Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.

Steric sea level variability (1993-2010) in an ensemble of ocean reanalyses and objective analyses

Quantifying the effect of the seawater density changes on sea level variability is of crucial importance for climate change studies, as the sea level cumulative rise can be regarded as both an important climate change indicator and a possible danger for human activities in coastal areas. In this work, as part of the Ocean Reanalysis Intercomparison Project, the global and regional steric sea level changes are estimated and compared from an ensemble of 16 ocean reanalyses and 4 objective analyses. These estimates are initially compared with a satellite-derived (altimetry minus gravimetry) dataset for a short period (2003–2010). The ensemble mean exhibits a significant high correlation at both global and regional scale, and the ensemble of ocean reanalyses outperforms that of objective analyses, in particular in the Southern Ocean. The reanalysis ensemble mean thus represents a valuable tool for further analyses, although large uncertainties remain for the inter-annual trends. Within the extended intercomparison period that spans the altimetry era (1993–2010), we find that the ensemble of reanalyses and objective analyses are in good agreement, and both detect a trend of the global steric sea level of 1.0 and 1.1 ± 0.05 mm/year, respectively. However, the spread among the products of the halosteric component trend exceeds the mean trend itself, questioning the reliability of its estimate. This is related to the scarcity of salinity observations before the Argo era. Furthermore, the impact of deep ocean layers is non-negligible on the steric sea level variability (22 and 12 % for the layers below 700 and 1500 m of depth, respectively), although the small deep ocean trends are not significant with respect to the products spread.

Ocean heat content variability and change in an ensemble of ocean reanalyses

Accurate knowledge of the location and magnitude of ocean heat content (OHC) variability and change is essential for understanding the processes that govern decadal variations in surface temperature, quantifying changes in the planetary energy budget, and developing constraints on the transient climate response to external forcings. We present an overview of the temporal and spatial characteristics of OHC variability and change as represented by an ensemble of dynamical and statistical ocean reanalyses (ORAs). Spatial maps of the 0–300 m layer show large regions of the Pacific and Indian Oceans where the interannual variability of the ensemble mean exceeds ensemble spread, indicating that OHC variations are well-constrained by the available observations over the period 1993–2009. At deeper levels, the ORAs are less well-constrained by observations with the largest differences across the ensemble mostly associated with areas of high eddy kinetic energy, such as the Southern Ocean and boundary current regions. Spatial patterns of OHC change for the period 1997–2009 show good agreement in the upper 300 m and are characterized by a strong dipole pattern in the Pacific Ocean. There is less agreement in the patterns of change at deeper levels, potentially linked to differences in the representation of ocean dynamics, such as water mass formation processes. However, the Atlantic and Southern Oceans are regions in which many ORAs show widespread warming below 700 m over the period 1997–2009. Annual time series of global and hemispheric OHC change for 0–700 m show the largest spread for the data sparse Southern Hemisphere and a number of ORAs seem to be subject to large initialization ‘shock’ over the first few years. In agreement with previous studies, a number of ORAs exhibit enhanced ocean heat uptake below 300 and 700 m during the mid-1990s or early 2000s. The ORA ensemble mean (±1 standard deviation) of rolling 5-year trends in full-depth OHC shows a relatively steady heat uptake of approximately 0.9 ± 0.8 W m−2 (expressed relative to Earth’s surface area) between 1995 and 2002, which reduces to about 0.2 ± 0.6 W m−2 between 2004 and 2006, in qualitative agreement with recent analysis of Earth’s energy imbalance. There is a marked reduction in the ensemble spread of OHC trends below 300 m as the Argo profiling float observations become available in the early 2000s. In general, we suggest that ORAs should be treated with caution when employed to understand past ocean warming trends—especially when considering the deeper ocean where there is little in the way of observational constraints. The current work emphasizes the need to better observe the deep ocean, both for providing observational constraints for future ocean state estimation efforts and also to develop improved models and data assimilation methods.

