Model inter-comparison between statistical and dynamic model assessments of the long-term stability of blanket peat in Great Britain (1940-2099)

We compared output from 3 dynamic process-based models (DMs: ECOSSE, MILLENNIA and the Durham Carbon Model) and 9 bioclimatic envelope models (BCEMs; including BBOG ensemble and PEATSTASH) ranging from simple threshold to semi-process-based models. Model simulations were run at 4 British peatland sites using historical climate data and climate projections under a medium (A1B) emissions scenario from the 11-RCM (regional climate model) ensemble underpinning UKCP09. The models showed that blanket peatlands are vulnerable to projected climate change; however, predictions varied between models as well as between sites. All BCEMs predicted a shift from presence to absence of a climate associated with blanket peat, where the sites with the lowest total annual precipitation were closest to the presence/absence threshold. DMs showed a more variable response. ECOSSE predicted a decline in net C sink and shift to net C source by the end of this century. The Durham Carbon Model predicted a smaller decline in the net C sink strength, but no shift to net C source. MILLENNIA predicted a slight overall increase in the net C sink. In contrast to the BCEM projections, the DMs predicted that the sites with coolest temperatures and greatest total annual precipitation showed the largest change in carbon sinks. In this model inter-comparison, the greatest variation in model output in response to climate change projections was not between the BCEMs and DMs but between the DMs themselves, because of different approaches to modelling soil organic matter pools and decomposition amongst other processes. The difference in the sign of the response has major implications for future climate feedbacks, climate policy and peatland management. Enhanced data collection, in particular monitoring peatland response to current change, would significantly improve model development and projections of future change.

Impacts of pollution and climate change on ombrotrophic Sphagnum species in the UK: analysis of uncertainties in two empirical niche models

A significant challenge in the prediction of climate change impacts on ecosystems and biodiversity is quantifying the sources of uncertainty that emerge within and between different models. Statistical species niche models have grown in popularity, yet no single best technique has been identified reflecting differing performance in different situations. Our aim was to quantify uncertainties associated with the application of 2 complimentary modelling techniques. Generalised linear mixed models (GLMM) and generalised additive mixed models (GAMM) were used to model the realised niche of ombrotrophic Sphagnum species in British peatlands. These models were then used to predict changes in Sphagnum cover between 2020 and 2050 based on projections of climate change and atmospheric deposition of nitrogen and sulphur. Over 90% of the variation in the GLMM predictions was due to niche model parameter uncertainty, dropping to 14% for the GAMM. After having covaried out other factors, average variation in predicted values of Sphagnum cover across UK peatlands was the next largest source of variation (8% for the GLMM and 86% for the GAMM). The better performance of the GAMM needs to be weighed against its tendency to overfit the training data. While our niche models are only a first approximation, we used them to undertake a preliminary evaluation of the relative importance of climate change and nitrogen and sulphur deposition and the geographic locations of the largest expected changes in Sphagnum cover. Predicted changes in cover were all small (generally <1% in an average 4 m2 unit area) but also highly uncertain. Peatlands expected to be most affected by climate change in combination with atmospheric pollution were Dartmoor, Brecon Beacons and the western Lake District.

Evaluating the potential for statistical decadal predictions of sea surface temperatures with a perfect model approach

We explore the potential for making statistical decadal predictions of sea surface temperatures (SSTs) in a perfect model analysis, with a focus on the Atlantic basin. Various statistical methods (Lagged correlations, Linear Inverse Modelling and Constructed Analogue) are found to have significant skill in predicting the internal variability of Atlantic SSTs for up to a decade ahead in control integrations of two different global climate models (GCMs), namely HadCM3 and HadGEM1. Statistical methods which consider non-local information tend to perform best, but which is the most successful statistical method depends on the region considered, GCM data used and prediction lead time. However, the Constructed Analogue method tends to have the highest skill at longer lead times. Importantly, the regions of greatest prediction skill can be very different to regions identified as potentially predictable from variance explained arguments. This finding suggests that significant local decadal variability is not necessarily a prerequisite for skillful decadal predictions, and that the statistical methods are capturing some of the dynamics of low-frequency SST evolution. In particular, using data from HadGEM1, significant skill at lead times of 6–10 years is found in the tropical North Atlantic, a region with relatively little decadal variability compared to interannual variability. This skill appears to come from reconstructing the SSTs in the far north Atlantic, suggesting that the more northern latitudes are optimal for SST observations to improve predictions. We additionally explore whether adding sub-surface temperature data improves these decadal statistical predictions, and find that, again, it depends on the region, prediction lead time and GCM data used. Overall, we argue that the estimated prediction skill motivates the further development of statistical decadal predictions of SSTs as a benchmark for current and future GCM-based decadal climate predictions.

