Linkage disequilibrium assessment via log-linear modeling of SNP haplotype frequencies

Analyses of high-density single-nucleotide polymorphism (SNP) data, such as genetic mapping and linkage disequilibrium (LD) studies, require phase-known haplotypes to allow for the correlation between tightly linked loci. However, current SNP genotyping technology cannot determine phase, which must be inferred statistically. In this paper, we present a new Bayesian Markov chain Monte Carlo (MCMC) algorithm for population haplotype frequency estimation, particulary in the context of LD assessment. The novel feature of the method is the incorporation of a log-linear prior model for population haplotype frequencies. We present simulations to suggest that 1) the log-linear prior model is more appropriate than the standard coalescent process in the presence of recombination (>0.02cM between adjacent loci), and 2) there is substantial inflation in measures of LD obtained by a "two-stage" approach to the analysis by treating the "best" haplotype configuration as correct, without regard to uncertainty in the recombination process. Genet Epidemiol 25:106-114, 2003. (C) 2003 Wiley-Liss, Inc.

Training conditional and cumulative risk judgements: the role of frequencies, problem-structure and Einstellung

Two experiments implement and evaluate a training scheme for learning to apply frequency formats to probability judgements couched in terms of percentages. Results indicate that both conditional and cumulative probability judgements can be improved in this manner, however the scheme is insufficient to promote any deeper understanding of the problem structure. In both experiments, training on one problem type only (either conditional or cumulative risk judgements) resulted in an inappropriate transfer of a learned method at test. The obstacles facing a frequency-based training programme for teaching appropriate use of probability data are discussed. Copyright (c) 2006 John Wiley & Sons, Ltd.

Precipitation and latent heating distributions from satellite passive microwave radiometry. Part I: improved method and uncertainties

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5°-resolution range from approximately 50% at 1 mm h−1 to 20% at 14 mm h−1. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%–80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5° resolution is relatively small (less than 6% at 5 mm day−1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%–35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%–15% at 5 mm day−1, with proportionate reductions in latent heating sampling errors.

Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

The effects of variation in snow properties on passive microwave snow mass estimation

Estimating snow mass at continental scales is difficult, but important for understanding land-atmosphere interactions, biogeochemical cycles and the hydrology of the Northern latitudes. Remote sensing provides the only consistent global observations, butwith unknown errors. Wetest the theoretical performance of the Chang algorithm for estimating snow mass from passive microwave measurements using the Helsinki University of Technology (HUT) snow microwave emission model. The algorithm's dependence upon assumptions of fixed and uniform snow density and grainsize is determined, and measurements of these properties made at the Cold Land Processes Experiment (CLPX) Colorado field site in 2002–2003 used to quantify the retrieval errors caused by differences between the algorithm assumptions and measurements. Deviation from the Chang algorithm snow density and grainsize assumptions gives rise to an error of a factor of between two and three in calculating snow mass. The possibility that the algorithm performsmore accurately over large areas than at points is tested by simulating emission from a 25 km diameter area of snow with a distribution of properties derived from the snow pitmeasurements, using the Chang algorithm to calculate mean snow-mass from the simulated emission. The snowmass estimation froma site exhibiting the heterogeneity of the CLPX Colorado site proves onlymarginally different than that from a similarly-simulated homogeneous site. The estimation accuracy predictions are tested using the CLPX field measurements of snow mass, and simultaneous SSM/I and AMSR-E measurements.

Microwave-assisted hydrogel synthesis: a new method for crosslinking polymers in aqueous solutions

It has been found that hydrogels may be formed by microwave irradiation of aqueous solutions containing appropriate combinations of polymers. This new method of hydrogel synthesis yields sterile hydrogels without the use of monomers, eliminating the need for the removal of unreacted species from the final product. Results for two particularly successful combinations, poly(vinyl alcohol) with either poly(acrylic acid) or poly(methylvinylether-alt-maleic anhydride), are presented. Irradiation using temperatures of 100–150 °C was found to yield hydrogels with large equilibrium swelling degrees of 500–1000 g g−1. Material leached from both types of hydrogel shows little cytotoxicity towards HT29 cells.

Quantitative precipitation estimation over ocean using Bayesian approach from microwave observations during the typhoon season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

A procedure for the simultaneous determination of total nitrogen and total phosphorus in freshwater samples using persulphate microwave digestion

In the absence of a suitable method for routine analysis of large numbers of natural river water samples for organic nitrogen and phosphorus fractions, a new simultaneous digestion technique was developed, based on a standard persulphate digestion procedure. This allows rapid analysis of river, lake and groundwater samples from a range of environments for total nitrogen and phosphorus. The method was evaluated using a range of organic nitrogen and phosphorus structures tested at low, mid and high range concentrations from 2 to 50 mg l-1 nitrogen and 0.2 to 10 mg l-1 phosphorus. Mean recoveries for nitrogen ranged from 94.5% (2 mg I-1) to 92.7% (50 mg I-1) and for phosphorus were 98.2% (0.2 mg l-1) to 100.2% (10 mg l-1). The method is precise in its ability m reproduce results from replicate digestions, and robust in its ability to handle a variety of natural water samples in the pH range 5-8.

