Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

Estigma e percepções dos médicos de Clínica Geral sobre a doença mental e o suicídio

RESUMO: INTRODUÇÃO: A OMS (2001) revela que cerca de 450 milhões de pessoas sofrem de perturbações mentais ou comportamentais em todo o mundo, mas apenas uma pequena minoria tem tratamento, ainda que elementar. Transformam-se em vítimas por causa da sua doença e convertem-se em alvos de estigma e discriminação. O suicídio é considerado como um grande problema de saúde pública em todo o mundo, é uma das principais causas de morte de jovens adultos e situa-se entre as três maiores causas de morte na população entre 15-34 anos (OMS, 2001). As perturbações mentais aumentam o risco de suicídio. A depressão, esquizofrenia, e a utilização de substâncias incrementam o risco de suicídio. Estudos (Sartorius, 2002; Magliano et al., 2012) mostram que os profissionais de saúde, tal como o público em geral, podem ter atitudes negativas e estigma em relação às pessoas com perturbações mentais, podendo agir em conformidade, uma vez feito e conhecido o diagnóstico psiquiátrico. Os clínicos gerais são os receptores das perturbações mentais e tentativas de suicídio nas principais portas de entrada no acesso a cuidados de saúde. As crenças, conhecimentos e contacto com a doença mental e o suicídio, podem influenciar a atenção clínica. OBJECTIVOS: Avaliar o estigma e as percepções dos médicos de clínica geral em relação às tentativas de suicídio, o suicídio e perturbações mentais bem como os possíveis factores associados a estes fenómenos. MATERIAIS E MÉTODOS: Estudo do tipo transversal, combinando métodos quantitativos e qualitativos. A amostra é constituída por 125 sujeitos, médicos de clínica geral. Utilizaram-se as versões adaptadas dos seguintes instrumentos: Questionário sobre Percepções e Estigma em Relação à Saúde Mental e ao Suicídio (Liz Macmin e SOQ, Domino, 2005) e a Escala de Atitudes sobre a Doença Mental (Amanha Hahn, 2002). Para o tratamento estatístico dos dados usou-se a estatística 1) descritiva e 2) Análise estatística das hipóteses formuladas (Qui Quadrado - 2) a correlação entre variáveis (Spearman: ρ, rho). Os dados conectados foram limpos de inconsistências com base no pacote informático e estatístico SPSS versão 20. Para a aferição da consistência interna foi usado o teste de Alfa de Cronbach. RESULTADOS: Uma boa parte da amostra (46.4%) refere que não teve formação formal ou informal em saúde mental e (69.35%) rejeitam a ideia de que “grupos profissionais como médicos, dentistas e psicólogos são mais susceptíveis a cometer o suicídio”. Já (28.0%) têm uma perspectiva pessimista quanto a possibilidade de recuperação total dos sujeitos com perturbação mental. Sessenta e oito(54.4%) associa sujeitos com perturbação mental, a comportamentos estranhos e imprevisíveis, 115 (92.0%) a um baixo QI e 35 (26.7%) a poderem ser violentas e e perigosas. Os dados mostram uma associação estatisticamente significativa (p0.001) entre as variáveis: tempo de serviço no SNS, recear estar perto de sujeitos com doença mental e achar que os sujeitos com doença mental são mais perigosos que outros. Em termos estatísticos, existe uma associação estatitisticamente significativa entre as duas variáveis(X2=9,522; p0.05): percepção de que “é vergonhoso ter uma doença mental” e os conhecimentos em relação à doença mental. Existe uma correlação positiva, fraca e estatisticamente significativa entre os conhecimentos dos clínicos gerais(beneficiar-se de formação em saúde mental) e a percepção sobre os factores de risco (0,187; P0,039). DISCUSSÃO E CONCLUSÕES: A falta de conhecimento sobre as causas e factores de risco para os comportamentos suicidários, opções de intervenção e tratamento, particularmente no âmbito da doença mental, podem limitar a procura de ajuda individual ou dos próximos. Percepções negativas como o facto de não merecerem prioridade nos serviços, mitos (frágeis e cobarde, sempre impulsivo, chamadas de atenção, problemas espirituais) podem constituir-se como um indicador de que os clínicos gerais podem sofrer do mesmo sistema de estigma e crenças, de que sofre o público em geral, podendo agir em conformidade (atitudes de afastamento ereceio). As atitudes são influenciadas por factores como a formação, cultura e sistema de crenças. Sujeitos com boa formação na área da saúde mental têm uma percepção positiva e optimista sobre os factores de risco e uma atitude positiva em relação aos sujeitos com doença mental e comportamentos suicidários.