The APE atlas

This Atlas presents statistical analyses of the simulations submitted to the Aqua-Planet Experiment (APE) data archive. The simulations are from global Atmospheric General Circulation Models (AGCM) applied to a water-covered earth. The AGCMs include ones actively used or being developed for numerical weather prediction or climate research. Some are mature, application models and others are more novel and thus less well tested in Earth-like applications. The experiment applies AGCMs with their complete parameterization package to an idealization of the planet Earth which has a greatly simplified lower boundary that consists of an ocean only. It has no land and its associated orography, and no sea ice. The ocean is represented by Sea Surface Temperatures (SST) which are specified everywhere with simple, idealized distributions. Thus in the hierarchy of tests available for AGCMs, APE falls between tests with simplified forcings such as those proposed by Held and Suarez (1994) and Boer and Denis (1997) and Earth-like simulations of the Atmospheric Modeling Intercomparison Project (AMIP, Gates et al., 1999). Blackburn and Hoskins (2013) summarize the APE and its aims. They discuss where the APE fits within a modeling hierarchy which has evolved to evaluate complete models and which provides a link between realistic simulation and conceptual models of atmospheric phenomena. The APE bridges a gap in the existing hierarchy. The goals of APE are to provide a benchmark of current model behaviors and to stimulate research to understand the cause of inter-model differences., APE is sponsored by the World Meteorological Organization (WMO) joint Commission on Atmospheric Science (CAS), World Climate Research Program (WCRP) Working Group on Numerical Experimentation (WGNE). Chapter 2 of this Atlas provides an overview of the specification of the eight APE experiments and of the data collected. Chapter 3 lists the participating models and includes brief descriptions of each. Chapters 4 through 7 present a wide variety of statistics from the 14 participating models for the eight different experiments. Additional intercomparison figures created by Dr. Yukiko Yamada in AGU group are available at http://www.gfd-dennou.org/library/ape/comparison/. This Atlas is intended to present and compare the statistics of the APE simulations but does not contain a discussion of interpretive analyses. Such analyses are left for journal papers such as those included in the Special Issue of the Journal of the Meteorological Society of Japan (2013, Vol. 91A) devoted to the APE. Two papers in that collection provide an overview of the simulations. One (Blackburn et al., 2013) concentrates on the CONTROL simulation and the other (Williamson et al., 2013) on the response to changes in the meridional SST profile. Additional papers provide more detailed analysis of the basic simulations, while others describe various sensitivities and applications. The APE experiment data base holds a wealth of data that is now publicly available from the APE web site: http://climate.ncas.ac.uk/ape/. We hope that this Atlas will stimulate future analyses and investigations to understand the large variation seen in the model behaviors.

Conditioning model output statistics of regional climate model precipitation on circulation patterns

Dynamical downscaling of Global Climate Models (GCMs) through regional climate models (RCMs) potentially improves the usability of the output for hydrological impact studies. However, a further downscaling or interpolation of precipitation from RCMs is often needed to match the precipitation characteristics at the local scale. This study analysed three Model Output Statistics (MOS) techniques to adjust RCM precipitation; (1) a simple direct method (DM), (2) quantile-quantile mapping (QM) and (3) a distribution-based scaling (DBS) approach. The modelled precipitation was daily means from 16 RCMs driven by ERA40 reanalysis data over the 1961–2000 provided by the ENSEMBLES (ENSEMBLE-based Predictions of Climate Changes and their Impacts) project over a small catchment located in the Midlands, UK. All methods were conditioned on the entire time series, separate months and using an objective classification of Lamb's weather types. The performance of the MOS techniques were assessed regarding temporal and spatial characteristics of the precipitation fields, as well as modelled runoff using the HBV rainfall-runoff model. The results indicate that the DBS conditioned on classification patterns performed better than the other methods, however an ensemble approach in terms of both climate models and downscaling methods is recommended to account for uncertainties in the MOS methods.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.

Evaluating multivariate forecast densities: a comparison of two approaches

We consider methods of evaluating multivariate density forecasts. A recently proposed method is found to lack power when the correlation structure is mis-specified. Tests that have good power to detect mis-specifications of this sort are described. We also consider the properties of the tests in the presence of more general mis-specifications.

Survival analysis statistics applied to threshold data obtained from the ascending forced-choice method of limits

Sensory thresholds are often collected through ascending forced-choice methods. Group thresholds are important for comparing stimuli or populations; yet, the method has two problems. An individual may correctly guess the correct answer at any concentration step and might detect correctly at low concentrations but become adapted or fatigued at higher concentrations. The survival analysis method deals with both issues. Individual sequences of incorrect and correct answers are adjusted, taking into account the group performance at each concentration. The technique reduces the chance probability where there are consecutive correct answers. Adjusted sequences are submitted to survival analysis to determine group thresholds. The technique was applied to an aroma threshold and a taste threshold study. It resulted in group thresholds similar to ASTM or logarithmic regression procedures. Significant differences in taste thresholds between younger and older adults were determined. The approach provides a more robust technique over previous estimation methods.