An ensemble of eddy-permitting global ocean reanalyses from the MyOcean project

A set of four eddy-permitting global ocean reanalyses produced in the framework of the MyOcean project have been compared over the altimetry period 1993–2011. The main differences among the reanalyses used here come from the data assimilation scheme implemented to control the ocean state by inserting reprocessed observations of sea surface temperature (SST), in situ temperature and salinity profiles, sea level anomaly and sea-ice concentration. A first objective of this work includes assessing the interannual variability and trends for a series of parameters, usually considered in the community as essential ocean variables: SST, sea surface salinity, temperature and salinity averaged over meaningful layers of the water column, sea level, transports across pre-defined sections, and sea ice parameters. The eddy-permitting nature of the global reanalyses allows also to estimate eddy kinetic energy. The results show that in general there is a good consistency between the different reanalyses. An intercomparison against experiments without data assimilation was done during the MyOcean project and we conclude that data assimilation is crucial for correctly simulating some quantities such as regional trends of sea level as well as the eddy kinetic energy. A second objective is to show that the ensemble mean of reanalyses can be evaluated as one single system regarding its reliability in reproducing the climate signals, where both variability and uncertainties are assessed through the ensemble spread and signal-to-noise ratio. The main advantage of having access to several reanalyses differing in the way data assimilation is performed is that it becomes possible to assess part of the total uncertainty. Given the fact that we use very similar ocean models and atmospheric forcing, we can conclude that the spread of the ensemble of reanalyses is mainly representative of our ability to gauge uncertainty in the assimilation methods. This uncertainty changes a lot from one ocean parameter to another, especially in global indices. However, despite several caveats in the design of the multi-system ensemble, the main conclusion from this study is that an eddy-permitting multi-system ensemble approach has become mature and our results provide a first step towards a systematic comparison of eddy-permitting global ocean reanalyses aimed at providing robust conclusions on the recent evolution of the oceanic state.

Interannual-decadal variability of wintertime mixed layer depths in the North Pacific detected by an ensemble of ocean syntheses

The interannual-decadal variability of the wintertime mixed layer depths (MLDs) over the North Pacific is investigated from an empirical orthogonal function (EOF) analysis of an ensemble of global ocean reanalyses. The first leading EOF mode represents the interannual MLD anomalies centered in the eastern part of the central mode water formation region in phase opposition with those in the eastern subtropics and the central Alaskan Gyre. This first EOF mode is highly correlated with the Pacific decadal oscillation index on both the interannual and decadal time scales. The second leading EOF mode represents the MLD variability in the subtropical mode water (STMW) formation region and has a good correlation with the wintertime West Pacific (WP) index with time lag of 3 years, suggesting the importance of the oceanic dynamical response to the change in the surface wind field associated with the meridional shifts of the Aleutian Low. The above MLD variabilities are in basic agreement with previous observational and modeling findings. Moreover the reanalysis ensemble provides uncertainty estimates. The interannual MLD anomalies in the first and second EOF modes are consistently represented by the individual reanalyses and the amplitudes of the variabilities generally exceed the ensemble spread of the reanalyses. Besides, the resulting MLD variability indices, spanning the 1948–2012 period, should be helpful for characterizing the North Pacific climate variability. In particular, a 6-year oscillation including the WP teleconnection pattern in the atmosphere and the oceanic MLD variability in the STMW formation region is first detected.

Evaluation of the Plant–Craig stochastic convection scheme (v2.0) in the ensemble forecasting system MOGREPS-R (24 km) based on the Unified Model (v7.3)

The Plant–Craig stochastic convection parameterization (version 2.0) is implemented in the Met Office Regional Ensemble Prediction System (MOGREPS-R) and is assessed in comparison with the standard convection scheme with a simple stochastic scheme only, from random parameter variation. A set of 34 ensemble forecasts, each with 24 members, is considered, over the month of July 2009. Deterministic and probabilistic measures of the precipitation forecasts are assessed. The Plant–Craig parameterization is found to improve probabilistic forecast measures, particularly the results for lower precipitation thresholds. The impact on deterministic forecasts at the grid scale is neutral, although the Plant–Craig scheme does deliver improvements when forecasts are made over larger areas. The improvements found are greater in conditions of relatively weak synoptic forcing, for which convective precipitation is likely to be less predictable.

Axillary bud development in pineapple nodal segments correlates with changes on cell cycle gene expression, hormone level, and sucrose and glutamate contents