-------------ABSTRACT: INTRODUCTION: The WHO (2001) reveals that about 450 million people suffer from mental or behavioral disorders worldwide, but only a small minority have access to treatment, though elementary. They become victims because of their disease and they become the targets of stigma and discrimination. Suicide is seen as a major public health problem worldwide, is a leading cause of death for young adults and is included among the three major causes of death in the population aged 15-34 years (WHO, 2001). Mental disorders increase the risk of suicide. Depression, schizophrenia, and the substances misuse increase the risk of suicide. Studies (Sartorius, 2002; Magliano et al, 2012) show that health professionals, such as the general public, may have negative attitudes and stigma towards people with mental disorders, and can act accordingly after psychiatric diagnosis is known. General practitioners are the main entry points of mental disorders and suicide attempts in the health sistem. Beliefs, knowledge and contact with mental illness and suicide, may influence clinical care. OBJECTIVES: To assess stigma and perceptions of general practitioners in relation to suicide attempts, suicide and mental disorders as well as possible factors associated with these phenomena. MATERIAL AND METHODS: This was a descriptive cross-sectional study, combining quantitative and qualitative methods. The sample consisted of 125 subjects, general practitioners. We used adapted versions of the following instruments: Questionnaire of Perceptions and Stigma in Relation to Mental Health and Suicide (Liz Macmin and SOQ, Domino, 2005) and the Scale of Attitudes on Mental Illness (Tomorrow Hahn, 2002). For the statistical treatment of the data we used: 1) descriptive (Data distribution by absolute and relative frequencies for each of the variables under study (including mean and standard deviation measures of central tendency and deviation), 2) statistical analysis of hypotheses using (Chi Square - 2, a hypothesis test that is intended to find a value of dispersion for two nominal variables, evaluating the association between qualitative variables) and the correlation between variables (Spearman ρ, rho), a measure of non-parametric correlation, which evaluates an arbitrary monotonic function can be the description of the relationship between two variables, without making any assumptions about the frequency distribution of the variables). For statistical analysis of the correlations were eliminated subjects who did not respond to questions. The collected data were cleaned for inconsistencies based on computer and statistical package SPSS version 20. To measure the internal consistency was used the Cronbach's alpha test. RESULTS: A significant part of the sample 64 (46.4%) reported no formal or informal training in mental health and 86 (69.35%) reject the idea that "professional groups such as doctors, dentists and psychologists are more likely to commit suicide." On the other hand, 42 (28.0%) have a pessimistic view of the possibility of full recovery of individuals with mental disorder. Sixty-eight ( 54.4 % ) of them associates subjects with mental disorder to strange and unpredictable behavior, 115 ( 92.0 % ), to low IQ, 35 ( 26.7 % ) and even to violent and dangerous behavior, 78 ( 62.4 % ) The data show a statistically significant (p = 0.001) relationship between the following variables: length of service in the NHS, fear of being close to individuals with mental illness and considering individuals with mental illness more dangerous than others. In statistical terms, there is a dependency between the two variables (X2 = 9.522, p> 0.05): the perception that "it is shameful to have a mental illness" and knowledge regarding mental illness. There is a positive and statistically significant weak correlation between knowledge of general practitioners (benefit from mental health training) and the perception of the risk factors (0,187; P0,039). DISCUSSION AND CONCLUSIONS: The lack of knowledge about the causes and risk factors for suicidal behavior, intervention and treatment, particularly in the context of mental illness options, may decreaseseeking for help by individual and their relatives. Negative perceptions such as considering that they dont deserve priority in services, myths (weak and cowards, always impulsive, seeking for attentions, spirituals problems) may indicate that general practitioners, may suffer the same stigma and beliefs systems as the general public, and can act accordingly (withdrawal and fear attitudes). Attitudes are influenced by factors such as education, culture and belief system. Subjects with good training in mental health have a positive and optimistic perception of the risk factors and a positiveattitude towards individuals with mental illness and suicidal behaviour.

