A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

The statistical properties of tropical ice clouds generated by the West-African and Australian monsoons from ground-based radar-lidar observations

In the present paper we characterize the statistical properties of non-precipitating tropical ice clouds (deep ice anvils resulting from deep convection and cirrus clouds) over Niamey, Niger, West Africa, and Darwin, northern Australia, using ground-based radar–lidar observations from the Atmospheric Radiation Measurement (ARM) programme. The ice cloud properties analysed in this paper are the frequency of ice cloud occurrence, cloud fraction, the morphological properties (cloud-top height, base height, and thickness), the microphysical and radiative properties (ice water content, visible extinction, effective radius, terminal fall speed, and concentration), and the internal cloud dynamics (in-cloud vertical air velocity). The main highlight of the paper is that it characterizes for the first time the probability density functions of the tropical ice cloud properties, their vertical variability and their diurnal variability at the same time. This is particularly important over West Africa, since the ARM deployment in Niamey provides the first vertically resolved observations of non-precipitating ice clouds in this crucial area in terms of redistribution of water and energy in the troposphere. The comparison between the two sites also provides an additional observational basis for the evaluation of the parametrization of clouds in large-scale models, which should be able to reproduce both the statistical properties at each site and the differences between the two sites. The frequency of ice cloud occurrence is found to be much larger over Darwin when compared to Niamey, and with a much larger diurnal variability, which is well correlated with the diurnal cycle of deep convective activity. The diurnal cycle of the ice cloud occurrence over Niamey is also much less correlated with that of deep convective activity than over Darwin, probably owing to the fact that Niamey is further away from the deep convective sources of the region. The frequency distributions of cloud fraction are strongly bimodal and broadly similar over the two sites, with a predominance of clouds characterized either by a very small cloud fraction (less than 0.3) or a very large cloud fraction (larger than 0.9). The ice clouds over Darwin are also much thicker (by 1 km or more statistically) and are characterized by a much larger diurnal variability than ice clouds over Niamey. Ice clouds over Niamey are also characterized by smaller particle sizes and fall speeds but in much larger concentrations, thereby carrying more ice water and producing more visible extinction than the ice clouds over Darwin. It is also found that there is a much larger occurrence of downward in-cloud air motions less than 1 m s−1 over Darwin, which together with the larger fall speeds retrieved over Darwin indicates that the life cycle of ice clouds is probably shorter over Darwin than over Niamey.

A combined engineering and statistical model of UK domestic appliance electrical load profiles

The development of a combined engineering and statistical Artificial Neural Network model of UK domestic appliance load profiles is presented. The model uses diary-style appliance use data and a survey questionnaire collected from 51 suburban households and 46 rural households during the summer of 2010 and2011 respectively. It also incorporates measured energy data and is sensitive to socioeconomic, physical dwelling and temperature variables. A prototype model is constructed in MATLAB using a two layer feed forward network with back propagation training which has a 12:10:24 architecture. Model outputs include appliance load profiles which can be applied to the fields of energy planning (microrenewables and smart grids), building simulation tools and energy policy.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Testing the statistical significance of sector & regional diversification

The question as to whether it is better to diversify a real estate portfolio within a property type across the regions or within a region across the property types is one of continuing interest for academics and practitioners alike. The current study, however, is somewhat different from the usual sector/regional analysis taking account of the fact that holdings in the UK real estate market are heavily concentrated in a single region, London. As a result this study is designed to investigate whether a real estate fund manager can obtain a statistically significant improvement in risk/return performance from extending out of a London based portfolio into firstly the rest of the South East of England and then into the remainder of the UK, or whether the manger would be better off staying within London and diversifying across the various property types. The results indicating that staying within London and diversifying across the various property types may offer performance comparable with regional diversification, although this conclusion largely depends on the time period and the fund manager’s ability to diversify efficiently.

Statistical monitoring of student performance: an early warning system

Weekly monitoring of profiles of student performances on formative and summative coursework throughout the year can be used to quickly identify those who need additional help, possibly due to acute and sudden-onset problems. Such an early-warning system can help retention, but also assist students in overcoming problems early on, thus helping them fulfil their potential in the long run. We have developed a simple approach for the automatic monitoring of student mark profiles for individual modules, which we intend to trial in the near future. Its ease of implementation means that it can be used for very large cohorts with little additional effort when marks are already collected and recorded on a spreadsheet.

Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods

A precipitation downscaling method is presented using precipitation from a general circulation model (GCM) as predictor. The method extends a previous method from monthly to daily temporal resolution. The simplest form of the method corrects for biases in wet-day frequency and intensity. A more sophisticated variant also takes account of flow-dependent biases in the GCM. The method is flexible and simple to implement. It is proposed here as a correction of GCM output for applications where sophisticated methods are not available, or as a benchmark for the evaluation of other downscaling methods. Applied to output from reanalyses (ECMWF, NCEP) in the region of the European Alps, the method is capable of reducing large biases in the precipitation frequency distribution, even for high quantiles. The two variants exhibit similar performances, but the ideal choice of method can depend on the GCM/reanalysis and it is recommended to test the methods in each case. Limitations of the method are found in small areas with unresolved topographic detail that influence higher-order statistics (e.g. high quantiles). When used as benchmark for three regional climate models (RCMs), the corrected reanalysis and the RCMs perform similarly in many regions, but the added value of the latter is evident for high quantiles in some small regions.

Statistical evaluation of the early-stage development of Jatropha energy plantations in Northeastern Mexico

A systematic evaluation of agricultural factors affecting the adaptation of the tropical oil plant Jatropha curcas L. to the semi-arid subtropical climate in Northeastern Mexico has been conducted. The factors studied include plant density and topology, as well as fungi and virus abundances. A multiple regression analysis shows that total fruit production can be well predicted by the area per plant and the total presence of fungi. Four common herbicides and a mechanical weed control measure were established at a dedicated test array and their impact on plant productivity was assessed.

Statistical decadal predictions for sea surface temperatures: a benchmark for dynamical GCM predictions

Accurate decadal climate predictions could be used to inform adaptation actions to a changing climate. The skill of such predictions from initialised dynamical global climate models (GCMs) may be assessed by comparing with predictions from statistical models which are based solely on historical observations. This paper presents two benchmark statistical models for predicting both the radiatively forced trend and internal variability of annual mean sea surface temperatures (SSTs) on a decadal timescale based on the gridded observation data set HadISST. For both statistical models, the trend related to radiative forcing is modelled using a linear regression of SST time series at each grid box on the time series of equivalent global mean atmospheric CO2 concentration. The residual internal variability is then modelled by (1) a first-order autoregressive model (AR1) and (2) a constructed analogue model (CA). From the verification of 46 retrospective forecasts with start years from 1960 to 2005, the correlation coefficient for anomaly forecasts using trend with AR1 is greater than 0.7 over parts of extra-tropical North Atlantic, the Indian Ocean and western Pacific. This is primarily related to the prediction of the forced trend. More importantly, both CA and AR1 give skillful predictions of the internal variability of SSTs in the subpolar gyre region over the far North Atlantic for lead time of 2 to 5 years, with correlation coefficients greater than 0.5. For the subpolar gyre and parts of the South Atlantic, CA is superior to AR1 for lead time of 6 to 9 years. These statistical forecasts are also compared with ensemble mean retrospective forecasts by DePreSys, an initialised GCM. DePreSys is found to outperform the statistical models over large parts of North Atlantic for lead times of 2 to 5 years and 6 to 9 years, however trend with AR1 is generally superior to DePreSys in the North Atlantic Current region, while trend with CA is superior to DePreSys in parts of South Atlantic for lead time of 6 to 9 years. These findings encourage further development of benchmark statistical decadal prediction models, and methods to combine different predictions.

A statistical approach to the problem of restoring damaged and contaminated images

We address the problem of automatically identifying and restoring damaged and contaminated images. We suggest a novel approach based on a semi-parametric model. This has two components, a parametric component describing known physical characteristics and a more flexible non-parametric component. The latter avoids the need for a detailed model for the sensor, which is often costly to produce and lacking in robustness. We assess our approach using an analysis of electroencephalographic images contaminated by eye-blink artefacts and highly damaged photographs contaminated by non-uniform lighting. These experiments show that our approach provides an effective solution to problems of this type.