Dominant components of the Thoroughbred metabolome characterised by 1H‐NMR spectroscopy: a metabolite atlas of common biofluids

Summary Reasons for performing study: Metabonomics is emerging as a powerful tool for disease screening and investigating mammalian metabolism. This study aims to create a metabolic framework by producing a preliminary reference guide for the normal equine metabolic milieu. Objectives: To metabolically profile plasma, urine and faecal water from healthy racehorses using high resolution 1H-NMR spectroscopy and to provide a list of dominant metabolites present in each biofluid for the benefit of future research in this area. Study design: This study was performed using seven Thoroughbreds in race training at a single time-point. Urine and faecal samples were collected non-invasively and plasma was obtained from samples taken for routine clinical chemistry purposes. Methods: Biofluids were analysed using 1H-NMR spectroscopy. Metabolite assignment was achieved via a range of 1D and 2D experiments. Results: A total of 102 metabolites were assigned across the three biological matrices. A core metabonome of 14 metabolites was ubiquitous across all biofluids. All biological matrices provided a unique window on different aspects of systematic metabolism. Urine was the most populated metabolite matrix with 65 identified metabolites, 39 of which were unique to this biological compartment. A number of these were related to gut microbial host co-metabolism. Faecal samples were the most metabolically variable between animals; acetate was responsible for the majority (28%) of this variation. Short chain fatty acids were the predominant features identified within this biofluid by 1H-NMR spectroscopy. Conclusions: Metabonomics provides a platform for investigating complex and dynamic interactions between the host and its consortium of gut microbes and has the potential to uncover markers for health and disease in a variety of biofluids. Inherent variation in faecal extracts along with the relative abundance of microbial-mammalian metabolites in urine and invasive nature of plasma sampling, infers that urine is the most appropriate biofluid for the purposes of metabonomic analysis.

A comparison of methods for treatment selection in seamless phase II/III clinical trials incorporating information on short-term endpoints

In an adaptive seamless phase II/III clinical trial interim analysis, data are used for treatment selection, enabling resources to be focused on comparison of more effective treatment(s) with a control. In this paper, we compare two methods recently proposed to enable use of short-term endpoint data for decision-making at the interim analysis. The comparison focuses on the power and the probability of correctly identifying the most promising treatment. We show that the choice of method depends on how well short-term data predict the best treatment, which may be measured by the correlation between treatment effects on short- and long-term endpoints.

Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

A new calibrated sunspot group series since 1749: statistics of active day fractions

Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [S_S] defined such that the observer is assumed to miss all of the groups with an area smaller than S_S and report all the groups larger than S_S. Next, using a Monte-Carlo method we construct, from the reference data set, a correction matrix for each observer. The correction matrices are significantly non-linear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot group records for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series displays secular minima around 1800 (Dalton minimum) and 1900 (Gleissberg minimum), as well as the Modern grand maximum of activity in the second half of the 20th century. The uniqueness of the grand maximum is confirmed for the last 250 years. It is shown that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the 18th and 19th centuries in some reconstructions.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

An ethnomedicinal survey of a Tashelhit-speaking community in the High Atlas, Morocco

Traditional knowledge about medicinal plants from a poorly studied region, the High Atlas in Morocco, is reported here for the first time; this permits consideration of efficacy and safety of current practices whilst highlighting species previously not known to have traditional medicinal use. Our study aims to document local medicinal plant knowledge among Tashelhit speaking communities through ethnobotanical survey, identifying preferred species and new medicinal plant citations and illuminating the relationship between emic and etic ailment classifications. Ethnobotanical data were collected using standard methods and with prior informed consent obtained before all interactions, data were characterized using descriptive indices and medicinal plants and healing strategies relevant to local livelihoods were identified. 151 vernacular names corresponding to 159 botanical species were found to be used to treat 36 folk ailments grouped in 14 biomedical use categories. Thirty-five (22%) are new medicinal plant records in Morocco, and 26 described as used for the first time anywhere. Fidelity levels (FL) revealed low specificity in plant use, particularly for the most commonly reported plants. Most plants are used in mixtures. Plant use is driven by local concepts of disease, including “hot” and “cold” classification and beliefs in supernatural forces. Local medicinal plant knowledge is rich in the High Atlas, where local populations still rely on medicinal plants for healthcare. We found experimental evidence of safe and effective use of medicinal plants in the High Atlas; but we highlight the use of eight poisonous species.