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.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

Incorporating Legacy Soil pH Databases into Digital Soil Maps

Soil data and reliable soil maps are imperative for environmental management. conservation and policy. Data from historical point surveys, e.g. experiment site data and farmers fields can serve this purpose. However, legacy soil information is not necessarily collected for spatial analysis and mapping such that the data may not have immediately useful geo-references. Methods are required to utilise these historical soil databases so that we can produce quantitative maps of soil propel-ties to assess spatial and temporal trends but also to assess where future sampling is required. This paper discusses two such databases: the Representative Soil Sampling Scheme which has monitored the agricultural soil in England and Wales from 1969 to 2003 (between 400 and 900 bulked soil samples were taken annually from different agricultural fields); and the former State Chemistry Laboratory, Victoria, Australia where between 1973 and 1994 approximately 80,000 soil samples were submitted for analysis by farmers. Previous statistical analyses have been performed using administrative regions (with sharp boundaries) for both databases, which are largely unrelated to natural features. For a more detailed spatial analysis that call be linked to climate and terrain attributes, gradual variation of these soil properties should be described. Geostatistical techniques such as ordinary kriging are suited to this. This paper describes the format of the databases and initial approaches as to how they can be used for digital soil mapping. For this paper we have selected soil pH to illustrate the analyses for both databases.

The spatial prediction of soil mineral N and potentially available N using elevation

The precision farmer wants to manage the variation in soil nutrient status continuously, which requires reliable predictions at places between sampling sites. Ordinary kriging can be used for prediction if the data are spatially dependent and there is a suitable variogram model. However, even if data are spatially correlated, there are often few soil sampling sites in relation to the area to be managed. If intensive ancillary data are available and these are coregionalized with the sparse soil data, they could be used to increase the accuracy of predictions of the soil properties by methods such as cokriging, kriging with external drift and regression kriging. This paper compares the accuracy of predictions of the plant available N properties (mineral N and potentially available N) for two arable fields in Bedfordshire, United Kingdom, from ordinary kriging, cokriging, kriging with external drift and regression kriging. For the last three, intensive elevation data were used with the soil data. The mean squared errors of prediction from these methods of kriging were determined at validation sites where the values were known. Kriging with external drift resulted in the smallest mean squared error for two of the three properties examined, and cokriging for the other. The results suggest that the use of intensive ancillary data can increase the accuracy of predictions of soil properties in arable fields provided that the variables are related spatially. (c) 2005 Elsevier B.V. All rights reserved.

Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Global observed changes in daily climate extremes of temperature and precipitation

A suite of climate change indices derived from daily temperature and precipitation data, with a primary focus on extreme events, were computed and analyzed. By setting an exact formula for each index and using specially designed software, analyses done in different countries have been combined seamlessly. This has enabled the presentation of the most up-to-date and comprehensive global picture of trends in extreme temperature and precipitation indices using results from a number of workshops held in data-sparse regions and high-quality station data supplied by numerous scientists world wide. Seasonal and annual indices for the period 1951-2003 were gridded. Trends in the gridded fields were computed and tested for statistical significance. Results showed widespread significant changes in temperature extremes associated with warming, especially for those indices derived from daily minimum temperature. Over 70% of the global land area sampled showed a significant decrease in the annual occurrence of cold nights and a significant increase in the annual occurrence of warm nights. Some regions experienced a more than doubling of these indices. This implies a positive shift in the distribution of daily minimum temperature throughout the globe. Daily maximum temperature indices showed similar changes but with smaller magnitudes. Precipitation changes showed a widespread and significant increase, but the changes are much less spatially coherent compared with temperature change. Probability distributions of indices derived from approximately 200 temperature and 600 precipitation stations, with near-complete data for 1901-2003 and covering a very large region of the Northern Hemisphere midlatitudes (and parts of Australia for precipitation) were analyzed for the periods 1901-1950, 1951-1978 and 1979-2003. Results indicate a significant warming throughout the 20th century. Differences in temperature indices distributions are particularly pronounced between the most recent two periods and for those indices related to minimum temperature. An analysis of those indices for which seasonal time series are available shows that these changes occur for all seasons although they are generally least pronounced for September to November. Precipitation indices show a tendency toward wetter conditions throughout the 20th century.

