An elastic net orthogonal forward regression algorithm

In this paper we propose an efficient two-level model identification method for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularization parameters in the elastic net are optimized using a particle swarm optimization (PSO) algorithm at the upper level by minimizing the leave one out (LOO) mean square error (LOOMSE). Illustrative examples are included to demonstrate the effectiveness of the new approaches.

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.

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.

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.

Equator-to-pole temperature differences and the extra-tropical storm track responses of the CMIP5 climate models

This paper aims to understand the physical processes causing the large spread in the storm track projections of the CMIP5 climate models. In particular, the relationship between the climate change responses of the storm tracks, as measured by the 2–6 day mean sea level pressure variance, and the equator-to-pole temperature differences at upper- and lower-tropospheric levels is investigated. In the southern hemisphere the responses of the upper- and lower-tropospheric temperature differences are correlated across the models and as a result they share similar associations with the storm track responses. There are large regions in which the storm track responses are correlated with the temperature difference responses, and a simple linear regression model based on the temperature differences at either level captures the spatial pattern of the mean storm track response as well explaining between 30 and 60 % of the inter-model variance of the storm track responses. In the northern hemisphere the responses of the two temperature differences are not significantly correlated and their associations with the storm track responses are more complicated. In summer, the responses of the lower-tropospheric temperature differences dominate the inter-model spread of the storm track responses. In winter, the responses of the upper- and lower-temperature differences both play a role. The results suggest that there is potential to reduce the spread in storm track responses by constraining the relative magnitudes of the warming in the tropical and polar regions.

Rheology of discrete failure regimes of anisotropic sea ice

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

Forecasting US output growth using leading indicators: an appraisal using MIDAS models

We evaluate the predictive power of leading indicators for output growth at horizons up to 1 year. We use the MIDAS regression approach as this allows us to combine multiple individual leading indicators in a parsimonious way and to directly exploit the information content of the monthly series to predict quarterly output growth. When we use real-time vintage data, the indicators are found to have significant predictive ability, and this is further enhanced by the use of monthly data on the quarter at the time the forecast is made

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

The dependence of radiative forcing and feedback on evolving patterns of surface temperature change in climate models

Experiments with CO2 instantaneously quadrupled and then held constant are used to show that the relationship between the global-mean net heat input to the climate system and the global-mean surface-air-temperature change is nonlinear in Coupled Model Intercomparison Project phase 5 (CMIP5) Atmosphere-Ocean General Circulation Models (AOGCMs). The nonlinearity is shown to arise from a change in strength of climate feedbacks driven by an evolving pattern of surface warming. In 23 out of the 27 AOGCMs examined the climate feedback parameter becomes significantly (95% confidence) less negative – i.e. the effective climate sensitivity increases – as time passes. Cloud feedback parameters show the largest changes. In the AOGCM-mean approximately 60% of the change in feedback parameter comes from the topics (30N-30S). An important region involved is the tropical Pacific where the surface warming intensifies in the east after a few decades. The dependence of climate feedbacks on an evolving pattern of surface warming is confirmed using the HadGEM2 and HadCM3 atmosphere GCMs (AGCMs). With monthly evolving sea-surface-temperatures and sea-ice prescribed from its AOGCM counterpart each AGCM reproduces the time-varying feedbacks, but when a fixed pattern of warming is prescribed the radiative response is linear with global temperature change or nearly so. We also demonstrate that the regression and fixed-SST methods for evaluating effective radiative forcing are in principle different, because rapid SST adjustment when CO2 is changed can produce a pattern of surface temperature change with zero global mean but non-zero change in net radiation at the top of the atmosphere (~ -0.5 Wm-2 in HadCM3).

Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models

We utilize energy budget diagnostics from the Coupled Model Intercomparison Project phase 5 (CMIP5) to evaluate the models' climate forcing since preindustrial times employing an established regression technique. The climate forcing evaluated this way, termed the adjusted forcing (AF), includes a rapid adjustment term associated with cloud changes and other tropospheric and land-surface changes. We estimate a 2010 total anthropogenic and natural AF from CMIP5 models of 1.9 ± 0.9 W m−2 (5–95% range). The projected AF of the Representative Concentration Pathway simulations are lower than their expected radiative forcing (RF) in 2095 but agree well with efficacy weighted forcings from integrated assessment models. The smaller AF, compared to RF, is likely due to cloud adjustment. Multimodel time series of temperature change and AF from 1850 to 2100 have large intermodel spreads throughout the period. The intermodel spread of temperature change is principally driven by forcing differences in the present day and climate feedback differences in 2095, although forcing differences are still important for model spread at 2095. We find no significant relationship between the equilibrium climate sensitivity (ECS) of a model and its 2003 AF, in contrast to that found in older models where higher ECS models generally had less forcing. Given the large present-day model spread, there is no indication of any tendency by modelling groups to adjust their aerosol forcing in order to produce observed trends. Instead, some CMIP5 models have a relatively large positive forcing and overestimate the observed temperature change.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