During the process of lateral organ development after plant decapitation, cell division and differentiation occur in a balanced manner initiated by specific signaling, which triggers the reentrance into the cell cycle. Here, we investigated short-term variations in the content of some endogenous signals, such as auxin, cytokinins (Cks), and other mitogenic stimuli (sucrose and glutamate), which are likely correlated with the cell cycle reactivation in the axillary bud primordium of pineapple nodal segments. Transcript levels of cell cycle-associated genes, CycD2;1, and histone H2A were analyzed. Nodal segments containing the quiescent axillary meristem cells were cultivated in vitro during 24 h after the apex removal and de-rooting. From the moment of stem apex and root removal, decapitated nodal segment (DNS) explants showed a lower indol-3-acetic acid (IAA) concentration than control explants, and soon after, an increase of endogenous sucrose and iP-type Cks were detected. The decrease of IAA may be the primary signal for cell cycle control early in G1 phase, leading to the upregulation of CycD2;1 gene in the first h. Later, the iP-type Cks and sucrose could have triggered the progression to S-phase since there was an increase in H2A expression at the eighth h. DNS explants revealed substantial increase in Z-type Cks and glutamate from the 12th h, suggesting that these mitogens could also operate in promoting pineapple cell cycle progression. We emphasize that the use of non-synchronized tissue rather than synchronous cell suspension culture makes it more difficult to interpret the results of a dynamic cell division process. However, pineapple nodal segments cultivated in vitro may serve as an interesting model to shed light on apical dominance release and the reentrance of quiescent axillary meristem cells into the cell cycle.

Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

Solução da equação de condução de calor bidimensional, em meios multicompostos, pelos métodos nodal, com parâmetros concentrados, e a técnica da transformada de Laplace

Neste trabalho, desenvolvemos uma metodologia semi-analítica para solução de problemas de condução de calor bidimensional, não-estacionária em meios multicompostos. Esta metodologia combina os métodos nodal, com parâmetros concentrados, e a técnica da transformada de Laplace. Inicialmente, aplicamos o método nodal. Nele, a equação diferencial parcial que descreve o problema é integrada, transversalmente, em relação a uma das variáveis espaciais. Em seguida, é utilizado o método de parâmetros concentrados, onde a distribuição de temperatura nos contornos superior e inferior é substituída pelo seu valor médio. Os problemas diferenciais unidimensionais resultantes são então resolvidos com o uso da técnica da transformada de Laplace, cuja inversão é avaliada numericamente. O método proposto é usado na solução do problema de condução de calor, em paredes de edificações. A implementação computacional é feita, utilizando-se a linguagem FORTRAN e os resultados numéricos obtidos são comparados com os disponíveis na literatura.

Expressão imuno-histoquímica da e-caderina e da ß-catenina em carcinoma epidermóide oral com e sem metástase nodal

The adhesion molecules E-cadherin and β-catenin have been studied as possible markers to distinguish carcinomas with and without metastatic potential. The objective of this research was to study the imunohistochemistry expression of the E-cadherin and β-catenin in oral squamous cell carcinoma (OSCC), aiming to contribute for the better understanding of the biological behavior of this lesion. The sample consisted of 30 cases of OSCC, being 15 of tongue and 15 of lower lip. The profile and intensity of labeling and semi quantitative analysis of the percentage of immunopositive tumoral cells in membrane for E-cadherin and β-catenin had been related with the anatomical localization of the lesion, the presence or not of nodal metastasis and the histological grade of malignancy in the invasive front area of the tumor. It was registered the presence or not of cytoplasmic and nuclear labeling of the β-catenin. The results had been submitted to the statistical analysis, being used the Mann-Whitney Test, the Fisher Test and the Spearman Correlation Coefficient (α=0, 05). The results showed that the expression in membrane for E-cadherin and β-catenin was, predominantly, the heterogeneous profile in the lower lip and tongue carcinomas, as well as in the cases with and without nodal metastasis. It was not observed significant statistical difference between expression profile and amount of immunopositive cells for E-cadherin, β-catenin and the anatomical localization of the lesion and for the presence or not of nodal metastasis. However, there was significant difference of the reduced expression of these proteins with the high score of malignancy. It was verified that the expression of the β-catenin in cytoplasm was present in 22 (73.33%) of the 30 analyzed cases, and 6 cases (20%) showed nuclear expression. The statistical analysis detected significant association between the expression of the β-catenin in the cytoplasm with the histological grade of malignancy, being this molecule more frequently present in the cytoplasm in the cases of high score of malignancy. It was concluded that the reduced immunoexpression of these proteins in membrane can be related with the lowest cellular differentiation, as well as with the pattern of invasion in nests and isolated cells, demonstrated in the cases of OSCC with high histological grade of malignancy

Técnica de parametrização geométrica para o fluxo de carga continuado baseado nas variáveis tensão nodal e fator de carregamento

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

Estudo comparativo dos métodos Nodal e Zbus para alocação de custos pelo uso do sistema de transmissão

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

Limit weierstrass points on nodal reducible curves

In the 1980s D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.