International evidence on the predictability of returns to securitized real estate assets: econometric models versus neural networks

The performance of various statistical models and commonly used financial indicators for forecasting securitised real estate returns are examined for five European countries: the UK, Belgium, the Netherlands, France and Italy. Within a VAR framework, it is demonstrated that the gilt-equity yield ratio is in most cases a better predictor of securitized returns than the term structure or the dividend yield. In particular, investors should consider in their real estate return models the predictability of the gilt-equity yield ratio in Belgium, the Netherlands and France, and the term structure of interest rates in France. Predictions obtained from the VAR and univariate time-series models are compared with the predictions of an artificial neural network model. It is found that, whilst no single model is universally superior across all series, accuracy measures and horizons considered, the neural network model is generally able to offer the most accurate predictions for 1-month horizons. For quarterly and half-yearly forecasts, the random walk with a drift is the most successful for the UK, Belgian and Dutch returns and the neural network for French and Italian returns. Although this study underscores market context and forecast horizon as parameters relevant to the choice of the forecast model, it strongly indicates that analysts should exploit the potential of neural networks and assess more fully their forecast performance against more traditional models.

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.

Modeling data with structural and temporal correlation using lower level and higher level multilevel models

Novel imaging techniques are playing an increasingly important role in drug development, providing insight into the mechanism of action of new chemical entities. The data sets obtained by these methods can be large with complex inter-relationships, but the most appropriate statistical analysis for handling this data is often uncertain - precisely because of the exploratory nature of the way the data are collected. We present an example from a clinical trial using magnetic resonance imaging to assess changes in atherosclerotic plaques following treatment with a tool compound with established clinical benefit. We compared two specific approaches to handle the correlations due to physical location and repeated measurements: two-level and four-level multilevel models. The two methods identified similar structural variables, but higher level multilevel models had the advantage of explaining a greater proportion of variation, and the modeling assumptions appeared to be better satisfied.

Evaluation of ice cloud representation in the ECMWF and UK Met Office models using CloudSat and CALIPSO data

Ice cloud representation in general circulation models remains a challenging task, due to the lack of accurate observations and the complexity of microphysical processes. In this article, we evaluate the ice water content (IWC) and ice cloud fraction statistical distributions from the numerical weather prediction models of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the UK Met Office, exploiting the synergy between the CloudSat radar and CALIPSO lidar. Using the last three weeks of July 2006, we analyse the global ice cloud occurrence as a function of temperature and latitude and show that the models capture the main geographical and temperature-dependent distributions, but overestimate the ice cloud occurrence in the Tropics in the temperature range from −60 °C to −20 °C and in the Antarctic for temperatures higher than −20 °C, but underestimate ice cloud occurrence at very low temperatures. A global statistical comparison of the occurrence of grid-box mean IWC at different temperatures shows that both the mean and range of IWC increases with increasing temperature. Globally, the models capture most of the IWC variability in the temperature range between −60 °C and −5 °C, and also reproduce the observed latitudinal dependencies in the IWC distribution due to different meteorological regimes. Two versions of the ECMWF model are assessed. The recent operational version with a diagnostic representation of precipitating snow and mixed-phase ice cloud fails to represent the IWC distribution in the −20 °C to 0 °C range, but a new version with prognostic variables for liquid water, ice and snow is much closer to the observed distribution. The comparison of models and observations provides a much-needed analysis of the vertical distribution of IWC across the globe, highlighting the ability of the models to reproduce much of the observed variability as well as the deficiencies where further improvements are required.

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.

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.

Validation of three new measure-correlate-predict models for the long-term prospection of the wind resource

The estimation of the long-term wind resource at a prospective site based on a relatively short on-site measurement campaign is an indispensable task in the development of a commercial wind farm. The typical industry approach is based on the measure-correlate-predict �MCP� method where a relational model between the site wind velocity data and the data obtained from a suitable reference site is built from concurrent records. In a subsequent step, a long-term prediction for the prospective site is obtained from a combination of the relational model and the historic reference data. In the present paper, a systematic study is presented where three new MCP models, together with two published reference models �a simple linear regression and the variance ratio method�, have been evaluated based on concurrent synthetic wind speed time series for two sites, simulating the prospective and the reference site. The synthetic method has the advantage of generating time series with the desired statistical properties, including Weibull scale and shape factors, required to evaluate the five methods under all plausible conditions. In this work, first a systematic discussion of the statistical fundamentals behind MCP methods is provided and three new models, one based on a nonlinear regression and two �termed kernel methods� derived from the use of conditional probability density functions, are proposed. All models are evaluated by using five metrics under a wide range of values of the correlation coefficient, the Weibull scale, and the Weibull shape factor. Only one of all models, a kernel method based on bivariate Weibull probability functions, is capable of accurately predicting all performance metrics studied.

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.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Regularized logistic models for probabilistic forecasting and diagnostics

Logistic models are studied as a tool to convert dynamical forecast information (deterministic and ensemble) into probability forecasts. A logistic model is obtained by setting the logarithmic odds ratio equal to a linear combination of the inputs. As with any statistical model, logistic models will suffer from overfitting if the number of inputs is comparable to the number of forecast instances. Computational approaches to avoid overfitting by regularization are discussed, and efficient techniques for model assessment and selection are presented. A logit version of the lasso (originally a linear regression technique), is discussed. In lasso models, less important inputs are identified and the corresponding coefficient is set to zero, providing an efficient and automatic model reduction procedure. For the same reason, lasso models are particularly appealing for diagnostic purposes.