On the weights of nations: assigning voting weights in a heterogenous union

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model.

Bayesian forecasting with highly correlated predictors

This paper considers Bayesian variable selection in regressions with a large number of possibly highly correlated macroeconomic predictors. I show that by acknowledging the correlation structure in the predictors can improve forecasts over existing popular Bayesian variable selection algorithms.

Wavelet analysis residual kriging vs. neural network residual kriging

This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method - wavelet analysis residual kriging (WARK) - is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.

Selecting statistical models to study the relationship between soybean yield and soil physical properties

Statistical models allow the representation of data sets and the estimation and/or prediction of the behavior of a given variable through its interaction with the other variables involved in a phenomenon. Among other different statistical models, are the autoregressive state-space models (ARSS) and the linear regression models (LR), which allow the quantification of the relationships among soil-plant-atmosphere system variables. To compare the quality of the ARSS and LR models for the modeling of the relationships between soybean yield and soil physical properties, Akaike's Information Criterion, which provides a coefficient for the selection of the best model, was used in this study. The data sets were sampled in a Rhodic Acrudox soil, along a spatial transect with 84 points spaced 3 m apart. At each sampling point, soybean samples were collected for yield quantification. At the same site, soil penetration resistance was also measured and soil samples were collected to measure soil bulk density in the 0-0.10 m and 0.10-0.20 m layers. Results showed autocorrelation and a cross correlation structure of soybean yield and soil penetration resistance data. Soil bulk density data, however, were only autocorrelated in the 0-0.10 m layer and not cross correlated with soybean yield. The results showed the higher efficiency of the autoregressive space-state models in relation to the equivalent simple and multiple linear regression models using Akaike's Information Criterion. The resulting values were comparatively lower than the values obtained by the regression models, for all combinations of explanatory variables.

Class of correlated random networks with hidden variables

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Outcome of smoking cessation counselling of HIV-positive persons by HIV care physicians.

OBJECTIVES: Smoking is the most prevalent modifiable risk factor for cardiovascular diseases among HIV-positive persons. We assessed the effect on smoking cessation of training HIV care physicians in counselling. METHODS: The Swiss HIV Cohort Study (SHCS) is a multicentre prospective observational database. Our single-centre intervention at the Zurich centre included a half day of standardized training for physicians in counselling and in the pharmacotherapy of smokers, and a physicians' checklist for semi-annual documentation of their counselling. Smoking status was then compared between participants at the Zurich centre and other institutions. We used marginal logistic regression models with exchangeable correlation structure and robust standard errors to estimate the odds of smoking cessation and relapse. RESULTS: Between April 2000 and December 2010, 11 056 SHCS participants had 121 238 semi-annual visits and 64 118 person-years of follow-up. The prevalence of smoking decreased from 60 to 43%. During the intervention at the Zurich centre from November 2007 to December 2009, 1689 participants in this centre had 6068 cohort visits. These participants were more likely to stop smoking [odds ratio (OR) 1.23; 95% confidence interval (CI) 1.07-1.42; P=0.004] and had fewer relapses (OR 0.75; 95% CI 0.61-0.92; P=0.007) than participants at other SHCS institutions. The effect of the intervention was stronger than the calendar time effect (OR 1.19 vs. 1.04 per year, respectively). Middle-aged participants, injecting drug users, and participants with psychiatric problems or with higher alcohol consumption were less likely to stop smoking, whereas persons with a prior cardiovascular event were more likely to stop smoking. CONCLUSIONS: An institution-wide training programme for HIV care physicians in smoking cessation counselling led to increased smoking cessation and fewer relapses.

