (re)insurance and large scale flood preparedness. Such global hazard maps can be generated using large scale physically based models of rainfall-runoff and river routing, when used in conjunction with a number of post-processing methods. In this study, the European Centre for Medium Range Weather Forecasts (ECMWF) land surface model is coupled to ERA-Interim reanalysis meteorological forcing data, and resultant runoff is passed to a river routing algorithm which simulates floodplains and flood flow across the global land area. The global hazard map is based on a 30 yr (1979–2010) simulation period. A Gumbel distribution is fitted to the annual maxima flows to derive a number of flood return periods. The return periods are calculated initially for a 25×25 km grid, which is then reprojected onto a 1×1 km grid to derive maps of higher resolution and estimate flooded fractional area for the individual 25×25 km cells. Several global and regional maps of flood return periods ranging from 2 to 500 yr are presented. The results compare reasonably to a benchmark data set of global flood hazard. The developed methodology can be applied to other datasets on a global or regional scale.

Conditioning model output statistics of regional climate model precipitation on circulation patterns

Dynamical downscaling of Global Climate Models (GCMs) through regional climate models (RCMs) potentially improves the usability of the output for hydrological impact studies. However, a further downscaling or interpolation of precipitation from RCMs is often needed to match the precipitation characteristics at the local scale. This study analysed three Model Output Statistics (MOS) techniques to adjust RCM precipitation; (1) a simple direct method (DM), (2) quantile-quantile mapping (QM) and (3) a distribution-based scaling (DBS) approach. The modelled precipitation was daily means from 16 RCMs driven by ERA40 reanalysis data over the 1961–2000 provided by the ENSEMBLES (ENSEMBLE-based Predictions of Climate Changes and their Impacts) project over a small catchment located in the Midlands, UK. All methods were conditioned on the entire time series, separate months and using an objective classification of Lamb's weather types. The performance of the MOS techniques were assessed regarding temporal and spatial characteristics of the precipitation fields, as well as modelled runoff using the HBV rainfall-runoff model. The results indicate that the DBS conditioned on classification patterns performed better than the other methods, however an ensemble approach in terms of both climate models and downscaling methods is recommended to account for uncertainties in the MOS methods.

Government spending and unemployment : An empirical study on Sweden, 1994-2012

The aim of the study was to see if any relationship between government spending andunemployment could be empirically found. To test if government spending affectsunemployment, a statistical model was applied on data from Sweden. The data was quarterlydata from the year 1994 until 2012, unit-root test were conducted and the variables wheretransformed to its first-difference so ensure stationarity. This transformation changed thevariables to growth rates. This meant that the interpretation deviated a little from the originalgoal. Other studies reviewed indicate that when government spending increases and/or taxesdecreases output increases. Studies show that unemployment decreases when governmentspending/GDP ratio increases. Some studies also indicated that with an already largegovernment sector increasing the spending it could have negative effect on output. The modelwas a VAR-model with unemployment, output, interest rate, taxes and government spending.Also included in the model were a linear and three quarterly dummies. The model used 7lags. The result was not statistically significant for most lags but indicated that as governmentspending growth rate increases holding everything else constant unemployment growth rateincreases. The result for taxes was even less statistically significant and indicates norelationship with unemployment. Post-estimation test indicates that there were problems withnon-normality in the model. So the results should be interpreted with some scepticism.

Cálculo do Value at Risk (VaR) para o Ibovespa, pós crise de 2008, por meio dos modelos de heterocedasticidade condicional (GARCH) e de volatilidade estocástica (Local Scale Model - LSM)

O objetivo deste estudo é propor a implementação de um modelo estatístico para cálculo da volatilidade, não difundido na literatura brasileira, o modelo de escala local (LSM), apresentando suas vantagens e desvantagens em relação aos modelos habitualmente utilizados para mensuração de risco. Para estimação dos parâmetros serão usadas as cotações diárias do Ibovespa, no período de janeiro de 2009 a dezembro de 2014, e para a aferição da acurácia empírica dos modelos serão realizados testes fora da amostra, comparando os VaR obtidos para o período de janeiro a dezembro de 2014. Foram introduzidas variáveis explicativas na tentativa de aprimorar os modelos e optou-se pelo correspondente americano do Ibovespa, o índice Dow Jones, por ter apresentado propriedades como: alta correlação, causalidade no sentido de Granger, e razão de log-verossimilhança significativa. Uma das inovações do modelo de escala local é não utilizar diretamente a variância, mas sim a sua recíproca, chamada de “precisão” da série, que segue uma espécie de passeio aleatório multiplicativo. O LSM captou todos os fatos estilizados das séries financeiras, e os resultados foram favoráveis a sua utilização, logo, o modelo torna-se uma alternativa de especificação eficiente e parcimoniosa para estimar e prever volatilidade, na medida em que possui apenas um parâmetro a ser estimado, o que representa uma mudança de paradigma em relação aos modelos de heterocedasticidade condicional.

Nucleon flavor asymmetry in a statistical quark model

A statistical model of linear-confined quarks is applied to obtain the flavor asymmetry of the nucleon sea. The model parametrization is fixed by the experimental available data, where a temperature parameter is used to fit the Gottfried sum rule violation. Results are presented for the ratios of light quark and antiquark distributions, d/u and (d) over bar/(u) over bar.