How much information is lost by using global-mean climate metrics? an example using the transport sector

Metrics are often used to compare the climate impacts of emissions from various sources, sectors or nations. These are usually based on global-mean input, and so there is the potential that important information on smaller scales is lost. Assuming a non-linear dependence of the climate impact on local surface temperature change, we explore the loss of information about regional variability that results from using global-mean input in the specific case of heterogeneous changes in ozone, methane and aerosol concentrations resulting from emissions from road traffic, aviation and shipping. Results from equilibrium simulations with two general circulation models are used. An alternative metric for capturing the regional climate impacts is investigated. We find that the application of a metric that is first calculated locally and then averaged globally captures a more complete and informative signal of climate impact than one that uses global-mean input. The loss of information when heterogeneity is ignored is largest in the case of aviation. Further investigation of the spatial distribution of temperature change indicates that although the pattern of temperature response does not closely match the pattern of the forcing, the forcing pattern still influences the response pattern on a hemispheric scale. When the short-lived transport forcing is superimposed on present-day anthropogenic CO2 forcing, the heterogeneity in the temperature response to CO2 dominates. This suggests that the importance of including regional climate impacts in global metrics depends on whether small sectors are considered in isolation or as part of the overall climate change.

Estimating reliability and resolution of probability forecasts through decomposition of the empirical score

References (20)Cited By (1)Export CitationAboutAbstract Proper scoring rules provide a useful means to evaluate probabilistic forecasts. Independent from scoring rules, it has been argued that reliability and resolution are desirable forecast attributes. The mathematical expectation value of the score allows for a decomposition into reliability and resolution related terms, demonstrating a relationship between scoring rules and reliability/resolution. A similar decomposition holds for the empirical (i.e. sample average) score over an archive of forecast–observation pairs. This empirical decomposition though provides a too optimistic estimate of the potential score (i.e. the optimum score which could be obtained through recalibration), showing that a forecast assessment based solely on the empirical resolution and reliability terms will be misleading. The differences between the theoretical and empirical decomposition are investigated, and specific recommendations are given how to obtain better estimators of reliability and resolution in the case of the Brier and Ignorance scoring rule.

Evaluating raw ensembles with the continuous ranked probability score

The continuous ranked probability score (CRPS) is a frequently used scoring rule. In contrast with many other scoring rules, the CRPS evaluates cumulative distribution functions. An ensemble of forecasts can easily be converted into a piecewise constant cumulative distribution function with steps at the ensemble members. This renders the CRPS a convenient scoring rule for the evaluation of ‘raw’ ensembles, obviating the need for sophisticated ensemble model output statistics or dressing methods prior to evaluation. In this article, a relation between the CRPS score and the quantile score is established. The evaluation of ‘raw’ ensembles using the CRPS is discussed in this light. It is shown that latent in this evaluation is an interpretation of the ensemble as quantiles but with non-uniform levels. This needs to be taken into account if the ensemble is evaluated further, for example with rank histograms.

A unifying framework for metrics for aggregating the climate effect of different emissions

Multi-gas approaches to climate change policies require a metric establishing ‘equivalences’ among emissions of various species. Climate scientists and economists have proposed four kinds of such metrics and debated their relative merits. We present a unifying framework that clarifies the relationships among them. We show, as have previous authors, that the global warming potential (GWP), used in international law to compare emissions of greenhouse gases, is a special case of the global damage potential (GDP), assuming (1) a finite time horizon, (2) a zero discount rate, (3) constant atmospheric concentrations, and (4) impacts that are proportional to radiative forcing. Both the GWP and GDP follow naturally from a cost–benefit framing of the climate change issue. We show that the global temperature change potential (GTP) is a special case of the global cost potential (GCP), assuming a (slight) fall in the global temperature after the target is reached. We show how the four metrics should be generalized if there are intertemporal spillovers in abatement costs, distinguishing between private (e.g., capital stock turnover) and public (e.g., induced technological change) spillovers. Both the GTP and GCP follow naturally from a cost-effectiveness framing of the climate change issue. We also argue that if (1) damages are zero below a threshold and (2) infinitely large above a threshold, then cost-effectiveness analysis and cost–benefit analysis lead to identical results. Therefore, the GCP is a special case of the GDP. The UN Framework Convention on Climate Change uses the GWP, a simplified cost–benefit concept. The UNFCCC is framed around the ultimate goal of stabilizing greenhouse gas concentrations. Once a stabilization target has been agreed under the convention, implementation is clearly a cost-effectiveness problem. It would therefore be more consistent to use the GCP or its simplification, the GTP.

