Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Probabilistic forecasting: why model imperfection is a poison pill

This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

A probabilistic analysis of the future potential of evaporative cooling systems in a temperate climate

The probabilistic projections of climate change for the United Kingdom (UK Climate Impacts Programme) show a trend towards hotter and drier summers. This suggests an expected increase in cooling demand for buildings – a conflicting requirement to reducing building energy needs and related CO2 emissions. Though passive design is used to reduce thermal loads of a building, a supplementary cooling system is often necessary. For such mixed-mode strategies, indirect evaporative cooling is investigated as a low energy option in the context of a warmer and drier UK climate. Analysis of the climate projections shows an increase in wet-bulb depression; providing a good indication of the cooling potential of an evaporative cooler. Modelling a mixed-mode building at two different locations, showed such a building was capable of maintaining adequate thermal comfort in future probable climates. Comparing the control climate to the scenario climate, an increase in the median of evaporative cooling load is evident. The shift is greater for London than for Glasgow with a respective 71.6% and 3.3% increase in the median annual cooling load. The study shows evaporative cooling should continue to function as an effective low-energy cooling technique in future, warming climates.

Influence of probabilistic climate projections on building energy simulation

The Chartered Institute of Building Service Engineers (CIBSE) produced a technical memorandum (TM36) presenting research on future climate impacting building energy use and thermal comfort. One climate projection for each of four CO2 emissions scenario were used in TM36, so providing a deterministic outlook. As part of the UK Climate Impacts Programme (UKCIP) probabilistic climate projections are being studied in relation to building energy simulation techniques. Including uncertainty in climate projections is considered an important advance to climate impacts modelling and is included in the latest UKCIP data (UKCP09). Incorporating the stochastic nature of these new climate projections in building energy modelling requires a significant increase in data handling and careful statistical interpretation of the results to provide meaningful conclusions. This paper compares the results from building energy simulations when applying deterministic and probabilistic climate data. This is based on two case study buildings: (i) a mixed-mode office building with exposed thermal mass and (ii) a mechanically ventilated, light-weight office building. Building (i) represents an energy efficient building design that provides passive and active measures to maintain thermal comfort. Building (ii) relies entirely on mechanical means for heating and cooling, with its light-weight construction raising concern over increased cooling loads in a warmer climate. Devising an effective probabilistic approach highlighted greater uncertainty in predicting building performance, depending on the type of building modelled and the performance factors under consideration. Results indicate that the range of calculated quantities depends not only on the building type but is strongly dependent on the performance parameters that are of interest. Uncertainty is likely to be particularly marked with regard to thermal comfort in naturally ventilated buildings.

Climate spectrum estimation in the presence of timescale errors.

We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1) the upper levels of the spectrum of the red-noise AR(1) alternative and (2) the uncertainty of the frequency of a spectral peak. Application of REDFITmc2 to ice core and stalagmite records of palaeoclimate allowed a more realistic evaluation of spectral peaks than when ignoring this source of uncertainty. The results support qualitatively the intuition that stronger effects on the spectrum estimate (decreased detectability and increased frequency uncertainty) occur for higher frequencies. The surplus information brought by algorithm REDFITmc2 is that those effects are quantified. Regarding timescale construction, not only the fixpoints, dating errors and the functional form of the age-depth model play a role. Also the joint distribution of all time points (serial correlation, stratigraphic order) determines spectrum estimation.

Case study part 2: probabilistic modelling of long-term effects of pesticides on individual breeding success in birds and mammals

Abstract: Long-term exposure of skylarks to a fictitious insecticide and of wood mice to a fictitious fungicide were modelled probabilistically in a Monte Carlo simulation. Within the same simulation the consequences of exposure to pesticides on reproductive success were modelled using the toxicity-exposure-linking rules developed by R.S. Bennet et al. (2005) and the interspecies extrapolation factors suggested by R. Luttik et al.(2005). We built models to reflect a range of scenarios and as a result were able to show how exposure to pesticide might alter the number of individuals engaged in any given phase of the breeding cycle at any given time and predict the numbers of new adults at the season’s end.

Bayesian estimation of the double hurdle model in the presence of fixed costs

We present a model of market participation in which the presence of non-negligible fixed costs leads to random censoring of the traditional double-hurdle model. Fixed costs arise when household resources must be devoted a priori to the decision to participate in the market. These costs, usually of time, are manifested in non-negligible minimum-efficient supplies and supply correspondence that requires modification of the traditional Tobit regression. The costs also complicate econometric estimation of household behavior. These complications are overcome by application of the Gibbs sampler. The algorithm thus derived provides robust estimates of the fixed-costs, double-hurdle model. The model and procedures are demonstrated in an application to milk market participation in the Ethiopian highlands.

Bayesian ranking and slection of fishing boat efficiencies

The steadily accumulating literature on technical efficiency in fisheries attests to the importance of efficiency as an indicator of fleet condition and as an object of management concern. In this paper, we extend previous work by presenting a Bayesian hierarchical approach that yields both efficiency estimates and, as a byproduct of the estimation algorithm, probabilistic rankings of the relative technical efficiencies of fishing boats. The estimation algorithm is based on recent advances in Markov Chain Monte Carlo (MCMC) methods— Gibbs sampling, in particular—which have not been widely used in fisheries economics. We apply the method to a sample of 10,865 boat trips in the US Pacific hake (or whiting) fishery during 1987–2003. We uncover systematic differences between efficiency rankings based on sample mean efficiency estimates and those that exploit the full posterior distributions of boat efficiencies to estimate the probability that a given boat has the highest true mean efficiency.

Conditionally unbiased estimation in phase II/III clinical trials with early stopping for futility

Seamless phase II/III clinical trials combine traditional phases II and III into a single trial that is conducted in two stages, with stage 1 used to answer phase II objectives such as treatment selection and stage 2 used for the confirmatory analysis, which is a phase III objective. Although seamless phase II/III clinical trials are efficient because the confirmatory analysis includes phase II data from stage 1, inference can pose statistical challenges. In this paper, we consider point estimation following seamless phase II/III clinical trials in which stage 1 is used to select the most effective experimental treatment and to decide if, compared with a control, the trial should stop at stage 1 for futility. If the trial is not stopped, then the phase III confirmatory part of the trial involves evaluation of the selected most effective experimental treatment and the control. We have developed two new estimators for the treatment difference between these two treatments with the aim of reducing bias conditional on the treatment selection made and on the fact that the trial continues to stage 2. We have demonstrated the properties of these estimators using simulations

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

Contrasting probabilistic scoring rules

There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion for preferring one proper scoring rule above another. This manuscript compares and contrasts some commonly used proper scoring rules and provides guidance on scoring rule selection. In particular, it is shown that the logarithmic scoring rule prefers erring with more uncertainty, the spherical scoring rule prefers erring with lower uncertainty, whereas the other scoring rules are indifferent to either option.