Correlated observation errors in data assimilation

Data assimilation provides techniques for combining observations and prior model forecasts to create initial conditions for numerical weather prediction (NWP). The relative weighting assigned to each observation in the analysis is determined by its associated error. Remote sensing data usually has correlated errors, but the correlations are typically ignored in NWP. Here, we describe three approaches to the treatment of observation error correlations. For an idealized data set, the information content under each simplified assumption is compared with that under correct correlation specification. Treating the errors as uncorrelated results in a significant loss of information. However, retention of an approximated correlation gives clear benefits.

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Relative proportions of polycyclic aromatic hydrocarbons differ between accumulation bioassays and chemical methods to predict bioavailability

Chemical methods to predict the bioavailable fraction of organic contaminants are usually validated in the literature by comparison with established bioassays. A soil spiked with polycyclic aromatic hydrocarbons (PAHs) was aged over six months and subjected to butanol, cyclodextrin and tenax extractions as well as an exhaustive extraction to determine total PAH concentrations at several time points. Earthworm (Eisenia fetida) and rye grass root (Lolium multiflorum) accumulation bioassays were conducted in parallel. Butanol extractions gave the best relationship with earthworm accumulation (r2 ≤ 0.54, p ≤ 0.01); cyclodextrin, butanol and acetone–hexane extractions all gave good predictions of accumulation in rye grass roots (r2 ≤ 0.86, p ≤ 0.01). However, the profile of the PAHs extracted by the different chemical methods was significantly different (p < 0.01) to that accumulated in the organisms. Biota accumulated a higher proportion of the heavier 4-ringed PAHs. It is concluded that bioaccumulation is a complex process that cannot be predicted by measuring the bioavailable fraction alone. The ability of chemical methods to predict PAH accumulation in Eisenia fetida and Lolium multiflorum was hindered by the varied metabolic fate of the different PAHs within the organisms.

Relative humidity changes in a warmer climate

Key climate feedbacks due to water vapor and clouds rest largely on how relative humidity R changes in a warmer climate, yet this has not been extensively analyzed in models. General circulation models (GCMs) from the CMIP3 archive and several higher resolution atmospheric GCMs examined here generally predict a characteristic pattern of R trend with global temperature that has been reported previously in individual models, including increase around the tropopause, decrease in the tropical upper troposphere, and decrease in midlatitudes. This pattern is very similar to that previously reported for cloud cover in the same GCMs, confirming the role of R in controlling changes in simulated cloud. Comparing different models, the trend in each part of the troposphere is approximately proportional to the upward and/or poleward gradient of R in the present climate. While this suggests that the changes simply reflect a shift of the R pattern upward with the tropopause and poleward with the zonal jets, the drying trend in the subtropics is roughly three times too large to be attributable to shifts of subtropical features, and the subtropical R minima deepen in most models. R trends are correlated with horizontal model resolution, especially outside the tropics, where they show signs of convergence and latitudinal gradients become close to available observations for GCM resolutions near T85 and higher. We argue that much of the systematic change in R can be explained by the local specific humidity having been set (by condensation) in remote regions with different temperature changes, hence the gradients and trends each depend on a model’s ability to resolve moisture transport. Finally, subtropical drying trends predicted from the warming alone fall well short of those observed in recent decades. While this discrepancy supports previous reports of GCMs underestimating Hadley Cell expansion, our results imply that shifts alone are not a sufficient interpretation of changes.

Pb-210-Ra-226 and Ra-228-Th-232 systematics in young arc lavas: implications for magma degassing and ascent rates

New data show that island arc rocks have (Pb-210/Ra-226)(o) ratios which range from as low as 0.24 up to 2.88. In contrast, (Ra-22S/Th-232) appears always within error of I suggesting that the large Ra-226-excesses observed in arc rocks were generated more than 30 years ago. This places a maximum estimate on melt ascent velocities of around 4000 m/year and provides further confidence that the Ra-226 excesses reflect deep (source) processes rather than shallow level alteration or seawater contamination. Conversely, partial melting must have occurred more than 30 years prior to eruption. The Pb-210 deficits are most readily explained by protracted magma degassing. Using published numerical models, the data suggest that degassing occurred continuously for periods up to several decades just prior to eruption but no link with eruption periodicity was found. Longer periods are required if degassing is discontinuous, less than 100% efficient or if magma is recharged or stored after degassing. The long durations suggest much of this degassing occurs at depth with implications for the formation of hydrothermal and copper-porphyry systems. A suite of lavas erupted in 1985-1986 from Sangeang Api volcano in the Sunda arc are characterised by deficits of Pb-210 relative to Ra-226 from which 6-8 years of continuous Rn-222 degassing would be inferred from recent numerical models. These data also form a linear (Pb-210)/Pb-(Ra-226)/Pb array which might be interpreted as a 71-year isochron. However, the array passes through the origin suggesting displacement downwards from the equiline in response to degassing and so the slope of the array is inferred not to have any age significance. Simple modelling shows that the range of (Ra-226)/Pb ratios requires thousands of years to develop consistent with differentiation occurring in response to cooling at the base of the crust. Thus, degassing post-dated, and was not responsible for magma differentiation. The formation, migration and extraction of gas bubbles must be extremely efficient in mafic magma whereas the higher viscosity of more siliceous magmas retards the process and can lead to Pb-210 excesses. A possible negative correlation between (Pb-210/Ra-226)(o) and SO2 emission rate requires further testing but may have implications for future eruptions. (C) 2004 Elsevier B.V. All rights reserved.

Making 'dirty' nations look clean? The nation state and the problem of selecting and weighting indices as tools for measuring progress towards sustainability

Pressing global environmental problems highlight the need to develop tools to measure progress towards "sustainability." However, some argue that any such attempt inevitably reflects the views of those creating such tools and only produce highly contested notions of "reality." To explore this tension, we critically assesses the Environmental Sustainability Index (ESI), a well-publicized product of the World Economic Forum that is designed to measure 'sustainability' by ranking nations on league tables based on extensive databases of environmental indicators. By recreating this index, and then using statistical tools (principal components analysis) to test relations between various components of the index, we challenge ways in which countries are ranked in the ESI. Based on this analysis, we suggest (1) that the approach taken to aggregate, interpret and present the ESI creates a misleading impression that Western countries are more sustainable than the developing world; (2) that unaccounted methodological biases allowed the authors of the ESI to over-generalize the relative 'sustainability' of different countries; and, (3) that this has resulted in simplistic conclusions on the relation between economic growth and environmental sustainability. This criticism should not be interpreted as a call for the abandonment of efforts to create standardized comparable data. Instead, this paper proposes that indicator selection and data collection should draw on a range of voices, including local stakeholders as well as international experts. We also propose that aggregating data into final league ranking tables is too prone to error and creates the illusion of absolute and categorical interpretations. (c) 2004 Elsevier Ltd. All rights reserved.

Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.