Toward multifactorial null models of range contraction in terrestrial vertebrates

The contraction of a species’ distribution range, which results from the extirpation of local populations, generally precedes its extinction. Therefore, understanding drivers of range contraction is important for conservation and management. Although there are many processes that can potentially lead to local extirpation and range contraction, three main null models have been proposed: demographic, contagion, and refuge. The first two models postulate that the probability of local extirpation for a given area depends on its relative position within the range; but these models generate distinct spatial predictions because they assume either a ubiquitous (demographic) or a clinal (contagion) distribution of threats. The third model (refuge) postulates that extirpations are determined by the intensity of human impacts, leading to heterogeneous spatial predictions potentially compatible with those made by the other two null models. A few previous studies have explored the generality of some of these null models, but we present here the first comprehensive evaluation of all three models. Using descriptive indices and regression analyses we contrast the predictions made by each of the null models using empirical spatial data describing range contraction in 386 terrestrial vertebrates (mammals, birds, amphibians, and reptiles) distributed across the World. Observed contraction patterns do not consistently conform to the predictions of any of the three models, suggesting that these may not be adequate null models to evaluate range contraction dynamics among terrestrial vertebrates. Instead, our results support alternative null models that account for both relative position and intensity of human impacts. These new models provide a better multifactorial baseline to describe range contraction patterns in vertebrates. This general baseline can be used to explore how additional factors influence contraction, and ultimately extinction for particular areas or species as well as to predict future changes in light of current and new threats.

Assessment and improvement of biotransfer models to cow’s milk and beef used in exposure assessment tools for organic pollutants

The aim of this study was to assess and improve the accuracy of biotransfer models for the organic pollutants (PCBs, PCDD/Fs, PBDEs, PFCAs, and pesticides) into cow’s milk and beef used in human exposure assessment. Metabolic rate in cattle is known as a key parameter for this biotransfer, however few experimental data and no simulation methods are currently available. In this research, metabolic rate was estimated using existing QSAR biodegradation models of microorganisms (BioWIN) and fish (EPI-HL and IFS-HL). This simulated metabolic rate was then incorporated into the mechanistic cattle biotransfer models (RAIDAR, ACC-HUMAN, OMEGA, and CKow). The goodness of fit tests showed that RAIDAR, ACC-HUMAN, OMEGA model performances were significantly improved using either of the QSARs when comparing the new model outputs to observed data. The CKow model is the only one that separates the processes in the gut and liver. This model showed the lowest residual error of all the models tested when the BioWIN model was used to represent the ruminant metabolic process in the gut and the two fish QSARs were used to represent the metabolic process in the liver. Our testing included EUSES and CalTOX which are KOW-regression models that are widely used in regulatory assessment. New regressions based on the simulated rate of the two metabolic processes are also proposed as an alternative to KOW-regression models for a screening risk assessment. The modified CKow model is more physiologically realistic, but has equivalent usability to existing KOW-regression models for estimating cattle biotransfer of organic pollutants.

On the ability of statistical wind-wave models to capture the variability and long-term trends of the North Atlantic winter wave climate

A dynamical wind-wave climate simulation covering the North Atlantic Ocean and spanning the whole 21st century under the A1B scenario has been compared with a set of statistical projections using atmospheric variables or large scale climate indices as predictors. As a first step, the performance of all statistical models has been evaluated for the present-day climate; namely they have been compared with a dynamical wind-wave hindcast in terms of winter Significant Wave Height (SWH) trends and variance as well as with altimetry data. For the projections, it has been found that statistical models that use wind speed as independent variable predictor are able to capture a larger fraction of the winter SWH inter-annual variability (68% on average) and of the long term changes projected by the dynamical simulation. Conversely, regression models using climate indices, sea level pressure and/or pressure gradient as predictors, account for a smaller SWH variance (from 2.8% to 33%) and do not reproduce the dynamically projected long term trends over the North Atlantic. Investigating the wind-sea and swell components separately, we have found that the combination of two regression models, one for wind-sea waves and another one for the swell component, can improve significantly the wave field projections obtained from single regression models over the North Atlantic.