Latitudinal variation of the effect of aviation NOx emissions on atmospheric ozone and methane and related climate metrics

We evaluate the response to regional and latitudinal changes in aircraft NOx emissions using several climate metrics (radiative forcing (RF), Global Warming Potential (GWP), Global Temperature change Potential (GTP)). Global chemistry transport model integrations were performed with sustained perturbations in regional aircraft and aircraft-like NOx emissions. The RF due to the resulting ozone and methane changes is then calculated. We investigate the impact of emission changes for specific geographical regions (approximating to USA, Europe, India and China) and cruise altitude emission changes in discrete latitude bands covering both hemispheres. We find that lower latitude emission changes (per Tg N) cause ozone and methane RFs that are about a factor of 6 larger than those from higher latitude emission changes. The net RF is positive for all experiments. The meridional extent of the RF is larger for low latitude emissions. GWPs for all emission changes are positive, with tropical emissions having the largest values; the sign of the GTP depends on the choice of time horizon.

How vegetation impacts affect climate metrics for ozone precursors

We examine the effect of ozone damage to vegetation as caused by anthropogenic emissions of ozone precursor species and quantify it in terms of its impact on terrestrial carbon stores. A simple climate model is then used to assess the expected changes in global surface temperature from the resulting perturbations to atmospheric concentrations of carbon dioxide, methane, and ozone. The concept of global temperature change potential (GTP) metric, which relates the global average surface temperature change induced by the pulse emission of a species to that induced by a unit mass of carbon dioxide, is used to characterize the impact of changes in emissions of ozone precursors on surface temperature as a function of time. For NOx emissions, the longer-timescale methane perturbation is of the opposite sign to the perturbations in ozone and carbon dioxide, so NOx emissions are warming in the short term, but cooling in the long term. For volatile organic compound (VOC), CO, and methane emissions, all the terms are warming for an increase in emissions. The GTPs for the 20 year time horizon are strong functions of emission location, with a large component of the variability owing to the different vegetation responses on different continents. At this time horizon, the induced change in the carbon cycle is the largest single contributor to the GTP metric for NOx and VOC emissions. For NOx emissions, we estimate a GTP20 of −9 (cooling) to +24 (warming) depending on assumptions of the sensitivity of vegetation types to ozone damage.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

The use of land-sea warming contrast under climate change to improve impact metrics

A favoured method of assimilating information from state-of-the-art climate models into integrated assessment models of climate impacts is to use the transient climate response (TCR) of the climate models as an input, sometimes accompanied by a pattern matching approach to provide spatial information. More recent approaches to the problem use TCR with another independent piece of climate model output: the land-sea surface warming ratio (φ). In this paper we show why the use of φ in addition to TCR has such utility. Multiple linear regressions of surface temperature change onto TCR and φ in 22 climate models from the CMIP3 multi-model database show that the inclusion of φ explains a much greater fraction of the inter-model variance than using TCR alone. The improvement is particularly pronounced in North America and Eurasia in the boreal summer season, and in the Amazon all year round. The use of φ as the second metric is beneficial for three reasons: firstly it is uncorrelated with TCR in state-of-the-art climate models and can therefore be considered as an independent metric; secondly, because of its projected time-invariance, the magnitude of φ is better constrained than TCR in the immediate future; thirdly, the use of two variables is much simpler than approaches such as pattern scaling from climate models. Finally we show how using the latest estimates of φ from climate models with a mean value of 1.6—as opposed to previously reported values of 1.4—can significantly increase the mean time-integrated discounted damage projections in a state-of-the-art integrated assessment model by about 15 %. When compared to damages calculated without the inclusion of the land-sea warming ratio, this figure rises to 65 %, equivalent to almost 200 trillion dollars over 200 years.

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.

The probability of sale and price premiums in withdrawn auctioned properties

This paper examines the impact of the auction process of residential properties that whilst unsuccessful at auction sold subsequently. The empirical analysis considers both the probability of sale and the premium of the subsequent sale price over the guide price, reserve and opening bid. The findings highlight that the final achieved sale price is influenced by key price variables revealed both prior to and during the auction itself. Factors such as auction participation, the number of individual bidders and the number of bids are significant in a number of the alternative specifications.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Forecast encompassing tests and probability forecasts

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models' parameters on these distributions. The small-sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Evaluating the Survey of Professional Forecasters probability distributions of expected inflation based on derived event probability forecasts

Techniques are proposed for evaluating forecast probabilities of events. The tools are especially useful when, as in the case of the Survey of Professional Forecasters (SPF) expected probability distributions of inflation, recourse cannot be made to the method of construction in the evaluation of the forecasts. The tests of efficiency and conditional efficiency are applied to the forecast probabilities of events of interest derived from the SPF distributions, and supplement a whole-density evaluation of the SPF distributions based on the probability integral transform approach.