Toward vicarious calibration of microwave remote-sensing satellites in arid environments

The Soil Moisture and Ocean Salinity (SMOS) satellite marks the commencement of dedicated global surface soil moisture missions, and the first mission to make passive microwave observations at L-band. On-orbit calibration is an essential part of the instrument calibration strategy, but on-board beam-filling targets are not practical for such large apertures. Therefore, areas to serve as vicarious calibration targets need to be identified. Such sites can only be identified through field experiments including both in situ and airborne measurements. For this purpose, two field experiments were performed in central Australia. Three areas are studied as follows: 1) Lake Eyre, a typically dry salt lake; 2) Wirrangula Hill, with sparse vegetation and a dense cover of surface rock; and 3) Simpson Desert, characterized by dry sand dunes. Of those sites, only Wirrangula Hill and the Simpson Desert are found to be potentially suitable targets, as they have a spatial variation in brightness temperatures of <4 K under normal conditions. However, some limitations are observed for the Simpson Desert, where a bias of 15 K in vertical and 20 K in horizontal polarization exists between model predictions and observations, suggesting a lack of understanding of the underlying physics in this environment. Subsequent comparison with model predictions indicates a SMOS bias of 5 K in vertical and 11 K in horizontal polarization, and an unbiased root mean square difference of 10 K in both polarizations for Wirrangula Hill. Most importantly, the SMOS observations show that the brightness temperature evolution is dominated by regular seasonal patterns and that precipitation events have only little impact.

Assessment of intercalibration methods for satellite microwave humidity sounders

Three methods for intercalibrating humidity sounding channels are compared to assess their merits and demerits. The methods use the following: (1) natural targets (Antarctica and tropical oceans), (2) zonal average brightness temperatures, and (3) simultaneous nadir overpasses (SNOs). Advanced Microwave Sounding Unit-B instruments onboard the polar-orbiting NOAA 15 and NOAA 16 satellites are used as examples. Antarctica is shown to be useful for identifying some of the instrument problems but less promising for intercalibrating humidity sounders due to the large diurnal variations there. Owing to smaller diurnal cycles over tropical oceans, these are found to be a good target for estimating intersatellite biases. Estimated biases are more resistant to diurnal differences when data from ascending and descending passes are combined. Biases estimated from zonal-averaged brightness temperatures show large seasonal and latitude dependence which could have resulted from diurnal cycle aliasing and scene-radiance dependence of the biases. This method may not be the best for channels with significant surface contributions. We have also tested the impact of clouds on the estimated biases and found that it is not significant, at least for tropical ocean estimates. Biases estimated from SNOs are the least influenced by diurnal cycle aliasing and cloud impacts. However, SNOs cover only relatively small part of the dynamic range of observed brightness temperatures.

Global snow mass measurements and the effect of stratigraphic detail on inversion of microwave brightness temperatures

Snow provides large seasonal storage of freshwater, and information about the distribution of snow mass as Snow Water Equivalent (SWE) is important for hydrological planning and detecting climate change impacts. Large regional disagreements remain between estimates from reanalyses, remote sensing and modelling. Assimilating passive microwave information improves SWE estimates in many regions but the assimilation must account for how microwave scattering depends on snow stratigraphy. Physical snow models can estimate snow stratigraphy, but users must consider the computational expense of model complexity versus acceptable errors. Using data from the National Aeronautics and Space Administration Cold Land Processes Experiment (NASA CLPX) and the Helsinki University of Technology (HUT) microwave emission model of layered snowpacks, it is shown that simulations of the brightness temperature difference between 19 GHz and 37 GHz vertically polarised microwaves are consistent with Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) and Special Sensor Microwave Imager (SSM/I) retrievals once known stratigraphic information is used. Simulated brightness temperature differences for an individual snow profile depend on the provided stratigraphic detail. Relative to a profile defined at the 10 cm resolution of density and temperature measurements, the error introduced by simplification to a single layer of average properties increases approximately linearly with snow mass. If this brightness temperature error is converted into SWE using a traditional retrieval method then it is equivalent to ±13 mm SWE (7% of total) at a depth of 100 cm. This error is reduced to ±5.6 mm SWE (3 % of total) for a two-layer model.

A variational approach to retrieve rain rate by combining information from rain gauges, radars, and microwave links

Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimate with greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Zürich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge and microwave link information.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.