The development of a new dust uplift scheme in the Met Office Unified Model

Aeolian mineral dust aerosol is an important consideration in the Earth's radiation budget as well as a source of nutrients to oceanic and land biota. The modelling of aeolian mineral dust has been improving consistently despite the relatively sparse observations to constrain them. This study documents the development of a new dust emissions scheme in the Met Office Unified ModelTM (MetUM) based on the Dust Entrainment and Deposition (DEAD) module. Four separate case studies are used to test and constrain the model output. Initial testing was undertaken on a large dust event over North Africa in March 2006 with the model constrained using AERONET data. The second case study involved testing the capability of the model to represent dust events in the Middle East without being re-tuned from the March 2006 case in the Sahara. While the model is unable to capture some of the daytime variation in AERONET AOD there is good agreement between the model and observed dust events. In the final two case studies new observations from in situ aircraft data during the Dust Outflow and Deposition to the Ocean (DODO) campaigns in February and August 2006 were used. These recent observations provided further data on dust size distributions and vertical profiles to constrain the model. The modelled DODO cases were also compared to AERONET data to make sure the radiative properties of the dust were comparable to observations. Copyright © 2009 Royal Meteorological Society and Crown Copyright

LiDAR mapping of tidal marshes for ecogeomorphological modelling in the TIDE project

The European research project TIDE (Tidal Inlets Dynamics and Environment) is developing and validating coupled models describing the morphological, biological and ecological evolution of tidal environments. The interactions between the physical and biological processes occurring in these regions requires that the system be studied as a whole rather than as separate parts. Extensive use of remote sensing including LiDAR is being made to provide validation data for the modelling. This paper describes the different uses of LiDAR within the project and their relevance to the TIDE science objectives. LiDAR data have been acquired from three different environments, the Venice Lagoon in Italy, Morecambe Bay in England, and the Eden estuary in Scotland. LiDAR accuracy at each site has been evaluated using ground reference data acquired with differential GPS. A semi-automatic technique has been developed to extract tidal channel networks from LiDAR data either used alone or fused with aerial photography. While the resulting networks may require some correction, the procedure does allow network extraction over large areas using objective criteria and reduces fieldwork requirements. The networks extracted may subsequently be used in geomorphological analyses, for example to describe the drainage patterns induced by networks and to examine the rate of change of networks. Estimation of the heights of the low and sparse vegetation on marshes is being investigated by analysis of the statistical distribution of the measured LiDAR heights. Species having different mean heights may be separated using the first-order moments of the height distribution.

A comparison of three canopy interception models for a leafless mixed deciduous forest stand in the eastern United States

Canopy interception of incident precipitation is a critical component of the forest water balance during each of the four seasons. Models have been developed to predict precipitation interception from standard meteorological variables because of acknowledged difficulty in extrapolating direct measurements of interception loss from forest to forest. No known study has compared and validated canopy interception models for a leafless deciduous forest stand in the eastern United States. Interception measurements from an experimental plot in a leafless deciduous forest in northeastern Maryland (39°42'N, 75°5'W) for 11 rainstorms in winter and early spring 2004/05 were compared to predictions from three models. The Mulder model maintains a moist canopy between storms. The Gash model requires few input variables and is formulated for a sparse canopy. The WiMo model optimizes the canopy storage capacity for the maximum wind speed during each storm. All models showed marked underestimates and overestimates for individual storms when the measured ratio of interception to gross precipitation was far more or less, respectively, than the specified fraction of canopy cover. The models predicted the percentage of total gross precipitation (PG) intercepted to within the probable standard error (8.1%) of the measured value: the Mulder model overestimated the measured value by 0.1% of PG; the WiMo model underestimated by 0.6% of PG; and the Gash model underestimated by 1.1% of PG. The WiMo model’s advantage over the Gash model indicates that the canopy storage capacity increases logarithmically with the maximum wind speed. This study has demonstrated that dormant-season precipitation interception in a leafless deciduous forest may be satisfactorily predicted by existing canopy interception models.

A comparison of the variability of biological nutrients against depth and potential density.

The main biogeochemical nutrient distributions, along with ambient ocean temperature and the light field, control ocean biological productivity. Observations of nutrients are much sparser than physical observations of temperature and salinity, yet it is critical to validate biogeochemical models against these sparse observations if we are to successfully model biological variability and trends. Here we use data from the Bermuda Atlantic Time-series Study and the World Ocean Database 2005 to demonstrate quantitatively that over the entire globe a significant fraction of the temporal variability of phosphate, silicate and nitrate within the oceans is correlated with water density. The temporal variability of these nutrients as a function of depth is almost always greater than as a function of potential density, with he largest reductions in variability found within the main pycnocline. The greater nutrient variability as a function of depth occurs when dynamical processes vertically displace nutrient and density fields together on shorter timescales than biological adjustments. These results show that dynamical processes can have a significant impact on the instantaneous nutrient distributions. These processes must therefore be considered when modeling biogeochemical systems, when comparing such models with observations, or when assimilating data into such models.

Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Childhood obesity: should primary school children be routinely screened? A systematic review and discussion of the evidence

Background: Population monitoring has been introduced in UK primary schools in an effort to track the growing obesity epidemic. It has been argued that parents should be informed of their child's results, but is there evidence that moving from monitoring to screening would be effective? We describe what is known about the effectiveness of monitoring and screening for overweight and obesity in primary school children and highlight areas where evidence is lacking and research should be prioritised. Design: Systematic review with discussion of evidence gaps and future research. Data sources: Published and unpublished studies ( any language) from electronic databases ( inception to July 2005), clinical experts, Primary Care Trusts and Strategic Health Authorities, and reference lists of retrieved studies. Review methods: We included any study that evaluated measures of overweight and obesity as part of a population-level assessment and excluded studies whose primary outcome measure was prevalence. Results: There were no trials assessing the effectiveness of monitoring or screening for overweight and obesity. Studies focussed on the diagnostic accuracy of measurements. Information on the attitudes of children, parents and health professionals to monitoring was extremely sparse. Conclusions: Our review found a lack of data on the potential impact of population monitoring or screening for obesity and more research is indicated. Identification of effective weight reduction strategies for children and clarification of the role of preventative measures are priorities. It is difficult to see how screening to identify individual children can be justified without effective interventions.

Tests of syntactic comprehension in aphasia: an investigation of task effects

Background: Consistency of performance across tasks that assess syntactic comprehension in aphasia has clinical and theoretical relevance. In this paper we add to the relatively sparse previous work on how sentence comprehension abilities are influenced by the nature of the assessment task. Aims: Our aims are: (1) to compare linguistic performance across sentence-picture matching, enactment, and truth-value judgement tasks; (2) to investigate the impact of pictorial stimuli on syntactic comprehension. Methods Procedures: We tested a group of 10 aphasic speakers (3 with fluent and 7 with non-fluent aphasia) in three tasks (Experiment 1): (i) sentence-picture matching with four pictures, (ii) sentence-picture matching with two pictures, and (iii) enactment. A further task of truth-value judgement was given to a subgroup of those speakers (n=5, Experiment 2). Similar sentence types across all tasks were used and included canonical (actives, subject clefts) and non-canonical (passives, object clefts) sentences. We undertook two types of analyses: (a) we compared canonical and non-canonical sentences in each task; (b) we compared performance between (i) actives and passives, (ii) subject and object clefts in each task. We examined the results of all participants as a group and as case-series. Outcomes Results: Several task effects emerged. Overall, the two-picture sentence-picture matching and enactment tasks were more discriminating than the four-picture condition. Group performance in the truth-value judgement task was similar to two-picture sentence-picture matching and enactment. At the individual level performance across tasks contrasted to some group results. Conclusions: Our findings revealed task effects across participants. We discuss reasons that could explain the diverse profiles of performance and the implications for clinical practice.

A systematic review of the routine monitoring of growth in children of primary school age to identify growth-related conditions

Objectives: To clarify the role of growth monitoring in primary school children, including obesity, and to examine issues that might impact on the effectiveness and cost-effectiveness of such programmes. Data sources: Electronic databases were searched up to July 2005. Experts in the field were also consulted. Review methods: Data extraction and quality assessment were performed on studies meeting the review's inclusion criteria. The performance of growth monitoring to detect disorders of stature and obesity was evaluated against National Screening Committee (NSC) criteria. Results: In the 31 studies that were included in the review, there were no controlled trials of the impact of growth monitoring and no studies of the diagnostic accuracy of different methods for growth monitoring. Analysis of the studies that presented a 'diagnostic yield' of growth monitoring suggested that one-off screening might identify between 1: 545 and 1: 1793 new cases of potentially treatable conditions. Economic modelling suggested that growth monitoring is associated with health improvements [ incremental cost per quality-adjusted life-year (QALY) of pound 9500] and indicated that monitoring was cost-effective 100% of the time over the given probability distributions for a willingness to pay threshold of pound 30,000 per QALY. Studies of obesity focused on the performance of body mass index against measures of body fat. A number of issues relating to human resources required for growth monitoring were identified, but data on attitudes to growth monitoring were extremely sparse. Preliminary findings from economic modelling suggested that primary prevention may be the most cost-effective approach to obesity management, but the model incorporated a great deal of uncertainty. Conclusions: This review has indicated the potential utility and cost-effectiveness of growth monitoring in terms of increased detection of stature-related disorders. It has also pointed strongly to the need for further research. Growth monitoring does not currently meet all NSC criteria. However, it is questionable whether some of these criteria can be meaningfully applied to growth monitoring given that short stature is not a disease in itself, but is used as a marker for a range of pathologies and as an indicator of general health status. Identification of effective interventions for the treatment of obesity is likely to be considered a prerequisite to any move from monitoring to a screening programme designed to identify individual overweight and obese children. Similarly, further long-term studies of the predictors of obesity-related co-morbidities in adulthood are warranted. A cluster randomised trial comparing growth monitoring strategies with no growth monitoring in the general population would most reliably determine the clinical effectiveness of growth monitoring. Studies of diagnostic accuracy, alongside evidence of effective treatment strategies, could provide an alternative approach. In this context, careful consideration would need to be given to target conditions and intervention thresholds. Diagnostic accuracy studies would require long-term follow-up of both short and normal children to determine sensitivity and specificity of growth monitoring.