Estimating surface CO2 fluxes from space-borne dry air mole fraction observations using an Ensemble Kalman filter

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

Space physics for graduate students: an activities-based approach

The geospace environment is controlled largely by events on the Sun, such as solar flares and coronal mass ejections, which generate significant geomagnetic and upper atmospheric disturbances. The study of this Sun-Earth system, which has become known as space weather, has both intrinsic scientific interest and practical applications. Adverse conditions in space can damage satellites and disrupt communications, navigation, and electric power grids, as well as endanger astronauts. The Center for Integrated Space Weather Modeling (CISM), a Science and Technology Center (STC) funded by the U.S. National Science Foundation (see http://www.bu.edu/cism/), is developing a suite of integrated physics-based computer models that describe the space environment from the Sun to the Earth for use in both research and operations [Hughes and Hudson, 2004, p. 1241]. To further this mission, advanced education and training programs sponsored by CISM encourage students to view space weather as a system that encompasses the Sun, the solar wind, the magnetosphere, and the ionosphere/thermosphere. This holds especially true for participants in the CISM space weather summer school [Simpson, 2004].

The effect of consumption volume on profile and liking of oral nutritional supplements of varied sweetness: sequential profiling and boredom tests

Oral nutrition supplements (ONS) are routinely prescribed to those with, or at risk of, malnutrition. Previous research identified poor compliance due to taste and sweetness. This paper investigates taste and hedonic liking of ONS, of varying sweetness and metallic levels, over consumption volume; an important consideration as patients are prescribed large volumes of ONS daily. A sequential descriptive profile was developed to determine the perception of sensory attributes over repeat consumption of ONS. Changes in liking of ONS following repeat consumption were characterised by a boredom test. Certain flavour (metallic taste, soya milk flavour) and mouthfeel (mouthdrying, mouthcoating) attributes built up over increased consumption volume (p 0.002). Hedonic liking data from two cohorts, healthy older volunteers (n = 32, median age 73) and patients (n = 28, median age 85), suggested such build-up was disliked. Efforts made to improve the palatability of ONS must take account of the build up of taste and mouthfeel characteristics over increased consumption volume.

Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Sequential genome-wide association studies for monitoring adverse events in the clinical evaluation of new drugs

Pharmacovigilance, the monitoring of adverse events (AEs), is an integral part in the clinical evaluation of a new drug. Until recently, attempts to relate the incidence of AEs to putative causes have been restricted to the evaluation of simple demographic and environmental factors. The advent of large-scale genotyping, however, provides an opportunity to look for associations between AEs and genetic markers, such as single nucleotides polymorphisms (SNPs). It is envisaged that a very large number of SNPs, possibly over 500 000, will be used in pharmacovigilance in an attempt to identify any genetic difference between patients who have experienced an AE and those who have not. We propose a sequential genome-wide association test for analysing AEs as they arise, allowing evidence-based decision-making at the earliest opportunity. This gives us the capability of quickly establishing whether there is a group of patients at high-risk of an AE based upon their DNA. Our method provides a valid test which takes account of linkage disequilibrium and allows for the sequential nature of the procedure. The method is more powerful than using a correction, such as idák, that assumes that the tests are independent. Copyright © 2006 John Wiley & Sons, Ltd.

Comparing correlations of continuous observations from two independent populations using a sequential approach

A sequential study design generally makes more efficient use of available information than a fixed sample counterpart of equal power. This feature is gradually being exploited by researchers in genetic and epidemiological investigations that utilize banked biological resources and in studies where time, cost and ethics are prominent considerations. Recent work in this area has focussed on the sequential analysis of matched case-control studies with a dichotomous trait. In this paper, we extend the sequential approach to a comparison of the associations within two independent groups of paired continuous observations. Such a comparison is particularly relevant in familial studies of phenotypic correlation using twins. We develop a sequential twin method based on the intraclass correlation and show that use of sequential methodology can lead to a substantial reduction in the number of observations without compromising the study error rates. Additionally, our approach permits straightforward allowance for other explanatory factors in the analysis. We illustrate our method in a sequential heritability study of dysplasia that allows for the effect of body mass index and compares monozygotes with pairs of singleton sisters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Melt structure and its transformation by sequential crystallization of the two blocks within poly(L-lactide)-block-poly(epsilon-caprolactone) double crystalline diblock copolymers

Sequential crystallization of poly(L-lactide) (PLLA) followed by poly(epsilon-caprolactone) (PCL) in double crystalline PLLA-b-PCL diblock copolymers is studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS). Three samples with different compositions are studied. The sample with the shortest PLLA block (32 wt.-% PLLA) crystallizes from a homogeneous melt, the other two (with 44 and 60% PLLA) from microphase separated structures. The microphase structure of the melt is changed as PLLA crystallizes at 122 degrees C (a temperature at which the PCL block is molten) forming spherulites regardless of composition, even with 32% PLLA. SAXS indicates that a lamellar structure with a different periodicity than that obtained in the melt forms (for melt segregated samples). Where PCL is the majority block, PCL crystallization at 42 degrees C following PLLA crystallization leads to rearrangement of the lamellar structure, as observed by SAXS, possibly due to local melting at the interphases between domains. POM results showed that PCL crystallizes within previously formed PLLA spherulites. WAXS data indicate that the PLLA unit cell is modified by crystallization of PCL, at least for the two majority PCL samples. The PCL minority sample did not crystallize at 42 degrees C (well below the PCL homopolymer crystallization temperature), pointing to the influence of pre-crystallization of PLLA on PCL crystallization, although it did crystallize at lower temperature. Crystallization kinetics were examined by DSC and WAXS, with good agreement in general. The crystallization rate of PLLA decreased with increase in PCL content in the copolymers. The crystallization rate of PCL decreased with increasing PLLA content. The Avrami exponents were in general depressed for both components in the block copolymers compared to the parent homopolymers. Polarized optical micrographs during isothermal crystalli zation of (a) homo-PLLA, (b) homo-PCL, (c) and (d) block copolymer after 30 min at 122 degrees C and after 15 min at 42 degrees C.

Ligand-centred reactivity of bis(picolyl)amine iridium: sequential deprotonation, oxidation and oxygenation of a "non-innocent" ligand

Treatment of [Ir(bpa)(cod)](+) complex [1](+) with a strong base (e.g., tBuO(-)) led to unexpected double deprotonation to form the anionic [Ir-(bpa-2H)(cod)](-) species [3](-), via the mono-deprotonated neutral amido complex [Ir(bpa-H)(cod)] as an isolable intermediate. A certain degree of aromaticity of the obtained metal-chelate ring may explain the favourable double deprotonation. The rhodium analogue [4](-) was prepared in situ. The new species [M(bpa-2H)(cod)](-) (M = Rh, Ir) are best described as two-electron reduced analogues of the cationic imine complexes [M-I(cod)(Py-CH2-N=CH-Py)](+). One-electron oxidation of [3](-) and [4](-) produced the ligand radical complexes [3]* and [4]*. Oxygenation of [3](-) with O-2 gave the neutral carboxamido complex [Ir(cod)(py-CH2-N-CO-py)] via the ligand radical complex [3]* as a detectable intermediate.