Low adiponectin is associated with increased ambulatory pulse pressure and activation of the renin-angiotensin system in subjects of African descent

Purpose: Adiponectin, arterial stiffness, as well components of the renin-angiotensin system are associated with cardiovascular risk. This study was aimed to investigate whether plasma adiponectin was directly linked with pulse pressure (PP), as a marker for arterial stiffness, and the renin-angiotensin system (RAS). Methods and materials: A family-based study in subjects of African descent enriched with hypertensive patients was carried out in the Seychelles. Fasting plasma adiponectin was determined by ELISA, plasma renin activity according to the antibody-trapping principle and plasma aldosterone by radioimmunoassay. Daytime ambulatory blood pressure (BP) was measured using Diasys Integra devices. PP was calculated as the difference between systolic and diastolic BP. The association of adiponectin with PP, plasma renin activity and plasma aldosterone were analyzed using generalized estimating equations with a gaussian family link and an exchangeable correlation structure to account for familial aggregation. Results: Data from 335 subjects from 73 families (152 men, 183 women) were available. Men and women had mean (SD) age of 45.4 ± 11.1 and 47.3 ± 12.4 years, BMI of 26.3 ± 4.4 and 27.8 ± 5.1 kg/m2, daytime systolic/diastolic BP of 132.6 ± 15.4 / 86.1 ± 10.9 and 130 ± 17.6 / 83.4 ± 11.1 mmHg, and daytime PP of 46.5 ± 9.9 and 46.7 ± 10.7 mmHg, respectively. Plasma adiponectin was 4.4± 3.04 ng/ml in men and 7.39 ± 5.44 ng/ml in women (P <0.001). After adjustment for age, sex and BMI, log-transformed adiponectin was negatively associated with daytime PP (-0.009 ± 0.003, P = 0.004), plasma renin activity (-0.248 ± 0.080, P = 0.002) and plasma aldosterone (-0.004 ± 0.002, P = 0.014). Conclusion: Low adiponectin is associated with increased ambulatory PP and RAS activation in subjects of African descent. Our data are consistent with the observation that angiotensin II receptor blockers increase adiponectin in humans.

Étude des maxima de champs gaussiens corrélés.

Ce mémoire porte sur l’étude des maxima de champs gaussiens. Plus précisément, l’étude portera sur la convergence en loi, la convergence du premier ordre et la convergence du deuxième ordre du maximum d’une collection de variables aléatoires gaussiennes. Les modèles de champs gaussiens présentés sont le modèle i.i.d., le modèle hiérarchique et le champ libre gaussien. Ces champs gaussiens diffèrent par le degré de corrélation entre les variables aléatoires. Le résultat principal de ce mémoire sera que la convergence en probabilité du premier ordre du maximum est la même pour les trois modèles. Quelques résultats de simulations seront présentés afin de corroborer les résultats théoriques obtenus.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.

The interannual variability of energy transports within and over the Atlantic Ocean in a coupled climate model

To gain a new perspective on the interaction of the Atlantic Ocean and the atmosphere, the relationship between the atmospheric and oceanic meridional energy transports is studied in a version of HadCM3, the U.K. Hadley Centre's coupled climate model. The correlation structure of the energy transports in the atmosphere and Atlantic Ocean as a function of latitude, and the cross correlation between the two systems are analyzed. The processes that give rise to the correlations are then elucidated using regression analyses. In northern midlatitudes, the interannual variability of the Atlantic Ocean energy transport is dominated by Ekman processes. Anticorrelated zonal winds in the subtropics and midlatitudes, particularly associated with the North Atlantic Oscillation (NAO), drive anticorrelated meridional Ekman transports. Variability in the atmospheric energy transport is associated with changes in the stationary waves, but is only weakly related to the NAO. Nevertheless, atmospheric driving of the oceanic Ekman transports is responsible for a bipolar pattern in the correlation between the atmosphere and Atlantic Ocean energy transports. In the Tropics, the interannual variability of the Atlantic Ocean energy transport is dominated by an adjustment of the tropical ocean to coastal upwelling induced along the Venezuelan coast by a strengthening of the easterly trade winds. Variability in the atmospheric energy transport is associated with a cross-equatorial meridional overturning circulation that is only weakly associated with variability in the trade winds along the Venezuelan coast. In consequence, there is only very limited correlation between the atmosphere and Atlantic Ocean energy transports in the Tropics of HadCM3