Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Detection of flood extent in urban areas using high resolution TerraSAR-X data

Flooding is a major hazard in both rural and urban areas worldwide, but it is in urban areas that the impacts are most severe. An investigation of the ability of high resolution TerraSAR-X data to detect flooded regions in urban areas is described. An important application for this would be the calibration and validation of the flood extent predicted by an urban flood inundation model. To date, research on such models has been hampered by lack of suitable distributed validation data. The study uses a 3m resolution TerraSAR-X image of a 1-in-150 year flood near Tewkesbury, UK, in 2007, for which contemporaneous aerial photography exists for validation. The DLR SETES SAR simulator was used in conjunction with airborne LiDAR data to estimate regions of the TerraSAR-X image in which water would not be visible due to radar shadow or layover caused by buildings and taller vegetation, and these regions were masked out in the flood detection process. A semi-automatic algorithm for the detection of floodwater was developed, based on a hybrid approach. Flooding in rural areas adjacent to the urban areas was detected using an active contour model (snake) region-growing algorithm seeded using the un-flooded river channel network, which was applied to the TerraSAR-X image fused with the LiDAR DTM to ensure the smooth variation of heights along the reach. A simpler region-growing approach was used in the urban areas, which was initialized using knowledge of the flood waterline in the rural areas. Seed pixels having low backscatter were identified in the urban areas using supervised classification based on training areas for water taken from the rural flood, and non-water taken from the higher urban areas. Seed pixels were required to have heights less than a spatially-varying height threshold determined from nearby rural waterline heights. Seed pixels were clustered into urban flood regions based on their close proximity, rather than requiring that all pixels in the region should have low backscatter. This approach was taken because it appeared that urban water backscatter values were corrupted in some pixels, perhaps due to contributions from side-lobes of strong reflectors nearby. The TerraSAR-X urban flood extent was validated using the flood extent visible in the aerial photos. It turned out that 76% of the urban water pixels visible to TerraSAR-X were correctly detected, with an associated false positive rate of 25%. If all urban water pixels were considered, including those in shadow and layover regions, these figures fell to 58% and 19% respectively. These findings indicate that TerraSAR-X is capable of providing useful data for the calibration and validation of urban flood inundation models.

Clustered Fox genes in lophotrochozoans and the evolution of the bilaterian Fox gene cluster

FoxC, FoxF, FoxL1 and FoxQ1 genes have been shown to be clustered in some animal genomes, with mesendodermal expression hypothesised as a selective force maintaining cluster integrity. Hypotheses are, however, constrained by a lack of data from the Lophotrochozoa. Here we characterise members of the FoxC, FoxF, FoxL1 and FoxQ1 families from the annelid Capitella teleta and the molluscs Lottia gigantea and Patella vulgata. We cloned FoxC, FoxF, FoxL1 and FoxQ1 genes from C. teleta, and FoxC, FoxF and FoxL1 genes from P. vulgata, and established their expression during development. We also examined their genomic organisation in C. teleta and L. gigantea, and investigated local syntenic relationships. Our results show mesodermal and anterior gut expression is a common feature of these genes in lophotrochozoans. In L. gigantea FoxC, FoxF and FoxL1 are closely linked, while in C. teleta Ct-foxC and Ct-foxL1 are closely linked, with Ct-foxF and Ct-foxQ1 on different scaffolds. Adjacent to these genes there is limited evidence of local synteny. This demonstrates conservation of genomic organisation and expression of these genes can be traced in all three bilaterian Superphyla. These data are evaluated against competing theories for the long-term maintenance of gene clusters.

The impact of uncertainty in satellite data on the assessment of flood inundation models

The performance of flood inundation models is often assessed using satellite observed data; however these data have inherent uncertainty. In this study we assess the impact of this uncertainty when calibrating a flood inundation model (LISFLOOD-FP) for a flood event in December 2006 on the River Dee, North Wales, UK. The flood extent is delineated from an ERS-2 SAR image of the event using an active contour model (snake), and water levels at the flood margin calculated through intersection of the shoreline vector with LiDAR topographic data. Gauged water levels are used to create a reference water surface slope for comparison with the satellite-derived water levels. Residuals between the satellite observed data points and those from the reference line are spatially clustered into groups of similar values. We show that model calibration achieved using pattern matching of observed and predicted flood extent is negatively influenced by this spatial dependency in the data. By contrast, model calibration using water elevations produces realistic calibrated optimum friction parameters even when spatial dependency is present. To test the impact of removing spatial dependency a new method of evaluating flood inundation model performance is developed by using multiple random subsamples of the water surface elevation data points. By testing for spatial dependency using Moran’s I, multiple subsamples of water elevations that have no significant spatial dependency are selected. The model is then calibrated against these data and the results averaged. This gives a near identical result to calibration using spatially dependent data, but has the advantage of being a statistically robust assessment of model performance in which we can have more confidence. Moreover, by using the variations found in the subsamples of the observed data it is possible to assess the effects of observational uncertainty on the assessment of flooding risk.